Quantitative Biological Raman Spectroscopy for Non-invasive Blood Analysis
By
Wei-Chuan Shih
M.S., Mechanical Engineering
National Chiao Tung University, 1999
B.S., Mechanical Engineering
National Taiwan University, 1997
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN PARTIAL
FULLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2007
@2007 Massachusetts Institute of Technology
All rights reserved
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Department of Mechanical Engineering
March 31, 2007
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Professor of Physics, Thesis Supervisor
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George Barbastathis
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chanical Engineering, Thesis Reader
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Lallit Anand
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 1 8 2007
LIBRARIES
AWAV"s
Quantitative Biological Raman Spectroscopy for Non-invasive Blood Analysis
by
Wei-Chuan Shih
Submitted to the Department of Mechanical Engineering
on March 31, 2007 in partial fulfillment of the
requirements for the degree of Doctor of Philosophy in
Mechanical Engineering
ABSTRACT
The long term goal of this project is the measurement of clinically-relevant analytes in the blood
tissue matrix of human subjects using near-infrared Raman spectroscopy, with the shorter term
research directed towards glucose measurements for diabetic patients. This optical technique
enables non-contact, painless measurements with no sample preparation and simultaneous
determination of multiple analytes. Such a technology could greatly impact the healthcare
practices for the entire population.
This thesis presents advances in quantitative biological Raman spectroscopy along three avenues:
instrument optimization, analyte-specific information extraction, and correction for sampling
volume variations. In the first category, we have built a high-throughput instrument that
integrates Raman and diffuse reflectance capabilities. Additionally, new algorithms have been
developed to enhance wavelength precision and stability. Using this instrument, we have
presented evidence of glucose-specific measurements in human and dog subjects. We believe
that this is the first time glucose-specific information is extracted transcutaneously in vivo using
Raman spectroscopy.
Toward our ultimate goal of prospective prediction, we have developed two novel techniques:
constrained regularization (CR) for improved information extraction and intrinsic Raman
spectroscopy (IRS) to correct for sampling volume variations. CR utilizes additional prior
information in the form of the target analyte spectrum during multivariate calibration, and thus
generates more analyte-specific models compared to the most widely used method, partial least
squares. IRS employs the newly-discovered relationship between measured Raman scattering
and diffuse reflectance in turbid media. This relationship was revealed via photon migrationbased analytical models and Monte Carlo simulations, and subsequently confirmed by in vitro
experiments.
Our recent advances and promising results from the in vivo studies demonstrate that Raman
spectroscopy is a viable technique for non-invasive blood analysis.
Thesis Supervisor: Michael S. Feld
Title: Professor of Physics
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ACKNOWLEDGEMENTS
First, I'd like to thank the other major contributors of this thesis: Prof. Michael S. Feld, my thesis
supervisor, and Dr. Kate L. Bechtel, the postdoc I have worked with. Without them, this thesis
would have been a waste of paper and carbon. I've learned a great deal from both of them. I
thank Prof. George Barbastathis for equipping me with the tools and skills in mathematics and
optics, which are essential to this thesis. I also thank my other thesis committee members, Prof.
Mark Arnold, Dr. Gary Horowitz, and Prof. Roy Welsch, for their insights and comments and
efforts coming to all the meetings. I thank Dr. Misha Rebec from Bayer HealthCare for his help
on the in vivo dog study and I thank NIH NCRR and Bayer Healthcare for funding this project.
Several MIT faculty members provided me advice and guidance on various aspects: Lallit Anand,
Daniel Blankschtein, Sang-Gook Kim, Martin Schmidt, and Peter So.
I thank my office mates, Kate Bechtel, Obrad Scepanovic, Zoya Volynskaya, and GP Singh, for
making the dull place much more sexy. I thank Luis Galindo, our best "machine shop," Zina
Queen, who makes sure we have cookies and other goodies during group meetings, and
Ramachandra Dasari, of course, as the behind-the-scenes provider of all that good stuff.
I thank MIT friends that I have either worked with, talked to, or consulted with at various points
during these past few years: Shih-Chi Chen, Matthew Dawson, Kunya Desjardins, Abi Haka,
Chun-Hung Liu, Greg Nielson, Jeankun Oh, Gabi Popescu, David Randall, Leslie Regan, Troy
Savoie, Tom Scecina, Dilan Seneviratne, Yong Shi, Andy Stein, Hung-Jen Wang, Tom Yeh,
Peng Yi, Chung-Chieh Yu, and Jin Zhou.
I thank friends from MIT ROCSA, in particular, Ling Chao, Jacky Chen, Nancy Chen, ChiaoLun Cheng, Hsu-Yi Lee, and Chia-Ling Pai. To me, most of you are like younger brothers and
sisters. I am grateful to have had the opportunity to work and play with you during my last year
at MIT. I hope that together we can continue to bring this student organization to the next level.
I thank some other friends outside MIT: Yin-Chu Chen, Ling-Yu Kan, and Chi Shen.
I thank friends from the Church in Cambridge for their prayers for me, in particular, brother
Philip Yaghmai, from whom I got the idea of baptism; brother Henry Hwang, for his long lasting
shepherding and caring.
The journey at MIT has obviously taken longer than I expected or would have liked it to, but it
turned out to be a great experience with the companionship of Iris and her understanding in
various ways. I thank my parents and my brother, who always support me and pray for me. I
also thank Iris' parents, especially my mother-in-law, for constantly reminding me that I have to
graduate and start a family.
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TABLE OF CONTENTS
Abstract .......................................................................................................... 3
Acknowledgements ........................................................................ 4
Table of C ontents ....................................
..................................................... 5
List of Figures ........................................................
.............................. 10
L ist of Tables ....................................................................................
List of Abbreviations .....................................
CHAPTER 1
1.1
15
.................................................. 16
INTRODUCTION ............................................................................................
19
Objectives .....................................................................................................................
20
1.1.1
Improving throughput, precision, and stability............................
......... 20
1.1.2
Correcting sampling volume variations ..................................... ..
......... 21
1.1.3
Optimizing information extraction .........................................
............ 21
1.2
M ajor accomplishm ents ..............................................................
1.3
Outline of the thesis ...................................................................................................
CHAPTER 2
2.1
............................ 22
BACKGROUND AND SIGNIFICANCE ......................................
Blood analytes encountered in this thesis ..................................... ..
24
....
. 27
............ 27
2.1.1
G lucose .................................................................................................................
28
2.1.2
Creatinine ..............................................................................................................
30
2 .1.3
U rea......................................
2.2
............................................................... .......... 3 1
Review of existing non-invasive optical techniques for glucose detection ........... 32
2.2.1
D irect approaches...........................................
2.2.1.1.
2.2.2
................................................. 33
Near infrared (NIR) absorption spectroscopy..........................
....... 33
Mid-infrared (MIR) absorption spectroscopy ................................................. 36
2.2.2.1.
Near infrared (NIR) Raman spectroscopy .....................................
2.2.2.2.
Optical activity and polarimetry ..................................... ..
2.2.3
Indirect approaches ...............................................................
37
........... 40
.......................... 40
2.2.3.1.
Diffuse reflectance spectroscopy (DRS)..................................
....... 40
2.2.3.2.
Optical coherence tomography (OCT)..................................
......... 41
2.2.4
2.3
2.3.1
O ther approaches ................................................................
............................ 41
Prior research in the MIT Spectroscopy Laboratory...........................
.......... 42
In vitro studies....................................................................................................... 42
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In vivo studies ............................................. .................................................... 43
2.3.2
........ 43
2.3.2.1.
Methods and experimental protocols .....................................
2.3.2.2.
Results and discussion .....................................................
Sum mary .....................................................................
2.4
45
........................................ 46
INTRODUCTION TO QUANTITATIVE BIOLOGICAL RAMAN
CHAPTER 3
SPEC TR O SC OPY ....................................................................................................................... 47
............................. 47
3.1
R aman spectroscopy ..................................................................
3.2
Biological considerations ...........................................................................................
3.2.1
Using near infrared radiation .....................................................................
3.2.2
Background signal in biological Raman spectra..............................
3.2.3
Heterogeneities in human skin................................................
49
49
....... 51
52
3.3
Quantitative consideration I: minimum detection error analysis.............................
53
3.4
Quantitative consideration II: multivariate calibration .......................................
55
..................................................... 55
3.4.1
B ackground ................................................
3.4.2
Introduction ...........................................................................................................
3.4.3
Multivariate calibration methods ..........................................
............. 58
3.4.3.1.
Explicit calibration methods ..........................................
............ 59
3.4.3.2.
Implicit calibration methods ..........................................
............ 59
3.4.3.3.
Hybrid methods.........................................
.............................................. 61
Model validation and performance evaluation .....................................
3.4.4
55
62
...
........................ 62
3.4.4.1.
M odel validation .............................................................
3.4.4.2.
Summary statistics for calibration model and prediction .......................... 63
. . . . ..
.... 65
3.4.5.1.
Theoretical and practical limits............................................
65
3.4.5.2.
Model dimensionality ......................................................
65
3.4.5.3.
Chance or spurious correlation ........................................
3.4.5.4.
"Visualize" glucose............................................................................
Is the calibration model based on glucose?............. ...........
3.4.5
Physical interpretation of the regression vector................................
3.4.6
CHAPTER 4
4.1
. ... . ...
............ 66
.....
67
. 68
IMPROVING THROUGHPUT, PRECISION, AND STABILITY .............. 71
Instrumentation considerations ..................................................................................
71
4.1.1
Excitation light source .................................................................................... 72
4.1.2
Light delivery ........................................................................................................
4.1.3
Light collection .................................................................
-6-
72
.............................. 73
4.1.4
L ight transport....................................................................................................... 74
4.1.5
Spectrograph and detector..................................................
74
Overview of our laboratory instrument...........................................
74
4.2
4.2.1
Excitation light source and light delivery .......................................
4.2.2
Light collection and transport, spectrograph, and detector.............................
4.3
....... 75
Software-based image curvature correction.........................................
76
79
4.3.1
Introduction ...........................................................................................................
79
4.3.2
Image curvature formation..................................................
81
4.3.3
Simulations ................................................ ..................................................... 83
4.3.4
M ethods................................................................................................................. 84
4.3.5
Results and discussion .............................................................
4.4
....................... 87
Instrument precision and stability .................................................................................
4.4.1
Intensity and temperature stability............................................
4.4.2
Wavelength drift detection and correction..............................
4.5
5.1
90
............ 92
Summary ..................................................
CHAPTER 5
90
96
CORRECTING SAMPLING VOLUME VARIATIONS ............................. 97
Background and introduction...................................................97
5.1.1
Optical properties of biological tissue ...............................................................
97
5.1.2
Optical property variations in biological tissue .........................................
98
5.1.3
Photon migration theory to model light-tissue interactions ............................... 99
5.2
Corrections based on photon migration ...............................................
............... 101
5.2.1
Correction for spectral distortions in fluorescence spectroscopy .......................
101
5.2.2
Correction for intensity distortions in Raman spectroscopy........................
102
5.3
Monte Carlo simulations for diffuse reflectance, fluorescence, and Raman scattering in
turbid media ..................................................
105
5.3.1
Monte Carlo method .......................................
5.3.2
Monte Carlo model for fluorescence and Raman ....................
5.3.3
Effects of turbidity variations .....................................
110
5.3.4
Model validation using Monte Carlo simulation .....................................
117
5.3.5
Geometry considerations .....................................
119
5.3.6
Elastic scattering anisotropy (g) considerations .....................................
121
5.4
5.4.1
Tissue phantom studies........................................................
Cuvette geometry ........................................
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105
.................... 107
................................. 124
124
5.4.1.1.
Methods.......................................................................................................
124
5.4.1.2.
Experimental results .................................
129
5.4.2
Dog ear geometry.................................
131
5.4.3
Prospective application of IRS..................................
133
5.5
Extraction of optical properties...............................
136
5.6
Summary and guidelines...............................
136
CHAPTER 6
OPTIMIZING INFORMATION EXTRACTION...........................
138
6.1
Data pre-processing ........................................
138
6.2
Multivariate calibration..............................
143
6.3
Constrained regularization: a hybrid method for multivariate calibration............... 143
6.3.1
Theory ................................................................................
Performance of CR compared to PLS and HLA.............
6.4
6.4.1
................
Numerical studies..................................
144
147
147
6.4.1.1.
Three-analyte clear model: uncorrelated and correlated analyte
concentrations ................................................................................................................. 147
6.4.1.2.
Ten-constituent model for human forearm skin: uncorrelated and correlated
constituent variations ........................................
151
6.4.1.3.
Three-analyte model: sensitivity to inaccurate constraints...................... 155
Experimental studies .......................................
6.4.2
157
Three-analyte clear model: uncorrelated and correlated analyte
6.4.2.1.
concentrations ................................................................................................................. 157
6.4.2.2.
Discussion ........................................
6.4.3
6.5
Three-analyte turbid model: uncorrelated concentrations ....................... 160
In vivo considerations -
162
CR vs. PLS using synthetic in vivo data ......................... 163
6.5.1
Background and background removal .....................................
163
6.5.2
Signal-to-noise ratio....................................
167
6.5.3
Reference concentration error .................................
168
6.5.4
Spectral overlap ........................................
169
6.6
Sum mary .....................................................................................................................
CHAPTER 7
7.1
IN VIVO DOG STUDY .....................................
170
172
D og study .................................................................................................................... 172
7.1.1
Protocol and experiment .....................................
172
7.1.2
Minimum detection error analysis .....................................
175
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7.2
Initial analysis using PLS............................................................................................
176
7.3
Applicability of constrained regularization .....................................
186
7.4
Applicability of intrinsic Raman spectroscopy.....................................................
187
7.4.1
Glucose-induced index change .....................................
187
7.4.2
Information in the Rayleigh peak .....................................
187
7.4.3
Information in the sapphire peaks................................
188
7.5
Summary and guidelines for future studies .....................................
CHAPTER 8
CONCLUSION AND FUTURE DIRECTIONS .........................................
190
192
8.1
Review of objectives and accomplishments .....................................
192
8.2
Future directions ........................................
193
8.3
Final remarks ..............................................................................................................
195
-9-
LIST OF FIGURES
Figure 2-1 Raman spectra of a-D-glucose (solid) and anomeric balanced D-glucose (dashed) in
30
water .
........................................................................
Figure 2-2 Raman spectra of anomeric balanced D-glucose (G), creatinine (C), and urea (U). .. 31
Figure 2-3 Volunteer sitting by the optical table with his forearm clamped at the instrument.... 44
Figure 2-4 Cross validated calibration results from each individual of the 17 volunteers
combined into one chart ................................................................................................................ 45
Figure 3-1 Energy diagram for Rayleigh, Stokes Raman, and anti-Stokes Raman scattering ..... 48
Figure 3-2 A Raman spectrum consists of scattered intensity plotted vs. energy. This figure uses
acetaminophen powder measured in a quartz cuvette as an example ...................................... 49
Figure 3-3 Absorption spectra of water, skin melanin, hemoglobin, and fat. Also shown is the
scattering spectrum of 10% Intralipid, a lipid emulsion often used to simulate tissue scattering.
50
Data are obtained from http:// omlc.ogi.edu/spectra/index.html. ......................................
Figure 3-4 Correlation between the OLS regression vector (boLs) and the glucose spectrum
versus m odel com plexity. ............................................................................................................. 54
Figure 3-5 Schematic showing primary steps of multivariate calibration ................................ 57
Figure 3-6 corr(bpLS, Sglucose) versus random noise for two levels of random error in reference
concentrations. (error standard deviation: solid 5%, dashed 2%; glucose is 0.2-0.5% of the total
69
Raman signal norm ).. .....................................................................................................
Figure 3-7 RMSEP versus random noise for two levels of random error in reference
concentrations. (error standard deviation: solid 5%, dashed 2%; glucose is 0.2-0.5% of the total
69
Raman signal norm). ............................................................
Figure 3-8 corr(bpLs, Sglucose) versus random noise for two levels of random error in reference
concentrations. (error standard deviation: solid 5%, dashed 2%; glucose is 0.2-0.5% of the total
70
Ram an signal norm). ..................................................................................................................
Figure 3-9 RMSEP versus random noise for two levels of random error in reference
concentrations. (error standard deviation: solid 5%, dashed 2%; glucose is 0.2-0.5% of the total
70
Ram an signal norm). ............................................................
Figure 4-1 Schematic of the present instrument. ........................................
............. 76
Figure 4-2 Schematic of the grating spectrometer with 4f imaging optics. For clarity, the focal
lengths of the lenses L1 and L2 are f The optical axis is indicated by dotted lines. k,, and kdff
are the wave vectors of the incident and the diffracted rays, and k9 is the grating vector. ......... 82
Figure 4-3 (a) Simulated impulse response of the system at 5 different wavelengths for an
infinitesimally narrow slit. The CCD is 1340(H) x 1300(V) pixels with 20x20 pm 2 pixel size.
" ": 830nm, "--": 880nm, "....": 905nm, "-.-.": 930nm, "cD": 970nm. (b) Curves in (a) shifted
such that their apexes are aligned and with the x-axis expanded to show detail. The largest
difference is 35 pixels if the whole CCD range is used. (c) After the first-order curvature
-10-
correction with pixel shifting. The uncorrected error is still approximately 15 pixels on either
side of the C CD ........................................ ............................................................................... 84
Figure 4-4 Raman spectrum of acetaminophen powder, used as the reference material in the
calibration step. Nine prominent peaks used as separation boundaries are indicated by arrows.. 86
Figure 4-5 CCD image of acetaminophen powder. Images were created with 5-pixel hardware
binning. (a) Raw image; (b) after applying pixel shift method; (c) zoom-in of the box in (b); (d)
after applying curvature map method; (e) zoom-in of the box in (d) ..................................... 88
Figure 4-6 Comparison of two spectra from the top (solid) and the center (dashed) row of the
CCD: (a) After applying pixel shift method; (b) after applying curvature map method; (c) zoomin of high wavenumber region of (a); (d) zoom-in of high wavenumber region of (b)............ 89
Figure 4-7 Temperature monitored at 5 key points for 18 hours .......................................
91
Figure 4-8 Laser intensity monitored forl8 hours .....................................................................
91
Figure 4-9 Wavelength drifts increase prediction error .......................................
92
........
Figure 4-10 Peaks chosen from the acetaminophen powder Raman spectrum. ........................ 93
Figure 4-11 Wavelength drifts in 9 acetaminophen peaks detected using the new algorithm in 42
measurem ents over 10 hours......................................................................................................... 95
Figure 4-12 Detected wavelength drifts in 4 representative peaks before (dashed) and after
(solid) application of the correction algorithm. .................................................................
96
Figure 5-1 Photon-medium interactions in the photon migration picture.............................
101
Figure 5-2 Flow chart of the new Monte Carlo code for diffuse reflectance, fluorescence, and
Ram an scattering...............................................................................................................
109
Figure 5-3 Steady-state fluence rate owing to excitation for three turbidity-induced sampling
volumes: (left) large; (middle) medium; (right) small sampling volume. ............................... 110
Figure 5-4 Radial profile of diffuse reflectance versus varying ts ............. ................... . . . ..... .
111
Figure 5-5 Total diffuse reflectance collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-4........... .......................................................................................................
112
Figure 5-6 Steady-state fluence rate owing to Raman scattering for three turbidity-induced
sampling volumes: (left) large; (middle) medium; (right) small sampling volume................ 112
Figure 5-7 Radial profile of Raman scattered light versus varying s.................................... 113
Figure 5-8 Total Raman scattered light collected from a spot of 0.5 cm radius for the 7 cases in
113
..................................................
Figure 5-7
Figure 5-9 Radial profile of diffuse reflectance versus varying a............................................. 114
Figure 5-10 Total diffuse reflectance collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-9 . ....................................................................
114
Figure 5-11 Radial profile of Raman scattered light versus varying pa. ....................................
115
Figure 5-12 Total Raman scattered light collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-11 ..................................................
115
-11-
Figure 5-13 Raman versus diffuse reflectance for various turbidities. Symbols code different
absorption coefficients. ............................................................................................................... 116
Figure 5-14 (Ram*lt)versus diffuse reflectance for various turbidities .................................... 117
Figure 5-15 (Ram*glt) versus (Rx-RR)/(ax-aR). The slope is the intrinsic Raman signal ......... 118
Figure 5-16 (Ram*lt) versus RR. The fit to the curve can be used to correct for sampling volume
variations. See text for details .................................................................................................... 119
Figure 5-17 Diffuse reflectance versus Pts/La for a 2 cm (r) by 2 cm (z) cylinder with three
120
collection spot radii: 2, 1, and 0.4 cm ......................................
Figure 5-18 Diffuse reflectance versus lts/ta for a 1 cm (r) by 1 cm (z) cylinder with three
120
collection spot radii: 1, 0.5, and 0.2 cm ......................................
Figure 5-19 Diffuse reflectance versus CIs/CLa for a 0.5 cm (r) by 1 cm (z) cylinder with three
120
collection spot radii: 0.5, 0.25, and 0.1 cm ......................................
Figure 5-20 (Ram*pt) versus RR for three sample sizes: 0.5 cm (r) by 1 cm (z), 2 cm (r) by 2 cm
121
(z), and semi-infinite. (Fixed g (0.8) for all cases.) .....................................
Figure 5-21 (Ram*lit) versus RR for four g's: 0.7, 0.9, 0.95, and 0.99. (Fixed sample size 2 cm (r)
by 2 cm (z) for all cases.)............................................................................................................ 122
Figure 5-22 Combined effect of the sample size and scattering anisotropy on the curvature.... 123
Figure 5-23 Correlations between the curvature and the sample size (left) and anisotropy (right).
12 3
.........................................................................
Figure 5-24 OLS model constituent spectra from (a) to (f) are: fluorescence, creatinine, Intralipid,
ink, w ater, and fused silica.......................................................................................................... 127
128
Figure 5-25 Representative spectrum, fit, and residual. .....................................
Figure 5-26 Normalized creatinine Raman signal of the 49 samples, represented by the
128
norm alized OLS fit coefficients versus s/ a..............................................................................
Figure 5-27 Integrated diffuse reflectance of the 49 samples normalized to the highest value
128
versus is/ita .a........................................... ...............................................................................
Figure 5-28 (Ram*lit) versus RR. Excellent agreement is observed between the experimental
data and M onte Carlo result ........................................................................................................ 129
Figure 5-29 Raman signal (OLS fit coefficient) of 49 samples before (open circle) and after
(solid square) correction. The gray line at constant 1 is the ideal prediction line. ................. 130
Figure 5-30 Histograms of Raman signal of all 49 samples before (upper panel) and after (lower
panel) correction............................................................... 131
Figure 5-31 Sapphire Raman signal serves as an external standard of the diffused reflectance. 132
Figure 5-32 (Ram*lit) versus RR. Excellent agreement is observed between the experimental
data and Monte Carlo results. ..................................................................................................... 132
Figure 5-33 Raman signal (OLS fit coefficient) of 49 samples before (open circle) and after
(solid square) correction. The gray line at constant 1 is the ideal prediction line. ................. 133
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Figure 5-34 (Ram*pt) versus RR for IRS calibration .....................................
134
Figure 5-35 Formation of the calibration (circle) and the prediction (solid square) sets. ...... 135
Figure 6-1 Twenty frame-by-frame Raman spectra of toluene acquired with 2 sec per frame.. 141
Figure 6-2 Calculated standard deviation of the 20 spectra (dotted) and the square root of the
Raman spectra in Figure 6-1 (solid)..................................
141
Figure 6-3 Measured Raman spectra of pure analytes dissolved in water and typical experimental
mixture spectra in clear and turbid samples: (G) glucose, (C) creatinine, (U) urea, (Sc)
representative clear sample spectrum, and (St) representative turbid sample spectrum. For the
turbid samples, the only clearly identifiable analyte peak is of creatinine at - 680 cm-1 . Traces
are normalized and offset for clarity .......................................
148
Figure 6-4 RMSEP values normalized to PLS results for glucose (G) and creatinine (C) obtained
from various methods in the first (Uncorrelated) and second (Correlated) numerical simulations.
See text for details....................................................................................................................... 149
Figure 6-5 (a) boLS (normalized, dashed line for visual guidance). Deviations of bpLs and bcR
from boLs: (b) bPLs- boLs, and (c) bcR- boLs. All b vectors are for glucose calibration with the
traces offset for clarity. ..........................................................
150
Figure 6-6 (a) Typical Raman spectrum of skin with background removed; (b) typical simulated
Raman spectra, 25 sample spectra are overlaid; (c) difference between the first two spectra in (b),
magnified 10X; (d) glucose Raman spectrum, 90 mg/dL, magnified 100X. The spectra are
displaced vertically for better visualization ......................................
151
Figure 6-7 Raman spectra of the ten constituents used in the simulation: (A): actin (1%); (CH):
cholesterol (2%); (CI): collagen I (49%); (CIII): collagen III (7%); (W): water (3%); (H):
hemoglobin (6%); (K): keratin (15%); (P): phosphatidylcholine (4%); (T): triolein (13%); (G):
glucose (0.2-0.6% ). ............................................................
152
Figure 6-8 RMSEP values normalized to PLS results for glucose obtained from various methods
in the uncorrelated and correlated numerical simulations using the 10-constituent model. See
text for details . ................................................................
154
Figure 6-9 RMSEP values (in arbitrary units) for glucose obtained from CR (4 bars on the left)
and HLA (4 bars on the right) for the three cases in the numerical simulation. The ideal values
from the first numerical simulation are plotted for comparison. ....................................
156
Figure 6-10 Glucose boLs (normalized, for visual guidance) and difference spectra between
averaged b vectors from CR and HLA and bOLs: (a) boLs, (b) bHLA- boLS, and (c) bcR - boLs. 157
Figure 6-11 RMSEP values normalized to PLS results for glucose (G) and creatinine (C)
obtained from various methods for clear sample experiments without (Uncorrelated) and with
(Correlated) analyte correlations. See text for details.............................
160
Figure 6-12 RMSEP values normalized to PLS results for glucose (G) and creatinine (C)
obtained from various methods for the turbid sample experiment. See text for details. ....... 161
Figure 6-13 Raman spectra of the in vitro turbid tissue phantom (top), and 50 mM glucose in
water (bottom, water subtracted). The samples were in a cuvette ........................................ 164
-13-
Figure 6-14 Raman spectra of the in vivo dog study (top), and 50 mM glucose in water (bottom,
water subtracted). The glucose sample was in a fake dog ear holder described in section 5.4.2.
.................................... 165
...............................................................................................................
Figure 6-15 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details......................... 166
Figure 6-16 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details......................... 167
Figure 6-17 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details......................... 168
Figure 6-18 Comparison between CR and PLS with different inaccuracy in the reference
concentration measurem ents ....................................................................................................... 169
Figure 6-19 Comparison between CR and PLS with different spectral overlaps. The scheme of
170
33- frame averaging was used.....................................
Figure 7-1 A dog subject lies on its stomach with the ear positioned over the sapphire window
173
aperture of the aluminum sample stage. .....................................
Figure 7-2 33-frame averaged sample spectra with -18.7 min in between 2 adjacent spectra. . 174
Figure 7-3 Sample spectra in Figure 7-2 after background removed using a fifth-order
175
polynom ial routine . .....................................................................................................
Figure 7-4 Variance spectrum calculated from 10 frames using the curvature correction
algorithm ........ ............................................................................................................ 176
Figure 7-5 Laser fluctuation (pixel 400 as an example): Raw data (upper left), raw data zoom-in
(upper right), filtered data (lower left), and filtered data zoom-in (lower right). .................... 177
Figure 7-6 33-frame averaged sample spectra (thin solid lines), smoothed spectra (solid lines
178
with cross), and extracted fixed pattern noise (dashed line) ......................................
Figure 7-7 RMSECV versus number of PLS factors ......................................
179
Figure 7-8 Clarke error grid of predicted glucose concentrations. ...................
.................... 180
Figure 7-9 Temporal profiles of reference and predicted glucose concentrations (-1.87 min
betw een tw o samples) ................................................................................................................. 180
Figure 7-10 Regression vector (top) and the glucose Raman spectrum (bottom). .................. 181
Figure 7-11 Rayleigh and Sapphire peaks before removing the slowly-varying backgrounds.. 189
Figure 7-12 Normalized Rayleigh and Sapphire peaks after removing the slowly-varying
189
backgrounds and plasma glucose concentration profile. .....................................
-14-
LIST OF TABLES
Table 2-1 Glucose measurements using NIR absorption spectroscopy ..................................... 36
Table 2-2 Glucose measurements using NIR Raman spectroscopy. .....................................
Table 2-3 Cross-validated results of calibration on eight analytes .....................................
39
. 43
Table 4-1 List of components in the present instrument versus the previous generation ............. 78
Table 5-1 Tissue phantom design: scattering coefficient, absorption coefficient, and the
calculated ratio.... .......................................................................................................
126
Table 7-1 Summary of the cross-validation analysis with various pre-processing and model
182
param eters........ ...........................................................................................................
Table 7-2 Summary of the level-splitting analysis with various pre-processing and model
param eters........ ...........................................................................................................
184
Table 7-3 Summary of the leave- one-level-out analysis with various pre-processing and model
param eters. ...................................................................
185
Table 7-4 Summary of the randomized concentration analysis ......................................
185
Table 7-5 Summary of the level-splitting analysis with various pre-processing and model
param eters........ ...........................................................................................................
186
-15-
LIST OF ABBREVIATIONS
Chapter 1
NIR/MIR/IR: near infrared/mid-infrared/infrared
CCD: charge coupled device
OLS: ordinary least squares
CLS: classical least squares
ILS: inverse least squares
PCA/PCR: principal component analysis/principal component regression
PLS: partial least squares
HLA: hybrid linear analysis
CR: constrained regularization
PRESS: prediction residual error sum of squares
RMSEP: root mean square error of prediction
RMSECV: root mean square error of cross validation
SEP: standard error of prediction
SECV: standard error of cross validation
r: correlation coefficient
r2: square of the correlation coefficient
Chapter 2
GFR: glomerular filtration rate
BUN: blood urea nitrogen
OCT: optical coherence tomography
PAS: photoacoustic spectroscopy
MAE: mean absolute error
SNR: signal-to-noise ratio
Chapter 3
UV: ultra violet
Chapter 4
-16-
ASE: amplified spontaneous emission
NA: numerical aperture
f/#: 1/(2*NA)
LN : liquid nitrogen
QE: quantum efficiency
FWHM: full width at half maximum
Chapter 5
IRS: intrinsic Raman spectroscopy
IFS: intrinsic fluorescence spectroscopy
DRS: diffuse reflectance spectroscopy
Chapter 6
NIPLS: nonlinear iterative partial least squares
SVD: singular value decomposition
PCSA: pure component selectivity analysis
Chapter 7
ISF: interstitial fluid
ECF: extracellular fluid
-17-
-18-
CHAPTER 1 INTRODUCTION
Applications of optical techniques to biological and biomedical problems have been rapidly
advancing in recent years. This thesis addresses one specific application among many others:
non-invasive blood analysis using near infrared (NIR) Raman spectroscopy.
Based on inelastic scattering, Raman spectroscopy, as a type of vibrational spectroscopy,
provides extremely rich molecular information about multiple analytes present in a
sample/specimen simultaneously. The intensity of Raman signal bears a linear relationship to
the analyte concentrations, and therefore, Raman spectroscopy can be used as a quantitative tool
in concentration measurements as well. Owing to the nature of low-energy optical radiation
impinging on the sample/specimen, there is no danger from exposure to ionizing radiation. In
addition, penetration depth of NIR light is significantly larger than other optical wavelengths,
mainly because of lower water and protein absorption. As a result, Raman spectroscopy satisfies
two critical prerequisites for a truly non-invasive technique. The ultimate application of this
technique will be non-invasive and continuous monitoring of clinically important blood analytes
in vivo. Nevertheless, non-invasive techniques of this kind will be valuable in a wide variety of
clinical settings and laboratory tests.
