| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Departments of 1 Medicine and of 2 Physiology and Biophysics, University of Washington, Seattle, Washington 98195-6522
 |
ABSTRACT |
|---|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
Numerical methods for determining end-capillary gas contents for ventilation-to-perfusion ratios were first developed in the late 1960s. In the 1970s these methods were applied to validate distributions of ventilation-to-perfusion ratios measured by the multiple inert-gas-elimination technique. We combined numerical gas analysis and fluorescent-microsphere measurements of ventilation and perfusion to predict gas exchange at a resolution of ~2.0-cm3 lung volume in pigs. Oxygen, carbon dioxide, and inert gas exchange were calculated in 551-845 compartments/animal before and after pulmonary embolization with 780-µm beads. Whole lung gas exchange was estimated from the perfusion- and ventilation-weighted end-capillary gas contents. Before lung injury, no significant difference existed between microsphere-estimated arterial PO2 and PCO2 and measured values. After lung injury, the microsphere method predicted a decrease in arterial PO2 but consistently underestimated its magnitude. Correlation between predicted and measured inert gas retentions was 0.99. Overestimation of low-solubility inert gas retentions suggests underestimation of areas with low ventilation-to-perfusion ratios by microspheres after lung injury. Regional deposition of aerosolized and injected microspheres is a valid method for investigating regional gas exchange with high spatial resolution.
ventilation heterogeneity; pulmonary blood flow; ventilation-perfusion matching; aerosol; fluorescent microspheres
| |
INTRODUCTION |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
THE PRIMARY DETERMINANT of gas exchange efficiency in
the lung is the matching of alveolar ventilation
(
A) and
blood flow (
) (5, 16). Ventilation-perfusion
(A/)
matching can be assessed by determining ventilation- and
perfusion-weighted A/
distributions in the lung by using the multiple inert-gas-elimination technique (MIGET) (24). This method is useful for determining the
amount of perfusion through
low-A/
areas and therefore the impact of
A/
heterogeneity on gas exchange; however, it cannot provide spatial
information about regional ventilation and perfusion distributions.
Recently, studies using intravenously embolized radioactive
microspheres have observed significant heterogeneity of regional
perfusion that increases as resolution improves (8, 9, 13). Efficient
gas exchange implies a similar degree of ventilation heterogeneity that
correlates well with regional perfusion, at least to the level of the
respiratory bronchiole. Below that level of scale, gas diffusion
increasingly dominates convective forces, and further perfusion
heterogeneity may be compensated for by diffusional gas mixing within
the gas-exchanging unit.
High-resolution measurements of regional lung expansion by radiopaque topographical markers (12) and computed tomography (19) have demonstrated significant spatial heterogeneity. However, these techniques measure static volume distribution during an inspiratory pause and may not represent true regional ventilation because gas redistributes between regions of different time constants after cessation of inspiratory flow. These methods also do not allow simultaneous measurement of regional perfusion and therefore cannot be validated by predictions of gas exchange as initially done with MIGET (15, 25).
Recently, Robertson and co-workers (17) reported
high-spatial-resolution measurements of regional ventilation by using
aerosolized 1-µm fluorescent microspheres. They showed that
simultaneously aerosolized pairs of microspheres yield regional
distributions with a high degree of correlation and with minimal
deposition in airways. They also demonstrated a high degree of
correlation between simultaneously aerosolized and intravenously
injected microsphere distributions. Although this suggests that
aerosolized microsphere deposition is an accurate marker of regional
ventilation, no calculations of gas exchange were done to confirm that
physiologically relevant
A/
distributions were measured.
To evaluate aerosolized 1-µm-microsphere deposition as a measurement
of regional ventilation, we measured
A/
distributions in five juvenile pigs with normal and abnormal gas
exchange by simultaneously using aerosolized and injected fluorescent
microspheres. These data are used to predict regional alveolar and
end-capillary tensions of both respiratory and inert gases of varying
solubility in multiple compartments of
~2-cm3 volume. Whole lung gas
exchange is determined from mean perfusion- and ventilation-weighted
end-capillary gas contents.
| |
METHODS |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
The experiments were approved by the Animal Care Committee at the University of Washington. Briefly, regional ventilation and perfusion were measured in five mechanically ventilated, normal pigs by using aerosolized 1-µm microspheres and injected 15-µm fluorescent microspheres. Measurements were repeated after vascular embolization with 780-µm polystyrene beads. Data were collected for MIGET analysis at all time points for the five animals. A complete description of the experimental protocol may be found in our companion paper (2).
