A Spectral Analysis Method to Quantify the Relative Contribution of Different Length
Scales to Heterogeneity in PET Images of Pulmonary Function
by
Daniel M. Call
B.S., Mechanical Engineering (1998)
Brigham Young University
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
June 2000
© Daniel Call
All rights reserved
The author hereby grants to MIT permission to reproduce and to
distribute publicly paper and electronic copies of this thesis document in whole or in part.
Signature of Author
Department of Mechanical Engineering
May 5, 2000
Certified by
A ocia
rofesso,
Jos6 G. Venegas
arvard-MIT Division of Health Science and Technology
Accepted by
Am. A onin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
A SPECTRAL ANALYSIS METHOD TO QUANTIFY THE RELATIVE
CONTRIBUTION OF DIFFERENT LENGTH SCALES TO HETEROGENEITY IN
PET IMAGES OF PULMONARY FUNCTION
by
DANIEL MARCUS CALL
Submitted to the Department of Mechanical Engineering
On May 5, 2000 in partial fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
The two-dimensional power spectrum of pulmonary function images was calculated and
used to assess relative contribution of different length scales to heterogeneity. The
method was tested on synthetic images to verify its capability to determine spectral
content of irregularly shaped lung images.
The method was then applied to ventilation and perfusion images in animal models of
bronchoconstriction and pulmonary emboli. The bronchoconstriction study examined the
effects of different positions (prone and supine) and inspiratory gas oxygen concentration
(FiO 2 ) on pulmonary function. Methacholine-induced bronchoconstriction caused a shift
in relative heterogeneity to longer length scales. 18-41 mm length scales increased
contributions to ventilation heterogeneity by 156 ± 42% in prone animals and 78 ± 20%
in supine animals. The same length scales increased in perfusion by 50 ±4%in prone
animals and 53 ± 19% in supine animals. Pulmonary embolism caused by 100-iim
diameter beads showed no uniform change in heterogeneity.
The method provides a useful tool for associating physiological structure to pulmonary
function.
Thesis Advisor: Jose G. Venegas, Ph.D.
Title: Associate Professor of Anesthesia (Bioengineering) Harvard Medical School and
Harvard-MIT Division of Health Science Technology
2
For Kirsti
3
Table of Contents
CHAPTER 1 .......................................................................................... 10
1.1 Introduction ................................................................................................... 10
1.2 Methods .......................................................................................................... 11
1.2.1 Image Analysis .......................................................................................... 11
1.3 Results ............................................................................................................ 17
1.3.1 Sensitivity ................................................................................................. 18
1.3.2 Lung Shape Effects ................................................................................... 19
1.4 Discussion ....................................................................................................... 22
1.4.1 Conclusion ................................................................................................ 27
CHAPTER 2 .......................................................................................... 28
2.1 Introduction ................................................................................................... 28
2.2 Methods ..........................................................................................................28
2.2.1 Anim al Preparation ................................................................................... 28
2.2.2 Bronchoconstriction Protocol ................................................................... 29
2.2.3 Pulm onary Embolus M odel ...................................................................... 30
2.2.4 PET Image Collection ............................................................................... 31
4
2.3 Results ............................................................................................................ 34
2.3.1 Bronchoconstriction M odel ...................................................................... 34
2.3.2 Pulmonary Embolism ................................................................................ 42
2.4 Discussion ....................................................................................................... 45
2.4.1 Conclusion ................................................................................................ 49
BIBLIOG RAPHY ................................................................................... 50
5
List of Figures
Figure 1.1: A transmission scan showing an axial slice of the lung in a supine sheep. The
image is brighter in areas of greater tissue density. The masking procedure locates
the lung field (cross-hatched above). ....................................................................
12
Figure 1.2: A) the original image, B) the quadratic surface best fit to the data using a least
squares problem, C) the difference between images A and B. The surface removes
both the gravitational gradient and any left-to-right lung differences. .................
14
Figure 1.3: Sensitivity of the spectral method to localized image changes was tested by
creating a synthetic lung image with known frequency content (A) and attenuating
specific regions (B ). ...............................................................................................
16
Figure 1.4: A comparison of the effects of general mask shape on accuracy in the FFT.
The square image and corresponding bar plot serve as the control. The lung-shaped
mask, despite some "smoothing," still shows peak regions appropriately. .......... 18
Figure 1.5: The length scales contributing to heterogeneity are clearly identified (A) in
the lung image (B) containing a frequency of 0.073 mm-'. The analysis also reveals
the lower frequency content (C) introduced by the three attenuated areas shown in
(D ). ............................................................................................................................
19
Figure 1.6: Different lung shapes, different signals and their corresponding heterogeneity
analysis. Column A corresponds to images in column B; column C corresponds to
images in column D. The ordinates of columns A and C are the frequencies in
nm1. While there is a noticeable change between the square mask and each lung
mask, changes between individual lung masks are insignificant..........................
6
21
Figure 1.7: The ideal filter attenuation is shown by the dotted line, while the solid line
shows the actual attenuation of filters with the cutoff frequencies corresponding to
the ideals. The attenuation of an ideal filter completely removes all image content
below the cutoff frequency, whereas a real filter only approximates this sharp line.
Actual amplitude response typically crosses the ideal response at roughly 0.25......26
Figure 2.1: Images of regional ventilation in supine and prone animals. Higher regional
ventilation rates are brighter than lower rates. The supine animal shows a vertical
gradient in the control image (A) and splotchy heterogeneity after
bronchoconstriction (B). The prone animal has more uniform ventilation distribution
in the control image (C) and decreased ventilation in the center and upper right
regions after bronchoconstriction (D). ..................................................................