Over the past few years, novel instrumentation and applications using NIR Raman spectroscopy
have been developed in the MIT Spectroscopy Laboratory. Quantitative analyte concentration
measurements have been demonstrated on multiple blood analytes in water solution, human
blood serum and whole blood, and in vivo human subjects. After the acquisition of the Raman
spectra together with the corresponding reference concentrations of the analyte of interest (the
calibration data), chemometric algorithms with internally consistent leave-one-out cross
validation were applied to extract concentration information relevant to the analyte of interest, a
-19-
procedure called "multivariate calibration." The outcome of the calibration process is the so
called "b vector," which summarizes the correlation between the measured spectra and the
reference concentrations.
This b vector can then be employed to predict the analyte
concentrations prospectively, i.e., future samples independent from the calibration data. Note
that calibration and prediction are two distinctive steps, and the associated errors should always
be explicitly specified. A good cross validation result is necessary but not sufficient for a good
prediction result.
The goal of this thesis is to address three major challenges when this technique is to be applied
prospectively: instrumental requirements, turbidity-induced sampling volume variations, and
analyte-specific information extraction.
This thesis will also serve as a resource for other
researchers who are interested in quantitative biological Raman spectroscopy. Glucose is chosen
as an example analyte because it is relatively easy to alter its concentration in vivo and for the
application's potential impact on diabetes.
1.1 Objectives
1.1.1
Improving throughput, precision, and stability
Since Raman scattering is an extremely weak phenomenon, it is imperative to have an instrument
with high throughput to acquire enough scattered photons in a reasonable period of time. Thus,
improvements in instrument throughput had to be made.
However, when a compact
spectrometer and large-area charge coupled device (CCD) detector are employed for high
throughput, image curvature is an inevitable artifact. A better method had to be developed to
transform 2D images into lD spectra without degrading spectral resolution. In addition, analyte
Raman features are usually a small portion compared to contributions from proteins and other
constituents in biological media and the entire Raman spectrum is often riding on a broadband
- 20 -
background.
These confounding factors make minute spectral variations owing to analyte
concentration changes easily masked by imprecise spectral pre-processing or source intensity
fluctuations. Therefore, wavelength precision and intensity stability had to be addressed.
1.1.2
Correcting sampling volume variations
One of the major challenges to apply any optical technique to biological media is turbidityinduced sampling volume variations. With fixed, finite collection geometry, the analyte Raman
signal is sensitive to the number of analyte molecules sampled and therefore errors are prone to
occur if sampling volume variations is not corrected.
physical parameters: scattering coefficient (.s)
Turbidity is the manifestation of two
and absorption coefficient (ta).
Significant
variations in these two parameters exist among biological media such as tissue or bodily fluids
owing to human physiological variations. Take whole blood as an example: depending on the
red blood cell density, gs and ta can vary significantly. Similarly, owing to differences in skin
morphology, Raman spectra acquired from different sites or individuals have various levels of
"built-in" turbidity distortions, a major hurdle for calibration transfer. To address this issue, a
corrective method had to be developed.
1.1.3
Optimizing information extraction
Quantitative analysis of spectroscopic data generally belongs to a field called chemometrics.
Since the spectral contribution from the analyte of interest is only a small portion of the entire
Raman spectrum and is always overlapped with other spectral interferents, concentration
information can not be obtained simply by measuring analyte-specific peak heights, i.e., via
univariate methods.
Multivariate calibration techniques take the full-range spectrum into
account and therefore fully exploit the multi-channel nature of spectroscopic data. Implicit
calibration methods are often the only choices when all the constituent spectra are not known.
-21-
Partial least squares (PLS) and principal component regression (PCR) are two widely adopted
methods. Fully based upon calibration data, these methods lack the capability of incorporation
of prior or additional information.
One direction to optimize information extraction is to incorporate prior information such as pure
analyte spectrum into the calibration process, and is thus called hybrid calibration. A potential
issue for hybrid methods is that the performance degrades when the prior information is
inaccurate, a common situation with biological media. Therefore, there is a need for developing
hybrid calibration that is robust against inaccurate prior information.
1.2
Major accomplishments
Results described in the following chapters show progress along the fore-mentioned three
directions. These are all my original contributions.
(1) To provide better throughput and alignment, several critical components have been
redesigned or replaced. A homebuilt photodiode has been added to the original instrument to
provide correction for laser intensity fluctuation and temperature probes have been added at key
positions. A new spectral pre-processing algorithm has been developed to make the originally
curved 2D images into 1D spectra. The new method calibrates on multiple Raman lines of a
reference material and therefore generates spectra with diffraction-limited spectral resolution and
reduced sensitivity to sample placement. Lastly, the error introduced by wavelength drifts was
evaluated and a new correction scheme has been devised.
(2) Intrinsic Raman spectroscopy (IRS) has been developed as a method to correct turbidityinduced sampling volume variations. The relationship between Raman and diffuse reflectance
has been studied using analytical models, Monte Carlo simulations, and tissue phantom
experiments, with designed turbidity variations.
- 22 -
Excellent agreement between modeling and
experiments has been observed.
Based on the observed functional relationship between
Raman*it, where tt is the total attenuation coefficient, and diffuse reflectance, the intrinsic
Raman signal can be obtained. Ordinary least squares (OLS) and Partial Least Squares (PLS)
has been applied to analyze the raw and corrected spectra, showing significant improvement in
concentration measurements after IRS correction.
(3) Constrained regularization (CR) has been developed as a new hybrid method for multivariate
calibration.
CR incorporates prior information in the form of pure analyte spectrum, and
therefore generates more analyte-specific calibration models compared to the most widely used
method, partial least squares (PLS). Compared to hybrid linear analysis (HLA), a method that
uses the pure analyte spectrum in a different way, CR shows improved robustness when the pure
analyte spectrum is not accurate. Inaccurate pure analyte spectra can be a result of several
causes: turbidity variations, co-existing anomeric forms (e.g., a- and P3-glucose), chemical with
multiple types (e.g., collagen), and instrumental drifts. We demonstrate both numerically and
experimentally with tissue phantoms that CR is more robust when turbidity variations are present.
Additionally, using data from a dog study, we investigate the relative performance of CR and
PLS for in vivo applications. We compare CR and PLS from several aspects, including the
presence of a strong fluorescence background with photobleaching, background removal, signalto-noise ratio, reference concentration error, and spectral overlap among constituents. We have
identified fluorescence background decay as the main reason that CR performed similarly to PLS
in the in vivo dog experiment.
(4) An in vivo dog study has been done in parallel with the other major accomplishments of this
thesis.
Using PLS, the concentration prediction error is approaching our theoretical limit
calculated for the experimental condition. We used the dog data and the modeling work in (2)
- 23 -
and (3) to identify issues for the applicability of CR and IRS. Guidelines are provided for future
in vivo studies.
1.3
Outline of the thesis
The work that has been performed is presented in the following sequence:
Chapter 2 Background and significance
This chapter provides background information about clinically relevant blood analytes that are
encountered in this thesis: glucose, creatinine, and urea. Their physiological concentrations are
within the millimolar (mM) range, suitable for non-invasive optical techniques.
A review
section is presented on existing non-invasive optical techniques. Previous accomplishments in
this project are also summarized, including, development of a sensitive instrument,
measurements of chemical concentrations in disposed human serum and whole blood, and a
transcutaneous study using human subjects.
Chapter 3 Introduction to quantitative biological Raman spectroscopy
This chapter introduces Raman spectroscopy, including the classical theory and interpretation of
Raman scattering and comparison of selection rules to absorption spectroscopy.
Biological
considerations such as excitation wavelength, background, light penetration depth, and skin
heterogeneity are discussed. Quantitative aspects including theoretical minimum detection error
based on signal-to-noise ratio and overlap factor are also discussed. An in-depth overview of
multivariate calibration is given to equip the reader with the necessary knowledge to evaluate
calibration results.
Chanter 4 Improving throughout. precision, and stability
-24 -
We present important considerations for building a high throughput Raman instrument. We also
describe the continual upgrade of our laboratory instrument for higher sensitivity.
Several
components have been replaced or redesigned to achieve this goal. In addition, we review the
image curvature problem owing to a high numerical aperture spectrograph with large CCD
detector and provide detailed analysis with an improved solution. We further describe addition
of a laser intensity monitoring photodiode and temperature probes at key positions. Lastly, the
error introduced by wavelength drifts is evaluated and a new correction scheme is implemented.
Chapter 5 Correcting sampling volume variations
This chapter first provides an overview of techniques to correct turbidity-induced spectral
distortions and sampling volume variations in fluorescence and Raman spectroscopy,
respectively. It introduces the methodologies of intrinsic Raman spectroscopy (IRS) to the field
of biomedical optics. Analytical models and Monte Carlo codes have been developed and
employed to give insights to the relationship between Raman and diffuse reflectance under
turbidity variations. Tissue phantom experiments are performed with results agreeing to the
modeling results. Based on the observed functional relationship between Raman*,tt, where pt is
the total attenuation coefficient, and diffuse reflectance, the intrinsic Raman signal can be
obtained. Ordinary least squares (OLS) and Partial Least Squares (PLS) are applied to analyze
the raw and corrected spectra, showing significant improvement in concentration measurements
after IRS correction.
Chapter 6 Optimizing information extraction
Data analysis is the immediate next step after spectral data and reference concentrations are
taken. In general, data analysis for quantitative biological Raman spectroscopy consists of three
- 25 -
major steps: pre-processing, multivariate calibration including model building and validation,
and prospective application of the model. This chapter describes each of the steps in detail. It
reviews traditional methods and novel ones that we have developed. Particularly, we present the
new hybrid multivariate calibration technique: constrained regularization.
The superior
performance of CR over PLS and HLA is demonstrated using both numerical and experimental
data.
In addition, using data from the dog study, we study the relative performance of CR and PLS for
in vivo applications. We compare CR and PLS from several aspects, including, the presence of
strong background with its intensity decay over time, background removal, signal-to-noise ratio,
reference concentration error, and spectral overlap among constituents.
Chapter 7 In vivo dog study
This chapter describes an in vivo dog study that has been done with our collaborators at Bayer
Healthcare. The dog study was performed on a beagle anaesthetized for -8 hours, during which
its blood glucose concentration was clamped at several different levels. Results demonstrate
feasibility of extracting glucose-specific information in vivo using our technique. Using PLS, the
concentration prediction error is approaching our theoretical limit calculated for the experimental
condition. We use the dog data and the modeling work in chapters 5 and 6 to identify issues for
the applicability of CR and IRS. More importantly, the analyses and results provide valuable
insights to improving our technique for future in vivo studies.
Chapter 8 Conclusion and future directions
The major accomplishments in this thesis research are summarized, and final remarks are given.
- 26 -
CHAPTER 2 BACKGROUND AND SIGNIFICANCE
This chapter provides background information on clinically relevant blood analytes that are
encountered in this thesis: glucose, creatinine, and urea. Their physiological concentrations are
within the millimolar (mM) range, suitable for non-invasive optical technologies. A brief review
of existing non-invasive optical techniques is given with emphasis on salient or unique features.
Previous accomplishments in this project are also summarized, including development of a
sensitive instrument, measurements of chemical concentrations in disposed human serum and
whole blood, and a transcutaneous study using human subjects.
2.1
Blood analytes encountered in this thesis
Blood analyte concentrations provide important clinical information in diagnostic procedures.
Most clinical chemistry techniques are performed in four steps: withdrawing blood from patients,
centrifuging blood to obtain serum or plasma, adding specific reagents for chemicals whose
concentrations are of interest, and measuring concentrations using spectrophotometric techniques.
Although these methods can be used to detect a wide variety of substances and have evolved to
the point where they can be done relatively quickly and accurately on small quantities of blood,
they usually require transport to a laboratory and multiple processes before analysis can be
initiated. Thus, from a practical perspective, clinicians can not obtain instant results from these
methods. There is great benefit in developing a technique capable of measuring clinically
important substances that does not require reagents for analysis and is non-invasive, as current
clinical chemistry methods still require blood withdrawal.
Non-invasive blood analysis is a technique for measuring blood analyte concentrations without
physically contacting the sample or subject. Among various candidates, optical technology
appears to be the most suitable modality compared to others. Optical technology enables non- 27 -
contact and painless measurements, virtually no sample preparation, is reagentless, and allows
for simultaneous determination of multiple analytes.
Glucose, creatinine, and urea are chosen as example analytes in this thesis and are reviewed
below.
2.1.1
Glucose
Glucose is the carbohydrate essential to all body cells as a major energy source. It is introduced
into the body by direct ingestion of glucose or digestion of other large carbohydrates molecules.1
Its concentration is regulated by a variety of hormones, the most important of which is insulin.
When the glucose level in the blood stream rises, insulin is secreted by the pancreas, which
enables the glucose to move into cells. In the absence, or lack, of insulin, the glucose cannot
move into the cells and therefore its level rises in the bloodstream, and the cells begin to
catabolize (break down) fat.2
The most prominent glucose-related disease is diabetes. There are two main types of diabetes:
Type 1 diabetes (insulin dependent diabetes) and type 2 diabetes (non-insulin dependent). Type
1 diabetes is primarily due to autoimmune-mediated destruction of pancreatic beta-cell islets,
resulting in absolute insulin deficiency. People with type 1 diabetes must take exogenous insulin.
People with type 2 diabetes, which accounts for over 90% of diabetes, are able to produce insulin
but are unable to use it properly. Diabetes itself may not be a serious disease but the real risks lie
in its complications such as heart disease and stroke, blindness, kidney disease, nerve disease,
amputations, and etc. Economically, these complications have led to huge cost and financial
burden.
Frequent measurements and tight control of blood glucose level will lower the risk of
complications. Thus, the American Diabetes Association recommends that glucose levels be
- 28 -
measured frequently and accurately in all diabetes patients. People with type 2 diabetes are
recommended to check daily blood glucose level by themselves at least once in a day.
Nevertheless, numerous studies and reports have indicated that more frequent measurements are
actually necessary. Type 1 people may require 3 or 4 times (before meals and at bedtime) for
tight control, since people with type 1 do not have the ability to produce insulin at all.
The glucose concentration in a normal human subject typically ranges from 45 to 180 mg/dL (2.5
to 10.0 mM) in plasma. 3 Glucose concentration is affected by the age and gender of the subject
and the delay between a meal and the measurement. Glucose concentrations higher than the
normal range are classified as hyperglycemia and glucose concentrations lower than the normal
range are classified as hypoglycemia. Extreme concentrations as high as 1000 mg/dL (56 mM)
have been observed.
Among all clinical chemistry techniques, enzymatic methods yield the maximum specificity for
glucose measurements. Glucose can be measured by the reaction of f3-D-glucose with glucose
oxidase, in which gluconic acid and hydrogen peroxide are generated. Hydrogen peroxide then
reacts with an oxygen acceptor in a reaction catalyzed by peroxidase to form a color, and
subsequently detected via spectrophotometry. One of the chief advantages of a glucose oxidase
method is its low cost.
Another useful approach is the glucose oxidase-oxygen electrode method. In this method, an
oxygen-sensing electrode monitors reaction of glucose with oxygen while generated hydrogen
peroxide is removed by reaction with ethanol and iodide. By determining the rate of oxygen
consumption, one can accurately estimate glucose. This method is precise, linear, and free from
important interferents, and has been widely used with variations, as reference methods.
- 29 -
Glucose in water solution has two anomeric forms with distinctive Raman spectra. Precautions
should be given to in vitro sample preparation or comparison to the regression vector that the
balanced form is used. Figure 2-1 shows the a-D-glucose and its anomeric balanced form
(mixture of a- and J3-D-glucose) at room temperature. It takes a few hours for the a form to
become the balanced form in water solution.
0.
0.
0.
0.
400
600
800 1000 1200 1400 1600
Raman shift (cm-1)
Figure 2-1 Raman spectra of a-D-glucose (solid) and anomeric balanced D-glucose (dashed) in
water.
2.1.2
Creatinine
Creatinine is a waste product from muscle activity that circulates in the bloodstream. The typical
serum creatinine concentration in an adult male is 1 mg/dL (88 [IM). Levels of creatinine in
serum are used in conjunction with other factors such as age, gender, and race to calculate the
glomerular filtration rate (GFR), a measure of the ability of the kidney to filter blood and
produce urine. The National Kidney Foundation has recommended that serum creatinine be
measured to monitor kidney function. However, there is significant inter-laboratory variation in
-30-
this measurement as a result of the methods used. The Raman spectrum of creatinine measured
in water is shown in Figure 2-2.
j
400
600
800 1000 1200 1400 1600
Raman shift (cm-1 )
Figure 2-2 Raman spectra of anomeric balanced D-glucose (G), creatinine (C), and urea (U).
2.1.3
Urea
Urea is synthesized in the liver during the deamination of protein (removal of nitrogen from
amino acids). Determination of plasma urea is used most frequently as a kidney function test.
This is because urea does not circulate for long in the bloodstream but rather is filtered through
the kidneys and excreted in the urine. With deterioration of kidney function, the rate and
effectiveness of filtration falls and the urea concentration increases.
Physicians use urea
concentration to screen for renal problems and to monitor their progression. 3
Historically, the nitrogen content of urea has been reported instead of the actual urea
concentration. Due to this reason, urea concentrations in blood are reported in concentrations of
"blood urea nitrogen" (BUN).
To convert a blood urea nitrogen concentration to a urea
concentration, the conversion factor 2.14 is multiplied. A typical concentration of urea nitrogen
-31-
is 8 - 23 mg/dL (2.9 - 8.2 mM) in plasma and 60 - 90 mg/dL (21.4 - 32.1 mM) in urine. Low
levels of urea in urine may indicate malnutrition and kidney dysfunction, whereas high levels
may indicate excessive protein intake. Raman spectrum of urea measured in water is shown in
Figure 2-2.
2.2
Review of existing non-invasive optical techniques for glucose detection
In the following, we present a general overview of direct and indirect optical techniques
employed for non-invasive measurements of glucose that have appeared in the peer-reviewed
literature within the past two decades. Direct approaches are based on glucose-specific intrinsic
molecular properties such as optical absorption, Raman scattering, and optical rotation. Indirect
approaches are based on glucose-induced changes in physiological or physical parameters such
as the index of refraction and the scattering coefficient.
Omar Khalil4 ' 5 has written two
comprehensive reviews spanning the period from 1989 to 2003. It is not our goal here to
conduct an exhaustive literature review, but to familiarize the reader with each technique.
Fundamental principles and salient features of each technique will be followed by a summary of
one or more representative studies, selected by considering the impact to the field and inclusion
of sufficient supporting evidence.
The cited literature includes a variety of study designs.
In all, it is essential that glucose
concentrations in the calibration samples vary over a wide range. For in vitro studies, this
requirement can be satisfied by the original sample diversity or by spiking the samples with a
glucose stock solution. For in vivo studies, one of three different experimental protocols is
typically followed: oral glucose or meal tolerance,5 time-randomized, or glucose clamping. 6 To
further increase the range of glucose variation, patients with diabetes have been involved in some
of the studies.
- 32 -
A concern exists that calibration results based on glucose tolerance protocols are likely to be
influenced by spurious correlations.7
Therefore, time-randomized and glucose clamping
protocols are better choices given that rigorous experimental design can be employed. However,
they are relatively more costly and require higher compliance from experimental subjects.
For brevity, results from selected in vitro and in vivo studies employing NIR absorption or
Raman spectroscopy, the most commonly used techniques, are documented in Table 2-1 and
Table 2-2. In the tables, error estimates are reported with either "CV" or "P" in parentheses,
indicating cross-validated or predicted results, respectively. For an explanation of these terms,
please refer to the section on multivariate calibration (section 3.4).
2.2.1
Direct approaches
2.2.1.1.
Near infrared (NIR) absorption spectroscopy
NIR absorption spectroscopy is one of the most widely pursued techniques for in vivo glucose
sensing because of the relatively low cost of the necessary instrumentation, data with high SNR,
and the penetration depth of NIR light into biological tissue, which can reach depths of mm - cm
in several windows within the 800-2500 nm (12500-4000 cm 1 ) NIR spectral region. Light at
these wavelengths is absorbed by IR-active overtone or combination vibrational transitions of
molecules.
IR-active transitions are associated with a change in the dipole moment of the
molecule. Because overtone and combination transitions are much weaker than fundamental
transitions, NIR light penetrates deeper into the tissue than longer wavelength regions in the midto far-infrared. The penetration depth in shorter wavelength regions is limited by hemoglobin
absorption and light scattering. Thus, the NIR region is ideal for probing biological tissues at
depth.
-33 -
The NIR spectral range can be roughly divided into three regions that have been explored for the
application of non-invasive glucose sensing. The shorter-wavelength region (14286-7300 cm-1 )
includes numerous higher order transitions such as OH (10654 cm-') and CH (8881 cm ')
overtones. The spectral region 6500-5500 cm'1 corresponds to an OH and CH combination band
(6510 cm -1) and a CH overtone (5924 cm-n). The higher-wavelength region (5000-4000 cm-')
includes CH stretch combination bands and CCH and OCH deformation bands at 4423 and 4300
cm'. These ring deformation bands may provide higher specificity for glucose as compared to
the other regions. Additional consideration should be given to interferents such as water, fat, and
hemoglobin when various spectral ranges are employed.4
Glucose absorption at physiological concentrations is several orders of magnitude lower than the
major background absorber in tissue, water. Additionally, molecular overtone and combination
bands are typically very broad, leading to spectra with a large degree of spectral overlap. As a
result, multivariate calibration is required to extract quantitative analyte-specific information.
A NIR absorption instrument typically consists of a tungsten-halogen lamp as the broadband
light source, intermediate optic elements to deliver and collect the light, a Fourier-Transform
spectrometer, and an InSb detector. An InGaAs photodiode array and a grating are sometimes
used in place of the Fourier-Transform spectrometer. Recently, Olesbergs demonstrated the use
of a tunable diode laser that could significantly increase the SNR as compared to lamp
illumination. Both transmission and reflectance modes have been realized, frequently with fiberoptic probes.
The reflection mode 9 has the advantage of being a single-ended instrument, i.e., the source and
detector are on the same side of the measuring site. This facilitates optical probe design and
allows for greater access to various tissue sites. The transmission mode1 o requires the tissue site
- 34 -
to be sandwiched between the source and detector and is therefore restricted by sample geometry
and available space. However, the optical path length is better defined in the transmission mode
than in the reflection mode, which may reduce error.
Early in vitro experiments in blood or plasma samples spiked with glucose demonstrated the
detection capabilities of NIR absorption spectroscopy.1,
12
Significantly better results were
obtained in plasma than in blood, likely owing to the higher background absorption and
scattering loss introduced by red blood cells.
Marbach 9 et al. analyzed in vivo diffuse reflectance spectra obtained from human inner lip and
discovered a lag time of-10 min for the glucose concentration in the optically probed volume to
reflect the plasma blood glucose concentration. This time lag has a profound impact on the
development of a non-invasive technique as a significant portion of the spectroscopic signal
originates from glucose molecules contained in the tissue interstitial fluid. Samann et aL.13
evaluated the long-term accuracy of a NIR calibration algorithm and the resulting wide range of
errors demonstrated the need for very stable instrumentation and algorithms robust enough to
accept changes in patient physiology. Maruo et al.14 employed a novel numerically simulated
calibration model to perform glucose concentration predictions within several hours of the
calibration phase. Using a glucose clamping protocol, Olesberg et al.15 found spectral residuals
similar to the glucose net analyte signal by removing principal components obtained during a
fasting condition from spectra obtained during a hyperglycemic period.
presence of glucose spectral information in the NIR measurements.
results from these and other selected NIR studies.
-35-
This suggests the
Table 2-1 summarizes
Table 2-1 Glucose measurements using NIR absorption spectroscopy.
In vitro
range [cm
tral-
Mode
Sample
# Samples
Protocol
Approx.
error
Haaland et al."
6600-4250
transmission
whole blood
various
number from
4 individuals
spiked
2 (CV)
Small et al.'2
5000-4000
transmission
bovine
plasma
69
spiked
0.4-0.5 (P)
# Subjects
Protocol
Approx.
error
Author
plasma
[mM]
In vivo
Site
range [cm]tral Mode
Author
range [c
Robinson
Robinson
et
et
[mM]
6600-4250
transmission
fingertip
1 diabetic
tolerance
1.1 (CV)
Marbach et al.9
9000-5500
reflection
inner lip
133
timerandomized
randomized
2.5-3 (CV)
Burmeister
al.
6
al.'
7000-5000
transmission
tongue
5 diabetics
timerandomized
> 3 (P)
al.
1_
et
e6
Samann et al.13
12500-7407
reflection
fingertip
10 diabetics
17
Maruo et al.
6667-5556
reflection
forearm
2 healthy
Maruo et al.14
6579-5882
reflection
forearm
Olesberg et al.•
5000-4000
transmission
rat back
2.2.2
5 healthy,
8 ICU
1
randomized
3.1-35.9 (P)
tolerance
1-2 (CV)
tolerance
1.5 (P)
clamp
2.2 (P)
Mid-infrared (MIR) absorption spectroscopy
To reduce the amount of spectra overlap, longer wavelength mid-infrared radiation in the 2.5-25
gm (4000-400 cm "1) spectral range can be used to measure the fundamental vibrations of glucose.
MIR tissue absorption spectra contain sharp peaks allowing for better molecular specificity.
However, the absorption of water in this spectral range is orders of magnitude higher than in the
NIR region, resulting in a much reduced penetration depth of light in biological tissue on the
-36-
order of 10-100 pm. Hence, glucose-containing fluid can not be easily sampled in in vivo
applications.
A MIR absorption instrument contains the same essential components as a NIR absorption
instrument, with the light source, optics, and detector optimized for the mid- infrared spectral
region.
Most of the reported MIR research was carried out in vitro, including those using dried samples 18
to reduce water absorption.
Although MIR absorption spectroscopy can extract clinical
information from blood or serum, 19 its penetration depth is severely limited and therefore
restricted to near-surface measurements in tissue. Heise et al.20 attempted to measure glucose in
oral mucosa and concluded that no clear evidence shows that glucose can be detected.
2.2.2.1.
Near infrared (NIR) Raman spectroscopy
Fundamental vibrational states of molecules can be probed with any wavelength of light by
Raman spectroscopy. In spontaneous Stokes Raman scattering, incident light scattered off a
molecule is shifted to longer wavelengths, with the difference in energy corresponding to
vibrational transitions of the molecule.
The selection rules for Raman scattering and IR
absorption are different, but the molecular information is the same.
IR-active vibrational
transitions alter the dipole of the molecule, whereas Raman-active vibrational transitions alter the
polarizability of the molecule. Further comparisons between NIR absorption spectroscopy and
Raman spectroscopy can be made concerning the data characteristics. NIR spectroscopy offers
high SNR data but with broad, indistinguishable features. Raman spectroscopy offers sharp
spectral features, but weak signals result in lower SNR data. In the following we focus on nonresonant spontaneous Raman scattering.
- 37 -
Because Raman shifts are independent of excitation wavelength, NIR radiation (typically 785 or
830 nm) is chosen for deeper penetration into biological tissue and to reduce the laser-induced
fluorescence background. However, NIR tissue fluorescence is still several orders of magnitude
larger than physiological glucose Raman signals.
Although Raman spectra possess sharp,
distinct peaks, the background fluorescence signal can often be a major limitation to this
technique because of its spectral variation and the associated detector noise.
Multivariate
calibration is required to extract glucose-specific concentration information.
A NIR Raman instrument consists of a laser source, optic elements for light delivery and
collection, and either a Fourier-Transform spectrometer with InGaAs detector, a grating with a
photodiode array, or a grating with a cooled CCD detector. Owing to the intrinsically weak
Raman signal, special considerations are often given to the design of the collection optics. A
microscope objective is the most common collection optic used, however, a paraboloidal mirror
has also been utilized to increase light collection. 21
In vitro measurements have been performed in filtered blood serum, 22' 23 blood serum, 24 and
whole blood. 21 Rohleder et al.23 discovered that measurements from serum are greatly improved
by ultrafiltration to remove macromolecules that cause intense Raman background and
subsequently impair measurement accuracy. Results from whole blood have greater error than
results from filtered or unfiltered serum, but are still within the clinically-acceptable range.1 7
Lambert et al.25 performed measurement in human aqueous humor, simulating measurements in
the eyes.
26' 27
Laser dosimetry concerns may preclude some in vivo applications. To date, only two groups
have reported successful in vivo studies on human subjects. Enejder et al.26 of our laboratory
reported measurements of glucose concentrations in 17 non-diabetic volunteers following an oral
-38 -
glucose tolerance protocol. Results based on individual and multiple volunteers demonstrated
that a glucose-specific calibration model was likely obtained. Chaiken et al.27 reported the
acquisition of whole blood Raman spectra in vivo using tissue modulation.
Glucose
concentrations were subsequently extracted via analysis of a particular spectral range of the
whole blood spectra. A calibration model derived from one individual was able to generate
meaningful predictions on independent data.
Table 2-2 summarizes these and other selected Raman spectroscopy studies. Most published
accounts utilize the same spectral range (-300-1800 cm') and thus specific ranges are not
reported here.
Table 2-2 Glucose measurements using NIR Raman spectroscopy.
In vitro
Excitation
in
[nm]
Sample
# Samples
et 830no
830
serum
66
Qu et al.22
785
serum
Enejder et al.21
830
Rohleder et al. 22
785
Author
al.24
Berger
Berger et al.
Pelletier et al28
Protocol
further sample
Approx.
Approx.
Error [mM]
1.5 (CV)
preparation
1.7 (P)
24
ultrafiltrated
0.38 (P)
whole blood
31
pre-selected
for
hyperglycemia
1.2 (CV)
serum
247
ultrafiltrated
0.4 (P)
aqueous
17
measured within
1-1.5 (P)
# Subjects
Protocol
humor
contact lens
In vivo
Excitation
[nm]
Author
Site
[nm]
26
Enejder et al.
27
Chaiken et al.
Approx.
Approx.
Error
830
forearm
17 healthy
tolerance
785
fingertip
25 diabetics
time-randomized
-39-
[mM]
0.7-1.5 (CV)
1.2 (P)
2.2.2.2.
Optical activity and polarimetry
Glucose is a chiral molecule that rotates the polarization of incident light. 29 The rotation angle
can be measured by polarimetry and is related to the glucose concentration. Polarimetry is often
performed at a single wavelength, therefore avoiding the need for multivariate calibration. 30
However, the analysis can be complicated when dealing with birefringent turbid biological
tissue.31
2.2.3
Indirect approaches
Light scattering in biological tissue is largely a result of refractive index mismatches across
physical boundaries. In the diffusion approximation, 32 the reduced scattering coefficient can be
expressed as a function of the number density and diameter of spherical scatterers and the
refractive index mismatch between the scatterers and the surrounding medium. 33 It is known that
concentration variations of tissue osmolytes change the index mismatch between the
extracellular fluid and structural scatterers such as cell membranes and protein matrix, therefore
creating measurable differences in the tissue scattering coefficient. Compared to other tissue
osmolytes such as potassium chloride (KC1), sodium chloride (NaC1), and urea, glucose has a
34 35
much greater effect in altering refractive index. ,
2.2.3.1.
Diffuse reflectance spectroscopy (DRS)
Instead of analyzing the frequency response of the light to extract molecular information as is
done in reflectance-mode absorption spectroscopy, diffuse reflectance spectroscopy (DRS)
extracts the bulk absorption and scattering coefficients by fitting the spectrum to a particular
model.36
-40-
A steady-state DRS instrument typically includes a broadband light source, intermediate optics,
spatially separated delivery-collection optical fiber probes, 37 and a CCD-based grating
spectrometer. Frequency-based approaches based on diffuse theory have also been pursued.38
Correlations between the glucose concentration and the tissue transport scattering coefficient
have been observed.37' 38
2.2.3.2.
Optical coherence tomography (OCT)
Optical coherence tomography (OCT) has been used to detect glucose and other analyte
concentrations in biological tissue. 35'
39-41
Based on interferometry, OCT provides reasonable
range (-mm) and depth resolution (-104m) for localized tissue reflectance measurements. An
OCT system consists of a broadband light source, intermediate optics, a Michaelson
interferometer, fiber-optical probes, and detector. In particular, Larin et al.40 demonstrated a
correlation between the slope of the OCT signal versus depth and glucose concentration in 15
healthy individuals. It is suggested that glucose-induced local changes in the index of refraction
is related to the slope of the OCT signal.
2.2.4 Other approaches
Thermal emission is based on measuring the fundamental absorption bands of glucose at -10 gpm,
using the body's naturally-emitted infrared radiation as the energy source.