Generation of
A/
Distributions from Microsphere Data
Numerical Gas Analysis
Data were analyzed by using an Excel 5.0 spreadsheet and macros written with Visual Basic for Applications (Microsoft, Redmond, WA). The program uses ventilation and perfusion data (ml/min) to determine theA/
distribution and its effect on respiratory and inert gas exchange. The
data may also be manipulated to allow comparison with the
50-compartment model of
A/
distribution provided by MIGET software.
Alveolar tensions of O2 and
CO2
(PAO2
and
PACO2,
respec-tively) and end-capillary
O2 and
CO2 contents
(CecO2 and
CecCO2,
respectively) for each lung piece are determined by solving mass
balance equations for each gas, given that piece's A/
(Fig. 1). A full discussion of the
calculations may be found in the
APPENDIX.
|
Once CecO2 and CecCO2 are calculated for each lung piece, they are weighted by each piece's perfusion, summed, and divided by the total cardiac output to calculate the arterial contents, CaO2 and CaCO2, respectively. The arterial gas tensions, PaO2 and PaCO2, are then calculated by using the developed software. The mixed PAO2 used to calculate the alveolar-arterial O2 difference (A-aDO2) is calculated by summing each piece's ventilation-weighted PAO2 and dividing by the total alveolar ventilation. Assuming complete equilibration between the alveolar gas and end-capillary blood, this gives
|
(1) |
i
is the alveolar ventilation to piece
i, n
is the number of pieces analyzed from the lung, and
PecO2 is the
end-capillary O2 tension. The
microsphere-estimated
A-aDO2 (A-aDO2 MS)
is compared with the
A-aDO2
calculated with the alveolar gas equation (3), the measured arterial
gas tensions, and the measured respiratory quotient
(A-aDO2 ABG).
The
A-aDO2 MS
includes only gas exchange abnormalities from
A/
heterogeneity, as opposed to the
A-aDO2 ABG,
which includes abnormalities caused by intracardiac and postpulmonary
shunt as well as any possible diffusion limitation.
The arterial retentions [arterial pressure (Pa)/mixed venous
pressure (
)] of the six inert gases
were estimated from the measured
A/
distribution. Because an inert gas does not interact with components of
blood, its end-capillary retention [end-capillary pressure
(Pec)/] depends only on the gas
solubility in plasma (
) and the
A/
of that particular lung compartment (18)
|
(2) |
|
(3) |
i
is the perfusion to piece i, and CO is
the total cardiac output. The calculated arterial retentions for each
inert gas were compared with the retentions measured on a gas
chromatograph (model 3300, Varian, Palo Alto, CA).
Statistics and Data Manipulation
All data, unless otherwise stated, are presented as means ± SD. Paired t-tests are used for statistical comparisons. Up to eight pieces were excluded from each data set because of unexplained, very high fluorescence signal, usually in the orange color. For numerical gas analysis, no pieces were excluded because of airway content; those with airway content
25%
generally had very low ventilation and perfusion signals and did not
significantly contribute to gas exchange.
| |
RESULTS |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
Aerosolized and injected microsphere distributions were measured in
551-851 pieces/animal. Nine measurements were made in normal lungs
and five measurements were made in lungs with abnormal gas exchange.
Only one measurement was made with normal gas exchange in the first
animal due to an aerosol generator malfunction. The developed software
found a solution for end-capillary gas contents for almost all lung
pieces. A solution was not found in 0-9 pieces/data set. This
occurred exclusively in pieces with low flow and a
A/ > 200; therefore, the impact on estimates of mixed arterial contents was negligible.
In the normal lungs, the mean microsphere-estimated PaO2 was 110 Torr (Fig. 2) and the mean PaCO2 was 33.3 Torr. Neither was significantly different from the measured values. The mean difference between A-aDO2 MS and A-aDO2 ABG of 0.36 was not significant (Table 1). MIGET consistently underestimated the PaO2 (Fig. 2) and overestimated PaCO2 in the normal lungs.
|
|
In the abnormal lungs, microsphere-measured ventilation and perfusion distributions predicted a decrease in PaO2 and an increase in PaCO2; however, the magnitude of these changes was consistently underestimated (Fig. 2). The A-aDO2 MS differed from the A-aDO2 ABG by a mean of 19.1. MIGET also consistently underestimated the degree of gas exchange abnormality after embolization but to a lesser degree (Fig. 2).
Microsphere-measured
A/
distributions predicted arterial retentions of inert gases of varying
solubilities with high precision. Grouping all animals and conditions
together, the correlation of microsphere-predicted retentions for six
inert gases with measured retentions is 0.992 (Fig.
3A).
When only preembolization data are evaluated, the correlation between
microsphere-estimated and measured retentions is 0.995, whereas, when
only postembolization data are considered, the correlation is 0.989. A
plot of the difference between measured and predicted retentions
against measured retentions (Fig.