35
Figure 2.2: Contribution of different length scales to total heterogeneity of ventilation at
FjO 2 = 0.5. Values are means ± SE of all (Nsupine= 8, Nprone= 4) animal studies..... 36
Figure 2.3: Images of regional perfusion in supine and prone animals. Higher perfusion
rates are brighter than lower rates. The control perfusion images (A,C) have more
low-frequency heterogeneity than the corresponding ventilation images
(Figure 2.1 A,C). The supine image shows a vertical gradient both in control (A)
and bronchoconstriction (B). The prone control (C) is more uniform than supine and
the prone bronchoconstriction (D) changes to match the distribution of ventilation
(Figure 2.1 D ).......................................................................................................
7
37
Figure 2.4: Contribution of different length scales to total heterogeneity of perfusion at
FiO 2 =
N prone
0.5 for supine and prone position. Values are means ± SE for all (Nsupine = 8,
= 4) anim als studied......................................................................................
39
Figure 2.5: Contribution of different length scales to ventilation (A,C) and perfusion
(B,D) heterogeneity in one subject. The heterogeneity content of the control images
for this subject varies dramatically, perhaps due to the injection of methacholine
between images, rather than the change in body position.....................................
41
Figure 2.6: Contributions to heterogeneity of regional ventilation images in four animals
prior to embolus insult, 1 hour after insult, and after administration of NO. Note the
lack of any strongly visible trends. ......................................................................
43
Figure 2.7: Contributions to heterogeneity of perfusion images in four animals prior to
embolus insult, 1 hour after insult, and after administration of NO. With the
exception of subject D, the heterogeneity of perfusion appears to change very little
between any of the stages of the experiment........................................................
8
44
List of Tables
Table 2.1: The relative contribution of the 18-41 mm length scales during
bronchoconstriction at FiO 2 = 0.5. *P < 0.05, control vs. bronchoconstriction. ....... 40
9
Chapter 1
1.1 INTRODUCTION
A new method of fractal analysis using low-pass filtering has recently been
developed (15). This method allows the calculation of fractal dimension from positron
emission tomographic (PET) images of pulmonary function. Fractal dimension,
however, is difficult to intuitively relate to lung structure. Rather, quantifying the relative
contributions of different length scales to heterogeneity in local function could be more a
useful analysis than fractal dimension. The ability to relate heterogeneity in function to
specific length scales allows a researcher or physician to consider the size of airways or
vessels being affected by insults or physiological interventions.
One of the significant problems faced by previous analyses of heterogeneity was
the inability to process the shape of the organ of interest. These methods were typically
applied by creating square regions of interest (ROI) within the organ of interest. This
forced the method to disregard a significant portion of the data at the edges of the organ.
A method to quantify perfusion and ventilation heterogeneity using the FFT on whole
lung functional images is described in this chapter.
10
1.2 METHODS
Animal preparation depended on the insult being studied and is explained in detail
in §2.2. Image collection and the creation of functional images is described in §2.2.4.
The methods in this chapter pertain solely to analyzing images.
1.2.1 Image Analysis
Determining the contribution of different length scales to heterogeneity in an
image involved the following steps: 1) masking the lung field, 2) de-trending the image
data with a second order polynomial surface to remove very low frequencies from rightto-left or dorsoventral gradients, 3) low-pass filtering the image to eliminate high spatial
frequencies from the lung edges and 4) generating the power spectral density (PSD) plot.
Masking was done to define the lung field within the PET images. Masking
created an image containing values of either 1 or 0, in voxels located inside and outside
the lung respectively. Mask images were created semi-automatically, by applying a
threshold to the tissue density (transmission) scans performed as part of the PET study.
Typically, a voxel with density less than 40-60% of maximum density of the scan was
used to define the lung field. In most cases, some manual processing was necessary to
smooth the edges of the mask and to better match the actual lung shape (Figure 1.1). The
mask image was multiplied voxel-by-voxel to the emission image to be analyzed, leaving
the data within the lung intact and all external voxels equal to 0.
11
Figure 1.1: A transmission scan showing an axial slice of the lung in a supine sheep.
The image is brighter in areas of greater tissue density. The masking procedure
locates the lung field (cross-hatched above).
In order to attenuate the effects of the lung shape on the FFT results, the image
was mean-normalized in the region of the mask and then reduced by 1, removing the DC
component. A quadratic surface was fitted to the data using a least-squares solution and
then subtracted from the lung data (Figure 1.2). This removed extremely low frequency
components caused by gravity or right-to-left lung differences. After reconstruction, the
PET images (159x159 voxels) had an effective resolution of 6 mm; therefore, image data
could only be valid in frequency ranges less than 0.0833 mm-1. In order to remove the
12
high frequencies introduced by the edges, the image was then low-pass filtered at a cutoff frequency of 0.0833 nm- 1.
13
A
B
C
Figure 1.2: A) the original image, B) the quadratic surface best fit to the data using
a least squares problem, C) the difference between images A and B. The surface
removes both the gravitational gradient and any left-to-right lung differences.
14
A two-dimensional FFT of the image was calculated after zero-padding it to
1024x 1024 voxels. The reasons for the padding were two-fold: 1) the 2" dimension
allowed the use of the FFT rather than the computationally slower discrete Fourier
transform, and 2) a smaller frequency step (2/N) obtained from zero padding gave more
precision in the ensuing analysis. The two-dimensional FFT generates a matrix of
magnitudes where the first and second quadrants are mirror images of the other two. The
first two quadrants of the matrix were converted to polar coordinates, and the power
between any two frequencies R1 and R2 was calculated as
P
XFI v 2(1.1)
i=R
j=O
where Fij is the matrix element and the difference between R1 and R2 was set at
0.0081 mm-1. This radius interval included 16 frequency steps yielded by the FFT. The
results of this transformation yielded a PSD plot that was displayed on a bar plot with
spatial frequency on the ordinate and percent of total power on the abscissa. Although 31
intervals from 0.0041-0.2556 mm 1 were summed, only frequencies less than 0.083 mm-1
were within the resolution of the camera and considered.