The detection
equipment is similar to that used for IR absorption spectroscopy. Malchoff et al.42 reported the
evaluation of a prototype that measures the infrared emission from the tympanic membrane.
Photoacoustic spectroscopy (PAS) is an alternative method to detect absorption in liquids and
gases or refractive index changes. The sample is excited by short nano-pico second laser pulses.
Light absorption and subsequent localized heating generates detectable ultrasonic waves, which
can be picked up by piezoelectric transducers.
-41-
PAS has been used to measure glucose
concentrations in vivo,43 but no advantage was shown over NIR absorption spectroscopy. PAS
can also be used as an indirect approach that detects refractive index changes.
2.3
Prior research in the MIT Spectroscopy Laboratory
2.3.1
In vitro studies
Our laboratory has pioneered the use of Raman spectroscopy in biological tissue, 44 including
human blood. Berger et al.24 demonstrated concentration measurements in biological media
reported measurement of multiple analytes including glucose, urea, cholesterol, triglyceride,
albumin, total protein and hematocrit in serum and whole blood samples from sixty-nine patients
over a seven-week period. The whole blood measurement errors were considerably higher than
the errors from serum measurements. This result was attributed to the reduced signal levels
obtained from whole blood owing to its high turbidity. An instrument was consequently built to
increase the signal collection capabilities by over a factor of 4.45
A subsequent whole blood study, Enejder et al.21 confirmed this hypothesis and they were able to
demonstrate the feasibility of measuring multiple analytes in whole blood. In this experiment,
whole blood samples from routine clinical diagnosis were collected from 31 patients. For each
sample, 30 consecutive 10-sec spectra were collected over a 5-min period. Conventional clinical
laboratory methods were used to measure the eight reference analyte concentrations in each
sample.
These reference concentrations were correlated with the recorded Raman spectra
through PLS with cross validation.
Table 2-3 lists the results for PLS leave-one-out cross
validation of the whole blood data set. To provide a sense of the significance of the RMSECV
values, a normal range for adult males in the United States is listed for each analyte. 46 All test
parameters show strong correlation between the predicted and the reference concentrations, with
r2 values of 0.93 or higher except for total cholesterol (r2=0.66). Generally, r2 values higher than
-42 -
0.9 indicate good correlation between the reference and the measured concentration values. Note
that is the r2 value is the correlation coefficient squared between two vectors. In this case, the
two vectors are the reference and the predicted concentrations.
Table 2-3 Cross-validated results of calibration on eight analytes.
Analyte (units)Cross-Validated
Error (RMSECV)
Normal Range
(adult males)
Glucose (mg/dL)*
21
45-180
0.97
Urea (mg/dL)
4.9
17-50
0.94
Cholesterol (mg/dL)
30
150-250
0.66
Triglycerides (mg/dL)
38
10-190
0.92
Total Protein (g/dL)
0.31
6-8.3
0.94
Albumin (g/dL)
0.11
3.2-4.5
0.98
Hemoglobin (g/dL)
0.66
13-17.5
0.94
Hematocrit (%)
1.7
35.9-50.4
0.94
2
* (For glucose: 1mM = 18 mg/dL)
2.3.2 In vivo studies
Enejder et al.26 conducted a transcutaneous study on 17 non-diabetic volunteers with glucose
challenge test. PLS with leave-one-out cross validation was used to analyze each individual.
Various group schemes were employed and the resulting b vector contains spectral information
of glucose.
2.3.2.1.
Methods and experimental protocols
For this study, a series of spectra were collected on the forearm of human volunteers in
conjunction with an oral glucose tolerance protocol. This test involves the intake of a highglucose containing fluid, after which the glucose levels are elevated to more than twice that
found under fasting conditions. Raman spectra and reference glucose concentrations from blood
samples were measured periodically during the 2-3 hour duration of the procedure for each
-43 -
volunteer. A Hemocue glucose analyzer provided the reference measurement for the blood
analysis via finger sticks.
Figure 2-3 Volunteer sitting by the optical table with his forearm clamped at the instrument.
A calibration model was generated individually from the data of each volunteer using PLS with
leave-one-out cross validation.47 '48 The glucose concentrations for all volunteers ranged from 68
to 223 mg/dL. Figure 2-3 shows a volunteer sitting with his arm fixed at the instrument. Raman
spectra in the range 1545-355 cm -' were selected for data analysis. Spectra collected in vivo
consisted of large, broad background superposed with small, sharp Raman features. The broad
background decays over time and is described as fluorescence photobleaching.
-44 -
Each 3-min
sample spectrum was subsequently smoothed with a 13-point Savitzky-Golay filter to increase
the SNR.
2.3.2.2.
Results and discussion
The combined background/Raman spectra from each volunteer were analyzed using PLS with
leave-one-out cross validation, based on which a b vector was obtained using 8 factors from each
individual. A mean absolute error (MAE) was 7.8% and the average r2 was 0.83. When data
from all 17 volunteers were combined, the MAE was 16.9%. An encouraging fact was that
multiple glucose spectral features were identified in the regression vectors, supporting that
glucose was indeed measured.
250
-1
E
200
-r%
0%
.1,J
(1)
C)
L-
LL
0
50
100
150
200
250
reference glucose, mg/dL
Figure 2-4 Cross validated calibration results from each individual of the 17 volunteers
combined into one chart.
-45 -
This study was an initial evaluation of the ability of Raman spectroscopy to measure glucose
non-invasively in vivo. Thus, the focus was on determining its capability on a range of subjects
rather than on long-term tracking. The protocol did not include measurement on the volunteers
over a number of days and thus independent data was not obtained. Note that a mean absolute
error based upon cross validated calibration provides only an indication of the calibration quality
and is not a measure of the expected accuracy over a longer term.
2.4
Summary
Optical detection is the most promising modality for developing a truly non-invasive technique
for blood analysis.
Among optical techniques, Raman spectroscopy offers great potential
because of its molecular specificity. This chapter reviewed clinically relevant blood analytes that
are encountered in this thesis.
Their concentrations are within the millimolar (mM) range,
suitable for non-invasive optical technologies. An in-depth overview of multivariate calibration
is given to equip the reader with necessary knowledge to evaluate calibration results in the
subsequent review section, in which we reviewed techniques including NIR and MIR absorption
spectroscopy, NIR Raman spectroscopy, polarimetry, diffuse reflectance spectroscopy, optical
coherence tomography, thermal emission spectroscopy, and photoacoustic spectroscopy.
The efforts of developing NIR Raman spectroscopy and previous accomplishments in the MIT
Spectroscopy Laboratory were reviewed, including, measurements of multiple blood analytes in
disposed human serum, whole blood, and human subjects using PLS with leave-one-out cross
validation. These results serve as the foundation of the work in this thesis. Note that the author
started working on this project during the data analysis phase of the human volunteer study.
-46 -
TO
CHAPTER 3 INTRODUCTION
BIOLOGICAL RAMAN SPECTROSCOPY
3.1
QUANTITATIVE
Raman spectroscopy
Raman spectroscopy is a way to measure fundamental molecular vibrational states through an
inelastic scattering process called Raman scattering. Raman scattering, discovered by Raman
and Krishna, 49 arises from photon-molecule interactions. In classical terms, the interaction can
be viewed as a perturbation of the electronic cloud of the molecule. When light is scattered from
a molecule the majority of photons are elastically scattered and give rise to Rayleigh scattering.
In elastic scattering, the scattered photon possesses the same energy as the incident photon, and
therefore, no frequency shift. In Raman scattering, on the other hand, photons can either transfer
energy to or gain energy from molecular vibrations. An incident photon, with energy hvL, where
h is Planck's constant and VL the frequency of the excitation laser, excites a molecule into a
virtual state that is lower in energy than an electronic transition. A new photon is created and
scattered from this "virtual state" and is called Stokes-Raman scattering.50 The Stokes-Raman
scattered light will have an energy of h(VL-VR), with frequency VR<VL. Similarly, a molecule can
begin in an excited vibrational state and proceed, via the virtual state, to the ground state. This
process generates an anti-Stokes-Raman scattered photon which has an energy of h(VL+VR), with
frequency VR>VL. The processes of Rayleigh, Stokes Raman, anti-Stokes Raman are depicted
schematically in Figure 3-1.
A Raman spectrum consists of scattered intensity plotted vs. energy, as shown in Figure 3-2 for
acetaminophen powder in a quartz cuvette. Each peak correspond to a given Raman shift from
the incident light energy hvL.
The energy difference between the initial and final vibrational
states, V, or Raman shift in wavenumbers (cm-'), is calculated by V= (vL -vR)/c, with c the
-47 -
speed of light. Raman shifts are always the same, regardless the frequency of the excitation laser.
This provides flexibility to select a suitable laser wavelength for a specific application.
Energy level
Virtual
energy
level
AEL=hvo
AEL=hvo
1st excited
vibration
state
Ground state
AEL=hvo
'
AEe=
-h(vo- VR)
'I
L
AEe=
-hvo
Rayleigh
AEe=
-h(vo+ VR)
Stokes Raman Anti-Stokes Raman
Figure 3-1 Energy diagram for Rayleigh, Stokes Raman, and anti-Stokes Raman scattering.
Infrared absorption also depends on molecular vibrations. Although Raman spectroscopy probes
vibrational transitions indirectly via scattering, the Raman shift has the same energy range as IR
absorption, and in many cases, the same energies are observed. The selection rules for Raman
and IR absorption are different, but the molecular information is the same.
IR absorption
measures vibrational frequencies that change the permanent dipole of the molecule. Raman
scattering measures vibrational frequencies that result in a change of polarizability.
-48 -
I
20.8
S0.6
0.4
Z 0.2
0
500
1000
Raman shift (cm- 1)
1500
Figure 3-2 A Raman spectrum consists of scattered intensity plotted vs. energy. This figure
uses acetaminophen powder measured in a quartz cuvette as an example.
Near-infrared (NIR) absorption spectroscopy is another technique relevant to the context of the
development of quantitative Raman spectroscopy. NIR is based on overtone and combination
bands of mid-IR transitions.
Such transitions are quantum mechanically "forbidden" and
significantly weaker than fundamental transitions. However, the higher energy photons involved
in NIR absorption are transmitted by common optical materials, and the method has a substantial
advantage in instrumentation.
3.2
Biological considerations
3.2.1
Using near infrared radiation
Raman shifts are independent of excitation wavelength and thus offers the flexibility to tailor the
excitation wavelength for specific applications. The choice of NIR excitation is justified by
three advantageous features for investigating biological samples: low-energy optical radiation,
-49 -
deep penetration depth, and reduced background fluorescence. Excitation wavelength in the NIR
region prevents hazardous ionization of sample constituents. The lack of prominent absorbers
present in the NIR region enables longer-range optical sampling, on the order of -1 mm. The
low fluorescence background associated with NIR excitation makes extraction of order-ofmagnitude lower Raman signal possible. As a result, we have chosen 830 nm as the excitation
wavelength to fully exploit the "diagnostic window" as shown in Figure 3-3 with acceptable
quantum efficiency of silicon-cased charge coupled device (CCD) detector.
3
2
=1 10.
-3
-4
500
1000
1500
2000
2500
Wavelength (nm)
Figure 3-3 Absorption spectra of water, skin melanin, hemoglobin, and fat. Also shown is the
scattering spectrum of 10% Intralipid, a lipid emulsion often used to simulate tissue scattering.
Data are obtained from http:// omlc.ogi.edu/spectra/index.html.
Figure 3-3 illustrates the absorption spectra of major endogenous tissue absorbers, namely, water,
skin melanin, hemoglobin, and fat. Also shown is the scattering spectrum of 10% Intralipid, a
lipid emulsion often used to simulate tissue scattering. The diagnostic window is depicted by the
dashed rectangle, in which a group of minima has been seen in the NIR region.
- 50 -
3.2.2
Background signal in biological Raman spectra
Raman spectra of biological samples are often accompanied by strong background. The source
of the background signal is often described as fluorescence, particularly when UV/visible laser
excitation is employed.
Several components present in biological tissue are fluorescent.
Macromolecules, such as proteins and lipids, contribute to the fluorescence background. 22 The
autofluorescence of skin with UV-visible light excitation has been applied to the diagnosis of
disease states such as psoriasis 51 and diabetes, in which changes in the autofluorescence of
collagen owing to glycation (single sugar such as glucose molecule, bonding to a protein or lipid
molecule without the controlling action of an enzyme.) was detected. 52 Furthermore, our lab
utilizes the autofluorescence of components in epithelial tissue to diagnose dysplasia. 53
The presence of the background and shot noise caused by the background limit ultimate
detection capability.
Further, background variation interferes with subsequent multivariate
analysis. As observed in the human study, the background decay is described as fluorescence
photobleaching. Zeng et al.54' 55 fit the signal decay from skin under UV-visible light excitation
with a double-exponential function, with the time constants ascribed as different photobleaching
rates of different fluorophores in the stratum corneum and dermis. On the other hand, Jongen
and Sterenborg 56 assert that the turbidity of tissue influences the decay characteristics of a single
fluorophore such that it does not follow a single exponential. Hence the decay profile does not
need to be described by additional exponentials with different time constants. The physical
reasoning for this argument is that the measured fluorescence signal for a multi-layered turbid
medium is the sum of the contributions from each layer. Fluorescence from a deeper-lying layer
will appear weaker and will photobleach at a slower rate because of the diminished laser power.
Thus, the relative contribution of fluorescence from deeper layers will appear as smaller signals
-51 -
that decay slower whereas the superficial layers have stronger signals that decay faster. This
illustrates the strong influence that optical properties of the sample can have on the observed
behavior of light.
While implicit multivariate calibration techniques can remove the detrimental effects of the
background to some extent, their efficacy is always impaired. Thus, it is desirable to either
reduce the background during data collection or remove it without introducing artifacts. Most
background removal methods in the literature are based on polynomial fit. Since the background
has little structure, a slowly-varying low-order polynomial can suffice to approximate the
background. 44, 57-59 These authors found that a fifth-order polynomial is the most effective
method to fit the background.
3.2.3
Heterogeneities in human skin
Uniform analyte distribution is often a good assumption for liquid samples such as blood serum
or even whole blood if stirring is continuous. For biological tissue, human skin in particular,
heterogeneity is a major factor. Detailed morphological structures and molecular constituents of
skin have been studied using confocal Raman spectroscopy. 60
The skin is a layered system with two principle layers: epidermis and dermis. The epidermis is
the outmost layer of skin and itself consists of multiple layers such as the stratum corneum,
stratum lucidum, and stratum granulosum. The major constituent of human epidermis is keratin,
comprising approximately 65% of the stratum corneum. The dermis is also a layered tissue
composed of mainly collagen and elastin. Blood capillaries are present in the dermis and thus
this region is targeted for optical analysis. However, it has been suggested that the majority of
the glucose molecules sampled by a non-invasive optical technique are present in the interstitial
fluid, which is usually found at the epidermis-dermis interface. 45
- 52 -
3.3
Quantitative consideration I: minimum detection error analysis
If all constituent spectra in a mixture sample are known, the minimum detection error can be
calculated via a simple formula derived by Koo et al.45 and Scepanovic et al.6 1 of our laboratory:
Ac = -olfk.
(3-1)
Sk
The first factor on the right hand side, o, describes the noise in the measured spectrum, while the
second factor, Sk, quantifies the signal strength, calculated as the norm of the kth model
constituent. The last factor, olfk, is termed the "overlap factor" and can take on values between 1
and oo.
The overlap factor indicates the amount of non-orthogonality (overlap) between the kth model
constituent and the other model constituents. Mathematically, the overlap factor for the kth
constituent is equal to the inverse of the correlation coefficient between the kth constituent
spectrum and the OLS regression vector (boLs):
1
olfk =
corr(bOLS,
)
(3-2)
boLs is the part in the kth constituent spectrum (sk) that is orthogonal to all interferents. Physical
interpretation can be gained by considering the following simple case: boLs is identical to the kth
constituent spectrum when no other interferents exist, and thus olfk = 1 / corr(boLs, sk) = 1 / 1 = 1.
When interferents exist, corr(boLs, Sk) is always smaller than one and therefore olfk is always
larger than 1.
Correlation between two vectors is calculated by:
n
corr(u,v)=
n
i=l
- 53 -
i
(3-3)
To estimate the overlap factor for glucose measurements in skin, we have built a 10-constituent
skin-mimicking model (detailed in section 6.4.1.2). Starting with a model of only glucose, other
constituents, including, collagen type I, keratin, triolein, actin, collagen type III, cholesterol,
phosphatidylcholine, hemoglobin, and water were added one at a time to increase the model
complexity. The correlation between boLs and the glucose spectrum changes from 1 to 0.73, as
shown in Figure 3-4.
1^
1
9'
0.95
9'
0.9
9'-.
9'\
0.85
O
9'\
F
0.8
9'
0.75
A'7
0
2
4
6
8
10
Model complexity (number of constituent)
Figure 3-4 Correlation between the OLS regression vector (boLs) and the glucose spectrum
versus model complexity.
Lower fluorescence background introduces less shot noise and therefore increases the Raman
SNR. High molecular specificity in the Raman spectra allows less spectral overlap and thus
reduces the olf for a specific analyte. Both features of NIR Raman spectroscopy contribute to
lower minimum detection error.
Equation (3-1) provides a practical way to estimate the
minimum detection error based on easily obtainable experimental parameters.
-54-
3.4
Quantitative consideration II: multivariate calibration
3.4.1
Background
Extracting analyte concentrations from spectra of complex systems containing multiple analyte
contributions with overlapping features requires more information than is obtainable in a single
wavelength measurement. Multivariate techniques take the full-range spectrum into account and
exploit the multi-channel (data at many wavelengths) nature of spectroscopic data to extract
4 8 62 63
concentration information from analytes at trace levels. , ,
Multivariate calibration is often treated as a black box because it can be mathematically
complicated. Here we present the fundamental ideas with minimum mathematics. The goal is to
familiarize the reader with the basic principles of multivariate calibration and, more importantly,
how to evaluate calibration results. More comprehensive treatment of this topic can be found in
the literature.4 8' 64-66
3.4.2
Introduction
The measured spectrum, s, of a complex mixture can be written as a linear combination of
analyte pure component spectra, p, in proportion to the analyte concentrations, c:
s= ct
*+Cnpn
1 -P +c2 TP2 +""
(3-4)
(In this section, lowercase boldface type denotes a column vector, uppercase boldface type a
matrix; and the superscript T denotes matrix transpose.) Multiple mixture spectra with varying
analyte concentrations can be written together in matrix form as:
S = PC,
(3-5)
where S is a (k x n) matrix of sample spectra with each sample spectrum occupying a column, P
is a (k x m) matrix of constituent spectra with each constituent spectra occupying a column, C is
-55-
a (m x n) matrix of constituent concentrations in the samples, and k is the number of the
resolution elements, e.g., pixels of a charge coupled device (CCD) detector.
For most spectroscopic applications, the goal of multivariate calibration is to predict the
concentration of a given analyte(s) in a future (prospective) sample using only its measured
spectrum and a previously-determined model. To do this we use inverse calibration in which Eq.
(3-5) is re-written as:
C = STB,
(3-6)
where B is an (k x m) matrix with the regression vector (b) for the mth constituent in column m.
In other words, the goal of (inverse) multivariate calibration is to obtain a "spectrum" of
regression coefficients, b, such that an analyte's concentration, c, can be accurately predicted by
taking the scalar product of b with a prospective spectrum, s:
c = bTs.
(3-7)
The regression vector, b, for each analyte is unique in an ideal noise-free linear system without
component correlations (i.e., two or more analytes that vary together).
Under realistic
experimental conditions, however, only an approximation to b for the experimental system of
interest can be found.
A thorough multivariate calibration procedure encompasses three primary steps: (1) model
building, (2) validation, and (3) prospective application, i.e., prediction. Step 1 utilizes a set of
data that includes multiple spectra with known concentrations, called calibration or training data,
to calculate the b vector. Among the calibration data, a subset are reserved for validation and
therefore not used in determining the b vector. Step 2 uses these reserved data as examples on
which to test the predictive capabilities of the b vector. Based on some prescribed criteria of
optimality, e.g., root mean square error of cross validation (see section 3.4.4), iterations can be
- 56 -
performed between model building and validation until the best model is obtained. Step 3 is
prospective application in which the optimal b vector is applied to future independent data to
determine the analyte concentration.
These primary steps in multivariate calibration are
presented schematically in Figure 3-5.
Step 1: Model Building
Mixture Raman spectra
Glucose
25
30
c = STb eq. (3-10)
Vch~
~n~nii
400
i
50
800
1200
1600
Raman Shift [cm-']
Step 2: Validation
Determine # factors
del
400
800 1200 1600
Raman Shift [cm-1]
Step 3: Prospective Application
Independent spectrum
b vector
concentration
prediction
Figure 3-5 Schematic showing primary steps of multivariate calibration.
- 57 -
3.4.3
Multivariate calibration methods
There are two categories of calibration methods: explicit and implicit. Explicit methods utilize
individual component spectra that can be measured or calculated. Examples are ordinary least
squares (OLS) and classical least squares (CLS). Explicit methods provide transparent models
with easily interpretable results.
However, highly controlled experimental conditions, high
quality spectra, and accurate concentration measurements of each component may be difficult to
obtain, particularly in biomedical applications.
When all of the individual component spectra are not known, implicit calibration methods are
often adopted. Among these, factor analysis methods such as principal component regression
(PCR) 67 and partial least squares (PLS) 68 are frequently used because they can function under
conditions in which the number of spectra used for calibration is less than the number of
wavelengths sampled. For example, a calibration set may include 30 spectra with each spectrum
having 500 data points (wavelengths).
Unlike explicit methods, the performance of implicit methods cannot be simply judged by
conventional statistical measures such as goodness of fit. As pointed out in the literature, 7
spurious effects such as system drift and co-variations among constituents can be incorrectly
interpreted as arising from the analyte of interest. This scenario has led to the development of
hybrid methods in which elements of explicit and implicit techniques are combined in order to
improve performance.
In the following we describe commonly used multivariate calibration methods in more detail.
-58-
3.4.3.1.
Explicit calibration methods
Ordinary least squares (OLS) can be employed if the spectra of all components can be measured.
For a pure component spectral matrix, P, the regression matrix, B, can be obtained by the
pseudo-inverse of P from Eq. (3-5):
BT = (pTp)-'pT .
(3-8)
OLS is a simple, yet powerful explicit calibration technique. Its result can be easily interpreted
with little ambiguity. However, the requirement that all spectral components be known reduces
the application of OLS to quantitative biological spectroscopy.
In some cases, it may be difficult to chemically separate individual components in order to
measure their spectra, but it may be possible to measure or estimate their concentrations. If so,
classical least squares (CLS) can be employed to obtain an estimate of the pure component
spectral matrix, P, through the pseudo-inverse of C inEq. (3-5):
P = SC T (CC T) - '.
(3-9)
OLS and CLS are complementary techniques. OLS calculates concentrations from a known set
of component spectra, and CLS calculates component spectra from a known set of concentrations.
The component spectra obtained by CLS can be used for OLS analysis of a new data set, as long
as the two data sets have the same components.
3.4.3.2. Implicit calibration methods
The limitation for explicit calibration methods is the requirement of complete knowledge of the
model components, either of their spectra or their concentrations. Implicit calibration methods
are particularly suited for cases where such complete information is not available.
Implicit calibration schemes require only a set of calibration spectra, S, with each spectrum
occupying a column of S, associated with several known concentrations of the analyte of interest
- 59 -
that are expressed as a column vector, c. Developing an accurate regression vector, b, requires
accurate values of c and S. The forward problem for implicit calibration method is defined by
the linear inverse mixture model for a single analyte:
c = ST b.
(3-10)
The goal of the calibration procedure is to use the set of data [S,c] to obtain an accurate b by
inverting Eq. (3-10).
The resulting b can then be used in Eq. (3-7) to predict the analyte
concentration, c, of an independent prospective sample by measuring its spectrum, s. The
"accuracy" of b is usually judged by its ability to correctly predict concentrations prospectively.
There are two primary difficulties in directly inverting Eq. (3-10). First, the system is usually
underdetermined, i.e., there are more variables (e.g., wavelengths) than equations (e.g., number
of calibration samples). Thus, direct inversion does not always yield a unique solution. Second,
even if a pseudo-inverse exists and results in a unique solution, the solution tends to be unstable
because all measurements contain noise and error. That is, small variations in c or S can lead to
large variations in b. Therefore, data reduction methods (e.g., factor analysis) are usually
applied to arrive at a substitute data set that can be easily inverted.
Principal component regression (PCR) and partial least squares (PLS) are two widely used
methods in this category. PCR decomposes the matrix of calibration spectra into orthogonal
principle components that best capture the variance in the data. These new variables eliminate
redundant information and, by using a subset of these principle components, filter noise from the
original data. With this compacted and simplified form of the data, Eq. (3-10) may be inverted
to arrive at b.
PLS is similar to PCR with the exception that the matrix decomposition for PLS is performed on
the covariance matrix of the spectra and the reference concentrations, while for PCR only spectra
- 60-
are used. PLS and PCR have similar performance if noise in the spectral data and errors in the
reference concentration measurements are negligible.
Otherwise, PLS generally provides
slightly better analysis than PCR.6 9
An important advantage of implicit methods such as PLS and PCR over OLS or CLS is their
ability to extract spectral components (called principal components in PCR, loadings in PLS, or,
more generally, factors) without knowledge of the actual physical constituents comprising the
spectrum. To a certain degree, this has encouraged users to treat implicit methods as a black box.
However, the extracted spectral components are usually not identical to the physical constituent
spectra.
Thus, caution should be taken when attempting to identify features of suspected
physical constituents in extracted spectral components.
Although these are powerful methods, they are not without their limitations.
implicit calibration methods can be susceptible to chance correlations.
In particular,
Thus, when the
calculated b is applied to a future spectrum in which those correlations are not present, increased
error is likely. It may be possible to improve implicit calibration and limit spurious correlations
by incorporating additional information about the system or analytes.
This combination of
features from implicit and explicit calibration methods is termed hybrid calibration.
3.4.3.3.
Hybrid methods
Incorporating additional information into implicit models has been extensively pursued in many
fields to enhance the functionality of calibration algorithms.
In the chemical and applied
spectroscopy literature, methods combining explicit and implicit schemes have been explored by
Haaland et al.,70 Wentzell et al.,71 Berger et al.,72 and Shih et al.73 Haaland et al.70 developed an
augmented CLS/PLS hybrid algorithm that can incorporate nonlinearities such as temperature
variations and known spectral components into the calibration process. This method was shown
-61-
to outperform PLS when the independent prediction spectra included un-modeled spectral
Wentzell et al.71 included information on measurement uncertainties in the
variation.
decomposition of the calibration spectral data, thereby optimizing data extraction. This method
was shown to outperform PCR and PLS when there is non-uniform error structure. Berger et
al.'o and Shih et al.73 utilized the pure component spectrum of the analyte of interest to build the
calibration model with higher specificity.
Berger et al. mathematically subtracted the pure
component spectrum from the calibration data according to reference concentrations before
performing PCR on the residuals.
Shih et al. included the pure component spectrum as a
nonlinear constraint in the regularized cost function. These methods were shown to outperform
PLS, particularly when spurious correlations were present.
All of these methods in principle outperform those without prior information.
However,
depending on how prior information is incorporated, these methods may be susceptible to
possible inaccuracies in the added information, which may reduce rather than enhance their
performance. 73
3.4.4
3.4.4.1.
Model validation and performance evaluation
Model validation
Validation of a calibration model is crucial before prospective application.
Two types of
validation schemes can be adopted: internal and external. Internal validation, or cross validation,
is used when the number of calibration samples is limited. In cross validation, a small subset of
calibration data is withheld from the model building step. After the model is tested on these
validation spectra, a different subset of calibration data is withheld and the b vector is
recalculated.
Various strategies can be employed for grouping spectra for calibration and
validation. For example, a single sample is withheld in a "leave-one-out" scheme, and the
- 62 -
calibration and validation process is repeated as many times as the number of samples in the
calibration data set.
In general, "leave-n-out" cross validation can be implemented with n
random samples chosen from a pool of calibration data.
The optimal model is determined by finding the minimum error between the extracted
concentrations and the reference concentrations. Cross validation is also used to determine the
optimal number of model parameters, e.g., the number of factors in PLS or principal components
in PCR, and to prevent over- or under-fitting.
Technically, because the data set used for
calibration and that for validation are independent in each iteration, the validation is performed
without bias. When a statistically sufficient number of spectra are used for calibration and
validation, the chosen model and its outcome, the b vector, should be representative of the data.
When the calibration data is not limited, external validation, i.e., prediction testing, can be
employed. As opposed to internal validation, external validation tests the calibration model and
optimizes the number of model parameters on data that never influences the model and therefore
provides a more objective measure than internal validation.
3.4.4.2.
Summary statistics for calibration model and prediction
In determining the optimal model via cross validation, the root mean square error of cross
validation (RMSECV) is calculated. RMSECV is defined as the square root of the average of
the squares of the differences between extracted and reference concentrations of nr samples, or:
,
RMSECV =
(3-11)
Where p is the number of estimated parameter. The RMSECV is calculated for a particular
choice of the number of model parameters. An iterative algorithm is often employed to vary the
number of parameters and recalculate the RMSECV. The statistically significant minimum
- 63 -
RMSECV and the corresponding number of model parameters are then chosen for determination
of the final calibration model.
Another important statistic is the correlation coefficient (r) between the extracted and the
reference concentrations, or:
(Cextracted,i - Cextracted)(Creference,i n
r(Cextractedi
Creferencei)
reference)
(3-12)
n
Cextractedi _
(cre
extracted )2
Vi
rnce,
-
Creference) 2
i
A higher correlation coefficient across a broad range of concentrations provides confidence that
the calibration model is accurate.
The b vector chosen by the validation procedure can be employed prospectively to predict
concentrations of the analyte of interest in independent data. Similar to the calculation of
RMSECV, root mean square error of prediction (RMSEP) for an independent data set is defined
as the square root of the average of the squares of the differences between predicted and
reference concentrations of np samples, or:
/
S " (Cpredicted,i --Creferencei )2
RMSEP = i
(3-13)
np
For feasibility studies, RMSECV is a good indicator of performance as long as the number of
calibration samples is statistically sufficient (see section 3.4.5.2). RMSEP, on the other hand,
provides the ultimate objective metric by which any technology can be evaluated.
Another frequently used statistic, called the mean absolute error (MAE), can be calculated by:
i
(extd Creference
MAE =
n
i=1
-64 -
Creference,i
3.4.5 Is the calibration model based on glucose?
Multivariate calibration models are often built on an underdetermined data set, i.e., more
wavelengths than samples. The powerful data reduction techniques employed make assessment
of the model validity an extremely important aspect of the analysis procedure. Here we present
four important criteria on which to judge the validity of results from multivariate calibration.
3.4.5.1.
Theoretical and practical limits
In spectroscopy, the analyte-specific signal is dependent on the number of analyte molecules
sampled by the incoming light. Therefore, the effective path length (in transmission mode) and
sampling volume (in reflection mode) of the light are important parameters in estimating
detection limit in turbid media. Modeling techniques such as diffusion theory 32 and Monte Carlo
simulation 74 have been employed to calculate fluence distribution inside the sample and the
angular and radial profile of the transmitted or reflected flux. Simple simulations with synthetic
data or experiments employing tissue-simulating phantoms can be of great value in determining
how close the theoretical limit can be realized practically.
In these studies, experimental
conditions (e.g., SNR, instrumental drifts) and tissue phantom composition (e.g., interferents,
concentrations) can be precisely controlled and the model components well characterized in
advance. Although in vitro experiments often present a 'best-case' scenario, proving that the
chosen technique and instrument can measure physiological levels of glucose in tissuesimulating phantoms is necessary but not independently sufficient to justify the in vivo results.
3.4.5.2.
Model dimensionality
In multivariate calibration, a large number of sample spectra can be reduced to fewer factors,
otherwise termed principal components in PCR or loading vectors in PLS. In practice, only a
subset of factors is significant in modeling the underlying analyte variations, while the others are
- 65 -
more likely to be dominated by noise and measurement errors. Although an apparently lower
RMSECV may be obtained by including more factors into the calibration model, the reduction in
error may be fortuitous and the resulting model may have less predictive capability. Therefore,
guidelines exist to help prevent over-fitting the data.
