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A/
measured by PET
Department of Anesthesia, Massachusetts General Hospital, and Harvard Medical School, Boston, Massachusetts 02114
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Treppo, Steven, Srboljub M. Mijailovich, and José G. Venegas. Contributions of pulmonary perfusion and ventilation to
heterogeneity in 
A/
measured by PET. J. Appl. Physiol. 82(4): 1163-1176, 1997. To estimate the contributions of the heterogeneity in regional
perfusion () and alveolar ventilation
(A) to that of ventilation-perfusion
ratio (A/), we have
refined positron emission tomography (PET) techniques to image local
distributions of and
A per unit of gas volume content
(s and sA,
respectively) and VA/ in
dogs. sA was assessed in two ways:
1) the washout of 13NN tracer after equilibration
by rebreathing (sAi), and
2) the ratio of an apneic image after a bolus intravenous
infusion of 13NN-saline solution to an image collected
during a steady-state intravenous infusion of the same solution
(sAp).
sAp was systematically higher than sAi in all
animals, and there was a high spatial correlation between
s and
sAp in both body positions
(mean correlation was 0.69 prone and 0.81 supine) suggesting that
ventilation to well-perfused units was higher than to those poorly
perfused. In the prone position, the spatial distributions of
s, sAp, and A/ were fairly
uniform with no significant gravitational gradients; however, in the
supine position, these variables were significantly more heterogeneous,
mostly because of significant gravitational gradients (15, 5.5, and
10%/cm, respectively) accounting for 73, 33, and 66% of the
corresponding coefficient of variation (CV)2 values. We
conclude that, in the prone position, gravitational forces in blood and
lung tissues are largely balanced out by dorsoventral differences in
lung structure. In the supine position, effects of gravity and
structure become additive, resulting in substantial gravitational
gradients in s and
sAp, with the higher
heterogeneity in
A/ caused by a
gravitational gradient in s, only partially compensated by that in sA.
positron emission tomography; body position; gas exchange; regional
ventilation-perfusion ratio; dog; pulmonary heterogeneity; functional
imaging
INTRODUCTION WILSON AND BECK (30) have recently outlined a
theoretical approach to assess the contributions of heterogeneities in
alveolar ventilation ( METHODS The experimental protocol for these animal experiments was approved by
the Massachusetts General Hospital Committee on Animal Care.
Experimental Setup
Animal Preparation
A) and regional
perfusion () to the heterogeneity of the
ventilation-perfusion ratio
(A/). Such an approach was illustrated with experimental data extrapolated from a compilation of reports by different investigators using different methodologies, leaving the quantitative validity of some of their conclusions in
question. A number of recent studies have measured and characterized the effect of body position on the spatial heterogeneity of
A (2, 15, 27) and (3,
11, 12), but the individual contributions of these variables to the
heterogeneity of A/ cannot be reliably assessed unless all variables are measured in the
same individual. We have supplemented the positron imaging technique to
measure A/ described by
Rhodes and co-workers (21, 22) with independent measurements of
and A per unit of gas
content (s and
sA, respectively) (17) using
13NN as the tracer gas. With the use of these techniques,
we have imaged the distributions of s,
sA, and
A/ and analyzed their
spatial correlation and heterogeneity, including the contribution of
gravitational gradients, in prone and supine dogs. The imaging data
were also analyzed to yield and characterize distributions of
A/ comparable to those
generated by the multiple inert-gas-elimination technique (MIGET). This
study provides the experimental data required by the method of Wilson
and Beck (30) to assess the contributions of heterogeneities in
A and to the
heterogeneity of A/.
Fig. 1.
Schematic representation of experimental apparatus. PET, positron
emission tomography; ACg, specific activity of labeled gas in rebreathing circuit; ACv, specific activity of systemic
blood; ACpa, specific activity of pulmonary artery blood;
ACi, specific activity of intravenous infusate.
[View Larger Version of this Image (13K GIF file)]
Imaging Scans
Image collection during mechanical ventilation was gated by using an electrical signal from the mechanical ventilator at the start of inspiration. The gating scheme consisted of a collection of two consecutive images of equal duration during the breathing cycle. Because inspiratory time was set at 30% of the total breathing period, the first image included all of inspiration and the initial part of exhalation, whereas the second image included the latter part of exhalation, in which expiratory flow was small and the lungs remained almost stationary at a lung volume close to resting functional residual capacity (FRC). Five animals were studied in the prone position and five in the supine position. A transverse cross section of the lungs intersecting the apex of the heart was selected for imaging. Such a position was determined after equilibrating the lungs with inhaled 13NN-labeled gas and advancing the lungs into the field of view of the camera until the highest count rate was recorded by the camera. This position corresponded to the slice of the lungs having the greatest cross-sectional area and provided consistency among animals. After positioning, the following scan sequences were performed: inhaled tracer, bolus infusion, constant infusion, blood pool scan, and transmission and uniformity scans. These scan sequences are described in detail below, and the average counts per voxel of the resulting PET images are given in Table 1.
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Blood pool scan. To estimate the contribution of counts originating from the pulmonary arterial blood per voxel during the constant-infusion (CI) imaging sequence, an additional blood pool scan was conducted. This was done by labeling the red blood cells with a temporary inhalation of 11C-labeled CO until the steady-state activity of the blood reached an adequate level. Two sequential images of 20-min duration were then collected. Blood samples were obtained at the beginning and the end of the imaging sequence to assess their respective specific activity needed to normalize the image and to correct for ventilatory losses of the CO tracer over the imaging time. Transmission and uniformity scans. To correct for gamma ray energy attenuation caused by the supporting structures and body tissues of the animal, a tubular ring, concentric to the PET camera's field, was filled with 18F-labeled water, and a gated transmission scan was collected during breathing. At the end of this scan, the animal and supporting structures were removed from the camera's field, and a final uniformity field scan was conducted.