In order to verify the method's capability to determine spectral content of data
within irregularly shaped lung images, 2D sinusoidal data of known frequency content
was used to create images with the following mask shapes: a square, a circle, and a
typical lung cross-section from an actual study. The known frequency signal was
composed of three sets of orthogonal sinusoids, with spatial frequencies of 0.026, 0.052,
and 0.078 mm-1 . This signal was used to create a 159x159 voxel image (Figure 1.4 A).
15
The circular mask was created by using a diameter of 79 voxels, approximately the
ventral-to-dorsal size of the lung. The lung mask was created using a transmission scan
from an actual study.
Another important step in validating our analysis technique was to test its
sensitivity to localized changes in the lung. To test this capability, an image was created
by multiplying two orthogonal signals at 0.073 mm-1 within the field of an actual lung
mask. The original image was analyzed and then altered by creating randomly located
two-dimensional gaussian-shaped regions of signal attenuation with a standard
attenuation of 8.66 mm. These regions had a maximal signal attenuation of 100% (Figure
1.3).
B
A
NA
Figure 1.3: Sensitivity of the spectral method to localized image changes was tested
by creating a synthetic lung image with known frequency content (A) and
attenuating specific regions (B).
It was also important to verify that the edges did not mask the signal content.
This was tested by using a variety of lung-shaped ROI's on two synthetic images. The
ROI's used in the test included five different lung shapes from actual subjects, as well as
16
a square ROL. The synthetic images were created in a manner similar to the above using
frequencies of 0.073 mm-1 and 0.022 mm-1 (6.85 and 22.73 mm length scales). The
square ROI introduced no shape effects and served as a comparison.
1.3 RESULTS
Analysis of a square synthetic image with heterogeneity of three distinct
frequencies showed a clean separation of power in three peaks (Figure 1.4A). This
separation was maintained after masking the image with a circular mask (Figure 1.4B) or
with a mask in the shape of a typical lung cross-section (Figure 1.4C).
17
A
30
0)
2).
20-
2
,
a)-0
0
xv,
V'A
1'_
%
_01
0
10
30
0.02
0.04
0.06
0.08
0.1
B
--
040)
W C
20-
4EW
(1)0
0)-
10
.
00
0.02
0.04
0.06
0.08
0.1
C
0)
0) a1)
CW
0
0
0.02
0.04
0.06
0.08
0.1
Frequency (mm")
Figure 1.4: A comparison of the effects of general mask shape on accuracy in the
FFT. The square image and corresponding bar plot serve as the control. The lungshaped mask, despite some "smoothing," still shows peak regions appropriately.
1.3.1 Sensitivity
Introduction of three discrete large-scale attenuations to a synthetic image in the
shape of a lung with heterogeneity of a single frequency yielded a distinct peak at a low
frequency (Figure 1.5).
18
8 0
C
M 60
2
40
0
20
Z
C
0
0
0.05
0.1
Frequency (mm-1)
D
(;0
60.
0
0
0-
0-.5
.
Frequency (mm')
Figure 1.5: The length scales contributing to heterogeneity are clearly identified (A)
in the lung image (B) containing a frequency of 0.073 mm 1 . The analysis also
reveals the lower frequency content (C) introduced by the three attenuated areas
shown in (D).
1.3.2 Lung Shape Effects
The PSD of the lung-shaped images had a wider distribution than the square
images (Figure 1.6). For the high frequency image, the relative contribution to
heterogeneity by the 6.5-7.2 mm length scales dropped by 25.1 ± 1% after the application
19
of the lung shape. In the low frequency image, the relative contribution to heterogeneity
by the 17.6-24.6 mm length scales dropped 39.5 ± 1.7% after the application of the lung
shape. In the low frequency image, the heterogeneity of the control image is spread
across two bins in the PSD plot (17.6-41.1 mm). The total relative contribution of these
length scales dropped 24.8 ± 2% after the lung shape was added.
20
A
100
B
50
50
0
0.05
0
0'-
0.1
0
0.05
0.1
0
100
CD
0.05
0.1
0.05
0.1
0
0.05
0.1
50 0
0.05
0.1
0.05
0.1
100
100
50
50
0
0.05
0.1
100
a)
D
C
100
50
a) 50
a,)
0
0
0.05
0.1
0
100
50
0
100
50
0
0.05
0.1
0
100
100
50
L
0
100F
0.05
.
0.1
0.05
0.1
100
50
0
Frequency (mm~1)
0
Frequency (mm- 1)
Figure 1.6: Different lung shapes, different signals and their corresponding
heterogeneity analysis. Column A corresponds to images in column B; column C
corresponds to images in column D. The ordinates of columns A and C are the
frequencies in mm-1. While there is a noticeable change between the square mask
and each lung mask, changes between individual lung masks are insignificant.
21
1.4 DISCUSSION
The results of testing the power spectral density method provide support for the
use of this analysis in quantifying changes in heterogeneity of lung-shaped images. This
analysis was accurate regardless of ROI shape and insensitive to typical changes in the
lung shape. These two qualities make it a useful tool in quantifying heterogeneity in lung
function and relating it to physiological structure.
One of the initial concerns presented by this method is the effect of lung shape on
the FFT. The sharp edges present at the perimeter of the lung introduced high
frequencies into the analysis; however, the limitations of the PET camera allow us to
discount any heterogeneity above 0.0833 mm-1. The best way to do this was to low-pass
filter the image prior to Fourier analysis. Such filtering would add artificial heterogeneity
to the image by blurring the edges outward and lower the values of the image just inside
the edge. In order to minimize this effect, we first normalized the image by its mean,
then subtracted 1. This attenuated the size of the step at the edge and lessened the
deleterious effect of the low-pass filter on true signal.