One such example is published by
American Society of Testing and Materials on infrared multivariate calibration 75 and states that a
minimum number of six independent samples is needed for each factor included in the model.
Extra scrutiny is given to data analysis that does not properly address model dimensionality.
3.4.5.3.
Chance or spurious correlation
Multivariate calibration algorithms are powerful yet somewhat misleading if used without
precaution. Owing to the nature of the underdetermined data set, any minute correlation present
in the data may be picked up by the algorithm as legitimate analyte-specific variations. For
example, Arnold et al.7 measured the near-infrared absorption spectra of tissue phantoms devoid
of glucose and used temporal glucose concentration profiles published by different research
groups to demonstrate that the calibration model could produce an apparent correlation with
glucose even though none was present. Calibration results such as these could actually satisfy
multiple criteria for judging the validity of a calibration model. The lesson here is that chance or
spurious correlations may be incorporated into the calibration model even when rigorous
validation procedures have been followed.
More seriously, if these chance or spurious
correlations exist in future measurements, even positive prediction results could be based on nonanalyte-specific effects.
Incorporation of prior or additional information has been shown to
provide more immunity to chance correlations. 70
- 66 -
73
3.4.5.4.
"Visualize" glucose
The difficulty in visualizing glucose-specific information in biological spectra makes it
challenging to verify the origin of the spectral information used by the calibration model and
confirm that positive results are actually based on glucose. However, some of this information
can be obtained by examination of the b vector. The b vectors obtained from spectroscopic data
contain spectral information of all model components and are not merely a collection of numbers.
Under ideal, noise-free conditions the regression vector bideal, can be explicitly derived from the
model component spectra, or implicitly obtained from the calibration sample set. This bideal is
termed the net analyte signal 76' 77 or the OLS b vector, boLs.
Mathematically, it can be
constructed by removing all parts of the glucose spectrum that are non-orthogonal to the
interferent spectra.
Physical interpretation can be gained from considering two simple examples.
First, bideal is
identical (within a scale factor) to the pure component spectrum of the analyte of interest, in this
case, glucose, if no other interferents are present. In other words, the regression vector should
"look" progressively more like the glucose spectrum as model complexity decreases.
For
example, when spectral overlap is low, such as in Raman spectroscopy, spectral features of
glucose have been identified in the experimentally-derived b vector as extra supporting
evidence. 2 1, 24 ,26 Second, bideal is orthogonal to all other interferents. This fact leads to a simple
checkpoint called pure component selectivity analysis (PCSA).7 8 In PCSA, the experimentallyderived b vector multiplied by the glucose spectrum should give the concentration of glucose,
and b multiplied by an interferent spectrum should equal zero.
Although a complete model is virtually never available for in vivo experiments, a good
approximation is often obtainable. Therefore, a theoretically "correct" regression vector (-bideal)
- 67 -
should be calculated and examined for spectral abnormalities. An explanation must be provided
to justify an experimentally-derived regression vector that deviates far from bideal.
Several papers in the literature have reported the successful measurement of glucose from in vivo
human spectra collected non-invasively. Unfortunately, the validity of these reports often can
not be judged based on the supplied information.
We believe that the burden is on all
investigators to prove that glucose is indeed measured following these four criteria for judgment.
3.4.6
Physical interpretation of the regression vector
Using the b vector as a "spectrum" is shown to be a good way to qualitatively judge whether the
implicit model is based on the constituent of interest. Because of the sharp and distinct Raman
peaks, the b vector is usually physically interpretable. Here our goal is to quantitatively interpret
b vector rather than pointing at several peaks and making qualitative claims. To this end, we
have to consider causes for an implicit b vector to deviate from the OLS b vector.
In PLS or PCR, the model is built on a set of calibration spectra with unknown constituents. If
we suppose that one knows all of the constituents, we showed in Figure 3-4, that as model
complexity increases, corr(boLs, sk) decreases in a predictable fashion (sk is the spectrum of the
analyte of interest). However, measurement noise causes bPLS/PCR to deviate from boLs. During
the inversion procedure, PLS/PCR trades bias for noise rejection.
Therefore, as long as
truncation of factors is done, the resulting bpLS/PCR, on average, is always slightly different from
boLs. In real applications, averaging is not always possible, and thus the noise in bPLS/PCR causes
further deviation from boLs. In principle, one can predict corr(bpLs/PCR, Sk) using a look-up table
that characterizes the noise-induced deviation. As an example, we used the 10-constituent model
- 68 -
(detailed in section 6.4.1.2) to study corr(bpLs,
Sglucose)
under different noise magnitudes with or
without exponential background decay.
RMSEP and corr(bpLs, Sglucose) versus spectral noise are plotted in Figure 3-6 and Figure 3-7,
respectively. The reference concentration error takes two values: 2% and 5%. It is shown that
random spectral noise or concentration error not only increases the RMSEP values but also
decreases the correlations because more bias is needed for noise rejection.
Ihi
0
140
160
180
Spectral noise counts (photoelectron)
200
140
160
180
200
Spectral noise counts (photoelectron)
Figure 3-6 corr(bpLs, Sglucose) versus random
noise for two levels of random error in
reference concentrations. (error standard
deviation: solid 5%, dashed 2%; glucose is 0.20.5% of the total Raman signal norm).
Figure 3-7 RMSEP versus random noise for
two levels of random error in reference
concentrations. (error standard deviation:
solid 5%, dashed 2%; glucose is 0.2-0.5% of
the total Raman signal norm).
The concentration correlation among either two components is 0.76 and the results are shown in
Figure 3-8 and Figure 3-9. We observe the correlations among constituents decreases corr(bpLS,
Sglucose) and increases RMSEP compared to the cases without constituent correlations.
A
thorough look-up table can be built and a good estimate of corr(bpLs, Sglucose) can in principle be
obtained and be used as a quantitative indicator of the quality of calibration models.
- 69 -
140
160
180
200
Spectral noise counts (photoelectron)
Spectral noise counts (photoelectron)
Figure 3-8 corr(bPLS, Sglucose) versus random
noise for two levels of random error in
reference concentrations. (error standard
deviation: solid 5%, dashed 2%; glucose is 0.20.5% of the total Raman signal norm).
- 70 -
Figure 3-9 RMSEP versus random noise for
two levels of random error in reference
concentrations. (error standard deviation:
solid 5%, dashed 2%; glucose is 0.2-0.5% of
the total Raman signal norm).
CHAPTER 4 IMPROVING THROUGHPUT, PRECISION, AND
STABILITY
This chapter first discusses important considerations for Raman instrumentation.
Then we
describe the continuing progress made to bring our transcutaneous Raman instrument to higher
sensitivity, stability, and precision.
An overview of the present instrument is provided and
critical components are discussed.
In addition, this chapter describes the image curvature
problem as a combinatorial effect of a high numerical aperture spectrograph and large area
charge coupled device (CCD). Detailed analysis with an improved solution is provided. This
chapter also describes addition of a laser intensity monitoring photodiode and temperature probes
at key positions. Lastly, the error introduced by wavelength drifts is evaluated and a new
correction scheme is presented.
4.1
Instrumentation considerations
As discussed previously, background fluorescence impedes observation of Raman signal from
biological tissue using UV-visible excitation wavelengths. To overcome this limitation, NIR
excitation was employed with Fourier-transform spectrometers in the late 1980s.7 9 With the
advent of high quantum efficiency CCD detectors and holographic diffractive optical elements,
researchers have increasingly employed CCD-based dispersive spectrometers. 21' 22, 24, 25, 27, 80-82
The advantages of dispersive NIR Raman spectroscopy are that compact solid-state diode lasers
can be used for excitation, the imaging spectrograph can be f-number matched with optical fibers
for better throughput, and cooled CCD detectors offer shot-noise limited detection.
As a tutorial for the selection of building blocks for a Raman instrument with high collection
efficiency, we present a summary of the key design considerations.
-71-
4.1.1
Excitation light source
Laser excitation at one of two wavelengths, 785 and 830 nm, is most common. The tradeoff lies
in that excitation at lower wavelengths has a higher efficiency of generating Raman scattering
but also generates more intense background fluorescence. The current trend is towards the use of
external cavity laser diodes because they are compact and of relatively low cost. In other
embodiments, argon-ion laser pumped titanium-sapphire lasers are used extensively.
The
titanium-sapphire laser can provide higher power output with broader wavelength tunability, but
is bulkier and more expensive to maintain than diode lasers.
Because Raman scattering occurs at the same energy shift regardless of the excitation
wavelength, narrowband excitation must be used to prevent broadening of the Raman bands.
Further, the wings of the laser emission (amplified spontaneous emission) can extend beyond the
cutoff wavelength of the notch filter used to suppress the elastically scattered light and obscure
low-wavenumber Raman bands. This problem is most severe in high power diode lasers and a
holographic bandpass or interference laser line filter with attenuation greater than 6 optical
density (OD) is usually required. Lastly, for quantitative measurements a photodiode is often
needed to monitor the laser intensity to correct for fluctuations.
4.1.2
Light delivery
The filtered laser light can be delivered to the sample either through free-space or through an
optical fiber. In the free-space embodiments, beam shaping is usually performed to correct for
astigmatism and other laser light artifacts. The incident light at the sample can be either focused
or collimated, depending on collection considerations. For biological tissue, the total power per
unit area is an important consideration and thus spot size on the tissue is an oft-reported
parameter.
- 72 -
Raman probes constructed from fused silica optical fibers have gained much attention recently.
Typically, low-OH content fibers are utilized to reduce the fiber fluorescence. The probe design
also includes filters at the distal end to suppress the fused silica Raman signal from the excitation
fiber and suppress the elastically scattered light entering the collection fibers.83 Commercial
probes are now available and they offer ruggedness and easy access to samples with various
special or geometrical constraints.
4.1.3
Light collection
As Raman scattering is a weak process, photons are precious and high collection efficiency is
desired for a higher signal-to-noise ratio. Specialized optics such as Cassegrain microscope
objectives and non-imaging paraboloidal mirrors have been employed to increase both the
collection spot size and the effective numerical aperture of the optical system. 45
The majority of photons that exit the air-sample interface are elastically scattered and remain at
the original laser wavelength. This light must be properly attenuated or it will saturate the entire
CCD detector. Holographic notch filters are extensively employed for this purpose and can
attenuate the elastically scattered light to greater than 6 OD, while passing the Raman photons
with greater than 90% efficiency. However, notch filters are very sensitive to the incident angle
of light and thus provides less attenuation to off-axis light. In some instances, the size of the
notch filter is one of the determining factors of the throughput of an instrument.
Specular reflection, light that is elastically scattered without penetrating the tissue, is also
undesirable. Strategies such as oblique incidence, 84 90 degree collection geometry,22 and a hole
in the collection mirror have been realized to reduce its effect.73
- 73 -
4.1.4
Light transport
After filtering out most of the elastically scattered light, the Raman scattered light must be
transported to the spectrograph with minimum loss. To match the rectangular shape of the
entrance slit of a spectrograph, the originally round-shape of the collected light can be relayed by
an optical fiber bundle with the receiving end arranged into a round shape and the exiting end
arranged linearly.21
4.1.5
Spectrograph and detector
In dispersive spectrographs for Raman spectroscopy, transmission holographic gratings are often
used for compactness and high dispersion.
Holographic gratings can be custom-blazed for
specific excitation wavelengths and provide acceptable efficiency. In addition, liquid nitrogen
cooled and more recently thermoelectric cooled CCD detectors offer high sensitivity and shotnoise limited detection in the near infrared wavelength range up to -1 ptm. These detectors can
be controlled using programs such as LabVIEW to facilitate experimental studies.
To increase light throughput in Raman systems, the CCD chip size can be increased vertically to
match the spectrograph slit height. However, large format CCD detectors show pronounced slit
image curvature that must be corrected in pre-processing (described below).
4.2
Overview of our laboratory instrument
The experimental system has been continually upgraded and redesigned from the first generation
for measurements in blood serum (low turbidity) samples 24 to the second generation for
measurements in whole blood (high turbidity) samples, 45 and then to the current generation
targeted for transcutaneous measurements. 26 Design goals and considerations on component
selection are described below.
-74 -
4.2.1
Excitation light source and light delivery
An 830-nm external cavity diode laser (PI-ECL-830-500, Process Instruments) is employed as
the Raman excitation source in the present instrument (Figure 4-1). The laser beam is passed
through a laser line filter (Maxline, Semrock, Inc.) to reduce amplified spontaneous emission
(ASE), directed toward a hole drilled in a gold-coated paraboloidal mirror (Perkin Elmer), and
focused onto the sample, with average power of -300 mW and a spot area of -1 mm 2. The laser
line filter has higher ASE and sideband attenuation, as well as a narrower spectral passband,
compared to the previously utilized holographic bandpass filter (Kaiser Optical Systems, Inc.).
In addition, the scheme with a hole in the mirror decouples the light delivery from collection
compared to the previous generation using a small prism. Previously, the paraboloidal mirror
was in both the light delivery and collection paths, and thus alignment was extremely difficult. 21
The present setup allows free beam shaping of the excitation light and ease of alignment.
Further, most of the specular reflection, lacking analyte information, escapes through the hole
without being collected. A home-built photodiode assembly was employed to monitor laser
power through a magnesium fluoride beam sampler, with power measurement accuracy of within
-0.1%.
- 75 -
Figure 4-1 Schematic of the present instrument.
4.2.2
Light collection and transport, spectrograph, and detector
Employing the so-called "180" ' geometry, 50 both backscattered Raman light and the "Rayleigh
peak" (i.e., elastically scattered light at 830 nm) were collected by the paraboloidal mirror and
passed through a holographic notch filter (42.5", Super Notch Plus, Kaiser Optical Systems, Inc.)
to attenuate the Rayleigh peak and prevent CCD saturation. The parabaloidal mirror was chosen
for its large collection angle and commercial availability. Detailed specifications of the mirror
are provided in reference 45.45
The filtered light is delivered to a modified spectrometer (Holospec f/1.4, Kaiser Optical
Systems, Inc.) with little loss by means of an optical fiber bundle (RoMack Inc.), which converts
the circular shape of the collected light to a single vertical row of fibers, 45 serving as the entrance
- 76 -
slit of the spectrometer. The spectra were collected as 2D images by a liquid nitrogen (LN)
cooled CCD array detector (VersArray 1300x1340b, Princeton Instruments). Image curvature
caused by the grating spectrometer was subsequently corrected by software and then binned in
the vertical direction, resulting in a spectrum (discussed in section 4.3). Spectral resolution of
the present instrument is -14.25 cm 1' (@ 907nm).
A few components have been upgraded for higher throughput: The 42" holographic notch filter
was replaced by a 42.5" filter with similar specifications, giving a -30% increase in throughput.
The original f/1.8 spectrometer was upgraded to f/1.4 by replacing the camera lenses; a larger
fiber bundle (65 f/1.4 fibers with core diameter 360 gm)was utilized to collect light originating
from a larger area and to fully exploit the vertical dimension of the CCD chip; a higher quantum
efficiency CCD chip was employed (CCD area -697 mm 2 with QE -60% @ 950 nm). Table 4-1
lists all components in the present instrument compared to the previous generation.
- 77 -
Table 4-1 List of components in the present instrument versus the previous
generation.
Component
Laser
Fiber bundle
Spectrometer
Specification
Wavelength (nm)
830
Power output (mW)
480
Power on sample (mW)
280
300
Core diameter (pm)
300
360
Circular end (mm)
Linear end (mm)
43.0
20.1
44.0
25
f/#
1.8
1.4
number of fibers
61
65
f/#
1.8
1.4
16.5 m/cm'
Dispersion
2
CCD area (mm )
CCD detector
Present
Previous
Pixel (gm2)
Quantum efficiency @ 950 nm
-78 -
425 (25x17)
697 (26x26.8)
22x22
20x20
30%
60%
4.3
Software-based image curvature correction
Increase of usable detector area is an effective way to improve light throughput in Raman
spectroscopy employing multi-channel dispersive spectrographs.
Owing to out-of-plane
diffraction, a problem arises - the entrance slit image is curved. Direct vertical binning of
detector pixels without correcting the curvature results in degraded spectral resolution. Among
possible solutions, this section presents a software approach that retains instrument spectral
resolution as if a small detector were used. Curvature correction is achieved in two steps:
calibration of the image curvature using a Raman active material, and application of corrective
algorithm to future curved images. The calibration step only has to be performed whenever the
spectrograph is reconfigured, offering great flexibility for instrument modifications.
4.3.1
Introduction
Multi-channel dispersive spectrographs are one of the most widely used tools for modem Raman
spectroscopy, owing to high efficiency and sensitivity. Unlike a monochromator, which employs
an exit slit and a single detector, a multi-channel spectrograph operates without an exit slit and
uses an array detector. Since Raman scattering is weak, it is important to optimize the SNR for
high quality spectra. In multi-channel spectrographs, a CCD camera is often employed in
conjunction with a tall grating to exploit the vertical dimension for increased throughput. Light
throughput, neglecting vignetting, is proportional to the number of operational CCD pixel rows.
Therefore, doubling the number of pixel rows increases the SNR approximately 1.4 times, given
a shot-noise-limited measurement. For non-imaging, low signal level experiments, this method
of "vertical binning" has been the most effective way to achieve higher throughput without
increasing laser power or modifying collection optics. However, given the use of a large area
- 79 -
CCD, a problem arises - slit image curvature, due to out-of-plane diffraction.8 5 If vertical
binning is applied directly, the resulting spectral resolution is degraded.
Various hardware approaches, such as employing curved slits84, 85 or convex spherical gratings,
have been pursued.86 In the curved slit approaches, fiber bundles have been employed as shape
transformers to increase Raman light collection efficiency. At the entrance end the fibers are
arranged in a round shape to accommodate the focal spot, and at the exit end in a curved line,
with curvature opposite that introduced by the remaining optical system. This exit arrangement
serves as the entrance slit of the spectrograph, and provides immediate first order correction of
the curved image, as described below. However, for quantitative Raman spectroscopy, with
substantial change of the image curvature across the wavelength range of interest (-150 nm) and
narrow spectral features, such first order correction is not always satisfactory.
As an alternative to the hardware approach, software can be employed to correct the curved
image, with potentially better accuracy and flexibility for system modification. In our past
research, we have developed a software method involving using a highly Raman active reference
material to provide a sharp image on the CCD.2 6 Using the curvature of the slit image at the
center wavelength as a guide, we determine by how many pixels in the horizontal direction each
off-center CCD row needs to be shifted in order to generate a linear vertical image. This method,
as well as the curved-fiber-bundle hardware approach, ignores the fact that the slit image
curvature is wavelength dependent.
The resulting spectral quality of our method is thus
equivalent to the curved-fiber-bundle hardware approach,"' as evidenced by the comparison of
our results with theirs. This issue becomes more important when large CCD chips and high-NA
spectrographs are employed for increasing the throughput of the Raman scattered light. In our
research, throughput considerations prompted us to employ an f/1.4 spectrometer with a CCD
- 80 -
array detector -1 inch 2 , much larger than that of our earlier CCD, for which the original method
was developed. Such a large CCD array provides excellent throughput. However, its large size
brings into question the effectiveness of the original curvature correction algorithm. Recently, a
software approach using multiple polystyrene absorption bands was developed for infrared
spectroscopy. 87 In this section we present a similar method, developed concurrently, which
calibrates on multiple Raman peaks, and demonstrate improvement over our original method.
4.3.2
Image curvature formation
A dispersive spectrometer is composed of a 4f optical system with the entrance slit placed at the
object plane, a diffraction grating at the Fourier plane, and a CCD camera at the imaging plane
(Figure 4-2). The entrance slit is imaged onto the CCD plane. However, for polychromatic
incident light, the spectral components are spread in the horizontal direction.
The grating
equation is: 88
,
sina + sino =
(4-1)
with a and p the incident and diffracted angles, m the diffraction order, X the wavelength, and p
the grating pitch. Note that this equation considers only incident and diffracted plane waves,
with wave vectors ki, and kdi respectively, in plane with the grating vector, k . For any plane
wave that emerges at an angle 0 with respect to the plane spanned by the optical axis and kg, the
modified grating equation reads:
sina + sin
=
cos
height.
from
emerging
finite
atoflight
aresult
term
slit
cosine
the
the
pwith
with the cosine term a result of light emerging from the slit at finite height.
-81 -
(4-2)
¢•rrrlila
sellr
7iarze
f
Figure 4-2 Schematic of the grating spectrometer with 4f imaging optics. For clarity, the focal
lengths of the lenses L1 and L2 aref. The optical axis is indicated by dotted lines. ki, and kdf
are the wave vectors of the incident and the diffracted rays, and k9 is the grating vector.
After Taylor expansion of Eq.(4-2) and keeping terms up to the second order term of cosine, the
diffraction angle as a function of 0 is obtained:
S= cos
(4-3)
2p -cospo0
where 30 is the diffraction angle of a fixed wavelength, for example, the center wavelength (905
nm) among the spectral range of interest in our system. Employing the paraxial approximation
by substituting 0 by yccD/f2 and 83 by xccD/f2, with f2 the focal length of the second lens in the 4f
system, we obtain the final expression for the first-order diffracted light:
X
2
XccD = 2p -coso •f2 YCCD '
- 82 -
(4-4)
with functional form of a parabola. We note that the curvature of this parabola is a function of
wavelength, the only variable in addition to the CCD coordinates, xCCD and YCCD.
4.3.3
Simulations
To simulate the response of our instrument, we use Eq. (4-4) and actual parameters from our
2 pixel size; the focal
instrument: The CCD dimensions 2.68 cm (H) x 2.6 cm (V) with 20x20 pmn
length 8.5 cm; and the spectral range 830-970 nm with 830 nm laser excitation.
The impulse response of the system for an infinitesimally narrow entrance slit is plotted in
Figure 4-3(a) for five representative wavelengths. To better examine the wavelength dependence
of the image curvature, each of the plotted curves is shifted to the 905 nm line with their vertexes
aligned (Figure 4-3(b)).
Without correction, vertical binning results in a highly degraded
spectrum with resolution - 36 pixels (-54 cm'l), full width at half maximum (FWHM). The
original method of simply shifting CCD rows assuming the curvature remains constant over the
entire spectral range results in the curves of Figure 4-3(c). The uncorrected error is as large as
±15 pixels (-±23 cm -') at both ends of the CCD using this pixel shifting method. Given a typical
Raman peak width of order -20 cm' from our instrument, such an error may cause significant
linewidth broadening.
- 83 -
200
(c)
600
400
600
800
Pixel: X-direction
Al 15
A27-
r 40 0
I
V
i
1
i
0
II
-400
I
i
'i
I
S-200
i
i!
I
S200
I
I
|
tT
'
'
0
1000
l•
I
";
-600
-600 -400 -200
0
200
Pixel: X-direction
4.3.4
400
600
20
40
00
80
Pixel: X-direction
100
Figure 4-3 (a) Simulated impulse response of
the system at 5 different wavelengths for an
infinitesimally narrow slit. The CCD is
2
1340(H) x 1300(V) pixels with 20x20 imn
pixel size. " ": 830nm, "--": 880nm, "....":
905nm, "-.-.": 930nm, "D": 970nm. (b)
Curves in (a) shifted such that their apexes are
aligned and with the x-axis expanded to show
detail. The largest difference is 35 pixels if
the whole CCD range is used. (c) After the
first-order curvature correction with pixel
shifting. The uncorrected error is still
approximately 15 pixels on either side of the
CCD.
Methods
As mentioned earlier, our instrument employs the fiber bundle approach with the exit fibers
arranged in a straight line (as opposed to the curved exit end approach described earlier.) The
fiber bundle is composed of 65 cladding-stripped fibers with 360 [lm core diameter. The linear
shape at the exit end serves as the entrance slit of the spectrometer, with equivalent dimensions
-0.4 mm (H) x 26 mm (V), and is imaged -1.1X onto the CCD. The Kaiser HoloSpec f/1.4
spectrometer was modified to incorporate the fiber bundle with the collimating stage removed.
- 84-
The pixel shifting method calibrates the image curvature at one wavelength and uses this
information to shift vertically off-center rows correspondingly.
The fact that the curvature
increases towards the higher dispersion end is ignored. Furthermore, we found that due to the
curvature change across the spectral range of interest, each row spectrum appears to be
"stretched" differently compared to the center-row spectrum. As a result, the same spectral
coverage occupies different number of pixels in each row, i.e., the center-row spectrum has the
fewest number of pixels whereas the top- or the bottom-row the most.
Our new curvature mapping method employs the following scheme. We first calibrate several
spectral lines (where peaks in a reference sample occur) and use these as boundaries to separate
the row spectra into several spectral segments. The chosen peaks are then aligned to their
respective locations in the center-row spectrum. Linear interpolation is then used to "compress"
each row spectrum back to the same length as the center-row spectrum for each segment, while
maintaining signal conservation. Finally, the compressed row spectra are vertically binned to
obtain the final spectrum.
We developed an algorithm to perform the two-step procedure described above: Image curvature
calibration and correction. For calibration, a full-frame image is taken with a reference material
that has prominent peaks across the spectral range of interest, for example, acetaminophen
powder. We chose nine prominent peaks across the wavelength range of interest, as depicted by
the arrows in Figure 4-4.
- 85 -
/·
1/
(
Y
0.8
0e /
0.6
0.4
0.2
j
U
0
'~iAA
"` "LI A~I'
"~ I
I
~
I
YI
500
1000
1500
Raman shift (cm' 1)
Figure 4-4 Raman spectrum of acetaminophen powder, used as the reference material in the
calibration step. Nine prominent peaks used as separation boundaries are indicated by arrows.
The calibration algorithm generates a map of the amount of shift for each CCD pixel and a scale
factor to maintain signal conservation in each CCD row. Once the map and the scale factor are
generated, usually when the system is first set up, the correction algorithm can be applied to
future measurements. We integrated the algorithm written in MATLAB (The MathWorks) with
LabVIEW (National Instruments) data acquisition software to streamline data processing.
Note that 2D image data were supplied as the input during the application step described above,
and the output is the corrected ID spectrum. Similarly, if the input is the 2D map of pixel
intensity variance calculated from a collection of frames, the output is the ID variance spectrum
and be subsequently used to, e.g., calculate the minimum detection error (see section 7.1.2).
- 86 -
4.3.5
Results and discussion
We have implemented both software curvature correction methods.
The raw and corrected
experimental full-frame Raman spectra of acetaminophen powder before software vertical
binning are shown in Figure 4-5.
There is significant improvement from pixel shifting to
curvature mapping, especially toward either side of the CCD, as can be seen by comparing
Figure 4-5(c) and Figure 4-5(e). The overall linewidth reduction in 14 prominent peaks is 7%
(FWHM). This improvement is significant considering that the equivalent slit width is -360 jim.
If a narrower slit is employed for better spectral resolution, the overall linewidth reduction will
be even more significant. Note that the images were taken with 5-pixel CCD hardware vertical
binning to reduce the amount of data, since the curvature is negligible within such a short range.
The error introduced by the hardware binning is much less than 1 pixel, and thus negligible.
To further evaluate the improvement of curvature mapping over pixel shifting, Figure 4-6(a)
shows the center-row spectrum and that of the top row after the application of the pixel shift
method. The error left uncorrected by pixel shifting show up as apparent peak drifts. Since the
curvature of the center wavelength was used for correction, the error becomes more significant
towards either side of the CCD. Spectra from the same two rows are plotted after the application
of the curvature map method in Figure 4-6(b), showing that the apparent peak drifts are greatly
reduced, as better visualized in Figure 4-6(c) and Figure 4-6(d) for the high wavenumber region.
The two spectra in Figure 4-6(b) differ mainly in their intensity levels due to vignetting. As
described above, system modifications simply require re-calibration to obtain the map and the
scale factor, a great gain in flexibility.
- 87 -
Corrected CCD image: Method I
Raw CCD image
200
/
200
1000
800
600
Pixel
400
Zoom-in of (b)
X
600
Pixel
800
1000
Corrected CCD image: Method 2
I J\
),d(
tC)
5
5(
"5 10
L 10(
15
15(
20
20(
25
(-'A.
82U
;4U
800
U
Pixel
9
25(
92U 94U
YZU
Corrected CCD image: Method 2, zoom-in
" 10
15
20
820
840
860
880
Pixel
jUU
40
300 b(
/00 ~OU 900 100UU0
Figure 4-5 CCD image of acetaminophen
powder. Images were created with 5-pixel
hardware binning. (a) Raw image; (b) after
applying pixel shift method; (c) zoom-in of
the box in (b); (d) after applying curvature
map method; (e) zoom-in of the box in (d).
5
25
200
Pixel
(e)
0
400
900
920
940
- 88 -
-
Top and center row spectra: Method 1
(a) 1--I
]
--
~
~-
0.8
0.6
0.4
A
0.2
£
lIIl
I 1W1W
Al
I I.
u""'"'
400
600
800
1000
I1k.].
I
~
1200
1400
Raman shift (cm ')
Raman shift (cm1')
Zoom-in of (a)
1200
1250
1300
1350
1200
Raman shift (cm1')
1250
1300
1350
Raman shift (cm-1)
Figure 4-6 Comparison of two spectra from the top (solid) and the center (dashed) row of the
CCD: (a) After applying pixel shift method; (b) after applying curvature map method; (c) zoomin of high wavenumber region of (a); (d) zoom-in of high wavenumber region of (b).
An important issue in implementation is how accurately the calibration algorithm identifies the
peaks serving as separation boundaries. We simulated scenarios for different amounts of random
noise and found that peaks with sharp and well-defined lineshape and higher SNR are more
resistant to noise distortion, i.e., the true peak positions could be more accurately identified.
Therefore, for practical implementation, the reference material must possess multiple distinctive
peaks across the wavelength range of interest and the reference image for calibration must have
superior SNR.
- 89 -
From both the simulations and the experimental spectra, we observe that pixel shifting provides
effective image curvature correction with fewer CCD rows, such as commercially available CCD
chips with 256 or 400 pixel rows. However, curvature mapping offers better correction when the
CCD height becomes larger, a trend in high-throughput Raman spectroscopy.
4.4
Instrument precision and stability
4.4.1
Intensity and temperature stability
We have improved the stability of our system with the following changes: a hole was drilled in
the parabaloidal mirror to replace the prism and stabilize the illumination beam. An enclosure
was added around the laser and isolated the laser air circulation loop from the rest of the system.
This eliminated a source of heat and a cause of temperature drift. Stray light entering the
spectrometer was reduced by constructing a tighter enclosure. This enclosure also suppresses
temperature fluctuation due to outside temperature changes. Baffling in the spectrometer was
added to prevent stray light that enters the spectrometer or is created in the incident side of the
spectrometer (before the grating) from entering the diffracted side and possibly hitting the CCD.
The CCD enclosure and the nitrogen tank were isolated from the system with thermal insulating
material. This reduced another source of temperature fluctuations. Temperature monitoring
probes were added (Thermocouples and OMB-DAQ-55 USB Data Acq Module, Omega
Engineering Inc.) at five key points in the system to identify any unusual changes in temperature
that would require a new reference measurement (Figure 4-7).
A new temperature stable
photodiode was added to monitor laser power, which later provides necessary power correction.
Figure 4-8 shows the photodiode reading for 18 continuous hours. Compared to the photodiode
temperature in Figure 4-7, we conclude that the laser intensity fluctuation is below 0.1% of its
average power.
- 90-
22
e21
;I
t .
o
pi
E
a
17
16
0
5
10
Time elapsed (Hr)
15
Figure 4-7 Temperature monitored at 5 key points for 18 hours.
6.815
6.814
6.813
S6.812
6.811
6.81
6.809
6.808
5
10
Time elapsed (Hr)
Figure 4-8 Laser intensity monitored forl 8 hours.
-91 -
15
4.4.2
Wavelength drift detection and correction
One important aspect of instrument stability is the repeatability of the wavelength axis at the
CCD plane.