Data Analysis
Image processing. PET images were initially corrected for camera sensitivity and for tissue attenuation. Image reconstruction was then performed with a convolution back-projection algorithm by using a Hanning filter yielding an effective spatial resolution of 10 mm determined from the width at one-half height of a point source image. This degradation of resolution length (from 4.5 mm of the camera) was needed to attenuate random noise to levels <5% of the measured coefficient of variation (CV)2 in most images processed. Resulting images consisted of an interpolated matrix of 159 × 159 voxels of 0.2 × 0.2 cm × 5 mm, or 57% of the resolution length. These reconstructed images of local counts per voxel were then processed following the methodology described in detail in the accompanying paper (17) and briefly discussed below, to yield functional images with voxel values in physical units (Table 2).
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A/
IMAGE.
A steady-state CI image was created by adding, on a voxel-by-voxel
basis, the last three images of the protocol sequence. An initial mask
was created by thresholding the CI image to exclude areas outside of
the lung field. A threshold of 30% was used initially and then refined
in increments until no areas outside the lung field were included in
the mask (mean threshold used was 33 ± 6%). A second mask was then
created by thresholding the blood pool (Vb) image to define the heart
and largest vessels. (This was also done in an iterative process where
mean threshold used was 55 ± 5%.) This second mask was subtracted
from the first one to exclude heart and vessels from further analysis.
The masked CI image was then corrected for the contribution of
pulmonary arterial blood activity with the algorithm described by
Rhodes and co-workers (21, 22), where the volume of radiolabeled
arterial blood is assumed to be 40% of the total pulmonary blood
volume assessed from the 11CO scan. Thus a bloodcorrection
image was subtracted voxel-by-voxel from the CI image. A temporary
image was formed from the ratio of uncorrected to blood-corrected CI
images, and the mask was further refined to exclude from the analysis
additional areas with very high correction values. These areas,
covering ~20 voxels out of 2,000 voxels on average, were typically
located in proximity to the heart and large blood vessels and
corresponded to overcorrected voxels by partial volume effects from the
Vb scan. These final masks were then applied to all
functional images analyzed. Cardiac output
(T) was calculated by using a mass
balance from the infusion flow rate and the 13NN specific
activities of the infusate and the pulmonary arterial blood.
ALVEOLAR GAS CONTENT.
An alveolar gas content per voxel image (VA) was obtained
by decay-correcting the voxel values of the equilibrated inhaled tracer
scan, normalized by the specific activity of a gas sample to create an
image in units of milliliters of gas content per cubic centimeter of
voxel.
.
Because of diffusion to neighboring regions and/or
readsorption of the tracer into capillary blood, the voxel tracer
concentration may have changed during the apneic period following the
bolus intravenous infusion of 13NN-labeled saline. An
estimation of, and correction for, these tracer kinetics effects was
conducted on a voxel-by-voxel basis by assessing the differences in
tracer content between the last two 30-s images of the sequence and
then extrapolating the activity level expected at the time of the
tracer's arrival to the alveoli (17). The tracer-kinetics-corrected
image was normalized by the ratio of total infused activity to
I to yield an image of local
in units of milliliter per minute of blood flow per cubic centimeter of
voxel volume. Finally, the image was divided in a
voxel-by-voxel manner by the VA image to yield an image of s (in units of s
1).
SA.
We derived images of regional sA by
using two independent methods. One method directly assessed the
kinetics of inhaled NN2 tracer during a washout maneuver
following an equilibration scan
(sAi), as described in the
accompanying paper (17). A second method indirectly assessed
ventilation (sAp) as the
ratio of the local concentration of the NN2 tracer, infused
during apnea (distribution of ), divided by the
local concentration of the tracer during CI of the tracer in saline
solution in steady-state breathing, after subtraction of activity from
the pulmonary arterial blood (distribution of
/sA) (17). The
resulting sAp image represented exclusively sA of
perfused units, since unperfused units would not receive tracer during
either of the two imaging protocols.
Assessment of spatial heterogeneity.
The spatial heterogeneity of the functional images was assessed from
the CV of the voxel data within the lung field defined as the SD
normalized by the mean value of the data
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or VA), the contribution of noise
to the CV2 was calculated as the random noise
(g2) caused by the finite counts
from the image. Thus, the noise-corrected CV (CVcr)
was
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) of the original PET image or
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A/,
sA, or s), the CV
of the ratio image [CV2(x/y)] was
corrected by the sum of random-noise contributions to the original
images, yielding
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and vs.
s; and s vs.
sAi and vs.
sAp.
In those cases where the pairs of functional images were originally
derived by using a common image, i.e., VA vs.
s, Rs was corrected to
eliminate the pseudocorrelation caused by imaging noise in the common
image VA.1
FRACTIONAL DISTRIBUTIONS.
Mean-normalized distribution histograms for VA,
, s,
sA, and
A/ and their
corresponding log-transformed versions were generated for each of these
functional images. Regional data were grouped by either fraction of
total voxels (lung fraction), VA,
A and/or
fractions. These distributions were then characterized by evaluating
the corresponding Pearson coefficient of skewness (Skx) and coefficient of kurtosis (
).
BIVARIATE DISTRIBUTIONS.
Mean-normalized bivariate-distribution histograms for log-transformed
mean-normalized s vs.
sA were also generated, in which
sA was calculated from either inhaled
or perfused tracer. These bivariate distributions were plotted as
three-dimensional surfaces with the z-axis corresponding to the
fraction of total voxels having the corresponding relative values of
sA and s. Distributions were then averaged within each group of animals.
Shunt Fraction
Because of the low solubility of nitrogen in blood and tissues, an index of overall lung venous admixture can be calculated from the fraction of tracer recirculating back into the lungs during the steady-state period of CI. Such a recirculation fraction (FR) can be estimated from the ratio between the peripheral CV and Cpa simultaneously measured during the steady-state part of the CI protocol
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Statistical Analysis
Comparisons between supine and prone positions were made by using single-tailed Student's t-test for independent samples. Comparisons between average and CV values of sAi and
sAp were made using
multivariate analysis of variance with body position and method as
factors. Statistical significance was taken at P < 0.05 level.