Further support for generally ignoring shape effects is evident from Figure 1.6.
Rather than adding spectral noise at a particular frequency or over a range of frequencies,
the mask simply spread the existing signal out over adjoining length scales. In the high
frequency example, 85.2 ± 1 % of the heterogeneity removed from the 6.5-7.2-mm length
scale interval moved to directly adjacent bins (5.9-8.2 mm). In the low frequency
22
example, 76.4 ± 1.7 % of the heterogeneity removed from the 17.6-24.6-mm length scale
moved to adjacent bins (13.7-41.0 mm). As evidenced by the small standard errors in
§1.3.2, the changes in distribution of heterogeneity imposed by the mask were very
consistent, regardless of mask shape. The length scale analysis can therefore be used
even when comparing different lung shapes.
FFT analysis has been previously used for texture analysis of medical images.
The method has been applied to sonographs, radiographs, PET, computed tomography,
and magnetic resonance images.
To analyze echo patterns in liver sonographs, Khoo (9) windowed square regions
of the liver, detrended them, and created a power spectral density plot similar to ours.
These steps, with the exception of the shape of the window, were the same as the steps
we used in analyzing lung images. He used this method to correlate the power in the
high-frequency portion of the spectrum with the degree of steatosis of the liver and the
extent of histological damage.
Katsuragawa (6-8) applied methods similar to Khoo's to lung radiographs. For
each image, he selected approximately twenty 6.4 mm 2 square regions between the ribs.
He detrended the regions, calculated and filtered their power spectra, and compared the
root-mean-square variation and the first moment of the power spectrum. He then
compared these texture measures in normal and interstitial diseased lungs.
Lloyd (10) proposed a morphological technique to quantify spottiness in
Technegas ventilation images. This method was applied over the entire image of the
lung, not just a square region of interest. Morphology changes pixel values according to
23
the values of surrounding pixels in a region defined by a structural element. Two
morphological operations were used in this study: erosion, which pushes down high
values; and dilation, which raises low values. After morphologically eroding and dilating
images using different structural elements, he was able to determine the proper
combination of the sum, standard deviation and coefficient of variation of the pixels to
algorithmically assess spottiness with accuracy comparable to a human observer.
To correlate breathlessness in respiratory failure with the heterogeneity of lung
perfusion obtained by SPECT images, Mitomo (12) defined a distribution index (D). The
fraction of functional lung volume containing values of blood flow from 10% to the
maximum flow was plotted, and change in the curve shape and integral were correlated
with breathlessness. A weakness of this method was that it gave no information
pertaining to the size or distribution of these different levels throughout the lung.
Our method of generating a PSD plot of the entire lung field has important
advantages over the above methods in that it both gives specific length scale information
and includes data from regions of the lung that would be ignored by square ROI's.
Prior to using the FF1' directly on lung images, we considered using a consecutive
series of low-pass filters, as used for the fractal analysis of lung function by Venegas and
Galletti (15). The low-pass filtering method used successively lower cutoff frequencies
to progressively remove heterogeneity from the image. The change in squared
coefficient of variation between two cutoff frequencies was then used to represent the
relative contribution to total heterogeneity by all length scales between those two. While
this method was promising when applied to fractal analysis, it was found inadequate to
24
quantify the contribution of different length scales to the total heterogeneity. A critical
weakness of the method was the practical difficulty of approximating an ideal low-pass
filter. An ideal low-pass filter removes all heterogeneity above the cutoff frequency
while leaving all heterogeneity below unattenuated. In practice, this is impossible to
implement, since some type of windowing of the data is always required. This
windowing spreads the level of attenuation over frequencies close to cutoff frequency.
This effect is particularly detrimental at the lower frequencies, or longer length scales
(Figure 1.7). For example, using cutoff frequencies corresponding to the 41-mm length
scale actually attenuates heterogeneity contributed by length scales over 128 mm long
and contains heterogeneity from length scales as short as 30 mm.
25
18
0.2-
20
40
60
80
100
120
Cutoff Length Scale (mm)
Figure 1.7: The ideal filter attenuation is shown by the dotted line, while the solid
line shows the actual attenuation of filters with the cutoff frequencies corresponding
to the ideals. The attenuation of an ideal filter completely removes all image content
below the cutoff frequency, whereas a real filter only approximates this sharp line.
Actual amplitude response typically crosses the ideal response at roughly 0.25.
The only way to improve on the actual performance of the low-pass filter at large
cutoff length scales is to increase the number of frequency steps (N) of the FFT.
Computationally, this is extremely expensive, increasing time in proportion to N to the
2.5 power.
26
Another method of texture analysis is fractal analysis (4, 5). Fractal analysis has
been used to show changes in lung fractal dimension resulting from diffuse nodular lung
disease (3), peripheral lung tumors (11), chronic obstructive pulmonary disease and aging
(17). Unfortunately, fractal dimension is difficult to intuitively relate to lung structure.
The ability to relate quantified changes in heterogeneity to lung structure is an important
benefit of length scale analysis. Knowing which length scales have significantly changed
their contributions to heterogeneity allows a researcher or physician to consider the size
of airways or vessels that are responding to insults or physiological interventions.
1.4.1 Conclusion
Application of power spectral analysis to lung-shaped images provides a
significant increase in usable data. Lung shape caused some spreading of spectral peaks,
but this effect was not sensitive to typical changes in lung shape, thus allowing
comparisons between lungs of different subjects. The method provides greater spectral
accuracy than the low-pass filtering method and more intuitive correlation between visual
inspection and analysis than the fractal analysis. The method should allow physicians and
researchers to more easily characterize the heterogeneity in images and to use that
knowledge to diagnose changes due to disease or injury.