Mainly owing to thermal expansion of the spectrometer grating and optical
aberrations, light of a specific wavelength does not always impinge at the same location on the
CCD. For quantitative studies, a crude "wavelength calibration" is usually performed to correct
drifts measured in pixels. To evaluate the detrimental effect of wavelength drift, we have built a
10-constituent skin-mimicking model. Using glucose in blood-tissue matrix as an example
analyte, we simulated PLS calibration performance for various wavelength drifts.
The
wavelength drift was varied from 0 to 2 pixels with other model parameters such as SNR,
glucose concentrations, and contributions from other tissue constituents identical. Figure 4-9
shows simulation results of prediction error vs. wavelength drift. Details of this model are
documented in section 6.4.1.2.
a
CIO
wavelength drift (pixel)
Figure 4-9 Wavelength drifts increase prediction error.
- 92 -
The results show that wavelength drift indeed has serious negative impact on performance of the
calibration, and a design goal of correcting drift <0.1 pixel was set.
To meet the goal required two items: first, a method of detecting peak positions at a higher
resolution than the one pixel CCD resolution, i.e., 0.01 pixels. Secondly, a method to detect and
correct for not only linear drifts (in which all wavelengths drift the same amount) but also
magnification type shift (where different parts of the spectrum drift different amounts) and the
two types of drifts occurring simultaneously.
Cu
200
400
600
800
1000
1200
CCD pixel
Figure 4-10 Peaks chosen from the acetaminophen powder Raman spectrum.
To achieve these requirements, we chose a stable reference (e.g., acetaminophen powder) with
peaks chosen across the wavelength range.
The spectrum of acetaminophen and the peaks
chosen are shown in Figure 4-10. To precisely detect the position of these peaks, the wavelength
axis was divided into 0.01 pixel increments. For each of the selected peaks, the measurements at
each pixel are fitted using a spline fit to a resolution of 0.01 pixels. That fitted, high resolution
- 93 -
curve is used to determine the peak position. Note that the selected peaks in Figure 4-10 in
principle can be the same peaks selected in Figure 4-4.
An initial measurement of the reference is made using a long measurement time to obtain a high
quality signal. The above procedure is performed on this measurement to form the baseline peak
positions for future correction.
For subsequent reference measurements, peak positions are
obtained and compared to the baseline peaks. The spectrum is divided into a number of sections,
separated by the selected peaks. In this example, there are 8 sections defined by nine peaks.
Within each section, the amount of correction required is determined by the position of newly
measured peaks at the section boundaries relative to the baseline positions. The spectrum is
corrected by shifting it by this amount. Linear interpolation is used to determine the correct
magnitude of shift for pixels between the section boundaries. Linear interpolation is also used to
determine the correct intensity at a wavelength resolution of 0.01 pixels.
This process was verified in a number of ways, with two reported here. The first tested the
sensitivity to measurement noise. In this test, random noise was added to a non-shifted spectrum.
A number of noise levels were added. These levels were multiples of our measured system noise:
1,2,4,8. For each level of noise, 100 spectra were created, each with a different pattern of
random noise. For each spectrum created, the positions of each peak were detected. Each peak
position was compared to the correct position to indicate to what degree noise gave the
appearance of wavelength shift. We examined 16 peaks and determined that 9 of them are
relatively more robust than others and therefore were chosen for the final algorithm (as shown in
Figure 4-10). These 9 peaks could be detected correctly within 0.1 pixel resolution when the
noise varied from 1 to 4 times the level of our system shot noise.
-94-
The second test utilized data from a previously run system stability test. In this test, the first
reference measurement was used as the baseline, i.e., no drift. The pixel positions of 9 peaks
were determined and recorded using the detection algorithm, and the results are plotted in Figure
4-11. We observe that there are indeed wavelength drifts from 0.2 to 0.4 pixels for different
peaks. In addition, each peak does not drift by the same amount, suggesting a linear correction is
not the optimal approach. After application of the correction algorithm, the detection algorithm
was run again to evaluate the performance of the correction. Results of four representative
samples were plotted in Figure 4-12 for all peaks. The results indicate that wavelength shifts can
be detected and corrected to within our goal of 0.1 pixels.
0.4
'0.3
& 0.2
o'tl
t•
'.€a
A
10
20
30
Sample index
40
Figure 4-11 Wavelength drifts in 9 acetaminophen peaks detected using the new algorithm in 42
measurements over 10 hours.
- 95 -
Sample 2
I'
0-,.
Sample 20
IVMN
c 0.3
= 0.2
.* 0.02
0.01
0
0.1
S0
(
o
2
Y
4
6
2
Peak index
Sample 25
4
6
Peak index
Sample 40
0.2
0.3
•0.2
0.1
- 0.1
•
.O
Li
0
W
2
4
6
8
Peak index
2
4
6
Peak index
Figure 4-12 Detected wavelength drifts in 4 representative peaks before (dashed) and after
(solid) application of the correction algorithm.
4.5
Summary
This chapter first discussed important considerations for Raman instrumentation.
We then
described the continual progress made to bring our instrument to higher sensitivity, stability, and
precision. A detailed instrument description with design considerations and component selection
was given. To overcome the image curvature problem in high numerical aperture spectrograph,
we presented a novel software based method to correct such distortions and demonstrated
diffraction limited spectral resolution and reduced sensitivity to sample re-positioning. This
chapter also described the addition of a laser intensity monitoring photodiode and temperature
probes at key positions. The monitored intensity can be used to correct laser fluctuations and the
temperature measurements enable us to evaluate systematic drifts. Lastly, the error induced by
wavelength drifts was evaluated and a new correction scheme was developed.
- 96 -
CHAPTER 5 CORRECTING
VARIATIONS
SAMPLING
VOLUME
This chapter provides an overview of techniques to correct turbidity-induced spectral and
intensity distortions in fluorescence and Raman spectroscopy, respectively.
It introduces
intrinsic Raman spectroscopy (IRS) to the field of biomedical optics. Analytical models and
Monte Carlo simulations have been developed and are employed to give insights into the
relationship between Raman signal and diffuse reflectance.
Tissue phantom experiments are
performed and results compared to the modeling results. Based on the observed functional
relationship between Raman* tt, where ptt is the total attenuation coefficient, and diffuse
reflectance, the intrinsic Raman signal can be obtained. Ordinary least squares (OLS) and partial
least squares (PLS) are applied to analyze the raw and corrected spectra, showing significant
improvement in concentration measurements after IRS correction.
5.1
Background and introduction
5.1.1
Optical properties of biological tissue
Light propagation in turbid media such as biological tissue is mainly governed by elastic
scattering and absorption of the media. Elastic scattering is a phenomenon in which the direction
of a photon is changed but not its energy, and is usually owing to discontinuities in material
properties (e.g. refractive index) of the media. Absorption is the conversion of light energy into
another form of energy (usually thermal energy).
Most analytical and numerical models employ macroscopic optical properties, including the
absorption coefficient, Ia (cm-l), the scattering coefficient, ps (cm~'), the single scattering angle 0,
and the elastic scattering anisotropy, g = <cosO>, the average cosine of the single scattering
angle. The absorption and scattering coefficients are the probability of a photon being absorbed
- 97 -
or scattered per unit path length. The sum of ga, and [ts is called the total attenuation coefficient,
lt, with
its inverse defined as the mean free depth. The reduced scattering coefficient is defined
as ps' = p~s(-g), also termed the transport scattering coefficient.
The reduced scattering
coefficient has great value in the photon diffusion approximation. 32 Penetration depth can be
defined as 8 = [3a(L-a+9ls')]
"0 '5.
The phase function is a probability density function of the
scattering deflection angle, describing the probability of a scattering angle at which single
scattering event occurs. For example, the Heyney-Greestein phase function in Eq. (5-11) is often
used to approximate tissue scattering.
In general, these optical properties are wavelength
dependent.
Many analytical models, numerical simulations, and experimental techniques were developed for
modeling and measuring light propagation for various illumination-collection and sample
geometries. 36, 74, 89-98 The published work provides foundations on which our models of both
diffuse reflectance and Raman scattering are based.
5.1.2
Optical property variations in biological tissue
Optical properties of biological tissue are known to be affected by physiological conditions,
tissue morphology, and laser irradiation. Different levels of hematocrit (red blood cell volume
percentage) in whole blood cause different absorption (hemoglobin) and scattering (red cells)
properties.
Similarly, different skin layer thickness, morphology, and melanin content cause
optical turbidity to vary.
Such turbidity variations exist across different tissue sites or
individuals, and are generally slowly-varying in time. On the other hand, laser irradiation can
cause quicker temporal variations in turbidity, typically as a result of heating. 94 In the literature,
much emphasis has been placed on large-scale temperature changes that result in tissue
denaturation or coagulation because of its occurrence in laser medicine. These changes are often
-98 -
irreversible and occur at temperatures above 50 degrees Celsius. Smaller, reversible changes of
optical properties occur at lower temperatures, including effects ranging from thermal lensing
(formation of refractive index gradient caused by localized heating) to thermal expansion of
tissue. Additionally, the absorption coefficient of water has been shown to be highly dependent
on temperature. 99 Differences in shape or size of scatterers results in variations in the reduced
scattering coefficient (ts').
Local dehydration may increase the anisotropy of the cells towards
forward scattering. 100
A limiting factor in non-invasive optical technology is variations in the optical properties of
samples under investigation that result in spectral distortions 53'
(effective optical path length) variability.4 '
104-108
97, 101-103
and sampling volume
These variations will impact a non-invasive
optical technique not only in interpretation of spectral features, but also in the construction and
application of a multivariate calibration model, if such variations are not accounted for. As a
result, correction methods need to be developed and applied prior to further quantitative analysis.
For Raman spectroscopy, nevertheless, relatively few correction methods appear in the literature.
Optical property variations will also have significant impact on the effectiveness of calibration
transfer. The optical properties of tissue from individual to individual and from site to site on the
same individual are significantly different and without a correction method, successful
calibration transfer is virtually impossible.
5.1.3 Photon migration theory to model light-tissue interactions
Light propagation in turbid media can be described by radiative transfer equation. 32 However,
the analytical solution to this integro-differential equation can be found only for very special
conditions and approximations.
Diffusion theory is one of the most extensively studied
approximations. The diffusion equation, along with appropriate boundary conditions dictated by
- 99-
the geometry of the problem, may be solved to provide the fluence distribution inside the sample
and the reflected flux. Diffusion theory is often used to model photons that experience multiple
scattering events and thus more "diffusive," usually with a certain amount of source-detector
separation. 32
Nevertheless, good results have been obtained with small source-detector
separation when additional calibration can be carried out. 96
Photon migration theory has been developed by Wu et al.97' 101 of our laboratory and is less
restrictive in source-detector separation. This method employs probabilistic concepts to describe
the scattering and absorption of light, and to set up a framework that allows the calculation of the
diffuse reflectance from semi-infinite turbid media. The total diffuse reflectance (Rd) from a
semi-infinite medium can be written as:
Rd ~-fn (g)*af,
(5-1)
with fn(g) the photon escape probability distribution, n the number of scattering events before
escaping, g the scattering anisotropy, and a the albedo (Is/([st+ a)).
Two fundamental
assumptions were made: 1) the photon escape probability distribution of a semi-infinite medium
only depends on the number of scattering events and anisotropy; 2) the lineshape of the escape
- g)"
probability distribution can be approximated by exponential function, i.e., fn(g) = k(g)ek(
Equation (5-1) can be approximated by integral form:
Rd = a"nk(g)e-k(g)ndn =
1Ina
0
(5-2)
k(g)
When a -1, this expression can be simplified as:
Rd
k(g)Cs
k(g)p,
+ia
where k(g) is an anisotropy and geometry dependent parameter that has to be calibrated.
- 100 -
(5-3)
Figure 5-1 shows various photon-medium interactions in the photon migration picture.
3n
•ln
Diffu
Raman scattered
Figure 5-1 Photon-medium interactions in the photon migration picture.
5.2
Corrections based on photon migration
5.2.1
Correction for spectral distortions in fluorescence spectroscopy
Many researchers have developed methods to correct for spectral distortions in biological
fluorescence spectroscopy.92,
102, 109, 110
Our laboratory has utilized diffuse reflectance
spectroscopy (DRS) in the development of intrinsic fluorescence spectroscopy (IFS) to correct
for turbidity, particularly, absorption-induced spectral distortions of the fluorescence lineshape. 53'
97, 101
Diffuse reflectance is the back-reflected light which undergoes numerous elastic scattering
events before escaping the tissue and thereby provides a metric for the amount of tissue
absorption and scattering. The optical properties of a given sample at a particular wavelength
can therefore be measured in situ by monitoring the diffuse reflectance at that wavelength.
Similarly, DRS can be employed to monitor optical properties at multiple wavelengths.
By measuring fluorescence and diffuse reflectance at the excitation wavelength and over the
fluorescence emission wavelengths using the same illumination-collection geometry, an
- 101-
algorithm can be developed to remove these distortions.
The underlying principle is that
fluorescence emission experiences similar distortions as diffuse reflectance in turbid media. For
IFS, the main goal is to remove distortions largely caused by the hemoglobin absorption peak
near 420 nm.
Based on photon migration theory, Wu derived an analytical equation relating measured
fluorescence (F) to the intrinsic fluorescence (IF), fluorescence as measured from a optically-thin
97
slice of tissue, through diffuse reflectance (R): , 101
IF(x
with a the albedo.
m) -
1
a x -a m
) FRx
m'
(5-4)
Subscripts x and m denote quantities at the excitation and emission
wavelengths, respectively. This expression can be re-written as the product of (1-Rx) and Rm
after using the integral form in Eq. (5-2):
IF(Xx, mX)
F
F
(IIF(Rx)Rm
(5-5)
(5-5)
Equation (5-5) states that for fixed excitation wavelength, the intrinsic fluorescence can be
recovered as the ratio of the measured fluorescence to the diffuse reflectance at the emission
wavelength.
This equation and its variants have been employed to recover turbidity-free
fluorescence spectra from various types of tissue. The correction facilitates interpretation of
53
underlying fluorophores and consequently improves the accuracy of disease diagnosis. ,97,
5.2.2
101
Correction for intensity distortions in Raman spectroscopy
The same general principle that applies for IFS should hold true for Raman spectroscopy as well.
Unlike in fluorescence spectroscopy, spectral distortion owing to prominent absorbers is less of
an issue in NIR wavelength range, 830-960 nm in particular.
This could be the reason
corrections for Raman was initially deemed unnecessary.24 However, for quantitative analysis,
-102 -
turbidity-induced sampling volume variations become very significant and usually dominates
over spectral distortions. Some researchers have applied corrections based on direct absorption
spectroscopy. 11', 2 For the application of diffuse reflectance, Waters extended the formalism
developed by Kubelka and Munk to relate the Raman signal to the measured diffuse reflectance
as a function of either the Kubelka-Munk absorption or scattering coefficient (not identical to
gta
and ps).113 This model assumes only one optical property is changing at a time. Thus, for
powdered samples where the size of the particles and therefore their scattering characteristic
change little over time, the effect of absorption from a progressively darkening sample on the
Raman signal can be sufficiently removed. 114', 115 However, the Kubelka-Munk formalism is not
necessarily applicable to biological tissue because it assumes isotropic scattering and biological
tissue is known to be anisotropic. 116
Therefore, the exact relationship between diffuse
reflectance and Raman in turbid biological media is a subject for our research.
Following Wu's derivation, measured Raman scattering (Ram) at various turbidities can be
written as:
Ram
x
IR Rx -RR
1s,X,+ Ita,xts,x ax -aR
IR R x -R
It,x
R
=,
a - aR
with IR the intrinsic Raman scattering coefficient, pt,x the sum of gs,x and
Ja,x,
(5-6)
and R the diffuse
reflectance. Subscripts x and R denote quantities at the excitation and the Raman wavelengths,
respectively. The intrinsic Raman signal is therefore:
ax
-aR
IR~-L,xRam R-RR
(5-7)
Note that the first part of Eq. (5-6) has an extra term is,x
in the denominator compared to Eq.
(5-4). This term addresses the turbidity-dependent probability of Raman scattering. It was not
included in the IFS scheme because all fluorescence spectra were normalized to their peaks and
- 103 -
therefore the absolute intensity information was irrelevant. In other words, the normalization
step essentially removes any intensity distortion owing to turbidity variations across samples,
thus it is only a semi-quantitative technique. The normalized form is then corrected for spectral
distortions. In the case of Raman spectra from complex systems, the choice of normalization as
in fluorescence spectroscopy is not available.
Without the normalization, information of
absolute intensity is kept, and thus the scattering term is needed. We have tested Eq. (5-7) using
Monte Carlo simulations under semi-infinite condition and excellent agreement was obtained
(detailed in section 5.3).
Equation (5-7) can be further simplified to relate the measured Raman signal to the product of
two diffuse reflectance using the integral form in Eq. (5-2): 97
Ram
IR - k(g)tt,x RxRR
(5-8)
with k(g) depending on the anisotropy and the specific illumination-collection geometry. Note
that Eq. (5-8) has been derived under the semi-infinite condition. Since most Raman instruments
rely on a notch filter to prevent CCD saturation by the intense laser line, diffuse reflectance at the
excitation wavelength is not directly available.
Monte Carlo simulations and experimental
results show that the intrinsic Raman signal for arbitrary sample, as well as collection geometries,
can be described by:
Ram
IR=,x (A+B*RCR)
(5-9)
Parameters (A,B,C) in Eq. (5-9) can be experimentally calibrated and employed to obtain the
intrinsic Raman signal, as will be demonstrated in section 5.4.
-104-
5.3
Monte Carlo simulations for diffuse reflectance, fluorescence, and Raman scattering
in turbid media
The Monte Carlo method has been one of the most effective and statistically accurate tools for
modeling light propagation in turbid media. However, most of the attention and efforts have
been placed on developing the model for elastic scattering in which incident light maintains its
original frequency. In addition, because of the statistical nature of the Monte Carlo method, a
large number of photons are needed to generate useful results. This makes simulations very time
consuming and thus renders the previously developed Monte Carlo program less useful in
practice. 45 In this section we briefly introduce the Monte Carlo method. We describe a recently
developed program based on an existing open source for diffuse reflectance and fluorescence by
Jacques. 98
5.3.1
Monte Carlo method
Monte Carlo simulation is a statistical method based on macroscopic optical properties that are
assumed to extend uniformly over small units of tissue volume (i.e., a voxel). A pre-defined grid
is employed to simulate photon-tissue interaction sites. Mean free path of the photon-tissue
interaction sites typically range from 10-1000 ýtm. This method does not consider the details of
energy distribution within voxels. Photons are treated as classical particles, and wave features
are neglected.32 ' 74 Since its early introduction as a tool to simulate photon elastic scattering,
capabilities such as polarization, 117'
118
temporal resolution, 119 fluorescence, 120 and Raman
scattering 45 have been developed.
Details of the Monte Carlo simulation for diffuse reflectance (the core program) are well
documented in the literature. 74 A brief description of a fixed-weight Monte Carlo simulation is
given below. Initially, a packet of photons at the excitation wavelength enters the sample. On
average, photons travel a distance 1/gPt,x (gtt,x is the total attenuation coefficient at the excitation
- 105 -
wavelength) between two adjacent tissue-photon interaction sites. In implementation, the step
size (s) is calculated by:
s=
ln5
I
(5-10)
where 4 is a random number sampled from a uniform probability density function between 0 and
1. Photon weights are fixed until an absorption or Raman event occurs. To calculate the
scattering deflection angle for each elastic scattering event, a phase function has to be selected.
121 22
In this code, the Henyey-Greenstein phase function is employed: ' 1
p(0)=(-g2 1+g2 -2gcosO)
3/2
,
(5-11)
where the anisotropy, g, equals <cosO>, and has a value between -1 and 1. A value of 0 indicates
isotropic scattering and a value near 1 indicates very forward directed scattering.
Jacques
determined experimentally that the function describes single scattering in tissue very well. 123
The deflection scattering angle is calculated by:
-[1
coso =
1-g
]2 if g >0
2
If g
ifg = 0
(5-12)
where 4 is a random number from a uniform probability density function between 0 and 1. The
azimuthal scattering angle, x, which is uniformly distributed over the interval 0 to 2nt, is sampled:
V= 2 4.
(5-13)
When a photon packet encounters the air-tissue interface (the top boundary), a statistical test for
total internal reflection is performed. The photon packet is either reflected back into the sample
and propagates further, or propagates across the boundary with direction adjusted by Snell's Law,
and is terminated and recorded. Recorded quantities are, for example, fluence rate distribution of
light inside the sample and exiting flux density at the top boundary. To obtain adequate SNR, a
million or more photons are usually needed.
- 106 -
5.3.2
Monte Carlo model for fluorescence and Raman
In this section, a steady-state Monte Carlo program for both diffuse reflectance and
fluorescence/Raman scattering is described. The program is based on an existing open source
code developed by Steve Jacques 98 for diffuse reflectance and fluorescence. The modified flow
chart is shown in Figure 5-2 with some features described below: a fixed-weight scheme was
employed for photon weight bookkeeping, i.e., the weight of a photon stays the same as long as
it is not absorbed or Raman scattered. When absorption or Raman scattering occurs, the photon
weight
is reduced to zero.
Secondary fluorescence/Raman
is
neglected,
i.e.,
a
fluorescence/Raman photon can not generate another fluorescence/Raman photon.
The simulation starts with injection of photon into the medium with a calculated step size. A
probability check (4<Pa) decides whether the photon is absorbed or scattered. If the photon is
absorbed and passes a fluorescence probability check (4<Pf), a new photon is launched at the
fluorescence wavelength and propagates until it exits or is absorbed, otherwise the absorbed
photon is terminated. If a photon is not absorbed, it is scattered (with probability Ps=1-Pa).
Similar to the fluorescence probability check, if a photon is scattered and passes a Raman
probability check (4<PR), a new photon is launched at the Raman wavelength and propagates
until it exits or is absorbed, otherwise the scattered photon continues to propagate without
wavelength shift.
Diffuse reflectance consists of the collected photons at the excitation
wavelength, and the fluorescence/Raman signal consists of the collected photons with
wavelength shift. In addition, angular resolution for the exiting light was added and finite
sample size was allowed. The probabilities mentioned above are given here:
-107-
Pa
Pa
l
afx
+
tt
Pf
L
ab
x
-
=
PR
gPafx
=
x
af
+
(5-14)
Pabx
pRRx
Jtsx
+LRx
where absorbers are considered either fluorescent (Pafx) or non-fluorescent (P'abx), and scatterers
either elastic (g,,x)
or Raman (pRx).
Similar considerations have been implemented in
fluorescence Monte Carlo simulation, 124 but not for Raman scattering.
The program consists of two components: (i) excitation and collection of diffuse reflectance, and
(ii) launch and collection of fluorescence/Raman photons. During excitation, photons sampled
from a collimated beam are launched into the sample. The locations of fluorescence/Raman
events and the angular- and radial-resolved exiting flux are recorded. The recorded locations of
fluorescence/Raman events inside the sample are later adopted as a "map" for launching
fluorescence/Raman photons.
The exiting flux is the diffuse reflectance which consists of
photons that are elastically scattered according to the sample optical properties.
During launching of fluorescence/Raman scattered photons, the program iteratively scans
through the recorded map and fluorescence/Raman photons are launched isotropically. These
photons experience elastic scattering according to the sample optical properties at the
fluorescence/Raman wavelength. In other words, after the initial isotropic launching event, the
program employs the same rules as for the excitation light (elastic and anisotropic) for further
propagation of the photons, however, at a different wavelength.
program is shared by both components of the program.
- 108 -
Therefore, the same core
Compared to the previous Monte Carlo program, 45 the new code simulates both fluorescence and
Raman simultaneously. It decouples the whole process into two parts, and therefore can be
significantly more efficient in computation.
Figure 5-2 Flow chart of the new Monte Carlo code for diffuse reflectance, fluorescence, and Raman
scattering.
-109-
5.3.3
Effects of turbidity variations
A series of Monte Carlo simulations and results are presented in this section. The goal is to
study the relationship between Raman scattering and diffuse reflectance under various amount of
turbidity. A detailed tissue phantom design is given in section 5.4 and briefly described below.
We simulated 49 tissue phantoms in water solutions, following a 7x7 matrix of scattering and
absorption properties with ranges similar to that found in biological tissue. 93 The scattering
coefficient, ýs, was varied from 18.4 to 99 cm' and the absorption coefficient,
Ia,
was varied
from 0.1 to 1.4 cm - . A Raman scatterer of constant strength was present in each sample to serve
as an indicator of the Raman signal. The excitation beam was collimated with 0.1 cm radius.
To demonstrate that turbidity variation causes changes in the sampling volume, we selected three
different turbidities that result in large, medium, and small sampling volumes. The optical
properties (ts,
ta)
for these three simulations are, from low turbidity to high, (18.4, 0.1), (62.57,
0.1), and (99.37, 0.1), all in cm-'. The simulated sample geometry was a 0.5 cm (r) by 1 cm (z)
cylinder. Figure 5-3 shows the steady-state light distribution inside the samples owing to the
excitation. We observe different sampling volumes as a result of the turbidity variations.
o
o
U
Ca
C
,00
N
0
0
,~,\
v
v.~
-0.5
rr
(cm)
Figure 5-3 Steady-state fluence rate owing to excitation for three turbidity-induced sampling
volumes: (left) large; (middle) medium; (right) small sampling volume.
-110-
Figure 5-4 depicts the radial profile of the exiting flux at the air/sample interface for 7 different
scattering levels with fixed absorption (0.1 cm-'). It is observed that in the high turbidity case
the radial distribution of the exiting light is much tighter and localized around the excitation
beam. As a result, for fixed collection geometry, a larger portion of the exiting light can be
collected in the small sampling volume case. Note that since the light delivery coincides with
collection in our instrument, the flux radial profile has taken into account the annulus area for
each radius. Figure 5-5 shows the total diffuse reflectance collected from a spot of 0.5 cm radius.
It is observed that with a fixed collection geometry, diffuse reflectance increases as the scattering
coefficient increases.
x 103
14
1(
lC
#, 8
4
0.1
0.2
0.3
0.4
r (cm)
Figure 5-4 Radial profile of diffuse reflectance versus varying ps.
-111-
0.5
0.6
0.5
0.4
o
o
x
*
+
18.4
36.8
50.6
62.6
73.6
87.4
0 99.4
0.3
0.2
o
Al1
0
20
40
60
80
100
os
Figure 5-5 Total diffuse reflectance collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-4.
Similar to Figure 5-3, a steady-state fluence rate inside the sample owing to the generated Raman
photons are plotted for the three cases in Figure 5-6, and the exiting fluxes of the Raman light are
plotted in Figure 5-7 (radial distribution) and Figure 5-8 (sum).
5
v.5
r
r (cmn)
C
Figure 5-6 Steady-state fluence rate owing to Raman scattering for three turbidity-induced
sampling volumes: (left) large; (middle) medium; (right) small sampling volume.
- 112-
3.5
3
2.5
2
1.5
1
0.5
0.1
0.2
0.3
0.4
0.5
r (cm)
Figure 5-7 Radial profile of Raman scattered light versus varying Ps.
I I I•
I,~I ~
V.02j
0.02
0.015
o 18.4
o 36.8
x 50.6
* 62.6
+ 73.6
* 87.4
o 99.4
0.01
0.005
20
40
60
80
100
As
Figure 5-8 Total Raman scattered light collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-7.
- 113-
Figure 5-9 depicts the radial profile of the exiting flux at the air/sample interface for 7 different
absorption levels with fixed scattering (62.57 cm-'). A phenomenon different to Figure 5-4 is
observed in that absorption decreases the radial distribution more evenly. Figure 5-10 shows the
total diffuse reflectance collected from a spot of 0.5 cm radius.
5
r (cm)
Figure 5-9 Radial profile of diffuse reflectance versus varying [La.
0.5
0.45
0.4
/
o
o
x
*
0.1
0.15
0.2
0.36
+
0.5
* 0.95
i 1.4
0.35 0.30.25
0.2 L
0
0.5
1.5
Figure 5-10 Total diffuse reflectance collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-9.
-114-
The exiting fluxes of the Raman light are plotted in Figure 5-11 and Figure 5-12.
6C
5(
4C
3C
2C
1(
5
r (cm)
Figure 5-11 Radial profile of Raman scattered light versus varying
1) x 10
n
4
-
Jta.
4
I
_
.
3.5
o
0
x
*
+
*
4
2.5
E
E
0.1
0.15
0.2
0.36
0.5
0.95
1.4
1.5
E
0.5
Pa
Figure 5-12 Total Raman scattered light collected from a spot of 0.5 cm radius for the 7 cases in
Figure 5-11.
-115-
Qualitatively, we observe that Raman intensity changes in accordance with the diffuse
reflectance, supporting the basic principle that both of them experience similar turbidity-induced
distortions. We will show quantitatively that the Monte Carlo results agree with the analytical
model.
Intuitively, one would expect a one-to-one relationship between the Raman and diffuse
reflectance for various turbidities. Such one-to-one relationship has been demonstrated in the
literature, 96 however, with either pi or
ýta
fixed while the other varies.
For fluorescence
spectroscopy in particular, fixed ps seems to be a good assumption. Figure 5-13 shows that the
one-to-one relationship does not hold when both optical properties are allowed to vary, a
situation where extra dependence on
ptt
has to be considered as stated in Eq. (5-7). When [it is
factored in, a new one-to-one relationship is revealed in Figure 5-14. This curve enables the IRS
correction when both optical are allowed to vary.
600(
500(
400(
300(
200(
100(
RR
Figure 5-13 Raman versus diffuse reflectance for various turbidities. Symbols code different
absorption coefficients.
-116-
5
x: 10o
5
~
x 10
o 0.1
5 a 0.15
* 0.2
4
* 0.36
3
0.5
* 0.95
I 1.4
=L
+
O
0.
* 0.95
2
a
.÷
1
0.1
o
0.2
0.3
'I.
0~
0.4
RR
0.5
0.6
Figure 5-14 (Ram*Plt) versus diffuse reflectance for various turbidities.
5.3.4
Model validation using Monte Carlo simulation
To test Eq. (5-7) using Monte Carlo simulation, the product (Ram* Pt) is plotted versus the ratio
(Rx-RR)/(ax-aR) in Figure 5-15. The intrinsic Raman signal can be obtained from the slope of the
linear fit. Note that Eq. (5-7) is only legitimate when the semi-infinite condition holds, but
expression Eq. (5-9) should be valid for arbitrary sample and illumination-collection geometry.
-117-
x 104
0
20
40
60
80
100
120
(Rx-RR) / (ax-a R)
Figure 5-15 (Ram*ptt) versus (Rx-RR)/(ax-aR). The slope is the intrinsic Raman signal.
To test Eq. (5-9), the product (Ram*ýpt) is plotted versus RR in Figure 5-16. The simulated
sample satisfies the semi-infinite condition. We observe that the Monte Carlo results can be well
fit using Eq. (5-9) Therefore, the intrinsic Raman signal can be obtained from the ratio of the
measured (Ram* it) to the fit, i.e., (A + B*RRC). It can be seen that this expression fits less well
in the presence of high absorption (lower Raman and reflectance).
However, such high
absorption cases in general are rare in biological tissue in the NIR spectral region.
Note that we chose the 3-parameter power law fit in Eq. (5-9) because of its simplicity and to
better retain the form in Eq. (5-8). In addition, as discussed below, sample size and anisotropy
influence the curvature, i.e., the parameter C in the fit. Nevertheless, this does not preclude
using other fitting function forms, such as the fourth order polynomial, which gives a better fit
even at high absorption.
- 118-
Semi infinite
Cu
0.
=L
o
0
0.2
0.4
0.6
0.8
1
Normalized RR
Figure 5-16 (Ram*,tt) versus RR. The fit to the curve can be used to correct for sampling
volume variations. See text for details.