RESULTS
Mean ± SE values for supine and prone positions of the average voxel
value within the imaged section for ,
s, VA,
sAp, sAi, and
A/ are presented in
Table 2. Of these parameters, only and
s were significantly greater in the supine compared with the prone position.
Measurement of Heterogeneity
The contributions from different factors to heterogeneity, such as noise or vertical gradients, are additive only when expressed in terms of CV2; thus the findings of this study are presented in Table 2 and Fig. 3 as CV2. Because the definition of CV (SD/mean) gives a more intuitive impression of the degree of heterogeneity, in the text we present the results in terms of the CV.
),
ventilation-perfusion ratio
(A/), and specific
alveolar ventilation measured from kinetics of perfused tracer
(sAp) images in 5 supine
(
) and 5 prone animals (
). Note that CV2 values of
supine dogs are higher that those in prone dogs and that in all animals
CV2 of A/
is lower than that of s.
A/.
Although there were substantial differences in spatial heterogeneity
among the different dogs (Fig. 3), the heterogeneity of
A/ was significantly
lower in the prone animals (CV = 0.14) compared with the supine
animals (CV = 0.34) (Table 2). This difference in heterogeneity was
partially accounted for by the presence of a systematic vertical
gradient in the supine position that accounted for 66% of the
CV2, whereby
A/ decreased by 10%/cm
distance in the direction of gravity. In contrast, the vertical
gradient in the prone position was not significantly different from
zero (0.63%/cm). After we removed the vertical gradient from the
images by linear regression, the differences in residual heterogeneity
between supine and prone positions were still statistically significant
but of a much lesser magnitude [CVr = 0.13 for
prone and 0.17 for supine positions (Table 2)].
.
T, measured from the specific
tracer activities of the pulmonary artery and the saline infusate
(ACpa and ACi) was 1.01 ± 0.180 l/min for prone and 1.27 ± 0.340 l/min for supine
animals. Mean values of average regional
were 0.031 ml · s1 · cm3 for
prone and 0.061 ml · s1 · cm3 for
supine dogs (Table 2). Regional distributions of
either normalized by voxel volume or by alveloar gas
volume s, were more heterogeneous in the supine than
in the prone position. CV and
CVs were 0.41 and 0.46 in supine and 0.25 and
0.18 in prone position, respectively (Table 2). The greater
heterogeneity of and s in the
supine position was due, in part, to consistent gravitational
gradients, whereby the respective variables increased by 9.5 and
15.1%/cm distance in the direction of gravity. These gradients
contributed to 38 and 73% of the total
CV 2 and
CVs2 , respectively. In contrast, there were no consistent vertical gradients
in the prone position.
When the regional distributions of s and
for each position were compared,
s was significantly less heterogeneous than in the prone position while the contrary was true in
the supine position (Table 2). Differences in the width of the
corresponding fractional distribution are consistent with this finding
(Fig. 4, B and C, right) by
showing that the average distribution of s in the
prone position is wider than the corresponding distribution of
, with the opposite happening in the supine position.
; B), and
(s; C) in prone (left) and supine (middle) positions. Height of surfaces over the x-y
plane represents relative value of corresponding variable. Plots on
right are fractional distributions of corresponding variables
averaged for all dogs studied. Overbars designate average values.
VA. As illustrated by a wider fractional distribution of VA (Fig. 4A, right), the spatial heterogeneity of local gas content was greater in the supine position compared with the prone position (CV was 0.28 for supine and 0.21 for prone; Table 2). The higher heterogeneity of the supine position was partially accounted for by a systematic vertical gradient, whereby gas content decreased by 5.1%/cm distance in the direction of gravity. This gradient contributed to 23.7% of the total CV2. In contrast, the prone position had smaller and not significant vertical gradients (
0.370%/cm), without significant contributions to the total
CV2 (1.2%).
sA.
sA was directly assessed with the
13NN tracer delivered by inhalation
(sAi), and, indirectly,
from the ratio of images with the 13NN delivered by
intravenous infusion
(sAp). Two-way analysis of
variance with repeated measures on the values of average
(
) for both
methods, including the fixed effect of body position, showed a
significant effect of method but not of body position. Student's
t-tests confirmed no statistical differences for
between supine (0.042 s1; Table 2) and prone (0.042 s1) positions and for
between supine (0.086 s1) and prone (0.070 s1) positions but demonstrated
to
be significantly greater than
for each position. There was, however, a significant correlation between the individual values of
and
,
and a linear fit between the two independent estimates of
sA had a slope of 1.66 and
R2 = 0.59 (Fig. 5).
plotted against corresponding
for each animal studied.
was consistently lower than
.
Local values of s
Ap on a
voxel-by-voxel basis were poorly correlated with, and consistently
higher than, those of sAi (Fig. 6). CV of
sAi of prone
(0.18 ± 0.09) was not significantly different from that of supine
position (0.22 ± 0.1), whereas the CV of
sAp of prone animals (0.16)
was significantly lower than that of supine dogs (0.25). Variations in
the width of the corresponding fractional distribution histograms of
sAp and
sAi illustrate these findings
(Fig. 7).
Ap vs.
sAi for a representative dog
in supine (A) and one in prone (B) position.
Ai
(A) and sAp
(B) in prone (left) and supine positions
(middle). Height of surfaces over the x-y plane
represents relative value of corresponding variable. Plots on
right are fractional distributions of corresponding variables averaged for all dogs studied.
A consistent difference between the spatial distributions of s
Ap and
sAi occurred in the supine
position where sAp presented a vertical gradient of 5.5%/cm length in the direction of gravity accounting for 33.2% of the total CV2, whereas
sAi had no significant
gradient (Table 2).
Spatial Correlations
was found to have a high and significant
spatial correlation with VA in the prone position
(RS = 0.74 ± 0.05) but none in the supine
position (RS = 0.23 ± 0.01) (Table
3). s was not spatially
correlated with sAi in either
position (RS = 0.036 ± 0.13 for prone, and
RS = 0.11 ± 0.23 for supine positions). In
contrast, s was highly correlated to
sAp in both prone and supine
positions (RS = 0.69 and 0.81, respectively).