27
Chapter 2
2.1 INTRODUCTION
Determining the contributions of different length scales to the heterogeneity of a
functional image can provide helpful insights into the relationship between the structure
and function of an organ. In Chapter 1, we demonstrated the power spectral analysis on
synthetic images. In this chapter, we present the results of analyzing PET images
obtained from two animal models: methacholine-induced bronchoconstriction and
pulmonary emboli induced by 100-ptm diameter polystyrene beads.
2.2 METHODS
2.2.1 Animal Preparation
The Massachusetts General Hospital subcommittee on animal research approved
all protocols and procedures. Sheep were anesthetized by an IV bolus of thiopental
(43.9 ± 2.8 mg/kg) and maintained under deep anesthesia by a continuous infusion of the
anesthetic (10-40 mg/kg/hr). A tracheostomy was performed for insertion of an
endotracheal tube. After inducing muscular paralysis with pancuronium bromide (4 mg),
mechanical ventilation was initiated with a ventilator (Harvard Apparatus, Millis, MA)
set at a breathing frequency of 10 breaths/min, an inspiratory time of 30% of the
breathing period, and a PEEP of 5 cmH 20. Tidal volume (VT) was set to maintain
28
normocapnic arterial blood gases (PCO 2 = 40.2 ± 1.4). The right femoral artery and vein
were cannulated for pressure monitoring, blood sampling, and administration of
intravenous fluids (2-3 mg/kg/hr) and intravenous nitroprusside. A pulmonary artery
thermodilution catheter (7-7.5 Fr, Baxter Healthcare Corporation, Irvine, CA) was
inserted in the left femoral vein for measurement of cardiac output (CO), pulmonary
arterial pressure, central venous and wedge pressures, and mixed venous blood gases. A
right jugular venous catheter was inserted to the superior vena cava for injection of the
Nitrogen- 13 ( 13 NN)-saline solution during positron emission tomography. Pancuronium
bromide was administered in 0.2-3 mg/kg intravenous doses as needed to prevent
respiratory efforts after adequate sedation was achieved. Heparin was initially given at
100 units/kg for 2 hr, with subsequent doses at 50 units/kg. Before each imaging run, the
lungs were inflated and sustained at a pressure of 30-40 cmH2 0 to standardize lung
volume history and minimize the occurrence of microatelectasis and the loss of
compliance. Airway, arterial and pulmonary artery pressures were continuously
monitored using a strip chart recorder (Hewlett Packard Inc, USA).
2.2.2 Bronchoconstriction Protocol
We used two different protocols of bronchoconstriction. The focus of the first
protocol was to examine the effect of FiO 2 on development of gas trapping and shunt
during bronchoconstriction, while the second was to examine the effect of animal
position.
29
In the first protocol, we studied 5 sheep (14.4 ± 0.6 kg) mechanically ventilated
with an FjO 2 of 0.5 in the supine position. After reaching a steady state, a set of
physiologic parameters and a set of control PET scans were acquired. Methacholine was
then infused sufficiently to increase airway pressure 50-100% (2.2-6.6 mg/hr), and after
30 minutes a second set of parameters and scans was acquired. FjO 2 was then increased
to 1.0, and after 30 minutes a third set of parameters and scans was acquired.
Transmission scans were collected for 20 minutes prior to each run.
In the second protocol, an FjO 2 of 0.5 was used at all times. Four sheep
(12.2 ± 0.8 kg) were initially studied in the prone position. After reaching a steady state,
a set of physiologic parameters and a set of control PET scans were acquired. Then an
infusion of methacholine was instituted to provoke response similar to the first protocol.
After 30 minutes, a second set of parameters and scans was acquired, the methacholine
infusion was suspended, and the animal was rotated to the supine position. The animal
was assumed to have recovered from methacholine when the peak airway pressure was
within 2 cmH 20 of the control. A third set of parameters and scans was acquired, and
methacholine was administered again to provoke an equivalent response. After
30 minutes, a fourth set of parameters and scans was acquired. Transmission scans were
collected for 20 minutes prior to each run.
2.2.3 Pulmonary Embolus Model
As a pulmonary embolus (PE) model, we used four Hampshire sheep (12-17 Kg).
The animals were studied in the supine position and mechanically ventilated with
30
FiO 2 =
1.0 and eucapnic ventilatory settings as above. After acquiring physiological data
and a set of PET scans under control conditions, PE was created by injecting a total dose
of 0.15 mg/kg of 100-prn (range 90-106 urm) diameter polystyrene spheres (Bangs Lab
Inc., Fishers, IN) suspended in 10 ml of normal saline in five equal injections. Each of
these injections was vigorously mixed before injection into the inferior vena cava. This
embolic insult resulted in an acute increase in the mean PA pressure of 50% or more.
One hour after the initial sphere injection, a second set of physiological data and scans
was acquired. Inhalation of NO gas (80 ppm) was initiated and after 20 minutes a third
set of physiological data and scans was collected. Transmission scans were collected for
20 minutes prior to each injection.
2.2.4 PET Image Collection
Sheep were initially placed supine or prone in the PET camera with the imaging
ring 1 inch inferior to the sternum. A 1-3-minute transmission scan was collected to
determine the region of the lungs being imaged, the animal was moved and the
transmission scan repeated until the myocardium apex was visible in the scan. This
image slice was selected because it provided the largest cross-section of the lung and
avoided inclusion of the diaphragm in the imaged volume.
A PET imaging run consisted of three steps. After steady state breathing, the
ventilator was stopped at end exhalation, maintaining the lung at FRC. Simultaneously, a
bolus of
13
NN in saline solution was injected into the jugular venous catheter, and the
camera began collecting a series of images. Six consecutive 5-second images were
31
collected during 30 seconds of apnea. At that point, mechanical ventilation was resumed
and four consecutive 30-second images were collected as the tracer washed out of the
lung.