3B) reveals a consistent bias to
underestimate the arterial retention of low-solubility gases,
suggesting an underestimation of
low-A/
units by the microsphere method. This bias increases when
gas exchange has been impaired.
|
High-resolution measurements of ventilation and perfusion allow the
effect of
A/
distribution on gas exchange to be evaluated with a number of novel
approaches. A scattergram of perfusion on the abscissa and ventilation
on the ordinate produces a plot with isopleths of constant
A/,
permitting evaluation of the contribution of individual pieces to
overall gas exchange (Fig. 4). For example,
a piece with high perfusion located along a
low-A/ isopleth will affect PaO2 more
than a piece with similar
A/ but lower perfusion. Pieces may also be grouped by
CecO2 to
construct a flow-weighted histogram (Fig.
5). Finally,
A/
data may be grouped into any number of perfusion- or
ventilation-weighted bins and plotted as a frequency polygon (Fig.
6). Using 50 compartments allows
direct comparison with
A/
measurements from MIGET.
|
|
|
| |
DISCUSSION |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
The primary finding of this study is that measurement of regional ventilation with aerosolized 1-µm microspheres, when combined with simultaneous measurement of regional perfusion, can predict whole lung gas exchange of both respiratory gases and inert gases of widely varying solubility.
In normal lungs, high-resolution measurements of ventilation and perfusion by microspheres accurately predict PaO2 and PaCO2. Because arterial blood is fully saturated in normal lungs, small differences in O2 content are associated with large differences in PaO2 due to the low solubility of O2 in plasma. Thus even small errors in the calculated CaO2 would be magnified when calculating PaO2.
In this study, MIGET significantly underestimated
PaO2 and overestimated
PaCO2, probably due to consistent
underestimation of the mean
A/
distribution. MIGET algorithms described a bimodal ventilation
distribution with a high
A/
component in the majority of animals studied. Given a fixed total
minute ventilation, this causes the perfusion-weighted distribution to shift to a lower mean
A/
and an underestimation of gas exchange. This erroneous identification
by MIGET of a
high-A/
mode may be caused by airway excretion of highly soluble gases,
particularly acetone (7, 22, 23).
The microsphere-measured
A/
distributions significantly underestimate gas-exchange impairment after
vascular embolization. Predicted PaO2 values
all decreased after embolization but were consistently overestimated.
There are three possible explanations for this systematic error. First,
the degree of
A/
heterogeneity may be underestimated by the microsphere method. This
could occur if a tissue cube receives blood flow from two different
vessels. If one vessel has reduced flow postembolization and the other has increased flow, our method does not measure this change and therefore underestimates
A/
heterogeneity within that tissue cube (Fig.
7A).
This type of error is possible because the lungs are not diced along
vascular boundaries. A second potential explanation for the
underestimated PaO2 is development of a
diffusion limitation postembolization. Calculation of
CaO2 in both our method and MIGET assumes equilibration between
PecO2 and
PAO2.
If flow redistribution increases transit time sufficiently for
some capillaries, this assumption may be invalid (Fig.
7B). Diffusion limitation has been
proposed as an explanation for overestimation of
PaO2 by MIGET in studies of pulmonary
embolism (4, 20). Given that both methods assume
end-capillary-alveolar equilibrium of gas tensions and that the
microsphere-estimated PaO2 is
consistently greater than MIGET-estimated
PaO2 after embolization, it is
unlikely that diffusion limitation is the sole explanation for our
overestimation of PaO2. A third possible
cause for our overestimatation of PaO2 could be an underestimation of right-to-left shunt. The microsphere technique measures intrapulmonary shunt
(A/ = 0) only if the entire lung region examined receives no
ventilation. Shunt occurring below this resolution would decrease the
cube's microsphere-measured A/
but causes an overestimation of the cube's
CecO2.
Similarly, microsphere measurements of pulmonary perfusion cannot
measure extrapulmonary shunt. Neither mechanism seems to be the source of error in our studies because MIGET does not demonstrate an increase
in shunt postembolization. Because MIGET is based on the retention of
intravenously infused inert gases in the arterial blood, it is not
limited by lung-piece size and does measure intracardiac shunt. MIGET
does not measure postpulmonary shunt caused by the bronchial
circulation or the Thebesian veins; however, gas-exchange abnormalities
due to postpulmonary shunt will be equally underestimated by MIGET and
cannot explain the disparity between the microsphere- and
MIGET-estimated PaO2.
|
Gas exchange may also be evaluated by the
A-aDO2.