This correlation is illustrated in the bivariate distributions (Fig. 8
and Fig. 9),
where most voxels contain combinations of
), where 
is average regional
s, and
log(sAp/)
that fall along a 45° projection (constant
A/).
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vs. log(s/)
averaged over all dogs studied in prone position. Height of surface
over the x-y plane in surface plot (bottom left)
represents average fraction of voxels containing respective combination
of relative sAp and
s. A contour plot (top right) illustrates
correlation between these variables (direction of constant
A/ isopleths is
45°).
vs. )
averaged over all dogs studied in supine position. Height of surface
over the x-y plane in surface plot (bottom left)
represents average fraction of voxels containing respective combination
of relative sAp and
s. A contour plot (top right) illustrates correlation between these variables (direction of constant
A/ isopleths is
45°).
Fractional Distributions
Mean-normalized fractional distributions of functional images originating from the ratio of two PET images (sAp, s,
and A/) were all
skewed to the right, as shown by the mean Skx significantly greater than zero at both body positions (Table 4). Logarithmic transformation of the data
results in unskewed fractional distributions with mean
Skx values not different from zero. The
log-transformed distributions were also mesokurtic, i.e., they had
coefficient of kurtosis that does not appreciably deviate from 3. This suggests that the regional distributions closely resemble the
shape of a log-normal distribution.
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In contrast, fractional distributions of functional images originating
from single PET images (VA, , and
A) were not skewed (Skx not different from zero) and were mesokurtic
while logarithmic transformation of the voxel data made the
distributions significantly skewed to the left
(Skx < 0).
Shunt Fraction
Reflecting the higher degree of venous admixture expected from a less uniformA/
distribution, the FR of the infused tracer recirculating back into the lungs during the CI protocol was
significantly higher in the supine position
(FR = 0.018 ± 0.005) compared with the prone
position (FR = 0.007 ± 0.005).
DISCUSSION
The most significant findings of this study were as follows.
1) The regional distribution of
A/ was more
heterogeneous in the supine position compared with the prone position.
The higher heterogeneity supine was due to a significant vertical
gradient that contributed more than one-half of the total
CV2. 2) Differences in the heterogeneities between
supine and prone in both and
A contributed to the differences in
A/ heterogeneity. 3) In both body positions, there was a high spatial correlation between s and
sAp while there was no
correlation between s and
sAi. Regional
and VA were positively correlated in the prone position but not in the supine position.
Methodology
Most issues related to the PET imaging methodology have either been discussed by the original proponents of the CI technique (7, 21, 22) or have been discussed in detail in the accompanying paper (17). A major methodological departure from the original method to assessA/ was in the
estimation of VA, where we imaged the lungs after
equilibration with inhaled 13NN gas instead of deriving
VA from the transmission scan as described by Rhodes et al.
(22). This modification improved the quality and signal-to-noise ratio
of the A/ images
because it largely canceled out systematic imaging artifacts and
because transmission scans with an equal number of events have greater
inherent noise than emission scans. As pointed out by Brudin et al.
(7), this improvement in image quality is only realized when imaging
normal lungs, since delayed equilibration in areas of very low
ventilation introduces errors in VA with the inhaled
13NN technique. Given the small size of our animals, it was
crucial to use this modification to obtain the highest possible spatial resolution of our instrument, compatible with an appropriate
signal-to-noise ratio.
Aside from the contributions of random noise to image heterogeneity,
there are systematic distortions introduced by PET imaging. For
example, the filtering involved in the convolution-back-projection algorithm not only affects the spatial resolution of the camera but
also results in smearing of the lung edges that artifactually increases
the estimated heterogeneity of an image that includes them. Voxel size
of our images was 0.2 cm × 0.2 cm × 5 mm with the average
amount of 37 ml of lung studied for the 10 animals (from an average of
2,000 voxels/animal). Maximal resolution of the instrument was 4.5 mm × 4.5 mm × 5 mm. The resolution length, defined as the width at
half maximum of a point source, was increased to 1 cm after filtering.
Other effects, such as imperfect uniformity calibration and
transmission corrections, also contribute to an increase in the
CV2 of images derived from single PET scans. Fortunately,
these systematic distortions cancel out in images obtained from the
voxel-by-voxel ratio of two independently acquired PET images such as
in sA, s, and
A/ (25). The
contribution of systematic imaging artifacts to the CV2 of
single PET images such as VA or
was also estimated by imaging a uniform
lung-like phantom and reconstructing, masking, and thresholding the
resulting images in the same way as our images. The CV2
measured from those images was 0.015, which corresponds to 34 and 25%
of the CV2 in the prone position and to 18 and 12% in the
supine position, measured for VA and ,
respectively.
Heterogeneity of A/
A/ was found to be
higher in supine (CV = 0.34) than in prone animals (CV = 0.14). In
the supine position, 66.0% of the CV2 was attributed to a
significant vertical gradient (10.3%/cm). The prone position, in
contrast, had no systematic vertical gradients in
A/, although there was
substantial interanimal variability with gradients ranging from 3.3
to +2.0 %/cm. The residual heterogeneity of the supine position, after
subtraction of the vertical effect, was still significantly greater
than that of the prone position. This might be attributed to the
inadequacy of the linear-regression model in describing nonlinear
vertical gradients. The CI technique to assess the distribution of
A/ was originally
described by Rhodes et al. (21). Although the authors did not study the effect of body position, they reported a CV = 0.21 for supine, spontaneously breathing normal humans. More recently, the same group of
investigators (5) reported a very modest vertical gradient in
A/, whereby
A/ decreased, on
average, by 2%/cm in the ventral-to-dorsal direction, with this
gradient explaining only 20% of the CV2. Remarkably, the
single patient studied in the prone position showed a more substantial
gradient in the direction of gravity than the group of supine patients.
The lower CV2 and gradients in humans compared with our
dogs could be due to a difference in distribution of ventilation
between spontaneously breathing and mechanically ventilated subjects
(20). Also, partial volume effects, exaggerated by a lack of
respiratory gating and poorer spatial resolution of their PET
instrument (1.7 cm) compared with ours (1 cm), must have also
accounted for lower CV in comparison with our study.