PET images were corrected for camera sensitivity and tissue attenuation, then
reconstructed using a convolution-backprojection algorithm. This resulted in a
159x159-voxel image, with each voxel representing a 1.925x1.925 mm square transverse
area with 1 cm axial depth. The effective resolution of the reconstructed images for this
camera was 6 mm, with the finer voxel resolution being created by interpolation.
2.2.4.1 Perfusion Images
Due to the low solubility constant of 1 3NN (X = 0.012), virtually all of the gas that
reaches aerated alveoli diffuses from the blood into the airspaces. Therefore, for healthy
aerated lung regions, the radioactivity is distributed in the lung in proportion to the local
rate of perfusion. In these regions, local activity reaches a plateau by the beginning of the
second image. Thus, the second through the sixth images were summed to obtain an
image with a higher signal-to-noise ratio (SNR). In lung regions manifesting shunt, local
activity reached a peak during the second image, and exponentially decreased to a plateau
during the rest of the apneic images as the tracer diffused back into the capillary blood
and was carried away from the lung (13). In these regions, data from the second image
was used as an approximation of relative pulmonary perfusion.
32
2.2.4.2 Ventilation Images
Regional ventilation of perfused and aerated regions was assessed from the
analysis of images collected during the washout period. The local specific ventilation
(slVA,)
was calculated using a modified Stewart-Hamilton equation (1) that uses the sum
counts collected in the washout period normalized by the pre-washout count rate to
calculate an exponential washout time constant (13). For each voxel, the local time
constant was therefore determined as
T wo
(2.1)
N+2
3
N
where Y WO is the sum of the counts collected in washout images and
N
is the
average count rate of the final N (usually four) apneic images. The time constant was
inverted to give sVAr for each voxel.
This equation works well under the assumption that there is no shunt and all of
the gas is removed by the end of the 2-minute washout period. If ventilation is poor in
some region and a substantial amount of tracer remains in the lung at the end of the
washout period, sVA, is underestimated. Also, in the presence of regional shunt, sVA, is
overestimated.
33
2.3 RESULTS
2.3.1 Bronchoconstriction Model
Methacholine infusion produced a pronounced effect on ventilation (Figure 2.1).
There was a large shift in the heterogeneity towards low frequencies. This effect was
uniform across all animals, allowing results to be plotted as means with standard error
bars (Figure 2.2). After bronchoconstriction, the percentage of the total heterogeneity at
spatial frequencies between 0.012 mm- and 0.028 mm-1 (18 to 41 mm length scales)
increased an average of 78 ± 20% in supine animals and 156 ± 42% in prone animals
(P < 0.05).
34
A
B
C
D
Figure 2.1: Images of regional ventilation in supine and prone animals. Higher
regional ventilation rates are brighter than lower rates. The supine animal shows a
vertical gradient in the control image (A) and splotchy heterogeneity after
bronchoconstriction (B). The prone animal has more uniform ventilation
distribution in the control image (C) and decreased ventilation in the center and
upper right regions after bronchoconstriction (D).
35
35-
35
Supine Control
Supine Methacholine
* 30
F) 30C:
a)"25-
2 25
T
a)
20
0
T
15
0
S15a)
a)
CD
CU 10
0)
0
35a -
C10
0
0
35-
a)205--
0.1
0.05
0
Prone Control
Prone Methacholine
)30-20
a - 35-35-15-
-5 30C20)
C
2O 25-
0.1
0.05
T
T
a)
X: 20-
CY
0
0
T
4-15
a) 0
a) 5
a)
a)
T
-
T
5
0
t
T
C
0--
0.05
Frequency (1/mm)
0
e
0.1
0
0.05
Frequency (1/mm)
,--- I
0.1
Figure 2.2: Contribution of different length scales to total heterogeneity of
ventilation at FjO 2 = 0.5. Values are means ± SE of all (Nupi. =8, Nprone = 4) animal
studies.
The effect of bronchoconstriction on perfusion heterogeneity was less pronounced
(Figure 2.3). As in the ventilation images, there was a shift in the heterogeneity towards
the lower frequencies. However, in perfusion images, the low frequencies contribute
36
more to heterogeneity in the control images than in ventilation. After
bronchoconstriction, the contribution to total heterogeneity between 0.012 mm~1 and
0.028 mm-1 (18 to 41 mm length scales) increased an average of 53 ± 19% (P < 0.05) in
supine animals and 50 ±4%in prone animals (Figure 2.4).
A
B
C
D
Figure 2.3: Images of regional perfusion in supine and prone animals. Higher
perfusion rates are brighter than lower rates. The control perfusion images (A,C)
37
have more low-frequency heterogeneity than the corresponding ventilation images
(Figure 2.1 A,C). The supine image shows a vertical gradient both in control (A)
and bronchoconstriction (B). The prone control (C) is more uniform than supine
and the prone bronchoconstriction (D) changes to match the distribution of
ventilation (Figure 2.1 D).
38
35-
35
Supine Control
30-
30-
a)
T
a)
25-
a)
0)
0
a)
Supine Methacholine
25T
0)
20-
T
15-
20
0
L.
a)
15-
0)
10-
10-
5-
5-
Tr
-1I
a.
0 0
00.05
0
0.1
Prone Control
a)
30-
a)
C
a)
0)
0
a)
a)
a)
4--
0
03 5-
0-
T
15-
0.1
Prone Methacholine
a)
0)
0 25a)
20-
0.05
-
0
a)
T
10
a)
0.
a)
5-
T
15-
a)
0)
10-
a.
0-
TT
5-
00
0.05
Frequency (1/mm)
0
0.1
0.05
Frequency (1/mm)
0.1
Figure 2.4: Contribution of different length scales to total heterogeneity of perfusion
at FjO 2 = 0.5 for supine and prone position. Values are means ± SE for all
(Nsupine = 8, Nprone = 4) animals studied.
