Origin of signals in tissue imaging
and spectroscopy
Andrew J. Berger
The Institute of Optics
University of Rochester
Rochester, NY 14627
A very brief outline
• Absorption
• Emission
• Scattering
Who are you? Why are you here?
(with apologies to Admiral Stockdale)
•
•
•
•
•
•
experienced in some branch of optics
biomedical not your main shtick
interested in survey of fundamentals
want introduction to applications
interested in following the later talks
want pointers to the literature
Fred the photon
photons
absorption events
I ( )
I 0 ( )
Absorption = molecular transition between states
• electronic
• vibrational
• rotational
• (translational)
Electronic transitions
What's quantized:
angular momentum  n  
Consequently:
me4
E 
8 0 h 2
 1

1
 2  2 
n

n
i
f


13.7 eV = 91 nm
energy
outer shell: n>1
Biologically: typically UV or blue
4
3
2
1
energy
Vibrational transitions
r
What's quantized:
oscillator levels : Enn1  

r  r0  0.5A
Representative values:
U  5 eV
r0
r
U  12 k r  r0   k ~ 6 10 2 J/m 2
  6 amu (2 carbon nuclei)
2
   k   2.5 1014 rad/sec
  6 m
mid-IR
Rotational transitions
What's quantized:
angular momentum L2  J J  1 2
Consequently:
2
EJ  J 1  2  J
r
Representative values:
  6 amu

r 1A
 2 10 3 eV
01  0.5 mm
microwave regime
How to talk about absorption
I0
I
L
I
a L
 cL
 10
e
I0
molar
extinction
concentration
 a  ln 10  c
"absorption coefficient" [1/length]
vibrational
electronic
courtesy V. Venugopalan, http://www.osa.org/meetings/archives/2004/BIOMED/program/#educ
rotational
DNA
biological
window
What's absorbing?
Hemoglobin
courtesy V. Venugopalan, http://www.osa.org/meetings/archives/2004/BIOMED/program/#educ
Typical tissue absorption!
adipose tissue ~ 1% blood
by volume
blood = 45% red
blood cells by volume
Hemoglobin molecular weight
= 65,000 mg/mmole
Hb concentration = 23 M
red blood cell =
1/3 hemoglobin
by weight
Hemoglobin
at isosbestic point,
 a  0.023 mM  0.09 mm -1 / mM  0.002 mm -1
Mean free absorption pathlength = 500 mm (!)
Hemodynamics calculations
single
absorber :
two
absorbers :
 a  ln 10  c
HbO2
Hb

1
1  Hb
  a1 
    ln 10   Hb  HbO2   c 
2
 2
 c HbO2 
 a2 


 

  
 

measure the
absorption
coefficients
parameters
of interest :
look up the molar extinction
coefficients (e.g.
http:/omlc.ogi.edu)
oxygen saturation:
total hemoglobin
HbO2 
Hb   HbO2 
Hb HbO2 
calculate the
concentrations
theory works
for N>2
chromophores,
too!
Further adventures of Fred the photon
absorption
photons
fluorescence
Fluorescence: level diagram
•
•
•
•
absorption:
internal conversion:
upper state lifetime:
emission:
fsec
fsec
psec-nsec
fsec
shift is to the RED (Stokes) of the excitation light
r0
r
Fluorescence Spectroscopy
Major biological fluorophores:
Ref. Mycek and Pogue, Handbook of Biomedical Fluorescence
B
Tryptophan
Porphyrins (Hp)
Pyridoxine
8
Fluorescence Intensity [a.u.]
• structural proteins: collagen
and elastin crosslinks
• coenzymes for cellular energy
metabolism (electron
acceptors):
• flavin adenine dinucleotide
(FAD)
• nicotinamide adenine
dinucleotide, reduced form
(NADH)
• aromatic amino acids: side
groups on proteins
• porphyrins: precursors to
heme
10
6
Collagen
Elastin
NADH
Flavins
4
2
0
300
350
400
450
500
550
600
650
700
Fluorescence emission wavelength [nm]
courtesy M.-A. Mycek
A fluorescence scenario
cellular epithelium
thickening
collagen support
healthy
trending towards cancer
• increased FAD fluorescence
• reduced collagen fluorescence
(farther from surface)
• polyp formation → neovasculature;
increased absorption & decreased
fluorescence
The time dimension
•
•
•
•
absorption:
internal conversion:
upper state lifetime:
emission:
fsec
fsec
psec-nsec
fsec
• radiative decay rate:
kr
• nonradiative loss rate:
knr
• knr varies with environment
• fluorescence decay lifetime
varies, too:
r0
r
 1 

  

 k 
not intensity-based!
combined spectral and temporal fluorescence measurements:
Pitts and Mycek, Rev. Sci. Inst. 72:7, 3061-3072 (2001).
More introductions to fluorescence
R. Redmond, "Introduction to fluorescence and
photophysics," in Handbook of Biomedical
Fluorescence (ed. Mycek and Pogue).
N. Ramanujam, "Fluorescence spectroscopy of
neoplastic and non-neoplastic tissues," Neoplasia,
2:1, 89-117 (2000).
Yet more adventures for Fred
scattering
photons
Stokes
Anti-Stokes
Raman scattering
Level diagram for Raman
energy
incident photon has
energy E
molecule gains
energy E
r0
r
scattered photon has
energy E -E
excitation usually in near-IR or <300 nm UV to avoid visible fluorescence
Basic mechanism of Raman scattering
cos t
cos t
induced
dipole
moment:



p  E   0 
r0 cos t  E0 cos t
r 0


product
term:
2 cos t cos t  cos  t  cos  t
STOKES
ANTI-STOKES
RNA bases
Raman shift (cm-1)
1580
amide I
aromatic amino acids
1651
C-H 2 def.
1457
1340
1211
1259
amide III
1092
902
1005
783
813
853
C-N, C-C str. 1127
phenylalanine
tyrosine
cytosine, uracil
phenylalanine 619
guanine 667
adenine
720
intensity (arb. units)
Typical spectrum (oral bacteria)
Applications for Raman
• Chemical analysis of tissue, in vitro or in vivo (breast,
artery, blood)
• Disease classification
topical review: Hanlon et al., “Prospects for in vivo Raman
spectroscopy,” Phys. Med. Biol. 45, R1-R59 (2000)
(or just talk to me!)
• High-resolution, molecularly specific microscopy
go to: FWN4, “CARS microscopy: coming of age,” Sunney
Xie, 2:45-3:15.
FWN5, “Interferometric contrast between resonant
CARS and nonresonant four-wave mixing,” Daniel
Marks, 3:15-3:30.
Fred keeps going, and going, and...
scattering
photons
elastic scattering
Elastic scattering
• caused by variations in refractive index
component
typical n in the vis/NIR
extracellular fluid
1.35 – 1.36
cytoplasm
1.36 – 1.375
nucleus
1.38 – 1.41
mitochondria
1.38 – 1.41
water
1.33
Drezek et al., Appl. Opt. 38:16, 3651-3661 (1999).
• various approaches to modeling:
full rigor
Mie theory
Maxwell’s equations (e.g. Drezek above)
plane wave on homogeneous sphere
(e.g., code at philiplaven.com)
van de Hulst
three-term approximation to Mie (larger spheres
and modest n values)
Rayleigh scattering very small particles (compared to λ)
Wavelength dependence varies w/ scatterer size
Polystyrene Spheres of Varying Diameters in Water
0
Mie Theory Scattering Coefficient (mm
-1
)
10
10
-1
2000
nm
1000
nm
200
nm
100
nm
20

500
600
nm
-4
700
800
Wavelength (nm)
courtesy Edward Hull, Rochester summer school lecture notes
900
1000
1100
A summary of scattering scales
Figure by Steve Jacques,
Oregon Medical Laser Center
http://www.omlc.ogi.edu/classroom
go to: FTuL1, “On the microscopic origin of light scattering
in tissue,” Peter Kaplan, 2:00-2:30.
incident plane wave
Spectral dependence of scattering
sin 2    sin    
~ 1


 




n2
n1
  d n2  n1 
sphere
van de Hulst
approximation to
Mie theory
d
n2  n1
F sin 2   
~
1  F sin 2   
d/2
etalon
(F = cavity finesse)
2
Spectral dependence of scattering
1-D etalon
• d=5 microns
• n1 = 1.36
• n2/n1 = 1.06
3-D sphere
wavelength / nm
Scattering spectroscopy
1
2

sin 2    sin    

2
~ d 1 

 






 


• spacing of peaks:
• depth of modulation:
mixture
 2  1
more rapid
oscillations
size of scatterer
number of such scatterers
superposition of
spectra
broadband
polarized
illumination
Scattering spectroscopy
polarizationresolved detection
normal colon cells
cancerous cells
Perelman et al., Phys Rev Lett 80:627 (1998) and following.
Angularly-resolved scattering
d
n1
n2
angular distribution
has interferometric
(oscillatory) behavior
as well
go to: FTuR1, “Real-time angle-resolved low-coherence
interferometry for detecting pre-cancerous cells,”
Adam Wax, 4:15-4:45.
FTuL4, “Elastic-scattering spectroscopy for cancer
detection: What have we learned from preliminary
clinical studies?” Irving Bigio, 3:00-3:30.
Bulk tissue interrogation
 s'
a
reduced scattering
coefficient [1/length]
• determine the absorption coefficient (spectroscopy)
• identify and characterize heterogeneities (functional imaging)
• note: scattering enables absorption studies in backscattering
geometry!
Absolutely basic photon migration
in the
limit of:
Detector
no
scattering
signal at detector decays
according to
e
  a ct
absorption
RMS distance from origin
(“random walk”)
increases according to
no
absorption
pulse
1
ct  Dct
'
3  s  a

scattering

diffusion
coefficient
[m2/sec]
The real deal: diffusion theory
scattering and
absorption
different source-detector separations
a = 0.001 mm-1
35 mm
25 mm
pulse
r = 15 mm
s' = 1 mm-1
n = 1.4
What are the diffusion measurements?
source(s)
detector(s)
• time domain: intensity vs. time
• frequency domain (amplitude-modulation):
modulation depth and/or phase vs. distance or frequency
• steady state: intensity vs. distance
go to: FTuK1, “Multidimensional diffuse optical imaging in
breast cancer detection,” Brian Pogue, 2:00-2:30.
FTuK5, “Functional imaging by optical topography,”
Randall Barbour, 3:15-3:45.
Still hungry?
• fluorescence:
multiphoton-excited microscopy
• second-harmonic:
ditto
• elastic scattering:
optical coherence tomography,
laser scanning confocal microscopy
• polarization:
surface-sensitive imaging, intrinsic
birefringence
• instrumentation:
Raman fiber probes,
fluorescence excitation-emission
matrices
Thanks to: Mary-Ann Mycek, Vasan Venugopalan, Edward Hull
Have a great rest of the conference!