Using MIGET, Beck and co-workers (3) reported values of lnSD for the
main A/ distribution
peak of 0.45 and 0.35 for the supine and prone positions, respectively.
For narrow distributions, the lnSD approximates the CV (30), and
the results from MIGET appear somewhat greater than our direct
measurement of CV for A/. Intrinsic
differences between PET and MIGET need to be considered before
discussing these results. MIGET distributions are understood to reflect
the overall heterogeneity of
A/ of the whole lung
and at all physiologically relevant length scales. In normal
experimental conditions, however, the capability of MIGET to resolve
narrow distributions of
A/ is limited to distributions with SDlog 0.2 to 0.3 (19, 29). In contrast, the
heterogeneity in A/
measured by PET in this study is based on actual topographical
distribution but is limited to detect heterogeneities with length
scales greater than the spatial resolution of our PET imaging method (1 cm) and to sampling a single transverse cross section of the lung.
Thus part of the higher CV seen by MIGET, compared with
PET, could possibly be attributed to the limited sampling
and spatial resolution of our study. Although for the supine position
the CV values measured by MIGET (0.45) and PET (0.34) do not appear to
be too different, for the prone position the CV for MIGET (0.35) was
more than double that measured by PET (0.14). Thus, at first glance,
one could attribute the greater CV recovered from MIGET to a limitation
of the technique to resolve narrow distributions (21). However,
considering that CV2, and not CV, is the proper parameter
to compare the differences in heterogeneity between PET and MIGET, our
results and those of Beck et al. (3) are remarkably consistent for
the supine [CV2(MIGET PET) = 0.087] and prone positions
[CV2(MIGET PET) = 0.103]. Thus the
difference in CV2 between MIGET and PET is consistent in
prone and supine animals and could be the result of either the limited
sampling of a single slice or the limited spatial resolution of PET.
In an attempt to estimate whether the limited sampling by a
single-slice camera was responsible for the low CV2
recovered with PET, we studied an additional animal in a multiring PET
camera that imaged 10 contiguous slices of 1-cm thickness. The data
covering >70% of the lung were analyzed with the same algorithms
used for the single-ring data, yielding mean and CV2 values
for each slice and for the ensemble of the 10 slices. Analysis of
VA, sAi,
sAp, s,
, and
A/ images showed that,
although there was substantial variation in
the CV2 among the 10 slices,2 the slice
corresponding to that imaged with our single-ring camera had a
CV2 that deviated by <13% from that of the ensembled
slices. This means that the CV2 of the basal section
selected for our study seems to be a reasonable estimate of the
CV2 of the lung as a whole. We have to conclude that the
difference in heterogeneity recovered by PET and MIGET is probably the
result of the limited spatial resolution of PET. An important corollary from this conclusion is that in the normal animals there must be a
component of heterogeneity in
A/ with a
length scale <1 cm that substantially adds to the in-plane
heterogeneity. The existence and magnitude of these sources of
heterogeneity cannot be assessed from our study.
Fractional A/
Distributions
, and A
distributions of log-transformed and mean-normalized
A/ derived from our
data are comparable with those derived from the MIGET technique (Fig.
10B). Remarkably, the skewness of
these distributions was minimal (Pearson's coefficient close to zero),
and their varied around 3 and 4 (Table 4). This finding means that
the A/ distributions
recovered with our method closely resemble log-normal distributions
and, therefore, give experimental support to the presentation of MIGET
A/ data in
logarithmic scales. Our results are different from those reported by
Rhodes and co-workers (21) for humans showing a normally distributed
dispersion of A/
without skewing when plotted on a linear scale. There are, however, two
methodological differences between the two studies. First, Rhodes et
al. averaged unnormalized
A/ distributions from
the various individuals, and it is possible that averaging of
A/ distributions with different means between subjects could have converged into a normal distribution. Second, to calculate
A/, Rhodes et al. used a method to derive VA from a measurement of tissue density
by using the transmission scan that propagates noise into the
A/ image.
A/ for an animal in
prone position (left) and for one in supine position
(right), where height of surface over the x-y plane
represents relative value of
A/. B:
distributions of A/
as a fraction of total (left), and total
alveolar perfusion (A) (right).
We also found that the spread and shape of the different
A/ distributions,
whether grouped by A, ,
or VA, were not appreciably different from those directly
based on the voxel distribution. This result agrees with the report by
Beck et al. (3) where the SDlog of the main peaks of the
A or distributions
of A/ were
not significantly different.
To separate the causes for the observed differences in heterogeneity of
A/, we discuss
independently the contributions of heterogeneities in VA,
A, and .
VA Distribution
In agreement with previous studies in dogs (15, 27), regional VA per voxel was found to be more uniform in the prone than in the supine position, with the greater heterogeneity in supine animals being mostly attributed to a vertical gradient. The prone position had lower vertical gradients that on average were not significantly different from zero.Distribution of
T between prone
and supine dogs, the mean value of local in supine
dogs (0.06 ml · s1 · cm3)
was substantially greater than that in prone dogs (0.03 ml · s1 · cm3).
These differences stem from the significant gradient in the distribution of local of the supine dogs, which
creates a bias in the estimate to the high--dependent
areas.
Using PET, Brudin et al. (5, 7) indirectly estimated
in healthy supine humans from independent
measurements of A (using 19Ne
inhalation) and A/
(using the CI of 13NN in saline solution), whereas Mintun
et al. (18) used 15O-labeled water intravenously infused
into dogs. Average values of local reported by
Brudin (mean 0.032 ml · s1 · cm3)
and Mintun (ranging from 0.01 to 0.05 ml · s1 · cm3)
were of the same order as our mean values for prone and supine dogs,
respectively.
represents the blood flow normalized by unit of
thorax volume, whereas s represents the blood flow
normalized per unit of VA. It is advantageous to normalize
local by regional gas content, s,
for the following reasons: 1) to be consistent with regional
specific ventilation, already normalized by VA,
has to be normalized by the same variable;
2) normalization by VA compensates for partial
volume effects in voxels with large amounts of nonalveolar tissues such
as large vessels and voxels close to the chest wall or the heart; and
3) systematic imaging artifacts present in single images are
canceled in a ratio image. The vertical gradient in VA of
the supine dog (decreasing gas content in the direction of gravity)
was of the opposite sign of that in , resulting in an
exaggeration of the vertical gradient in s
compared with in the supine position. These findings
suggest that, in the prone position, gravitational forces that would
tend to drive blood flow to dependent regions are largely balanced out
by structural features of the lung while the additive effects of
gravity and structure result in a substantial gravitational gradient in
the supine position.