5.3.5
Geometry considerations
Under the semi-infinite condition with all escaped light collected, it is known that the diffuse
reflectance from various turbidity can be described by a function of the ratio
scale invariance. 96'
respect to
125, 126
/Itýa according to
Here we vary the turbidity and study the diffuse reflectance with
t/Da. Three sample geometries were simulated with various collection spot radii. We
observe a general trend in the results shown in Figure 5-17 -
Figure 5-19 that the diffuse
reflectance approaches a function of only the ratio CPt/Pa when the sample or the collection spot
radii becomes larger. A lesson we have learned is that strictly speaking, the scale invariance is
only preserved when both the sample and the collection radius are semi-infinite. Note that in
principle the sample has to be larger than 88 (8 is the penetration depth defined earlier) in any
dimension to be considered truly semi-infinite without any boundary effect. 1 27 The average
-119-
penetration depth in our tissue phantom design is 0.33 cm and thus the 88 criterion is often
violated, however, we observe that the diffuse reflectance can be well approximated by a oneparameter function using a 2 x 2 sample with a 2-cm radius collection spot, but not with a small
collection radius such as 0.4 cm. Given that the collection spot size is -0.3 cm (r) in our
instrument, we do not expect to see a semi-infinite like diffuse reflectance.
Rdvs.P IP (vol:2x 2,col:2)
M.
(vol: 2 x 2, co: 0.4)
Rd vs. P
o
0c0
008
0.6
Rdvs. s P (vol: 2 x 2, col: 1)
6
0.5
0.4so
0 002
0 o
0.3
0.3/
0.201
0.12
200
600
400
P.I. La.
800
800
600
400
P./ it.
200
200
400
600
P./Ip
800
Figure 5-17 Diffuse reflectance versus P.•/ha for a 2 cm (r) by 2 cm (z) cylinder with three
collection spot radii: 2, 1, and 0.4 cm.
Rdvs. P
I
RdV. s
.(vol: I x 1, col:1)
I
(vol:1 x 1, ol: 0.5)
Rd S. p p
0.41
(VOl:
I X 1, oal:0.2)
'
o'
o
00.2
o
a?
00o
0.244o o
200
400
600
800
200
P./Pit
400
600
800
400
600
P./IlP.
200
800
P./IP
Figure 5-18 Diffuse reflectance versus 9P.sta for a 1 cm (r) by 1 cm (z) cylinder with three
collection spot radii: 1, 0.5, and 0.2 cm.
Rdvs. p
(Pol:
0.5 x 1, col:0.5)
Rdvs.Ps
/
(vol:0.5 x 1, col: 0.25)
0.5
o
00
o00
03
o
Rd
0
o
.4
0 a
0
0
0
o
o
o
0
u
o
o
0.05
0.04
0
0
0
00
o
0.03. 0
S0.2
0
0.2
0.1
0.1
200
P.avs.
I (vol: 0.5 x 1, eol: 0.1)
0
0o
400
600
ILL/ILp
800
0
o o
0
0
o
0.020o0
0oo
200
0.01
400
I,
6600
P00
800
co
o
O 0o
200
600
400
P=IPi
800
Figure 5-19 Diffuse reflectance versus Ps•ta for a 0.5 cm (r) by 1 cm (z) cylinder with three
collection spot radii: 0.5, 0.25, and 0.1 cm.
-120-
Although diffuse reflectance versus pts/Ia varies significantly with sample size and collection
spot radius, Eq. (5-9) is still applicable.
Figure 5-20 shows the evolution of the curvature
mentioned previously from small sample size to semi-infinite. We observe that the exponent in
the power law fit (or the curvature) increases when sample size varies from finite to semi-infinite.
0.2
Normalized 1
0.2
0.4
0.6
U.6
0.8
1
Normalized RR
Semi infinite
0
0.4
Figure 5-20 (Ram*gtt) versus RR for three
sample sizes: 0.5 cm (r) by 1 cm (z), 2 cm (r)
by 2 cm (z), and semi-infinite. (Fixed g (0.8)
for all cases.)
0.8
1
Normalized Rs
5.3.6 Elastic scattering anisotropy (g) considerations
From Monte Carlo simulations we have learned that the curvature of (Ram*pt) versus RR
increases when the sample becomes more semi-infinite.
An analog phenomenon can be
observed in Figure 5-21 when the anisotropy (g) is varied from 0.99 to 0.7. In the high
anisotropy (g=0.99) case, the photons are nearly all "ballistic," resulting in an effective path
much shorter compared to the low anisotropy case, and thus the exponent is lower as in the more
- 121 -
semi-infinite case. Further, the fact that the relationship between (Ram*Pt) and RR becomes
close to linear suggests that Raman and diffuse reflectance becomes more closely related in
terms of effective path length. This is certainly the case when light propagation is more ballistic.
g = 0.99
g = 0.95
Normalized RR
Normalized RR
g = 0.7
g = 0.9
I
0.8
S0.6
Z 0.2i
0.2
0.4
0.6
Normalized 1
0.8
1
Normalized RR
Figure 5-21 (Ram* Pt) versus RR for four g's: 0.7, 0.9, 0.95, and 0.99. (Fixed sample size 2 cm
(r) by 2 cm (z) for all cases.)
The effect of sample size and scattering anisotropy on the curvature (parameter C in Eq. (5-9))
can be studied collectively using the Monte Carlo results shown in Figure 5-22. Influence of
either the sample size or the anisotropy can be studied using Figure 5-23. Considerations on
these two parameters and the interplay between them will be important for implementation. For
example, it is known that whole blood is highly forward scattering with s,> 300 cm -' and g
- 122 -
-0.99.128 This implies that parameter C in Eq.(5-9) will be close to 1 and therefore the fit will be
more linear.
6
0
1
size (cm)
U.1
0
Anisotropy (g)
Figure 5-22 Combined effect of the sample size and scattering anisotropy on the curvature.
5-
I
I
5
4-
-
I
I
I
4
"'
"'
3
"'
''
'"
"'
''
''
2
21-
I
0
0.5
1
1.5
Sample size (cm)
0
2
I
·'
·'
1
0.9
I
0.8
Anisotropy (g)
tl
0.7
Figure 5-23 Correlations between the curvature and the sample size (left) and anisotropy (right).
- 123 -
5.4
Tissue phantom studies
5.4.1
Cuvette geometry
5.4.1.1.
Methods
A correction scheme using Eq. (5-9) is presented in this section. The details of the instrument
employed in this chapter are given in section 4.2, except the addition of a tungsten-halogen white
light source. The laser and the white light source share a common delivery path after a beam
combiner and shutters are programmed to alternate between Raman and diffuse reflectance
measurements. We prepared 49 tissue phantoms in water solutions, following a 7x7 matrix of
scattering and absorption properties with ranges similar to that found in biological tissue. 93 The
scattering coefficient, p•, was varied from 18 to 99 cm-' at 830 nm by altering the concentration
of Intralipid (Baxter Healthcare), an anisotropic elastic scatterer commonly used to simulate
tissue scattering.
The anisotropy of Intralipid is -0.8 at 830 nm91 and is closed to skin
anisotropy.129 The absorption coefficient, gPa, was varied from 0.1 to 1.4 cm -' at 830 nm by
altering the concentration of India ink (Super Black India Ink, Speedball Art Products Company),
124
which possesses a nearly flat absorption profile in our spectral region of interest. ,
130, 131
Optical properties of representative tissue phantoms were subsequently determined by
integrating sphere measurements. A constant 50 mM concentration of creatinine was included in
each sample to serve as an indicator of the Raman signal. The relatively high concentration of
creatinine enabled higher absorption values to be studied while retaining an adequate SNR. A
complete matrix of the tissue phantom design is given in Table 5-1.
Care was taken to ensure that the Rayleigh peak did not saturate the CCD detector in all samples.
Spectra were accumulated with 2-second integration time, and 10 sequential spectra were
collected for each sample. Identical excitation-collection geometry was maintained throughout
-124-
the experiment by fixing the cuvette position. Samples were replaced via pipette following a
water rinse and two rinses of the sample of interest to minimize concentration errors. Data were
processed off-line for image curvature correction, summation, and removal of cosmic rays.
Spectra from 280-1700 cm -1 (850-966 nm) were used in all data analysis.
- 125 -
Table 5-1 Tissue phantom design: scattering coefficient, absorption coefficient, and the
calculated ratio.
j, (cm 1)
•p(cmn-)
Ps/ga
Is (cm
1
')
9a (cm
'1
)
Pt'a
1
18.41
0.10
184.00
26
62.57
0.50
125.14
2
18.41
0.15
122.67
27
62.57
0.95
65.86
3
18.41
0.20
92.00
28
62.57
1.40
44.69
4
18.41
0.36
51.11
29
73.61
0.10
736.10
5
18.41
0.50
36.80
30
73.61
0.15
490.73
6
18.41
0.95
19.37
31
73.61
0.20
368.05
7
18.41
1.40
13.14
32
73.61
0.36
204.47
8
36.81
0.10
368.00
33
73.61
0.50
147.22
9
36.81
0.15
245.33
34
73.61
0.95
77.48
10
36.81
0.20
184.00
35
73.61
1.40
52.58
11
36.81
0.36
102.22
36
87.41
0.10
874.10
12
36.81
0.50
73.60
37
87.41
0.15
582.73
13
36.81
0.95
38.74
38
87.41
0.20
437.05
14
36.81
1.40
26.29
39
87.41
0.36
242.81
15
50.61
0.10
506.00
40
87.41
0.50
174.82
16
50.61
0.15
337.33
41
87.41
0.95
92.01
17
50.61
0.20
253.00
42
87.41
1.40
62.44
18
50.61
0.36
140.56
43
99.37
0.10
993.70
19
50.61
0.50
101.20
44
99.37
0.15
662.47
20
50.61
0.95
53.26
45
99.37
0.20
496.85
21
50.61
1.40
36.14
46
99.37
0.36
276.03
22
62.57
0.10
625.70
47
99.37
0.50
198.74
23
62.57
0.15
417.13
48
99.37
0.95
104.60
24
62.57
0.20
312.85
49
99.37
1.40
70.98
25
62.57
0.36
173.81
- 126 -
Data were analyzed via ordinary least squares (OLS) 48 using a seven-constituent model,
including fused silica (cuvette), water, Intralipid, India ink, creatinine (as measured in water,
with the background subtracted), fluorescence (from impurities in the cuvette - obtained by
subtracting the tenth spectrum from the first spectrum for a representative sample), and a DC
offset to account for the increased or decreased signal level due to scattering or absorption,
respectively. The OLS model constituents are shown in Figure 5-24. Each spectrum was fit
individually to account for varying levels of fluorescence and offset and the creatinine fit
coefficients for the 10 spectra in each set were averaged for each sample. A representative
spectrum, OLS fit, and residual are shown in Figure 5-25. The residual contains no appreciable
structure, supporting the assertion that spectral shape distortions owing to optical property
variations over our collected wavelength range are minimal.
3.5
32.5
2
1.5
1
0.5 400
(e
600
800
1000 1200 1400 1600
Raman shift (cm-1)
Figure 5-24 OLS model constituent spectra from (a) to (f) are: fluorescence, creatinine,
Intralipid, ink, water, and fused silica.
-127 -
4
x 10
10
8
6
4
2
0
400
600
800
1000 1200 1400 1600
Raman shift (cm-1)
Figure 5-25 Representative spectrum, fit, and residual.
OO
0
000
000
&
o
00
0.6
0.4
nA
.,-
ooo
oO 00
8
III
200
400
600
800
1000
0
200
400
600
As / Aa
800
1000
Figure 5-26 Normalized creatinine Raman signal Figure 5-27 Integrated diffuse reflectance of
of the 49 samples, represented by the normalized the 49 samples normalized to the highest
OLS fit coefficients versus 9Is/JIa.
value versus 9ts/ýIa.
The normalized creatinine Raman signal, represented by the normalized OLS fit coefficients, are
shown in Figure 5-26. The diffuse reflectance within the same spectral range was integrated for
each spectrum, averaged for each sample, and then normalized to the highest value, which
occurred for the sample with highest scattering and lowest absorption (Figure 5-27).
- 128 -
5.4.1.2.
Experimental results
The creatinine Raman signal, indicated by the OLS fit coefficients, is hereafter referred to as the
measured Raman signal. In the absence of turbidity, this value should be a constant for all
samples, as the concentration of creatinine was constant. However, owing to optical property
changes, measured values ranged from 0.48 to 1.88, a deviation of over 140%. (Ram*ptt) is
plotted versus RR in Figure 5-28, excellent agreement to the Monte Carlo simulation result is
observed.
i
N
0
t•
Oll
Normalized RR
Figure 5-28 (Ram* tt) versus RR. Excellent agreement is observed between the experimental
data and Monte Carlo result.
The intrinsic Raman signal can be obtained using Eq. (5-9) with the fit parameters. Figure 5-29
shows the measured and the intrinsic Raman signal plotted versus
Jts/Pa.
We observe that the
intrinsic Raman signal clusters much tighter around a constant value (1) for all samples,
regardless of the optical property variations, indicating that sampling volume variations have
-129-
been rectified. As a result, the prediction accuracy is significantly improved, with the RMSEP
for the raw data at 41.6% versus an RMSEP for the corrected data at 10.4%.
0
00
PS//
a
Figure 5-29 Raman signal (OLS fit coefficient) of 49 samples before (open circle) and after
(solid square) correction. The gray line at constant 1 is the ideal prediction line.
Figure 5-30 displays the histograms of the measured and the intrinsic Raman signal. We observe
a much tighter distribution around a constant value (1), the ideal prediction, after correction.
-130-
15
= Measured Raman
10A
GA
4.4
o, 5
6.4
0.6
0.8
1
1.2
| "•.
........
Id
1.4
-
1.6
1.8
2
Intrinsic Raman
P 10
U,
5U
0t
AI
6.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
OLS fit coefficient
Figure 5-30 Histograms of Raman signal of all 49 samples before (upper panel) and after (lower
panel) correction.
5.4.2 Dog ear geometry
To test the applicability of IRS on dog ear geometry (a disk shape), we have done a tissue
phantom experiment simulating the dog ear. A special sample holder was built to allow the
tissue phantom to be contained in a 1.5 cm (r) x 0.2 cm (z) disk sandwiched by two sapphire
windows. The sapphire window not only serves as a reference plane but also a measure of
diffuse reflectance. In other words, as depicted in Figure 5-31, the upper sapphire window plays
the role of an external standard with its Raman signal (Ramiaser) excited by first the incident laser,
and then the diffuse reflectance exiting the tissue phantom (RamDR). Since the laser excitation
spot is much smaller than the diffused light traveling backward, Ramaser can be treated as a small,
fixed background.
The same protocols were followed for tissue phantom preparation and
experiment as in the previous section. One important difference is that there was no additional
white light source in this experiment.
- 131 -
Ramlaser
Excitation
laser
m
RamDR
Zt
DR
Tissue phantom
Figure 5-31 Sapphire Raman signal serves as an external standard of the diffused reflectance.
(Ram*ptt) is plotted versus RR in Figure 5-32.
Excellent agreement with the Monte Carlo
simulation result is observed. Figure 5-33 shows the measured and the intrinsic Raman signal
plotted versus kts/ýta. We observe improvement similar to the results from the cuvette experiment.
The prediction accuracy (RMSEP) is improved from 49% to 3.9%. It is thus demonstrated that
the IRS correction also works for the dog ear geometry.
a+.
=L
0
zc
0.2
0.4
0.6
Normalized RR
0.8
1
Figure 5-32 (Ram*ýpt) versus RR. Excellent agreement is observed between the experimental
data and Monte Carlo results.
-132 -
0
2.2
00 0
O0
O
Ov
2
0 O 0
O
O
1.8
B 1.6-0
0 1.4-~ ~o
6I-P
I
li
-
•
II"
,•
11
200
400
600
800
1000
'
I
1200
Ps / Ia
Figure 5-33 Raman signal (OLS fit coefficient) of 49 samples before (open circle) and after
(solid square) correction. The gray line at constant 1 is the ideal prediction line.
5.4.3
Prospective application of IRS
An important limitation for multivariate calibration or any machine learning algorithm is that it is
generally difficult to extrapolate a calibration model. Extrapolation here refers to prospective
accommodation of variability that is not present in the calibration data, and the origin of the new
variability can be additional interferents or other non-analyte-specific variations. For example,
the b vector obtained from the three-analyte model used in chapter 6 does not predict well if the
prospective sample has a fourth constituent. Similarly, the b vector obtained from clear samples
does not work for turbid samples even though the three underlying analytes are the same.
One way to address the extrapolation limitation is to incorporate potential variability into the
calibration data.
This method is effective, but has two drawbacks: incorporation of more
variability may be experimentally costly.
In addition, the detection limit can be degraded
because of the increased model complexity. This can be understood, for example, via Eq. (3-1):
- 133 -
more interferents result in higher overlap factor and thus higher AC. Another method to get
around this limitation is to simply reduce or eliminate such variability in both calibration and
prediction sets.
Using turbidity variations and IRS as an example, we designed an in vitro experiment with
protocol similar to the one described in section 5.4.1. We prepared 51 tissue phantoms with
various ts,
(37-73 cm - ) and
ýIa
(0.1-0.2 cm'). Glucose and creatinine were used as Raman
scatterers with random concentration from 5-30 mM.
Figure 5-34 shows the experimental results and the fit to Eq. (5-9) with (A,B,C) equal to (0.3, 0.7,
3.7).
Then the 51 samples are separated into two groups according to their ps/ýta, which
characterizes the relative strength of scattering versus absorption in each sample (Figure 5-35).
0.
0.
0.
0.
0.
0.
t)RR
versus
for
IRS
calibration.
Figure 5-34 (Ram*ýtt) versus
RR
for IRS calibration.
- 134-
1
1
I
0.95
0
'0
- 0.9
0.85
oO
0
'o
0.8
0
A
0
mdo
I
I
I
I
I
200
250
300
350
400
I
450
sa'
Figure 5-35 Formation of the calibration (circle) and the prediction (solid square) sets.
The IRS correction was then applied on the reference concentration measurements, as it has been
previously implemented for the tissue phantom studies, where no prominent absorption feature
exist. In this case, each reference concentration value, [Cref], can be converted to [Cconverted] via:
[Cref]
[Cconverted]
tx (A+B*RC)
(5-15)
Then the converted concentration is used as the concentration in PLS with leave-one-out analysis.
Note that another conversion step in the reversed direction has to take place after predictions are
made.
The resulting b vector was used to predict glucose concentration in the prediction set. Compared
to PLS without IRS correction, the prediction error was improved from 0.99 to 0.57 mM. The
results demonstrated that the calibration model based on samples with lower
sis/La did
not predict
well on samples with higher pts/pta. However, after IRS correction the dependence on ps/4a was
greatly reduced.
In other words, PLS alone did not predict well because the sample
- 135 -
characteristics in turbidity has changed in the prediction set compared to the calibration set.
After IRS correction, the turbidity-induced variability was greatly reduced and thus the
prediction result was significantly improved.
Without IRS, the only way to address the
limitation on extrapolation is by incorporation of more sample variability into the calibration set.
As discussed earlier, this strategy is costly and sacrifices accuracy. IRS is presented as a solution
to address the dilemma between the incorporation of more variability (for better model
extrapolation capability) and the reduction of non-analyte-specific variability (for better
accuracy).
5.5
Extraction of optical properties
To apply IRS, one needs to know kt of the samples. Extraction of optical properties has been
studied by many researchers.36' 96, 129, 132, 133 The majority of methods are based on diffusion
theory or variants of it.
Our laboratory extracts optical properties from biological tissue
routinely in other wavelength ranges and a similar method could be employed for this purpose. 96
Nevertheless, the errors in estimating ýtt will impact the performance of IRS.
5.6
Summary and guidelines
This chapter provides an overview of techniques to correct turbidity-induced spectral and
intensity distortions in fluorescence and Raman spectroscopy, respectively. Turbidity-induced
sampling volume variation is one of the major obstacles for obtaining accurate quantitative
information in spectroscopic measurements in biological tissue. Analytical models and a Monte
Carlo code have been developed and employed to study the relationship between Raman and
diffuse reflectance. Experimentally, tissue phantoms have been employed and the result agrees
well with the models and simulations. An algorithm has been developed to correct turbidity-
136 -
induced sampling volume variations.
The result shows significant improvement in analyte
concentration measurements.
Guideline for application of IRS in vivo
Too apply IRS in future in vivo studies, the following two-step procedure can be taken:
calibration of the IRS curve and application. In the calibration step, a tissue phantom experiment
like the ones described in section 5.4 has to be performed under conditions tailored for the
particular in vivo study, i.e., similar ranges of optical properties, identical excitation-collection
geometry, etc. The data can then be fit using Eq. (5-9). Note that if prominent absorption
features exist, the fit has to be done on a wavelength basis, that is, one IRS curve is obtained for
each wavelength. The calibration step of IRS is then completed.
In the application step, total attenuate coefficient has to be obtained from the in vivo DRS spectra.
From here, there are two ways of performing IRS. The first method is to perform IRS on the
reference concentration measurements, as it has been previously implemented for the tissue
phantom studies, where no prominent absorption features exist.
The other method is to form a spectrum of ratios by calculating, for each wavelength,
(Ram*ýtt)/(A + B*RRC), where Ram and RR are the in vivo Raman and DRS spectra, respectively.
This "ratio" spectrum will then replace the measured Raman spectrum for multivariate
calibration.
- 137 -
CHAPTER 6
OPTIMIZING INFORMATION EXTRACTION
Data analysis is the immediate next step after spectral data and reference concentrations are
taken. In general, data analysis for quantitative biological Raman spectroscopy consists of three
major steps: pre-processing, multivariate calibration including model building and validation,
and prospective application of the model. This chapter describes traditional methods and novel
ones that we have developed for data analysis.
Particularly, we present a new hybrid
multivariate calibration technique: constrained regularization. The superior performance of CR
over PLS and HLA is demonstrated using both numerical and experimental data. In addition,
using data from the dog study (detailed in chapter 7), we study the relative performance of CR
and PLS for in vivo applications. We compare CR and PLS from several aspects, including the
presence of strong fluorescence background with and without photobleaching, background
removed spectra via fifth-order polynomial curve fitting, signal-to-noise ratio, reference
concentration error, and spectral overlap.
For more discussion on multivariate calibration, the reader is referred to section 3.4.
6.1
Data pre-processing
Spectral range selection
Multivariate calibration methods attempt to find the spectral constituents based on variance in
data. The presence of a spectral region with large non analyte-specific variations may cause the
algorithm to neglect the variance in other regions, where analyte-specific variations reside. In
our studies, we usually choose the Raman shift from -300-1700 cm-' to cover a significant
portion of the usable CCD range and be safely far from the notch filter cutoff region.
Cosmic ray removal
- 138-
Cosmic rays hit random pixels of the CCD array at random times with arbitrary intensity. As a
result, sharp spectral features of arbitrary intensities appear on top of Raman spectra, generating
artifacts that are not analyte-specific.
Our solution is based on the assumption that the spectrum does not change its intensity from
frame to frame other than due to noise and cosmic rays. Therefore, by comparing multiple
neighboring frames, a statistical algorithm can be used to identify cosmic rays. This algorithm
eliminates pixel values that are 2.22*IQR (interquartile range) above the third quartile. The
value 2.22 is chosen because it is equivalent to 3 standard deviations for a normal distribution.
The average pixel value from other frames without the cosmic ray is used to replace the
contaminated pixel value. This algorithm may not be appropriate for in vivo data owing to the
strong decrease in the background from frame to frame.
Thus, auxiliary methods must be
developed, which also compare adjacent pixels in the same CCD frame.
Background subtraction
Even at NIR excitation wavelengths, tissue Raman spectra often consist of sharp Raman peaks
and a broad background owing to fluorescence or other origins. The fluorescence background
can be from optical components in the system and the quartz cuvette, but mainly from proteins,
lipids, or tissue constituents. The background contributes to a significant part of the shot noise,
and its variation impairs subsequent multivariate calibration.
Although implicit calibration
methods can reduce the detrimental effects from such background or its variation, it is desirable
to completely remove the background to improve detection limit
If the background is already present in the data, only solutions through software can be sought.
A key feature of the background is that it is spectrally much broader and more slowly varying
-139-
compared to the sharp Raman peaks. Therefore, polynomials up to the fifth order have been
utilized to fit the background.44 The polynomial subtraction removes most of the background,
leaving sharp Raman features.
For in vivo Raman spectra, the background intensity level seems to decrease following multiple
exponential decay rates, closely resembling photobleaching of fluorophores.
Since each
fluorophore has different time constant, not only the background intensity decreases, but its
shape also deforms. It has been noted that using fifth-order-polynomial-corrected spectra does
not improve the calibration results. 26 A plausible explanation is that the low-order polynomial
does not fully account (or over-accounts) for the shape change of the background and thus
generates non analyte-specific artifacts.
Random noise rejection and suppression
Photon shot-noise-limited performance can be achieved using a liquid nitrogen cooled CCD
camera. When a detector is shot-noise-limited, the random noise can be estimated by the square
root of the measured intensity. Twenty 2-sec frames of Raman spectra of toluene are acquired
and plotted in Figure 6-1. In Figure 6-2, the standard deviation of the 20 spectra (dotted) is
compared to the square root of the Raman spectra in Figure 6-1 (solid). The observed good
agreement verifies that our instrument can be operated under the shot-noise-limited condition.
Note that this comparison is recommended to be done using units of photoelectron counts rather
than CCD counts.
-140-
...... STD
-SQRT
500
400
I
8
300
U
iii1
200
1
100
ki~L~k~
~JlrCbri~
400
600
800
1000
400
Pixel
600
800
1000
Pixel
Figure 6-1 Twenty frame-by-frame Raman Figure 6-2 Calculated standard deviation of
spectra of toluene acquired with 2 sec per the 20 spectra (dotted) and the square root of
frame.
the Raman spectra in Figure 6-1 (solid).
The most effective way to increase the SNR under shot-noise-limited condition is to increase the
integration time of the CCD or the throughput of the instrument. They both have obvious
limitations. Further, extending the integration beyond a certain length offers no extra benefit.4 5
This is possibly a result of other error sources dominating the performance.
Once the data are collected, signal processing appears to be the only way to further enhance SNR.
Pixel binning along the wavelength axis is one of the ways to increase SNR and the result in the
past suggests an optimal number of binning.4 5 However, a drawback is the degradation in
spectral resolution. Savitzky-Golay smoothing method has been employed to smooth the data
with the benefit that the data length does not change after smoothing. One important parameter
in data smoothing is the spectral range for each smoothing operation. Given the entrance slit
width of a spectrograph, one can estimate the diffraction limited spectral resolution, which is a
good choice for the smoothing range
White light correction and wavelength calibration
- 141 -
When spectra collected from different instruments or on different days are to be compared, white
light correction and wavelength calibration are required. White light correction is performed by
dividing the Raman spectra to a spectrum measured using a calibrated light source, a calibrated
tungsten-halogen lamp in our set up, under identical conditions. Combinatorial spectral response
of the optical components, the diffraction grating, and the CCD camera can be effectively
removed.
Wavelength calibration is to transform the pixel-based axis into a wavelength-based one (or
wavenumber-based). It allows for comparison of Raman features across instruments and time.
In general, unless data measured by different instruments or on different days are to be combined,
wavelength calibration is not performed before further data analysis.
Wavelength selection
Although in most experiments Raman spectra are acquired over a continuous wavelength range,
analyte-specific information can be distributed non-uniformly across the range. In addition, the
overlap factor can change if different wavelengths are chosen for multivariate calibration.
Further, because of the background, the shot noise is usually not a constant across the entire
spectral range. These factors combined suggests that there might be advantages when particular
wavelength channels (e.g., CCD pixels) are excluded from the spectra. The theoretical basis of
wavelength selection and algorithms to perform such selection have been studied. 134- 138 In our
laboratory, wavelength selection has not been implemented, but it should be considered in future
studies.
-142-
In analysis of data presented in this thesis, spectral range selection, cosmic ray removal, and
smoothing were always performed.
Details for these and other pre-processing steps are
mentioned when they are applied.
6.2
Multivariate calibration
As discussed previously, although Raman spectroscopy provides good molecular specificity,
spectral overlap is inevitable with the presence of multiple constituents. Further, the glucose
Raman signal is only 0.3% of the total skin Raman signal. 139' 140 Taken into consideration with
the varying fluorescence background and random noise, it is not feasible to quantify the glucose
signal by recording the skin Raman spectrum at only a few wavelengths.
For quantitative
analysis, multivariate techniques, which utilize the full-range spectra, are employed.
In
multivariate calibration, a set of calibration spectra and the associated glucose concentrations are
used to calculate a regression vector. This regression vector, or b vector, can be applied to a
future independent spectrum with unknown glucose content to extract the concentration.48 ' 62, 63
The introduction to multivariate techniques is given in section 3.4.
6.3
Constrained regularization: a hybrid method for multivariate calibration
This section presents a new method to merge prior spectral information with calibration data in
an implicit calibration scheme. Starting with the inverse mixture model as the forward problem,
we define the inverse problem with solution b. Instabilities associated with the inversion process
are removed by means of a technique known as regularization, 14 1 and prior information is
included by means of a spectral constraint. We thus call the method constrained regularization
(CR).73 We study the effectiveness of CR using numerical simulations and demonstrate its
performance using experimental Raman spectra. We show that with CR the root mean square
error of prediction (RMSEP) is lower than methods without prior information, such as PLS, and
- 143 -
is less affected by analyte co-variations and thus more analyte-specific. We further show that
CR is more robust than our previously developed hybrid method, HLA, when there are
inaccuracies in the applied constraint, as often occurs in complex or turbid samples such as
biological tissue.
It should be mentioned that the terms prior information and spectral constraints are used
interchangeably for both CR and HLA in this section.
6.3.1
Theory
Multivariate calibration can be viewed as an inverse problem. Regularization methods, 141 also
known as ridge regression in the statistical literature,142 are mostly used on ill-conditioned
inverse problems such as tomographic imaging, inverse scattering and image restoration. These
methods seek to obtain a source distribution in the presence of noisy (system-corrupted) data. In
our application the noise is assumed to be uncorrelated, which simplifies the analysis.
As described in section 3.4, the goal of implicit calibration is to invert the forward problem
defined in Eq. (3-10):
c = STb.
(3-10)
The inversion process may be viewed in terms of singular value decomposition (SVD), 143 in
which the spectra of the sample set, S, are decomposed into principal component directions, vj,
with amplitudes given by their respective singular values, aj. Most of the information in S is
captured in the principle components with large aj. The singular values with small amplitudes,
although potentially important, are the main cause of instability.' 44 Methods to alleviate such
144
instabilities are based on reducing the influence of these small singular values, '
145
accomplished by means of a regularization parameter, A. The regularized solution for b is given
by:
- 144 -
b=
P u-c
f
vj ,
(6-la)
,
(6-1b)
oj
j=1
with
2
f2
oj +A
,uj and vj are the eigenvectors of STS and SST, respectively, and p is the rank of S. Note that for
oj >> A, fj
1, and for oj << A, fj = aj2/A 2. Thus, one can interpret regularization as providing a
smoothing filter fj that limits the importance of the small singular values. For A=0, Eq. (6-1)
reduces to the least squares solution for b. In PCR, A=0 and only the k largest singular values
(k<p) are used. In Wiener filtering, 14 6 A is chosen to be the noise-to-signal ratio.
Equation (6-1) is the regularized solution of Eq. (3-10), i.e., no prior information is included
except by forcing the solution to be finite. However, Eq. (6-1) can be modified to incorporate
prior information. A convenient way to accomplish this is by viewing regularization as the
minimization of a quadratic cost function, (D:144
(D(A,b 0) = I/STb -cl 2 + Allb -b 0 2 ,
with
(6-2)
hIall
the Euclidean norm (i.e., magnitude) of a, and bo a spectral constraint that introduces
prior information about b. The first term of QD is the model approximation error, and the second
term the norm of the difference between the solution and the constraint, which controls the
smoothness of the solution and its deviation from the constraint. If bo is zero, the solution to
minimize D is given by Eq. (6-1). As mentioned above, for A=0 the least squares solution is
then obtained. In the other limit, in which A goes to infinity, the solution is simply b=bo. In the
following, we adopt a calibration method in which regularization with a properly chosen spectral
constraint, bo, is employed, hence the name constrained regularization (CR).
- 145 -
The CR solution, a generalization of Eq. (6-1), can be analytically derived in SVD form as: 14 5
b=
P
fj(A)--J + (1- fj(A))vjbe v j.
(6-3)u
(6-3)
A reasonable choice for b0 is the spectrum of the analyte of interest because that is the solution
for b in the absence of noise and interferents.