Both ventilation and perfusion images manifest similar changes during
bronchoconstriction. In the control images, the percentage of total heterogeneity
contributed by the 18-41 mm length scales was affected by animal position. After
39
inducing bronchoconstriction, these length scales had similar relative contributions to
total heterogeneity of both ventilation and perfusion, regardless of position (Table 2.1).
Position
Prone
Supine
Function
Perfusion
Ventilation
Perfusion
Ventilation
Control
Mean
SE
31.7%
6.5%
20.9%
6.1%
33.1%
3.3%
26.1%
2.5%
Bronchoconstriction
Mean
SE
47.4%
9.6%
47.5% *
7.9%
47.9% *
2.0%
43.3% *
3.7%
Table 2.1: The relative contribution of the 18-41 mm length scales during
bronchoconstriction at FiO 2 = 0.5. *P < 0.05, control vs. bronchoconstriction.
For the animals imaged in the prone and supine positions, supine position was
always studied after the prone position. Thus, the control condition supine was imaged
after bronchoconstriction in the prone position. In one subject, it was expected that the
over one hour interval between the end of the methacholine infusion prone and the
collection of the control scans supine was sufficient to reverse the effects of
methacholine, since the peak airway opening pressure had returned to within 2 cmH 2O of
the control conditions. However, PSD analysis showed that the contribution to
heterogeneity in the supine ventilation image by 25-41 mm length scales was 166%
higher than the equivalent prone image (Figure 2.5 A,C). The contribution to
heterogeneity in the supine perfusion image by 25-41 mm length scales in this subject
was 57% higher than the equivalent prone image (Figure 2.5 B,D). Both of these results
suggest the presence of lingering methacholine effect.
40
A
B
40-
40Prone Control Ventilation
Supine Control Ventilation
35-
CD
C
a)
235 -
0)30
0
CD30
0
a)
-
25-
(25-
20
20 020015
oa) 15-
0)
U0)
4-
U 10
C)
C
a)5
a5-
0--
a) -
0--
0
01
0.05
Frequency (1/mm)
0.1
C 40--
>4o-
Prone Control Perfusion
.535a)
0 030
a)
0.05
Frequency (1/mm)
0
0-
0.1
Supine Control Perfusion
35-
-
0
)-
a25-
(D25-
CU 020 -
o20-
4-
o 0)15-
a)
U 0)
a)
a)
C.)
0a)5-
0 -
0+
'I
0
0.05
Frequency (1/mm)
5
0.1
'I
0
0.05
Frequency (1/mm)
I
0.1
Figure 2.5: Contribution of different length scales to ventilation (A,C) and perfusion
(B,D) heterogeneity in one subject. The heterogeneity content of the control images
for this subject varies dramatically, perhaps due to the injection of methacholine
between images, rather than the change in body position.
41
2.3.2 Pulmonary Embolism
Changes in the PSD of perfusion and ventilation images caused by small size
(100 pm) emboli were much less uniform from animal to animal than those of
bronchoconstriction (Figures 2.6 and 2.7).
42
Control
35
30
25
20
15
10
5
0
1 Hour Post
5
0
5
0
0
5
25
205-
0
0.05
0.1
35
30
25
20
15
10
5
0
1
10
0
1
51
5 _
0 _
0
55
0_
0.05
0.-
35
30
25
20
15
10
5
0
0
0.05
0.
0.05
0.
0.05
0.
5
0
0
50.0
0 _
0
Post NO
5
1
1
0.05
0.'
0.05
0.1
0-15-105
0
0
5_
0
0
5
05-_
1046
1
55
0-5-
04w
0-
0
0.05
0. 1
35
30
25
20
15
10
5
5
0
0
R5
30
25
20
15
10
5
0
5 -A
0
00
0.05
0.1
Frequency (1/mm)
0
0
0.05
0.1
Frequency (1/mm)
11..I I I I "
0
0.1
0.05
Frequency (1/mm)
Figure 2.6: Contributions to heterogeneity of regional ventilation images in four
animals prior to embolus insult, 1 hour after insult, and after administration of NO.
Note the lack of any strongly visible trends.
43
3530
2520
15 _
10
5
0
0
3530-2520
15
10
5
0
0
35-30
25:
20
15
10
5
0
0
3530
257
207
157
10
50
0
Control
0.05
0.05
0.05
0.05
Frequency (1/mm)
,--I
0.1
,--1
0.1
-r-1
0.1
3530_
25
20:
15
10
50
0
3530
25
20-15:
10
5
01
0
3530
25
20
15
10
51
0
0
3530_
2520
15
105
01
0.1
0
1 Hour Post
0.05
,1-i
0.1
Post NO
35
30
25
20
15
10
5
0
,-1
0
0.05
0.1
0
0.05
0.
0.05
-- 1
0.1
3530
25
20
15
10
5
0
0.05
0.05
0.05
Frequency (1/mm)
0.1
,-I
0.1
30
25
20
15
10
5
01
0
3530
25
20
15
10
5
01
0
0.1
0.05
Frequency (1/mm
0.1
Figure 2.7: Contributions to heterogeneity of perfusion images in four animals prior
to embolus insult, 1 hour after insult, and after administration of NO. With the
44
exception of subject D, the heterogeneity of perfusion appears to change very little
between any of the stages of the experiment.
2.4 DISCUSSION
The most important findings of this study are as follows: 1) bronchoconstriction
resulted in an increase in contribution of lower frequencies to total heterogeneity of
ventilation and perfusion images and 2) small pulmonary emboli produced a smaller and
inconsistent response from animal to animal.
Before discussing the implications of these results, it is important to consider
methodological issues. A primary limitation of using spectral analysis to assess changes
in local functional response in these studies is the two-dimensional nature of the data
from our single-slice PET camera. Thus, length scale contribution to heterogeneity was
only determined in one transverse section, and it is not possible to ascertain the length
scale of heterogeneity extending beyond the range of the single slice (1 cm).