The heterogeneity of in the supine dogs is in close
agreement with that measured by Brudin and co-workers (5) in supine normal humans using PET, with a CV for of 0.47 and
consistent ventral-to-dorsal gradients in of 11%/cm
explaining 61% of the total CV2. The demonstrated
similarity in the distribution of between supine dogs and humans means that the differences in
A/ between the species
must be attributed to the corresponding differences in regional
ventilation distribution.
Glenny et al. (11), using radioactively labeled microspheres within
transverse planes for the supine position, have reported values of
heterogeneity for dry-tissue-weight-normalized (CV = 0.44) that lie between our CV values for (0.41) and
s (0.47), whereas their CV for the prone position
(0.39) was much greater than our respective findings for
(0.25) or for s (0.18). Beck et
al. (3) also measured with radiolabeled microspheres and reported CV values in of 0.28 and 0.45 for the
prone and supine positions, respectively, in closer agreement with our
results. Glenny and co-workers (13) found vertical gradients in
perfusion with an average of 7%/cm in the supine position and
nonsignificant gradients in the prone position accounting for <6% of
the total heterogeneity. Beck et al. (3) also reported significant
vertical gradient in (6%/cm) for the supine
position that explained as much as 33% of the total heterogeneity in
, whereas there were no significant gradients in the
prone position. The differences between supine and prone CV values of
both and s became smaller after
the removal of the vertical gradient with linear regression. The
residual CV values for supine and
s of 0.32 and 0.24, respectively, were close to the
residual CV reported by Beck et al. (3) (0.30) but, again, much smaller
than those reported by Glenny (10) (0.44).
Part of the reason for the somewhat greater vertical gradient in the
supine position measured with PET by us and Brudin et al. (5), compared
with those measured from injected microspheres, could be due to the
gravitational gradient in VA at FRC. The lower gradient in
recovered by the microsphere technique in the supine position could be caused by the inflation of the lungs to total lung
capacity (TLC), since, in the supine dog, greater local expansion of
dorsal regions (15) has been found, compared with that of ventral
regions. Thus, after inflation to TLC, the relative number of
microspheres per piece in the dependent region should be lower than the
relative blood flow per voxel measured by PET in vivo. In other words,
for the supine position, normalization of by VA should tend to exaggerate the gravitational gradient in
, whereas normalization per local tissue mass should
underestimate it.
Recently, Brudin and co-workers (5, 6) proposed that the vertical
gradients in regional blood content (Vb) could be the link between
VA, , and A
by affecting regional lung weight and by competing for space with
VA. Although this mechanism could possibly explain the
gradients in the supine position, it fails to explain the positive
spatial correlation between the variables in the prone position. Active
mechanisms by which regional differences in VA could affect
or control the distributions of are not known, but
it is possible that regional differences in parenchymal smooth muscle
tone or transpulmonary pressure could be mechanistically affecting the
distributions of .
There are other methodological differences between our measurement with PET and those performed with microspheres, which need to be considered when comparing these studies. First, the fractal approach of Glenny and Robertson (13) suggests that a smaller sample size should result in greater measured heterogeneity. Our resolution voxels were of 1 cm2 and a slice thickness of 5 mm, resulting in a voxel volume of 0.5 cm3, whereas Glenny and Robertson's pieces were cubes of 1.3-cm side (1.9 cm3), much greater than Beck's cylindrical pieces of 0.5-cm diameter and 1.5-cm length (0.3 cm3). If one accounts that the lung pieces from the microsphere studies were obtained from excised lungs inflated to TLC, thus having a smaller volume at FRC, and if the longest dimension of the sample is used as an estimator of the spatial resolution of the method, all three studies would have had a similar spatial resolution close to 1.0 cm. This could explain the similarities in CV values between methodologies without necessarily contradicting the fractal characteristics proposed by Glenny and Robertson (13).
A second difference is that with PET we are considering a single cross
section of the lungs, whereas the microsphere studies sample the entire
lung. As mentioned, experimental data from a multislice PET camera have
shown that heterogeneity in measured by PET from a
single basal slice appears to reflect the heterogeneity of the rest of
the lung, meaning that this is an unlikely cause of any differences.
Finally, one could argue that homogenization of the PET images of
could have taken place by convective mixing in the
lung during imaging because of cardiogenic oscillations. To assess the
magnitude of this potential effect, we examined the differences in
CV2 between the two sequential 30-s images acquired during
apnea. In the prone position, we found no statistical difference
between the CV2 of those two images or that after the
tracer kinetics correction, described in the companion paper (17). Thus
little or no significant homogenization occurred in the prone position
at the length scales visible by our method (1 cm). However, in the
supine position, where intraregional gradients in tracer content were
much greater than those in the prone position, there was a small but
significant (P < 0.03) drop in the CV2 of 16.0 ± 7.0% between the first and the second 30-s image. Although this
finding supports the argument that intraregional mixing during the
apneic period partially homogenized the distribution of the tracer in
the lungs, the correction for tracer kinetics yielded a
image with a CV2 that was not
significantly different from that of the first 30-s image. This
demonstrates that the voxel-by-voxel tracer kinetics correction
successfully compensated for the drop in heterogeneity measured between
the first and the second image.
Spatial Correlations
vs. VA.