Another choice is the net analyte signal 76
calculated using all of the known pure analyte spectra. Such flexibility in the selection of bo is
owing to the manner in which the constraint is incorporated into the calibration algorithm. For
CR, the spectral constraint is included in a nonlinear fashion through minimization of cD, and is
thus termed a "soft" constraint. On the other hand, there is little flexibility for methods such as
HLA, in which the spectral constraint is algebraically subtracted from each sample spectrum
before performing PCA. We term this type of constraint a "hard" constraint. In the experimental
section, we use CR and HLA as examples to show that the type of constraint affects the
robustness of hybrid methods concerning the accuracy of the constraint.
Once b0 is chosen, application of CR is straightforward, as Eq. (6-3) is a direct solution of b and
easy to evaluate. A trial value of A is selected and b is calculated from Eq. (6-3) using leaveone-out cross validation' 42 on the calibration data set to obtain a trial prediction residual error
sum of squares (PRESS):
PRESS = (ci
2
(6-4)
where ci and Ci are reference and predicted concentrations, respectively, and i denotes the
sample index. A is then varied until the minimum PRESS value is obtained. The resulting value
of A is then used with the full calibration data set, [S,c], to calculate b. This regression vector
can then be used to predict the concentrations of prospective samples. Because we compare
-146-
several methods in this chapter, it is convenient to denote the b vector obtained from a particular
method as bmethod.
6.4
Performance of CR compared to PLS and HLA
This section provides both numerical and experimental evidence showing that CR is more
advantageous than PLS with clear samples. CR is also more advantageous than HLA with turbid
samples, one of the major motivations for developing CR. In all studies, glucose and creatinine
were chosen as analytes of interest, while urea was always present as an additional active Raman
spectral interference. Since the goal of these studies is not to champion detection limit, results
are normalized to PLS results, an objective baseline.
6.4.1
Numerical studies
6.4.1.1.
Three-analyte clear model: uncorrelated and correlated analyte concentrations
Methods
Numerical spectra were generated by forming linear combinations of constituent analyte spectra
of glucose (G), creatinine (C), and urea (U) as measured in our Raman instrument reviewed in
section 4.2 (Figure 6-3). Spectra from 280-1750 cmn1 occupying 1051 CCD pixels were binned
every 2 adjacent pixels to produce Raman spectra of 525 data points each, reducing the size of
the data set for more rapid computation. Random concentrations uniformly distributed between
0 and 10 were used to generate 60 mixture sample spectra, with zero-mean Gaussian white noise
generated by MATLAB superimposed on the spectra. The SNR, defined here as the ratio of the
major Raman peak magnitude to the mean noise magnitude, was -9.
The uniform noise across
the spectra and the SNR are consistent with typical Raman spectra used for these types of
analytical measurements. Half of the noise-added spectra formed the calibration set, and the
other half the prospective set. Different calibration methods were applied to the calibration set to
- 147 -
generate the b vectors by minimizing the respective PRESS through leave-one-out cross
validation. The b vectors were then used to calculate the RMSEP among the prospective set.
Repeating this entire procedure, we obtained average RMSEP values and b vectors for different
methods. In all calibrations, 3 factors were needed to obtain optimal prediction in PLS and HLA.
The respective pure analyte spectrum was used as the spectral constraint for CR and HLA.
Additionally, because all sample-generating constituent analytes were known, OLS was used to
establish the best achievable prediction.
2.
0
400
600
800 1000 1200 1400 1600
Raman shift (cm-l )
Figure 6-3 Measured Raman spectra of pure analytes dissolved in water and typical
experimental mixture spectra in clear and turbid samples: (G) glucose, (C) creatinine, (U) urea,
(Sc) representative clear sample spectrum, and (St) representative turbid sample spectrum. For
the turbid samples, the only clearly identifiable analyte peak is of creatinine at - 680 cm - .
Traces are normalized and offset for clarity.
Two numerical simulations have been performed to evaluate the different methods under
uncorrelated and correlated conditions. In the first simulation, all analyte concentrations varied
148 -
randomly.
In the second simulation, the glucose concentrations correlated to creatinine
concentrations with r2 - 0.5 in the calibration set but not the prediction set.
Results
Uncorrelated As mentioned in the Methods section, two numerical simulations were performed
on spectra generated from measured constituent analyte spectra. The first simulation, in which
analyte concentrations were uncorrelated, demonstrates that CR significantly outperforms PLS
when all analyte concentrations vary in a random fashion. The results, summarized in Figure 6-4
(Uncorrelated), show that with the aid of prior information, CR generates lower RMSEP values
than PLS.
Simulations
Uncorrelated
0.5
PLS HLA CR OLS
G
PLS HLA CR OLS
C
Correlated
0.5gX
0
PLS HLA CR OLS
G
PLS HLA CR OLS
C
Figure 6-4 RMSEP values normalized to PLS results for glucose (G) and creatinine (C)
obtained from various methods in the first (Uncorrelated) and second (Correlated) numerical
simulations. See text for details.
-149-
The reason for the superior performance of CR over PLS is visualized in Figure 6-5, in which we
plot the deviation of bPLs and bcR from the ideal boLs. We observe that bCR better converges to
boLS, therefore improving prediction over PLS. It is expected that HLA is only slightly inferior
to OLS because the constraints are absolutely correct in simulations.
0
rI.
"0
400
600
800 1000 1200 1400 1600
Raman shift (cm - 1)
Figure 6-5 (a) boLs (normalized, dashed line for visual guidance). Deviations of bPLs and bcR
from bOLS: (b) bPLS- boLs, and (c) bcR- boLs. All b vectors are for glucose calibration with the
traces offset for clarity.
Correlated
The second simulation, in which correlations between analytes were introduced,
demonstrates that CR is less susceptible than PLS to spurious correlations among co-varying
analytes. We modified the calibration data set such that the concentration of glucose correlated
to creatinine with r2 - 0.5. The prospective set remained uncorrelated. The results are displayed
in Figure 6-4 (Correlated), in which CR possesses a much lower RMSEP value relative to PLS.
Again, it is expected that HLA is little affected by analyte correlations because the constraints
- 150-
are absolutely correct in simulations and therefore any correlations are broken after removing the
pure analyte contributions.
6.4.1.2.
Ten-constituent model for human forearm skin: uncorrelated and correlated
constituent variations
Methods
Uncorrelated
The numerical data were chosen to closely simulate the human data.
The
predominant Raman spectral features sampled from the forearm are indicative of skin (Figure
6-6(a)).
To simulate the forearm spectrum, we employed a model composed of nine
representative constituents of the skin-blood-tissue matrix and the spectrum of glucose dissolved
in water (Figure 6-7).
9
7
C5
3
1
400
600
800
1000 1200
Raman shift (cm-')
1400
Figure 6-6 (a) Typical Raman spectrum of skin with background removed; (b) typical simulated
Raman spectra, 25 sample spectra are overlaid; (c) difference between the first two spectra in
(b), magnified 10X; (d) glucose Raman spectrum, 90 mg/dL, magnified 100X. The spectra are
displaced vertically for better visualization.
- 151 -
30
25
K-
20
15
_
~W
_
C(I
10
,,
l
C(
'
AI
5
400
600
800
1000 J200
Raman shift (cm- )
1400
Figure 6-7 Raman spectra of the ten constituents used in the simulation: (A): actin (1%); (CH):
cholesterol (2%); (CI): collagen I (49%); (CIII): collagen III (7%); (W): water (3%); (H):
hemoglobin (6%); (K): keratin (15%); (P): phosphatidylcholine (4%); (T): triolein (13%); (G):
glucose (0.2-0.6%).
The choice of these constituents was based on the known composition of skin, and the relative
amplitudes were chosen to approximate those of the skin-blood-tissue matrix. Glucose was
included at physiological concentrations of 70 to 210 mg/dL.
The resulting simulations
exhibited Raman signal ratios of glucose to the total matrix varying from 0.2 to 0.6%, which is
the typical range measured in skin. 139' 140 These relative amounts of glucose were confirmed by
studies in our laboratory employing minced samples of porcine skin, a good spectral model of
human skin, with elevated levels of glucose. In simulating sample-to-sample variations, we
varied all of the background constituent concentrations in a random fashion (standard deviation
-5% of the design spectral weights in parentheses in Figure 6-7, ensuring that there is no
significant correlation between pairwise model constituents (r2 -0.02). An appropriate amount of
- 152 -
Gaussian random noise (standard deviation -130 counts), estimated from the volunteer data, was
added to each noiseless sample. We define the signal as the norm of the spectrum of interest.
Total Raman SNR (12,000) and glucose Raman SNR (24-72) can then be calculated by dividing
the norm of the total Raman signal (1.5x10 6 counts) and the glucose signal (3,120-9,360 counts)
by the noise magnitude (130 counts), respectively. Finally, to simulate reference concentration
measurement error, Gaussian random error (standard deviation -6 mg/dL) was added to the
glucose concentrations, as well.
Since these parameters are similar to their experimentally
observed counterparts, we expect the numerical data to closely simulate the in vivo Raman
spectra.
A typical Raman spectrum of human skin is shown in Figure 6-6(a). The broad slowly-varying
background was fit to a fifth-order polynomial and subtracted from the spectrum. Twenty five
simulated Raman spectra are shown in Figure 6-6(b), with glucose and other constituents varied
within the above design constraints. As can be seen, they approximate the observed features of
skin Raman spectra very well.
Figure 6-6(c) shows the difference between the first two
simulated spectra, magnified 10X, and Figure 6-6(d) shows the model glucose spectrum at 90
mg/dL, magnified 100X. The Raman signature of glucose is not apparent in either the sample
spectra nor their difference, thus necessitating the use of multivariate calibration techniques.
Correlated In the uncorrelated case, all model constituents were varied in an approximately
random fashion. To study the effectiveness of CR with spurious correlations present, a second
numerical study was performed, with significant constituent co-variations present in the
calibration sample set: strong correlation (r2 -0.72)
between hemoglobin and glucose
concentrations, and exponential decays in the total Raman signal level from the first sample to
153 -
the last. (The volunteer spectra manifested behavior of this type.) 26 All other model parameters
were identical to those of the three-analyte numerical study.
Simulations
Uncorrelated
1
I
I
0.5
0-
PLS
CR
OLS
Correlated
1
II
S0.5
0
PLS
CR
OLS
Figure 6-8 RMSEP values normalized to PLS results for glucose obtained from various
methods in the uncorrelated and correlated numerical simulations using the 10-constituent
model. See text for details.
Results
Figure 6-8 summarizes the results from the application of each calibration method to the
numerical data, using the results of PLS with 9 factors as a baseline. We observe significant
improvement in prediction accuracy using CR in either the uncorrelated or the correlated case.
Similar to the simulation results using the three analyte model, CR becomes more advantageous
than PLS when analyte covariation exists. Note that although the number of PLS factors seem
inappropriate with 25 samples, it does not pose a problem for simulations since we know there
are ten constituents changing in the model.
- 154-
6.4.1.3.
Three-analyte model: sensitivity to inaccurate constraints
Methods
This simulation is designed to address a practical issue for hybrid methods such as CR and HLA
-- robustness against inaccurate prior information, e.g., the measured spectrum of the analyte of
interest (bo) is inconsistent with the measured data. Examples of possible causes of this are: 1)
instrument drifts; 2) spectral distortions due to sample turbidity, i.e., wavelength dependent
absorption and scattering profiles; 3) coexistence of different molecular forms of the same
analyte, e.g., anomeric a- and f- D-glucose with different Raman spectra (section 2.1.1); and 4)
the use of a wrong constraint.
We used glucose as an example analyte and simulated the above four cases by modifying the
calibration and prospective sets described in the three-analyte model in the following ways. In
case one, calibration and prospective data sets, but not the spectral constraint, were shifted -5
cm- , a relatively small value compared to the instrument resolution of -15 cm- . In case two, the
calibration and prospective data sets, but not the spectral constraint, were multiplied by a linear
slope function decreasing from 1 to 0.9 over the spectral range. This effect simulates distortions
due to a wavelength dependent sample absorption profile that did not exist while the spectral
constraint was measured. In case three, the constraint used was the a-D-glucose spectrum as
opposed to the more appropriate anomeric-equilibrium D-glucose spectrum, mimicking an
extreme case for coexisting analyte forms. In case four, creatinine was used as the constraint
although the analyte of interest was glucose.
Results
Figure 6-9 summarizes the RMSEP values for the first three possible mechanisms leading to
inaccurate constraints. We observe that CR is more robust to inaccurate constraints than HLA in
- 155 -
all cases.
When the constraint becomes progressively more inaccurate, unlike HLA, the
performance of CR is maintained. The results of case 4 are not shown because HLA completely
breaks down (very high errors), whereas CR achieves the performance of PCR. The results
demonstrate that CR is more robust against inaccurate constraints.
j
C=4
W
cn
E
EL
I
(1) (2)
(3)
I
(1) (2) (3)
Scenario
Figure 6-9 RMSEP values (in arbitrary units) for glucose obtained from CR (4 bars on the left)
and HLA (4 bars on the right) for the three cases in the numerical simulation. The ideal values
from the first numerical simulation are plotted for comparison.
Figure 6-10 shows the differences (bcR - boLS) and (bHLA - bOLS) and the normalized boLs for
visual guidance for the third case with a-D-glucose as the constraint. We observe that bHLA
deviates more from bOLS, and thus generates higher RMSEP than CR, but it still possesses
excellent SNR. Therefore, judging calibration performance based on the quality of the b vector
can be misleading.
- 156-
0
oa
·c:
400
600
800
1000 1200 1400 1600
Raman shift (cm-1)
Figure 6-10 Glucose bOLs (normalized, for visual guidance) and difference spectra between
averaged b vectors from CR and HLA and bOLS: (a) boLs, (b) bHLA - boLs, and (c) bcR- boLs.
6.4.2
Experimental studies
6.4.2.1.
Three-analyte clear model: uncorrelated and correlated analyte concentrations
Methods
Uncorrelated
In the first experiment, Raman spectra were acquired from 84 water-dissolved
mixture samples composed of glucose, creatinine, and urea, each with randomized concentration
profiles from 0 to 50 mM, with respective mean -25 mM. Half of the samples were acquired on
day 1 and the rest on day 2 to allow instrumental drifts to be incorporated into the model. All
samples were measured in a 1-cm path length quartz cuvette using a Raman instrument described
previously in section 4.2. Each spectrum was acquired in 2 s with laser power equivalent to -12
mW/mm 2 and a 1 mm 2 spot size at the sample. 90 spectra of each water-dissolved analyte and of
water were acquired and averaged for better SNR. Pure analyte spectra were obtained by
- 157-
subtracting the water plus quartz spectrum from the water-dissolved analyte spectra.
A
representative sample spectrum (Sc) is displayed in Figure 6-3.
For data analysis, 21 samples randomly chosen from each day formed the calibration set, and the
other 42 samples formed the prospective set. b vectors obtained using different calibration
methods were applied to the prospective set to calculate RMSEP and the randomized calibrationprediction procedure was repeated 400 times for each method. In all calibrations with leave-oneout cross validation, 5 factors were needed to obtain optimal predictions in both PLS and HLA.
The pure analyte spectra were used as the spectral constraints for both CR and HLA. Because of
measurement errors in the pure analyte concentrations (estimated < 1%), as well as to fully
exploit HLA, we allowed the amplitude of the pure analyte spectra to vary within 1%.
Correlated In the second experiment, Raman spectra were acquired from 84 water-dissolved
mixture samples composed of glucose, creatinine, and urea. Analyte concentrations were varied
between 0 and 50 mM with mean -25 mM. In 42 samples, the glucose concentrations correlated
to creatinine concentrations with r2 - 0.5, and in the other 42 they varied randomly. The urea
concentration was random in all 84 samples. Half of the correlated samples (21) and the random
samples (21) were acquired on day 1 and the rest on day 2 to allow instrumental drifts to be
incorporated into the model. For data analysis, the 42 samples with the design correlation
formed the calibration set and the 42 random samples formed the prediction set. Owing to the
limited number of correlated samples, no randomized calibration-prediction sets were attempted.
Other details are similar to the first experiment.
Results
- 158-
Uncorrelated Mean RMSEP values for glucose and creatinine obtained from PLS, HLA, and CR
in the first experiment are summarized in Figure 6-11 (Uncorrelated). Using PLS as a reference
technique, all other RMSEP values are normalized to the PLS RMSEP values. OLS results are
not listed because the three-constituent model does not account for all experimental variations,
e.g. low amounts of fluorescence from the quartz cuvette; therefore, OLS no longer provides the
best achievable performance.
Among the implicit calibration techniques, substantial
improvement over PLS is observed using the hybrid methods. CR and HLA generate similar
RMSEP values, suggesting that these two methods have comparable performance under highly
controlled experimental conditions with clear samples and without analyte correlations. The
calculated 99% confidence intervals for the differences in means are RMSEPPLS-CR (0.28, 0.33)
and RMSEPHLA-CR (-0.02, 0.02) for glucose, and RMSEPPLS-CR (0.06, 0.13) and RMSEPHLA-CR
(0.02, 0.09) for creatinine, indicating that the results in comparison to PLS are statistically
significant.
Correlated Mean RMSEP values for glucose and creatinine obtained from PLS, HLA, and CR in
the second experiment are summarized in Figure 6-11 (Correlated).
Among the implicit
calibration techniques, substantial improvement over PLS is observed using the hybrid methods.
CR and HLA generate similar RMSEP values, suggesting that these two methods have
comparable performance under highly controlled experimental conditions with clear samples and
with analyte correlations. In principle, HLA should be less affected by analyte correlations than
CR, however, this is not observed in this experiment. Possible explanations include imperfect
experimental conditions and the higher sensitivity of HLA to inaccurate constraints (discussed
below).
-159-
Experiment - Clear
Uncorrelated
0.
F'L3
"IrT
tiL-
IL3
LAK
G
r
IILA
C
/I-'!1F
LK
Correlated
I-
1
[
[
T
I
t-
1
0.5
0
PLS HLA CR
G
PLS HLA CR
C
Figure 6-11 RMSEP values normalized to PLS results for glucose (G) and creatinine (C)
obtained from various methods for clear sample experiments without (Uncorrelated) and with
(Correlated) analyte correlations. See text for details.
6.4.2.2.
Three-analyte turbid model: uncorrelated concentrations
Methods
In the third experiment, the same protocol as in the clear experiment was followed, but with the
addition of Intralipid and India ink to increase turbidity.
The analyte concentrations were
uncorrelated. Raman spectra were acquired from 84 water-dissolved mixture samples composed
of glucose, creatinine, urea, India ink, and Intralipid with randomized concentration profiles.
Analyte concentrations were varied between 0 and 50 mM with mean -25 mM.
The
concentration of India ink was varied such that the sample absorption coefficients ranged from
0.1 to 0.2 cm -' with mean -0.15 cm'. The concentration of Intralipid was varied such that the
sample scattering coefficients ranged from 35 to 75 cm~' with mean -55 cm -'. The range of
- 160 -
optical property changes agree well with reported values measured from human skin. 129 A
representative sample spectrum (St) is displayed in Figure 6-3. In all calibrations with leave-oneout cross validation, no more than 6 factors were needed to obtain optimal prediction in both
PLS and HLA.
Results
Mean RMSEP values for glucose and creatinine obtained from PLS, HLA, and CR in the third
experiment with turbid samples are summarized in Figure 6-12. Substantial improvement over
both PLS and HLA is observed using CR. The performance of HLA is significantly impaired as
a result of the turbidity-induced sampling volume variations of the analyte of interest.
Experiment - Turbid
j
PI
W
v,
E
PLS HLA CR
PLS HLA CR
G
C
Figure 6-12 RMSEP values normalized to PLS results for glucose (G) and creatinine (C)
obtained from various methods for the turbid sample experiment. See text for details.
In HLA, the analyte of interest is assumed to be present in the data according to the reference
concentrations. This assumption leads to the first and most important step: the removal of the
spectral contribution of the analyte of interest from the data by subtracting the known spectrum
of the analyte according to its concentration in each sample. As a result, the performance
critically depends on the "accuracy" of the constraint, as well as the legitimacy of the assumption.
- 161 -
In CR, however, the constraint only guides the inversion, allowing the minimization algorithm to
arrive at the optimal solution, thereby reducing its dependency on the accuracy of the constraint.
Further, unlike HLA, which models the residual data after removing the analyte contribution, CR
retains data fidelity and is unlikely to produce false built-in analyte spectral features in the b
vector. The calculated 99% confidence intervals for the differences in means are RMSEPPLS-CR
(0.18, 0.23) and RMSEPHLA-CR (0.31, 0.37) for glucose, and RMSEPPLS-CR (0.09, 0.15) and
RMSEPHLA-CR (0.32, 0.38) for creatinine, indicating that the results are statistically significant.
6.4.3
Discussion
The results presented here demonstrate that there is a tradeoff between maximizing prior
information utilization and robustness concerning the accuracy of such information. Multivariate
calibration methods range from explicit methods with maximum use of prior information (e.g.
OLS, least robust when accurate model is not obtainable), hybrid methods with a hard constraint
(e.g. HLA), hybrid methods with a soft constraint (e.g. CR), and implicit methods with no prior
information (e.g. PLS, most robust, but is prone to be misled by spurious correlations). We
believe CR achieves the optimal balance between these ideals in practical situations.
Constrained regularization is a new hybrid method for multivariate calibration. Strictly speaking,
it should be categorized as an implicit calibration method with one additional piece of
information, the spectrum of the analyte of interest.
In the broader context, regularization
methods may perform somewhat better than either PLS or PCR 147 for certain data structures. A
heuristic explanation is that regularization provides a continuous "knob", and therefore can be
used to find a better balance between model complexity and noise rejection. Our results show
that in addition to this plausible intrinsic advantage, solid improvement can be obtained by
incorporating a meaningful solution constraint.
- 162 -
CR significantly outperforms methods without prior information such as PLS and is less
susceptible to spurious correlations with co-varying analytes.
Compared to HLA, CR has
superior robustness with inaccurate spectral constraints. This robustness is crucial for hybrid
methods because it is difficult, if not impossible, to quantify high-fidelity pure analyte spectra in
complex systems such as biological tissue. Further, CR naturally extends to situations in which
pure spectra of more than one constituent are also known.
In that case a better choice of
constraint (bo) might be the net analyte signal calculated from all the known pure spectra. CR is
thus able to include more prior information without sacrificing the principal advantage of
implicit calibration: that only the reference concentrations of the analyte of interest are required
in addition to the calibration spectra.
6.5
In vivo considerations -
CR vs. PLS using synthetic in vivo data
We have conducted an in vivo dog study with our collaborators at Bayer Healthcare.
Experimental protocols and details are given in section 7.1. PLS and CR were both applied to
analyze the data and similar performances were obtained. This prompts us to more carefully
investigate the possible scenarios encountered in vivo and examine the relative performance of
CR and PLS. In this section, we use similar background and random noise levels as observed in
the in vivo data and the three-analyte model with glucose, creatinine, and urea.
6.5.1
Background and background removal
Fluorescence background with photobleaching
The most outstanding difference between the in vivo data and earlier in vitro data in this chapter
is the presence of the background and its decay over time, attributed to photobleaching. Figure
6-13 shows the spectra of the turbid tissue phantom (top) and 50 mM glucose in water (bottom).
The ratio of the maximum glucose peak height to the average background intensity is -2.6%.
- 163 -
However, as shown in Figure 6-14, the ratio for the in vivo data is -0.027%, 100X smaller than
the in vitro data. Further, such an intense background is decreasing during the course of the
experiment.
Since multivariate calibration techniques look for spectral component based on
variance, the background becomes the first candidate under investigation. In this section CR and
PLS are compared in the following aspects: with noise equivalent to the in vivo data but without
the background, with both the equivalent noise and background, and background removed using
fifth-order polynomial curve fitting.
x 104
1.5
400
Ra
400
600
s
800
m
1000 1200 1400 1600
Raman shift (cm'1)
S200
o 100
0
400
600
800
1000 1200 1400 1600
Figure 6-13 Raman spectra of the in vitro turbid tissue phantom (top), and 50 mM glucose in
water (bottom, water subtracted). The samples were in a cuvette.
-164-
x 105
14
o8
06
10
4
400
600
400
600
800 1000 1200 1400 1600
Raman shift (cm-1)
250
200
150
0 100
50
'
800
1000 1200 1400 1600
Figure 6-14 Raman spectra of the in vivo dog study (top), and 50 mM glucose in water (bottom,
water subtracted). The glucose sample was in a fake dog ear holder described in section 5.4.2.
The in vivo backgrounds are approximated by heavily smoothing the in vivo spectra. Three steps
in the simulation are described here: First, a set of sample spectra without background is formed
by summation of unit concentration glucose spectrum times the corresponding glucose
concentration,
unit concentration
creatinine
and urea spectra times their respective
concentrations (random within similar range to glucose), and random noise generated by the
backgrounds. CR and PLS are applied and results are shown in the first two columns of Figure
6-15. Then the approximate backgrounds are added to the previous dataset to form the second
dataset. CR and PLS are applied with results shown in the third and fourth columns of Figure
6-15.
Finally, a third dataset is obtained by running a fifth-order polynomial background
removal routine on the second dataset. Then CR and PLS are applied with results shown in the
- 165 -
fifth and sixth columns of Figure 6-15. For better comparison to in vivo data analysis, the size of
the calibration set was 90 and each sample spectrum was obtained by averaging 33 frames.
2.6
'2.4
S2.2
12
1.8
CR
PLS
CR/BG PLS/BG CR/5op PLS/5op
Figure 6-15 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details.
We observe that with the background-generated noise, CR still performs much better than PLS.
However, the difference between CR and PLS is significantly reduced with the presence of
background. This suggests that the performance of implicit calibration is degraded not only by
the background-generated random noise, but also by the background itself. Nevertheless, CR's
performance is much more impaired because of the background. Further, we observe only a
slightly lower RMSEP after background removal, suggesting the fifth-order polynomial type of
background removal routine eliminates only a small portion of the detrimental background effect.
This agrees with our conclusion for the earlier in vivo human study that background subtraction
offers no substantial improvement.
-166-
6.5.2 Signal-to-noise ratio
The signal-to-noise ratio was fixed in the previous three-step study for clarity. In this section,
two additional factors are brought in: the size of the calibration sample (ns) set and the number
of frames averaged. Both factors influence the signal-to-noise ratio of the calibration data. We
simulated 4 different frame averaging schemes and 3 different sample sizes. Results shown in
Figure 6-16 and Figure 6-17 suggest that in general the advantage of CR relative to PLS
decreases when SNR increases either by averaging more frames or including more samples in a
calibration set. This is expected since all implicit calibration techniques should result in the ideal
OLS b vector under noise-free condition.
33 spectra averaged
C,,
CR
PLS
CR/BG PLS/BG CR/5op PLS/5op
40 spectra averaged
¶c
C-
CR
PLS
CR/BG PLS/BG CR/5op PLS/5op
Figure 6-16 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details.
- 167 -
50 spectra averaged
C-
CR
PLS
CR/BG PLS/BG CR/5op PLS/5op
60 spectra averaged
PLS
CR/BG PLS/BG CR/5op PLS/5op
6
44
2~
CR
Figure 6-17 Comparison between CR and PLS in various cases: without background, with
decreasing background, and after background removal. See text for details.
6.5.3
Reference concentration error
There are always errors in the reference concentrations.
We simulated three different error
magnitudes (2%, 4%, and 6%) and compare CR to PLS. Results shown in Figure 6-18 suggest
that with errors at the magnitude similar to our experimental condition, the relative advantage of
CR over PLS should remain.
This may imply that the spectral noise dominates over the
concentration error.
- 168 -
30 samples, 33 spectra averaged
4.4
2.2
...........
2%
E-
g 3.4
6%
CR
PLS
60 samples, 33 spectra averaged
m
nm·
S2.2-W
•
''
----- 4%
6%
•1.1
3.4
2.2
CR
PLS
90 samples, 33 spectra averaged
S...........
2%
------ 4%
-
16%
CR
PLS
Figure 6-18 Comparison between CR and PLS with different inaccuracy in the reference
concentration measurements.
6.5.4 Spectral overlap
Two more datasets were created and subsequently analyzed using CR and PLS. The first dataset
consists of only glucose and random noise, and thus without any spectral interferent. The second
dataset contains glucose with creatinine added as an interferent. Results from these two data sets
(Figure 6-19) can be compared with earlier results (Figure 6-16 top panel), suggesting that CR
works the best when the constraint is accurate, and fewer samples are needed to generate a good
calibration model. On the other hand, as demonstrated in section 6.3, CR is more robust than
HLA when the constraint becomes progressively inaccurate.
-169-
G only
A A
-
-• 3.3
ns=30
ns
2.2
11
L
CR
PLS
G&C
S2.8
S2.8
w
CR
PLS
Figure 6-19 Comparison between CR and PLS with different spectral overlaps. The scheme of
33- frame averaging was used.
6.6
Summary
This chapter described the data analysis in detail. Traditional methods and novel ones that were
developed in this laboratory were reviewed. Particularly, we present a new hybrid multivariate
calibration technique: Constrained Regularization. The superior performance of CR over PLS
and HLA is demonstrated using both numerical and experimental data. Compared to PLS, CR
less susceptible to spurious correlations. Compared to HLA, CR is more robust when the pure
analyte spectrum is not accurate, as is the case in turbid biological media.
Further, using data from the dog study, we studied the relative performance of CR and PLS for in
vivo applications. We compared CR and PLS in several circumstances, including the presence of
strong fluorescence background with and without photobleaching, background removed spectra
via fifth-order polynomial curve fitting, signal-to-noise ratio, reference concentration error, and
spectral overlap. We found that the intense decaying background impairs both CR and PLS, and
- 170-
largely washes out the intrinsic advantage of CR. This can be the reason why similar results
were obtained on the dog data via either method. Therefore, it is imperative to find a way to
mitigate the effects of the background and its variations.
- 171 -
CHAPTER 7 IN VIVO DOG STUDY
This chapter describes an in vivo dog study performed with our collaborators at Bayer Healthcare.
The dog study was performed on a beagle anaesthetized for -8 hours, during which its blood
glucose concentration was clamped at several different levels. Raman spectra were continuously
acquired from the ear and reference blood glucose measurements were taken via venous blood
and interstitial fluid withdraws.
Results from PLS analyses demonstrate that the calibration
model can predict samples that were not included in the calibration set, a step forward toward
prospective application. In addition, this study allows us to evaluate and analyze how CR and
IRS can be implemented in in vivo applications and develop protocols for future experiments
7.1
Dog study
An important aspect of our collaboration with Bayer Healthcare is to employ dogs as an
experimental subject for the development of our Raman technique. Dog subjects provide several
attractive features such as similar physiological glucose response to human, no motion artifacts
owing to the anesthesia that can be administered, and the flexibility to perform glucose clamping
studies. Several dog studies have been done over the past few years and the results have been
very encouraging. This section describes details and analysis of the most recent study carried out
collaboratively at the former Bayer facility in Elkhart, IN.
7.1.1
Protocol and experiment
As part of this collaboration, a second Raman instrument was constructed and transported to
Bayer for use in dog glucose clamping studies.
The geometry of light delivery path was
modified to allow the excitation laser to have normal incidence from beneath the dog ear through
a hole in the paraboloidal mirror which subsequently collects and collimates the back-scattered
Raman signal. The dog ear was placed in contact with a sapphire window, the backside of which
- 172 -
serves as a reference plane.
The optimal distance between the reference plane and the
paraboloidal mirror was determined by maximizing Intralipid Raman signal from tissue phantom
contained in a sample holder simulating dog ear geometry, i.e., a 1.5 (radius) x 0.2 (thickness)
cm cylindrical tissue phantom solution with optical properties and thickness close to the dog ear
(tissue phantom described in chapter 5). Figure 7-1 shows an aluminum sample stage that a dog
subject can lie on its stomach with the ear positioned over the sapphire window aperture.
Figure 7-1 A dog subject lies on its stomach with the ear positioned over the sapphire window
aperture of the aluminum sample stage.