Another issue is the error introduced into ventilation images by incomplete
washout of the
1NN
from the lungs during the imaging period. During the washout, the
count rate in each voxel plotted against time creates a "washout curve." The "mean
transit time" (MTT) of a particular region for a washout maneuver is defined as the total
number of counts collected in that region during the washout, divided by the equilibration
count rate measured from that region. If the instantaneous count rate (c(t)) is assumed to
be a continuous function of time, MTT can be defined as
45
MT =
- c(t)
'=0 C(O)
(2.2)
This represents the mean residence time of a molecule of 13NN in that particular area of
the lungs during a washout. Venegas (14) has shown that the MTT for a monoexponential washout curve is identical to its time constant, which is inverted to give
sVA,.
The modified Stewart/Hamilton method, preferred for its rapid computation, uses
the area under the imaged washout curve, normalized by the perfusion, to determine
MTT. Because the imaged washout curve occupies only a finite time, this method
underestimates MTT by not including the fraction of the area under the washout curve
from the completion of imaging to infinity. However, this error is insignificant when the
MTT is small. In areas that have gas-trapping or extremely slow washouts, the
Stewart/Hamilton method underestimates MTT, and ventilation rates calculated this way
are artificially fast. In these poorly ventilated cases, the washout curve can be
extrapolated beyond the end of the imaging period. Venegas (14) developed a solution
for the MTT
IWO=MTT
1=-M
e
(2.3)
where I WO is the sum of the washout images and Tf is the duration of the washout
period. MTT can be solved for as
MTT =
I
(2.4)
-Tf
L
eYj
( M
Y"'
WWO+
46
where L( ) is Lambert's W function. Lambert's W function L(Y) is the solution for X
in XeX = Y (2). This method is superior to the modified Stewart/Hamilton at calculating
slow ventilation regions.
The disadvantage of extrapolating the washout curve is the drastic increase in
computing time necessary to calculate
sVAr.
Therefore, we used the modified
Stewart/Hamilton to create all ventilation images.
Analysis of images containing shunting regions brings additional problems.
When the dissolved
13
NN is passes through the lung in a shunting region, it is unable to
diffuse to the airspaces and is carried away from the imaged volume. This results in peak
activity early in the apneic period, with an exponential decay thereafter. In animals with
shunt, the second 5-second image (5-10 seconds into apnea) was used to estimate
perfusion. This results in a lower SNR. In this study, only one animal, from the
pulmonary embolus model, manifested shunt.
To interpret our results it is useful to relate the histograms to the usual terms for
qualitative description of images after visual inspection. The lower values on the
ordinate (low spatial frequencies) correspond to heterogeneity at the larger length scales;
an image with a high percentage of its heterogeneity found in this range is generally
described as "splotchy." In contrast, images with a higher percentage of heterogeneity at
the higher frequency values are generally described as having a "broken glass" look. It is
the quantification of such vague terms that this analysis ventures to provide.
In both the prone and supine position, bronchoconstriction by IV infusion of
methacholine induced a dramatic shift in the length scales contributing to total
47
heterogeneity in ventilation. The increase in heterogeneity in length scales between 18
and 41 mm was 156 ± 42%. The increase in heterogeneity in the same length scales in
supine animals was 78 ± 20%. The abated response in supine animals may have been
caused by the existing non-uniformities in heterogeneity in the control cases (Figure 2.2),
where the initial contributions of the 18-41 mm length scales was higher in the supine
animals than that in prone by 5 ±.08%(P <0.05).
The relative contributions of the 18-41 mm length scales, for both ventilation and
perfusion heterogeneity after the administration of methacholine, regardless of body
position, were remarkably similar (Table 2.1). The uniform response of the lung at the
examined length scales suggests that a structural interpretation may be possible.
The shift to the 18-41 mm length scales in contribution to heterogeneity is
supported by previous research into the nature of bronchoconstriction in humans.
Verbanck et al (16) used multiple breath washouts of N 2 to find the relative contributions
of conductive airways (Scond) and acinar airways
(Sacin)
to ventilation inhomogeneity. He
found that histamine bronchoprovocation resulted in 200 to 400% increases in Scond and
almost no change in Sacin. This allowed him to conclude that airways proximal to the
acini were responsible for most airway narrowing.
The power of this analysis in quantifying changes in pulmonary function is further
illustrated by one of the animals studied in the prone and supine positions (Figure 2.5).
The PSD plots of the control ventilation and perfusion images suggest that the effects of
the methacholine had not abated sufficiently when the second control image was
collected. The physiological data collected at the time of the image also supports this
48
explanation with an increase in both pulmonary capillary wedge pressure from 2 to
6 mmHg and mean pulmonary arterial pressure from 13 to 21 mmHg.
The most significant result in the PE study was the lack of any consistent
response. Studies in dogs have shown that 100-pm beads produce no increase in shunt,
low VA/
areas, or deadspace (18). Therefore, control of ventilation and perfusion
probably occurs at a level well below the 6 mm resolution of the camera. The power
spectral analysis of the perfusion and ventilation images showed no evidence of any
secondary effects at length scales larger than this resolution.
2.4.1 Conclusion
PSD analysis can provide useful insights into the relationship of lung structure
and function. In a bronchoconstriction model, this analysis revealed a major contribution
of 18-41 mm length scales to increased heterogeneity in ventilation, suggesting that
relatively large airways (2 to 4-mm diameter) may be the primary site for
bronchoconstriction or airway closure. In pulmonary micro-embolus studies, the spectral
analysis method gives results consistent with previous research: there was no systematic
change in perfusion or ventilation heterogeneity. Application of this method in patients
with chronic obstructive pulmonary disorder, cancer, or other pulmonary diseases may
provide information on the structures involved in those disorders at an early stage.
49
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