In the prone position, there was a high degree of spatial correlation
(R = 0.74) among these variables, meaning higher blood flow
to areas of greater gas content. In the supine position, the
correlation between and VA was much
lower (R = 0.23) because the gravitational gradients in
were of opposite sign and, therefore, canceled, in
part because of the nongravitational correlation. Hakim et al. (14)
reported substantial radial gradients in , and Glenny
et al. (12) found that radial gradients explained as much
as 13% of the total heterogeneity. Although visual inspection of our
images appeared to demonstrate lower in the lung
periphery compared with that in the center, these apparent radial
gradients were also present in the VA image and canceled
out completely in the s image (Fig. 4). Because no
radial gradients were seen in the
A/ images,
their physiological importance is questionable.
sA vs. s.
Perfused areas had sAp highly
correlated with s. This correlation was not merely
due to the random noise of the common image, since a
correction was applied to eliminate this effect, as described in
METHODS. The fact that s and
sAi were not correlated could
be due to the presence of noise in
sAi (due to relatively lower
number of counts in the washout image) and to the ventilation of serial
and alveolar dead spaces included in
sAi and not in
sAp.
Differences Between sAi
and sAp
A from these indexes of lung expansion
may not be accurate. An index of effective specific
A per unit of alveolar volume, i.e.,
sA, has been estimated from the
steady-state distribution of a rapidly decaying inhaled isotope gas
such as neon (5, 6) or from the washout rate of a previously
equilibrated inhaled tracer gas such as 13NN (27, 28, 31).
Both of these methods truly assess a rate of gas transport into or out
of a resolution element but include in the calculation transport from
nonalveolar and nonperfused spaces that do not necessarily participate
in the exchange of respiratory gases.
We assessed the distribution of sA from
the kinetics of the tracer 13NN measured by two different
methods: from the washout after equilibrated inhalation of the tracer
(sAi), as in the past (27,
28, 31), and also by the ratio of local ,
measured from the apneic distribution of an intravenously infused
13NN-labeled saline bolus, divided by the local tracer
content during the constant-rate infusion protocol
(sAp). Because voxel
13NN content after equilibration is proportional to
intraregional gas volume, sAi
represents a volume-weighted mean
A of all intraregional
gas-filled areas including distal alveoli as well as unperfused alveoli
and serial dead space. In contrast, 13NN after an
intravenous bolus infusion should mostly reside in distal perfused
alveolar units. Thus sAp can
be taken to represent a perfusion-weighted mean
A of intraregional perfused alveoli. We speculate that sAi and
sAp should measure
related but different physiological entities affected in different ways
by heterogeneity of A and
at subresolution length scales, since, for
sAi and
sAp to be equal, the
distribution of A has to be either uniform or totally uncorrelated with .
Using that intersubject variability in ventilation we found that the
mean value of local sAi
within the lung field
i) was correlated with, but systematically lower than, those from sAp, suggesting that,
although related, the inhaled-tracer method underestimated ventilation
measured by perfused-tracer method. In terms of the spatial
distribution of sA, both methods yielded similar values of CV and showed lower heterogeneity in the prone position compared with supine. In the prone position, there were no
significant vertical gradients in
sAi or in
sAp. However, in the supine
position, sAp showed
significant vertical gradients, whereas
sAi did not. We
speculate that the difference in results between these methods could be
attributed to the effects of local dead space (stratified and alveolar)
and to intraregional heterogeneity of local
A being spatially correlated with that of
at length scales below the spatial resolution of the
instrument. This interpretation would be consistent with, and explain
why, local values of sAp were
greater than those of sAi.
Furthermore, given the vertical gradient in seen in
the supine position, this interpretation could also explain the
corresponding gradient in sAp
in that position. However, to reconcile and understand the differences between sAp and
sAi further experimentation
is needed.
Relative Contributions of A and
to
A/ Heterogeneity
A
and to the heterogeneity of the
A/. For small
levels of CV2, and to a first-order approximation, the
heterogeneity of A/ (CV 2A/) was estimated from the heterogeneities of
A
(CV 2A)
and
(CV2)
following the equation
|
is the spatial correlation between A and
. This approach was applied to data
compiled from various investigators for the gas-exchange variables.
To cancel the effects of reconstruction artifacts that cause a
correlation between A and
, the above relationship was expressed in terms of
ratio images by normalizing the variables A and by regional gas
content
|
(0.2) and
CV 2sA
(0.06) in the supine position, compared with our respective
CV2 values of 0.22 and 0.06. For the prone position,
however, their estimates for
CV 2s
(0.08) and
CV 2sA
(0.04) are substantially higher than our respective values of 0.034 and
0.026. Also, the degree of spatial correlation between
sA and s, estimated by
Wilson and Beck to be negligible in the prone position, was found to be
quite high in both prone
(RsA,s = 0.69) and supine
(RsA,s = 0.81) positions. On the bivariate distributions of
log(sA) vs. log(s) (Fig. 8), the height of the surface over the x-y
plane represents the fraction of voxels containing a given combination
of sA and s. Because
the data is mean-normalized and log-transformed, isopleths of constant
A/ are straight lines
on the x-y plane running 45° form the x-axis, and the
A/ distribution
corresponds to the integral projection of the distribution along these
isopleths. The fact that most of the distributions data lay parallel to
constant A/
isopleths in both supine and prone positions illustrates the high
degree of correlation between
sAp and s
and explains why the heterogeneity of
A/ is lower than if
these variables had not been correlated (Fig. 3).
We can conclude that the higher heterogeneity of
A/ in supine
compared with prone position was primarily caused by a consistent gravitational gradient in regional that is only
partially compensated by a gradient in
A. Our data support the concept that, in
the prone position, gravitational forces acting on blood and
parenchymal tissues are largely balanced out by dorsoventral
differences in lung structure avoiding vertical gradients in
VA, A, and
. In the supine position, the additive effect of
gravity and structure results in substantial gravitational gradients in
VA, A, and .
ACKNOWLEDGEMENTS
We thank Dr. C. A. Hales for his support and contributions to this project. We also thank Nikolai Alguri and Desmond Seow for their efforts to acquire and process the data from the multiring PET camera and Dr. A. Zaslovski for statistical advice.