Protocol
The dog was anesthetized before the data collection began. Its blood glucose concentration was
clamped at several different levels by controlled injection of both glucose and insulin. Plasma
and interstitial fluid (ISF) glucose concentrations were measured every five minutes using an
Analox glucose analyzer and a Bayer proprietary ISF glucose analyzer, respectively. The dog's
glucose concentration was clamped at 8 different levels within the range 5.6-25.6 mM (100-460
mg/dL). Each clamping level lasted for -35 min. During the course of the experiment, Raman
- 173 -
spectra were collected continuously with 1.8 sec per frame and 1.6 sec data transfer time, giving
a frame every 3.4 sec. (The duty cycle was limited by data transfer.) The laser was not shuttered
during file transfer as in past experiments. Each frame has dimension 260(V)*1340(H) as
hardware binning of every 5 vertical pixels was chosen. After data collection, the curvature
correction algorithm (described in section 4.3) was applied to all frames before vertical binning.
Since various frame-averaging schemes were adopted, the individual spectra are referred to as
"frames" though they are one dimensional, and the subsequent averaged spectra are referred to as
"sample spectra."
x 105
12
10
46
4
400
600
800
1000 1200 1400 1600
Raman shift (cm-1)
Figure 7-2 33-frame averaged sample spectra with -18.7 min in between 2 adjacent spectra.
Figure 7-2 shows examples of the 33-frame averaged sample spectra with -18.7 min between
successive spectra.
Apparent sapphire Raman peaks and a broadband decreasing background
are observed. To better accentuate Raman peaks from the dog ear, a fifth-order polynomial
background subtraction routine was employed with results shown in Figure 7-3.
-174-
x 104
6
-2
400
600
800
1000 1200 1400 1600
Raman shift (cm l)
Figure 7-3 Sample spectra in Figure 7-2 after background removed using a fifth-order
polynomial routine.
7.1.2 Minimum detection error analysis
As outlined in section 3.3, the minimum detection error can be estimated using experimental
parameters such as SNR and overlap factor. The dog data were acquired with 1.8 s/frame. To
estimate spectral random noise, we calculated the variance of each pixel among 10 adjacent
frames (frame 6485-6494). The reason for selecting these frames is to minimize the apparent
variance owing to the background decay, which was much reduced at later time during the
experiment. The calculated 2D variance map was then processed by the curvature correction
algorithm described previously and a single spectrum of variance was obtained and shown in
Figure 7-4. The estimated noise, 360, was then obtained from the average across the square root
of the variance spectrum.
- 175 -
x 105
E
=j
5
o
PI
rn
a
u
(d
· r(
k
400
600
800 1000 1200 1400 1600
Raman shift (cm-')
Figure 7-4 Variance spectrum calculated from 10 frames using the curvature correction
algorithm.
The Raman spectrum of glucose was measured from a 50 mM glucose water solution contained
in the dog-ear-like sapphire sample holder. The norm of glucose was calculated to be -56 mM 1
using either pixel range 240-1040 or 200-1200.
The overlap factor for the experiment was
estimated to be - 1.2-1.4 using the nine component model described earlier. Using Eq. (3-1), the
minimum detection error based on these experimental parameters is -8.36-9 mM (using raw
frames). If frame averaging is performed, AC is 1.46-1.57 and 1.04-1.11 for 33- and 65- frame
averaged, respectively. Note that the AC formalism considers only random noise in the predicted
spectra, not the calibration spectra nor the reference concentration, i.e., an absolutely correct
model. The estimated detection limit can be improved by optimizing sample placement as
described in section 8.2.
7.2
Initial analysis using PLS
Pre-processing
- 176 -
Among the 6498 frames, we observed that the laser intensity fluctuated at two fixed frequencies,
causing fluctuations at the same frequencies in the collected frames.
Fourier filtering was
employed to effectively remove the slowly-varying laser intensity fluctuations.
Figure 7-5
shows the temporal intensity at an example pixel (pixel 400) before and after Fourier filtering
using two frequency notches.
6
x 10
1 o r-
1.Uo)
x 10
1.6
1.06
S1.4
1.055
-...
Q 1.2
1.05
1 0A45
2000
4000
6000
2000
Frame index
2050
2100
2150
Frame index
6
6
x 10
x 10
1.0U6
1.6
1.06
1.4
1.055
1.2
1.05
1
"---~
2000
1 0A4
4000
6000
Frame index
2000
2050
2100
2150
Frame index
Figure 7-5 Laser fluctuation (pixel 400 as an example): Raw data (upper left), raw data zoomin (upper right), filtered data (lower left), and filtered data zoom-in (lower right).
Owing to high SNR, CCD fixed pattern noise is very significant. We first heavily smoothed the
sample spectrum and then subtracted the smoothed spectrum from the original sample spectra to
identify the fixed pattern noise. The fixed pattern noise in individual frames was subsequently
removed according to intensity levels. Figure 7-6 shows before and after fixed pattern noise
reduction.
- 177 -
.. ,xl0
6
I,
E '·
o
P,
v,
1
"100
750
800
Raman shift
850
900
(cm-1)
Figure 7-6 33-frame averaged sample spectra (thin solid lines), smoothed spectra (solid lines
with cross), and extracted fixed pattern noise (dashed line).
PLS analysis with cross validation
Various datasets were formed for PLS analysis using leave-one-out cross validation with
differences in the following aspects: numbers of frame averaged, with or without 25-pt SavitzkyGolay smoothing, spectral range selection, and reference concentration selection.
It is well known that the interstitial glucose lags the plasma glucose concentration from 5-30 min
in humans. Since our Raman technique is measuring mostly glucose in the ISF, both ISF and
plasma glucose concentrations were measured. In the following analyses, we will specify which
is used as the reference concentration.
The results give us a general evaluation of the performance of our technique. Figure 7-7 Figure 7-10 show example results from one analysis with 33-frame averaging, 25-pt smoothing,
and the plasma glucose as reference concentration. Figure 7-7 shows the calculated RMSECV
- 178 -
versus the number of PLS factors. The observed minimum indicates that the optimal calibration
model contains 8 factors. The Clarke error grid is plotted in Figure 7-8 using the predicted
concentrations in the cross validation procedure. This type of grid is used by physicians to
evaluate the performance of non-invasive glucose techniques. Predictions falling in zones A and
B are considered clinically acceptable.
Figure 7-9 compares the reference to the predicted
glucose concentration over time (-1.87 min between two samples). The regression vector and
glucose Raman spectrum are plotted in Figure 7-10. Great similarities are observed between the
two, indicating that glucose was indeed measured because there was no prior glucose spectral
information supplied to the PLS model.
Q
5
10
15
Number of PLS factors
Figure 7-7 RMSECV versus number of PLS factors.
-179-
20
EGA plot
25
20
15
5
10
20
Reference glucose (mM)
Figure 7-8 Clarke error grid of predicted glucose concentrations.
0
Sn
0
so
u
E
0
Sample index
Figure 7-9 Temporal profiles of reference and predicted glucose concentrations (-1.87 min
between two samples).
-180-
0.5
S0
OuV
-0.5
-1
400
600
800
1000 1200
Raman shift (cm 1)
1400
Figure 7-10 Regression vector (top) and the glucose Raman spectrum (bottom).
- 181 -
Table 7-1 lists all results from the cross-validation analyses with various calibration set
formations.
Table 7-1 Summary of the cross-validation analysis with various pre-processing and
model parameters.
RMSECV (mM)
r
Corr(b,g)
65f, plasma, 365-1519 cm t'
2.03
0.89
0.34
65f, ISF-2, 365-1519 cm' l
1.98
0.87
0.35
Statistics
Preprocessing
65f, plasma, 25-pt, 365-1519 cm-1
1.84
0.91
0.45
"
1.79
0.90
0.47
65f, plasma, 25-pt, 297-628 cm '
2.91
0.77
0.32
65f, plasma, 25-pt, 297-1703 cm-
1.56
0.93
0.51
65f, plasma, 25-pt, 1-1703 cm-1
1.83
0.79
0.31
65f, ISF-2, 25-pt, 297-628 cm'
2.88
0.72
0.30
65f, ISF-2, 25-pt, 297-1703 cm -1
1.64
0.90
0.51
1.70
0.76
0.34
65f, plasma, 25-pt, 297-1703 cm ' 5op
1.72
0.92
0.47
65f, ISF-2, 25-pt, 297-1703 cmr' 5op
1.74
0.90
0.48
33f, plasma, 365-1519 cm "1
2.06
0.89
0.37
33f, ISF-2, 365-1519 cm 1
2.05
0.87
0.37
33f, plasma, 25-pt, 365-1519 cm'
.1.87
0.91
0.47
33f, ISF-2, 25-pt, 365-1519 cm "
1.86
0.89
0.48
1
3.10
0.74
0.32
1.65
0.93
0.53
1.67
0.93
0.37
3.04
0.65
0.30
33f, ISF-2, 25-pt, 297-1703 cm-
1.74
0.90
0.53
33f, ISF-2, 25-pt, 1-1703 cm-'
1.61
0.82
0.46
1.76
0.92
0.52
1.81
0.89
0.51
65f, ISF-2, 25-pt, 365-1519 cm
65f, ISF-2, 25-pt, 1-1703 cm i"
1
"
33f, plasma, 25-pt, 297-628 cm
33f, plasma, 25-pt, 297-1703 cm l'
1
33f, plasma, 25-pt, 1-1703 cm '
33f, ISF-2, 25-pt, 297-628 cmd '
1
33f, plasma, 25-pt, 297-1703 cm-, 5op
'
33f, ISF-2, 25-pt, 297-1703 cm" 5op
-182 -
PLS analysis with cross validation and prediction
We then picked one set of parameters, i.e., 33-frame averaging and 25-pt smoothing, to perform
further analysis with level splitting. Since the 65-frame averaging scheme did not give much
improved RMSECV previously and results in fewer samples, analyses here were done using 33frame averaging. All the samples collected at the clamping levels were divided into a calibration
set and a prediction set. Building calibration models solely based on the leveled data avoids
additional confounding factors during the glucose rise and fall phases.
PLS was performed on the calibration set to calculate RMSECV and the b vector, which was
subsequently used to predict on the prediction set with RMSEPI. The b vector was then used to
predict on all samples except the calibration samples, including the samples during glucose rise
or fall phases, to calculate RMSEP 2 and r2 . Note that RMSECV -1.2 mM was obtained,
suggesting a lower bound for the prediction error.
Table 7-2 lists all results from the level-splitting analysis.
The higher values observed in
RMSEP 2 suggests that there were indeed more interferents during the glucose rise and fall phases,
which were not accounted for using the calibration models based on leveled regions. These
RMSEP values are slightly higher than the estimated minimum detection error (- 1-1.6 mM) in
section 7.1.2, suggesting that there is room for improvement in our experiment.
- 183 -
Table 7-2 Summary of the level-splitting analysis with various pre-processing and
model parameters.
Statistics
RMSEP 2
r2
Corr(b,g)
(mM)
(mM)
1.78±0.18
1.77±0.22
2.19±0.24
0.93±0.01
0.47±0.02
1.78±0.18
1.77±0.22
2.19±0.24
0.94±0.01
0.53±0.04
1.47+0.14
1.4±0.12
2.06±0.09
0.94±0.01
0.56±0.02
1.8±0.17
1.83±0.21
2.13±0.2
0.92±0.01
0.47±0.03
1.82±0.21
1.73±0.24
2.15±0.18
0.92±0.02
0.52±0.04
1.73±0.22
1.51±0.17
2.12±0.11
0.92±0.01
0.68±0.02
RMSECV
RMSEP1
(mM)
Reference
Wavenumber range
Blood,
365-1519 cm -1
Blood,
l
297-1703 cmn
Blood,
297-1703 crmf, 5op
ISF-2,
365-1519 cm'
ISF-2,
297-1703 cmf'
ISF-2,
297-1703 cmni, 5op
The next analysis was to form the calibration set with one level entirely left out, and then predict
on the left-out level (RMSEPI) and all samples not included in the calibration set (RMSEP 2).
Results are summarized in Table 7-3. It is observed that RMSEP 2 for level 1 is much higher than
for other levels. This is because fluorescence photobleaching was most significant during that
time and also the instrument and experimental subject needed time to come to equilibrium.
-184-
Table 7-3 Summary of the leave- one-level-out analysis with various pre-processing and
model parameters.
r2
Corr(b,g)
4.83±2.55
0.83±0.08
0.49±10.04
1.88±0.26
2.66±0.55
0.92±0.03
0.47±0.03
1.84±0.24
1.88±0.26
2.81±0.49
0.91±0.03
0.47±0.02
Level 4
1.89±0.19
1.85±0.23
2.82±0.54
0.91±0.03
0.47±0.03
Level 5
1.83±0.42
1.76±0.27
2.73±0.34
0.90±0.03
0.43±0.03
Level 6
1.89±0.34
1.83±0.55
2.25±0.58
0.93±0.02
0.48±0.03
Level 7
1.88±0.14
1.82±0.26
2.38±0.27
0.92±0.02
0.44±0.03
Level 8
1.63±0.14
1.63±0.23
3.08±0.29
0.87±0.03
0.37±0.04
Statistics
RMSECV
RMSEP 1
RMSEP 2
(mM)
(mM)
(mM)
Level 1
1.81±0.17
1.84±0.29
Level 2
1.9±0.25
Level 3
Preprocessing
Finally, two randomized concentration profiles were used to demonstrate that the previous
calibration models are indeed predictive.
In the first case, random concentrations in the
experimental range were paired with measured spectra. In the second case, the order of the
reference concentration measurements was randomly scrambled.
Result from these tests
suggests RMSEP >135 mg/dL with a model that lacks prediction capability. Therefore, results
from previous calibration models are predictive for glucose concentration.
Table 7-4 Summary of the randomized concentration analysis.
Sýtatistics
RMSEP 2
r2
Corr(b,g)
7.6±0.5
7.7±0.5
0.06±0.07
0.06±0.08
7.9±0.6
7.7±0.5
0.01±0.07
0.04±0.07
RMSECV
RMSEP,
Preprocessing
(mM)
(mM)
Scheme 1
7.6±0.8
Scheme 2
7.8±0.8
- 185 -
(mM)
7.3
Applicability of constrained regularization
Constrained regularization was applied to the dog data. Here we only show the level-splitting
analysis because it provides the best evaluation of performance. Similar values were obtained in
most statistics except the correlation coefficient of the b vector and glucose spectrum. It may
indicate that the CR calibration models captured more glucose-specific spectral features,
however, it is not clear why error was not improved. Perhaps other error sources, such as
reference error or background noise were higher.
The OLS b vector calculated using the
measured constituent spectra (sapphire, extracted background, glucose, water, and DC offset)
was also employed as the spectral constraint in CR and similar results were obtained. Table 7-5
summarizes the results of application of CR in the level-splitting analysis.
Table 7-5 Summary of the level-splitting analysis with various pre-processing and
model parameters.
Statistics
Reference
Corr(b,g)
RMSECV
RMSEPI
RMSEP 2
(mM)
(mM)
(mM)
1.79±0.22
1.75±0.14
2.2±0.14
0.93±0.01
0.52±0.04
1.66±0.13
1.66±0.21
2.18±0.18
0.93±0.01
0.61±0.04
1.36±0.08
1.44±0.13
2.23±0.17
0.93±0.01
0.64±0.04
1.43±0.13
1.42±0.1
2.13±0.1
0.94±0.01
0.57±0.03
1.81±0.15
1.98±0.3
2.32±0.43
0.91±0.02
0.55±0.07
1.79±0.11
1.7±0.2
2.18±0.14
0.91±0.01
0.62±0.03
1.51±0.12
1.62±0.13
2.24±0.13
0.92±0.01
0.64±0.08
Wavenumber range
Blood,
365-1519 cm'
Blood,
297-1703 cm'_
Blood,
297-1703 cm', 5op
Blood, boLs
297-1703 cm', 5op
ISF-2,
365-1519 cm
l
'
ISF-2,
-
297-1703 cm '
ISF-2,
-,
297-1703 cm ' 5op
-186-
As discussed in section 6.5, in the dog data, the background signal level is more than 4 orders of
magnitude higher than the glucose Raman spectrum at physiological level. This is the most
probable cause for CR to perform similarly to PLS. Therefore, it is imperative to reduce or
eliminate this background and its variations as it impairs analysis.
7.4
Applicability of intrinsic Raman spectroscopy
Intrinsic Raman spectroscopy corrects for turbidity-induced sampling volume variations. It is
our expectation that this technique will provide more accurate measurements across different
sites or individuals, among which turbidity variations can be significant.
As a result, the
applicability of IRS can not be properly evaluated based on this dog study, with a single subject,
on a single site.
Nevertheless, we have discovered and explored several issues that are
potentially critical to successful implementation of IRS in the future.
7.4.1
Glucose-induced index change
Light scattering in biological tissue is mainly owing to discontinuities in refractive index. It is
well known that the variation of concentration of different tissue osmolytes produces changes in
the refractive index mismatch between the extracellular fluid (ECF) and structural scatterers such
as cell membranes and protein matrix and, therefore, affects the tissue scattering coefficient.
Among several tissue osmolytes such as potassium chloride (KC1), sodium chloride (NaC1), and
urea, glucose has a much greater effect in changing refractive index. As reviewed in section
2.2.3, correlation between glucose concentration and reflectance was found using diffuse
reflectance spectroscopy and optical coherence tomography.
7.4.2 Information in the Rayleigh peak
As mentioned in Appendix A, the Rayleigh peak may be used as an alternative probe for diffuse
reflectance given that the Raman instrument located at Bayer does not have an additional white
- 187 -
light source. Figure 7-11 shows the Rayleigh peak (area under the peak) versus time. The
background (fit by a quadratic function) subtracted signal is plotted in Figure 7-12, overlaid with
the plasma glucose concentration profile. Anti-correlation is observed between the two signals (r
- -0.3). This can be explained by the rise of glucose concentration reducing the index mismatch
between ECF and scatterers and therefore the scattering coefficient. Using the spectral range of
the Rayleigh peak alone also demonstrated predictability in PLS analysis.
7.4.3
Information in the sapphire peaks
Similar to the Rayleigh peak, in section 5.4.2 the sapphire peak was employed as the "diffuse
reflectance" and IRS was demonstrated. Sapphire serves as not only the reference plane but an
external standard. In the dog study, however, the sapphire peaks are embedded in the intense
decreasing background.
Quadratic fit was used within a small spectral range close to the
sapphire peaks and the extracted peak area is plotted in Figure 7-11. After removing the slowlyvarying background, it is plotted in Figure 7-12. Strong correlation was expected to be observed
between the Rayleigh and the sapphire peaks because both of them contain information of
diffuse reflectance. However, little correlation is observed in Figure 7-12 and the cause has to be
investigated further.
- 188-
x 108
1.035
1.03
1.025
1.02
1.015
1.01
1.005
1
2
3
4
5
6
Time elapsed (Hr)
Figure 7-11 Rayleigh and Sapphire peaks before removing the slowly-varying backgrounds.
-Plasma
.---. Rayleigh
........ Sapphire 2
f
I
'
\I'
Y
:"`
...
_..
""'.•
,.: -'
1
S,
.
-•..•.•.
.
..
. "
2
3
-
.4
".t . :..
.
..
4
.
,
5
6
Time elapsed (Hr)
Figure 7-12 Normalized Rayleigh and Sapphire peaks after removing the slowly-varying
backgrounds and plasma glucose concentration profile.
- 189-
7.5
Summary and guidelines for future studies
This chapter describes an in vivo dog study that was accomplished with our collaborators at
Bayer Healthcare. The dog study was performed on a beagle anaesthetized for -8 hours, during
which its blood glucose concentration was clamped at several different levels. Glucose clamping
study allows better disentangling systematic effects from real glucose changes. Raman spectra
were continuously acquired from the ear and reference blood glucose measurements were taken
via venous blood and interstitial fluid withdraw. Using only the level data, RMSEP on the order
of 1.5-2 mM was obtained, agreeing with the minimum detection error analysis.
Great
similarities were observed between the resulting b vector and the glucose Raman spectrum
measured in water, indicating that glucose was indeed measured.
Results from this study
demonstrate the feasibility of detecting glucose in vivo using Raman spectroscopy. In addition,
the analyses and results provide valuable insights for improving our technique for future studies.
The reason that CR and PLS performed similarly on the in vivo data is mainly attributed to the
intense background and its variations. As demonstrated in section 6.5, CR shows significant
advantage at the same noise level without the background.
As a result, any method that
effectively removes or reduces the background and its variations will be critical in future studies
for CR to be applied successfully. Further, based on the minimum detection limit analysis, shot
noise generated by the intense background is one of the fundamental limitations of our technique.
So it is imperative to address the background issue if improved detection limit is sought.
It is our expectation that IRS will provide more accurate measurements across different sites or
individuals, among which turbidity variations can be significant. As a result, the applicability of
IRS can not be properly evaluated based on one dog study. Nevertheless, we have discovered
plausible anti-correlation between the Rayleigh peak and the glucose concentration, suggesting
- 190 -
the glucose-induced refractive index change was observed. Attempt to identify similar anticorrelation to glucose concentration in the sapphire peaks was not successful. Nevertheless, the
magnitude of temporal changes in either the Rayleigh or the sapphire peaks was smaller than 1%,
suggesting that optical property variations during the course of the experiment was much lower
compared to variations across sites or subjects, which can be on the order of 10%.
In addition, the position of the sapphire reference plane was determined based on maximizing
Intralipid Raman peaks using a tissue phantom. Concern was raised with regard to the accuracy
of such determination because major Raman-active skin constituents were not observed in the
spectra, which suggest that the probing depth was too shallow. A more accurate criterion to
determine probing depth and a repeatable sample positioning apparatus have to be in place for
future studies.
Furthermore, the main cause of the curvature in the background signal is the instrumental
response, i.e., the grating and CCD uneven spectral sensitivities. White light correction can
make the background shape more flat and may render the background removal algorithms more
effective. Therefore, a calibrated white light measurement is necessary in future studies.
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CHAPTER 8
8.1
CONCLUSION AND FUTURE DIRECTIONS
Review of objectives and accomplishments
The goal of this thesis is to advance quantitative biological Raman spectroscopy for non-invasive
blood analysis. To achieve that, our objectives are three-fold: improving throughput, precision,
and stability, correcting sampling volume variations, and optimizing information extraction. The
work related to achieving these goals were presented in chapters 4-6.
In Chap. 4, we described the improvements in the instrument, including increased throughput,
better wavelength precision and stability. Specifically, a novel algorithm has been developed for
curvature correction and wavelength drift detection. It resulted in better spectral resolution and
precision and less apparent wavelength drift due to sample placement.
In Chap. 5, the issue of turbidity-induced sampling volume variations was addressed. Analytical
and numerical models were developed to study the relationship between diffuse reflectance and
Raman scattering.
Tissue phantom experiments were carried out to develop a corrective
algorithm using the diffuse reflectance. Significant improvement in SEP was obtained after the
correction.
Chapter 6 described constrained regularization, a novel multivariate calibration technique.
Numerical simulations and tissue phantom experiments were used to demonstrate that CR is
more advantageous than PLS. In addition, we demonstrated that CR is more robust than HLA
when the pure analyte spectrum is not accurate. Further, we used data synthesized from the in
vivo dog study (chapter 7) to study the relative performance of CR and PLS in such applications.
We found that the intense background and its variations wash out most of the intrinsic advantage
- 192 -
of CR over PLS. Therefore, in order to fully exploit CR's superiority over PLS, the background
issue has to be dealt with.
An in vivo dog study was described in chapter 7.
PLS was applied to data with various
formation schemes of calibration set. Different sample-splitting schemes were also investigated
for model validation and prediction. The results agree with the minimum detection error analysis.
Application of CR to the dog data gave results similar to PLS analyses because of the intense
background and it variations over time. Application of IRS was not carried out because there
was not enough optical property variation in a single-dog study. Nevertheless, we believe that
the glucose-induced refractive index change has been observed in the Rayleigh peak. We also
found that the sapphire peaks can potentially be used as an external standard when a white light
measurement is not performed.
8.2
Future directions
To further advance quantitative biological Raman spectroscopy as a viable technique for noninvasive blood analysis, future development should focus on demonstration of prospective
applicability. This thesis has explored areas including instrumentation, correction for skin/tissue
diversity, and optimization of information extraction. Remaining important topics that have yet
to be explored by future researchers are: accurate reference concentrations, fluorescence
background removal and its temporal variations, optimal probing depth through accurate sample
positioning, motion artifacts and skin heterogeneity, and optimal site determination for data
collection.
Accurate reference concentration measurements
An additional factor that greatly affects the performance of the calibration algorithm is the
accuracy of the reference measurements. In spectroscopic techniques such as Raman, a large
- 193 -
portion of the collected glucose signal likely originates from the glucose molecules in the
interstitial fluid (ISF). In addition, it is well known that the interstitial glucose lags the plasma
glucose concentration from 5 to 30 minutes in humans. 14 8 As a result, using plasma glucose as
the reference concentration may introduce errors. Methods of extracting interstitial fluid for
glucose reference measurements should be explored.
Fluorescence background and its variations over time
The intense fluorescence background and its variations over time have been identified not only
as a fundamental limitation to detection accuracy, but an additional confounding factor to
multivariate calibration.
There are two issues with the background and can be dealt with
separately: Its intensity and variations.
One approach may be using pre-photobleaching
combined with intentional motion by, for example, scanning the illumination spot around an area
slightly larger than the spot itself. With such a scheme, the apparent background can be lower to
start with, and the photobleaching can be reduced. However, this may take more time than is
available. Ideally, prospective measurements should take less than 5 minutes each. Another
possible approach is to characterize the decay profile and apply correction based on time
constant of the decay.
Optimal probing depth through accurate sample positioning
The probing depth and sample positioning are critical for optimal collection of glucose-specific
Raman scattered photons and calibration transfer. In experiments, the optimal probing depth can
be estimated from extracted optical properties, and therefore the correct distance between the
sample-and the collection optic can be determined for each measurement site. To address this, a
fundamental study of morphological and layer structures at the probing site should be carried out
- 194-
with a computer-controlled 3-axis precision stage, as has been done on particular parts of skin.60
Because most Raman scatterers have specific spatial distribution in skin, such as keratin in the
epidermis, collagen in the dermis, etc., a two-layer model can be developed and utilized. Given
such distinctive spatial distributions between keratin and collagen, we can obtain information
about the probing depth and even layer thickness by comparing the relative magnitude of keratin
and collagen Raman signals. By knowing the exact sampling volume and its coverage of various
skin morphological structures, we can estimate how much of the glucose-containing region
(dermis in the two-layer model) is sampled. This information can effectively lead to better
reference concentrations, improving the calibration accuracy.
Motion artifacts and skin heterogeneity
A key component to obtaining accurate and robust calibrations is the sample interface. The
sample interface should ideally limit motion while maintaining a constant pressure and
temperature.
One approach to combat inadvertent motion artifacts is to intentionally build
motion into the calibration model. This can be achieved by scanning the laser spot within a
larger area.
Optimal data collection site
Individual calibration models based on cross validation can be established for several candidate
sites such as forearm, fingernail, etc, and the results can be compared. The minimum detection
error analysis can also be employed to evaluate different sites.
8.3
Final remarks
In conclusion, this research presented in this thesis has shown the feasibility of using quantitative
biological Raman spectroscopy as a tool for non-invasive blood analysis. We have explored
- 195 -
three areas including instrumentation, turbidity-induced sampling volume variations, and
analyte-specific information extraction, and developed novel techniques in each area.
An
improved curvature correction algorithm has been developed for diffraction limited spectral
resolution; intrinsic Raman spectroscopy has been developed for sampling volume correction;
constrained regularization has been developed for optimal information extraction. We believe
these techniques not only bring us closer to our ultimate goal, prospective applications, but also
contribute to the scientific field.
-196-
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Appendix A
Alternative approach for IRS- Using the Rayleigh peak
An empirical correction scheme using the "Rayleigh" peak is presented in this section.
Although the physical basis of this method is not fully understood, it appears to provide decent
corrective capability. However, the robustness of this empirical method is questionable when
sample or collection geometry varies.
The Rayleigh peak refers to the elastically scattered light at the excitation wavelength, which is
the specular plus diffuse reflection at 830 nm. In highly scattering samples, a significant portion
of the Rayleigh light can pass through the notch filter and be collected by the CCD, and thus
provides us a probe for optical properties. This scheme is very convenient because no additional
light source is required. Since the laser is employed for both Raman excitation and diffuse
reflectance, the illumination geometries are guaranteed to be identical for both Raman and
diffuse reflectance.
It works particularly well in our wavelength range of interest where no
prominent absorption or scattering feature exists.
Contributions to the Rayleigh peak from specular reflections are insubstantial owing to our
experimental design with the hole in the paraboloidal mirror.
In addition, linear intensity
response of the notch region of the notch filter was experimentally verified.
As mentioned in section 5.3.5, with certain collection-excitation geometries diffuse reflectance
may be characterized by a single parameter: the ratio 4s/ýta. A simple exponential model for
diffuse reflectance has been derived by Jacques 125 and shown to be representative of
experimentally-obtained diffuse reflectance by Fabbri: 126
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Rd = exp
-A
3((A-1)
A
13(1+Ps /ýtj
The A parameter in this expression depends on the refractive index mismatch and the ratio ýps/ta.
To determine the optimal value of A in order to fit this function to our Rayleigh peak area data,
an iterative procedure based on least-squares fitting was employed. Because we measure relative
and not absolute reflectance values, the normalization factor for the Rayleigh peak area data was
also determined by the iterative process. The values for A and the normalization factor were
found to be 6 and 0.84, respectively. The normalized Rayleigh peak and the fit to Eq. (A-1) are
plotted in Figure A-i versus P/Pa.
0
e~
0m
200
400
600
--
800
0.2
Ps / Pa
--
--
--
0.4
0.6
0.8
2
Normalized Rayleigh
·
1
Figure A-1 Rayleigh peak area (open circles) Figure A-2 The measured Raman signal
and calculated diffuse reflectance, Rd, (solid correlates with the Rayleigh peak area
squared. The straight line is linear fit.
line) plotted versus the ratio ps,/ta.
The excellent agreement between data and the calculated reflectance suggests that the "semiinfinite" condition was somehow largely met. Although the exact cause is unknown to us, we
believe it is because of the notch filter's angular response (discussed later).
Figure A-2 reveals an approximate linear relationship between the measured Raman signal and
the Rayleigh peak area squared.
Using the approximate linear relationship to correct the
- 205 -
variations in Raman intensity, the prediction accuracy is significantly improved from an RMSEP
-41.6% to -7.4%.
Note that the correction using the Rayleigh peak does not require the knowledge of optical
The quasi-semi-infinite behavior of the Rayleigh peak may be explained by the
properties.
angular response of the notch filter. Since the notch filter is designed to work with strictly
collimated light, it blocks much more efficiently the diffuse reflectance originating from the
center portion of the collection spot. This radial dependent attenuation can be simulated using a
donut-shape collection spot. Figure A-3 and Figure A-4 show the results of solid and donutshape collection spots, respectively.
We observe that the diffuse reflectance approaches a
function of the ratio (ps/la) better with the donut-shaped collection spot. A plausible explanation
is that the donut-shape collection spot collects more of the diffusive photons and thus satisfies
better the semi-infinite condition.
Rd vs. As /
a
(vol: 0.5 x 1, col: 0.5)
0
0.5
0.5
0%oo
o
S 00
o
@0
0.3
0
0o
0.3
0.25
0
o
0.2
oP
0.15
r o00
0
0
0o
0
0
0o0
o
0
0.15
0.2 0
a/
a (vol: 0.5 x 1, col: 0.125-0.5)
0.3
0o
0
0
oo0 o o
00 0 0
0.4
o0
0
o
0 0
Rd vs. Ps
0.1
0
1
200
0
400
600
s
800
0
200
400
600
s
a
800
a
Figure A-3 Diffuse reflectance from a solid Figure A-4 Diffuse reflectance from a donutcollection spot with radius 0.5 cm.
shape collection spot with inner and outer
radii 0.125 and 0.5 cm, respectively.
- 206 -
Kan-Ping Chin received the BS degree in mechanical engineering from National Taiwan
University in 1982, and the MS and PhD degrees in mechanical engineering from MIT in 1988
and 1991, respectively. He was an associate professor at National Chiao Tung University. Dr.
Chin was the author's MS thesis advisor during 1997-1999, and encouraged the author to pursue
the doctoral degree at MIT. Dr. Chin passed away on 8 February 2002 owing to pneumonia.
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