FOOTNOTES
and Y X, where X = log X and Y = log Y. Suppose
X = x + ex and Y = y + ey, where x and y are noise-free values of the logged variable, ex and
ey are noise with estimated variances
2ex and
2ey, respectively, and let 
= y x. Then we can estimate
2x
= covariance (x,
) = covariance (X, Y X) 2ex, 2 = variance
( y x) = variance
(Y X) 2ey 2ex, and
2y = variance ( y) = variance (Y) 2ey. Finally, we can use these
estimates to calculate a corrected correlation coefficient
Rs = 2x/(x).
2
CV2 ranged from 0.036 to 0.31 for
A/, from 0.084 to 0.48 for , and from 0.073 to 0.55 for
s.
Received 22 March 1995; accepted in final form 12 November 1996.
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M. F. V. Melo, R. S. Harris, J. D. H. Layfield, and J. G. Venegas Topographic Basis of Bimodal Ventilation-Perfusion Distributions during Bronchoconstriction in Sheep Am. J. Respir. Crit. Care Med., April 1, 2005; 171(7): 714 - 721. [Abstract] [Full Text] [PDF]
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W. A. Altemeier, S. McKinney, M. Krueger, and R. W. Glenny Effect of posture on regional gas exchange in pigs J Appl Physiol, December 1, 2004; 97(6): 2104 - 2111. [Abstract] [Full Text] [PDF]
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D. Rimeika, S. Nyren, N. P. Wiklund, L. R. Koskela, A. Torring, L. E. Gustafsson, S. A. Larsson, H. Jacobsson, S. G. E. Lindahl, and C. U. Wiklund Regulation of Regional Lung Perfusion by Nitric Oxide Am. J. Respir. Crit. Care Med., August 15, 2004; 170(4): 450 - 455. [Abstract] [Full Text] [PDF]
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J. Petersson, A. Sanchez-Crespo, M. Rohdin, S. Montmerle, S. Nyren, H. Jacobsson, S. A. Larsson, S. G. E. Lindahl, D. Linnarsson, R. W. Glenny, et al. Physiological evaluation of a new quantitative SPECT method measuring regional ventilation and perfusion J Appl Physiol, March 1, 2004; 96(3): 1127 - 1136. [Abstract] [Full Text] [PDF]
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M. F. Vidal Melo, D. Layfield, R. S. Harris, K. O'Neill, G. Musch, T. Richter, T. Winkler, A. J. Fischman, and J. G. Venegas Quantification of Regional Ventilation-Perfusion Ratios with PET J. Nucl. Med., December 1, 2003; 44(12): 1982 - 1991. [Abstract] [Full Text] [PDF]
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J. C. Richard, M. Janier, F. Lavenne, V. Berthier, D. Lebars, G. Annat, F. Decailliot, and C. Guerin Effect of position, nitric oxide, and almitrine on lung perfusion in a porcine model of acute lung injury J Appl Physiol, December 1, 2002; 93(6): 2181 - 2191. [Abstract] [Full Text] [PDF]
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G. Musch, J. D. H. Layfield, R. S. Harris, M. F. V. Melo, T. Winkler, R. J. Callahan, A. J. Fischman, and J. G. Venegas Topographical distribution of pulmonary perfusion and ventilation, assessed by PET in supine and prone humans J Appl Physiol, November 1, 2002; 93(5): 1841 - 1851. [Abstract] [Full Text] [PDF]
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G. G. Galletti and J. G. Venegas Tracer kinetic model of regional pulmonary function using positron emission tomography J Appl Physiol, September 1, 2002; 93(3): 1104 - 1114. [Abstract] [Full Text] [PDF]
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D. B. Willey-Courand, R. S. Harris, G. G. Galletti, C. A. Hales, A. Fischman, and J. G. Venegas Alterations in regional ventilation, perfusion, and shunt after smoke inhalation measured by PET J Appl Physiol, September 1, 2002; 93(3): 1115 - 1122. [Abstract] [Full Text] [PDF]
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K. Suga, N. Ogasawara, M. Okada, T. Tsukuda, N. Matsunaga, and M. Miyazaki Lung perfusion impairments in pulmonary embolic and airway obstruction with noncontrast MR imaging J Appl Physiol, June 1, 2002; 92(6): 2439 - 2451. [Abstract] [Full Text] [PDF]
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R. S. Harris, D.-B. Willey-Courand, C. A. Head, G. G. Galletti, D. M. Call, and J. G. Venegas Regional VA, Q, and VA/Q during PLV: effects of nitroprusside and inhaled nitric oxide J Appl Physiol, January 1, 2002; 92(1): 297 - 312. [Abstract] [Full Text] [PDF]
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K. C. Beck and T. A. Wilson Variance of ventilation during exercise J Appl Physiol, June 1, 2001; 90(6): 2151 - 2156. [Abstract] [Full Text] [PDF]
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C. Marcucci, D. Nyhan, and B. A. Simon Distribution of pulmonary ventilation using Xe-enhanced computed tomography in prone and supine dogs J Appl Physiol, February 1, 2001; 90(2): 421 - 430. [Abstract] [Full Text] [PDF]
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J. G. Venegas and G. G. Galletti Low-pass filtering, a new method of fractal analysis: application to PET images of pulmonary blood flow J Appl Physiol, April 1, 2000; 88(4): 1365 - 1373. [Abstract] [Full Text] [PDF]
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C. M. Mann, K. B. Domino, S. M. Walther, R. W. Glenny, N. L. Polissar, and M. P. Hlastala Redistribution of pulmonary blood flow during unilateral hypoxia in prone and supine dogs J Appl Physiol, June 1, 1998; 84(6): 2010 - 2019. [Abstract] [Full Text] [PDF]
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S. M. Mijailovich, S. Treppo, and J. G. Venegas Effects of lung motion and tracer kinetics corrections on PET imaging of pulmonary function J Appl Physiol, April 1, 1997; 82(4): 1154 - 1162. [Abstract] [Full Text] [PDF]
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