An increase in
A-aDO2
is caused by
A/
heterogeneity, shunt, or a diffusion limitation.
A/
heterogeneity increases the
A-aDO2
because PAO2
is calculated by a ventilation-weighted average of the equilibrated
oxygen tension in each piece, whereas
PaO2 is calculated by a flow-weighted
average of oxygen tension in each piece. Thus pieces with high
A/
that have higher
PecO2 contribute more to the
PAO2,
and pieces with a low
A/ that have lower
PecO2
contribute more to PaO2. Although a
significant difference does not exist between the
A-aDO2 ABG
and the
A-aDO2 MS in the normal lungs, the individual data provide interesting insights. First, in five of the nine preembolization measurements, the
A-aDO2 MS was lower than the
A-aDO2 ABG.
Because diffusion limitation is not believed to occur in the normal
lung, the difference can only be explained by underestimation of low
A/
perfusion or shunt by the microsphere method. The normal presence of a
small shunt from the Thebesian vessels and the bronchial circulation
will contribute to this discrepancy; however, the lower estimate of A-aDO2
by microspheres raises the possibility that
A/
heterogeneity is being underestimated. Of note, three of the nine
A-aDO2 ABG preembolizations are negative, which is physiologically impossible. This is likely the result of a summation of errors in measurements of
PaCO2 and the respiratory quotient used
in the alveolar gas equation. The
A-aDO2 MS
increased postembolization in all five animals, consistent with the
increased
A/
heterogeneity seen with both microsphere and MIGET methods. However,
the
A-aDO2 MS was consistently less than the
A-aDO2 ABG,
most likely resulting from unmeasured
A/
heterogeneity below the scale of resolution for this method.
Predicting inert gas exchange for a given
A/
distribution has several advantages over respiratory gas exchange.
First, inert gases do not interact with blood components or each other; therefore, gas-exchange prediction only involves solving mass balance
equations without iterative techniques. Second, by examining the
predictions of gas exchange for gases of varying solubilities, some
inference may be made as to sources of error. Figure
3B shows that the microsphere
technique consistently underestimates the arterial retention of gases
that are poorly soluble in blood (sulfur hexafluoride and ethane).
Because these gases are readily excreted into the alveoli when exposed
to ventilation, this finding suggests an underestimation of
low-A/
perfusion by the microsphere method. Underestimation of
heterogeneity occurring below the microsphere method's resolution
implies that there should be a consistent overestimation of retentions
of high-solubility gas (e.g., acetone) due to unmeasured high
A/
units. Figure 3B suggests that the microsphere method tends to overestimate acetone retention.
The calculated inert gas retentions support the hypothesis that
unmeasured
A/
heterogeneity exists below the present resolution of the microsphere
method. The measured heterogeneity of regional perfusion is scale
dependent and increases as resolution improves beyond the resolution
obtained in these experiments (8). Similarly, regional ventilation has
scale dependence with increasing heterogeneity, at least to the
resolution obtained in these experiments (1). A similar volume of human
lung at total lung capacity would have ~10 acini (10); therefore,
2.0-cm3 lung pieces from a 14-kg
pig has >10 acini, suggesting that measured regional ventilation
heterogeneity could increase at smaller resolutions. Because
A/
heterogeneity is determined by the individual heterogeneities of the
regional perfusion and ventilation distributions minus a component
determined by the correlation of regional perfusion and ventilation
(27), resolution-dependent underestimation by microspheres of the true
heterogeneity of regional perfusion and of regional ventilation will
likely result in overestimation of gas exchange.
The results of this study support the use of aerosolized microspheres to measure regional ventilation. In normal lungs, the 2.0-cm3 regional measurements obtained in this study provide adequate resolution for evaluating gas exchange. The overestimation of arterial oxygen tension in embolized lungs is likely due to the presence of resolution-dependent underestimation of the true heterogeneity of ventilation and perfusion. These results emphasize the importance of regional perfusion and ventilation heterogeneity on a small scale in determining gas exchange. Studies with higher resolution are warranted to determine whether the accuracy of microsphere prediction of gas exchange in abnormal lungs can be improved. This technique will also be useful in determining whether regional heterogeneity in perfusion and ventilation are as important in gas exchange abnormalities of other disease models and in exploring the relative importance of correlation between regional ventilation and perfusion.
| |
APPENDIX |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
Numerical Gas Analysis
The mass balance equation for O2 is
|
(4) |
I is the
inspired regional ventilation,
A is the
expired regional ventilation,
O2
is the O2 content of mixed venous
blood, and k is a
temperature-dependent factor that converts between
STPD and
BTPS units. Because the inspired
partial pressure of CO2 is ~0,
the term
I/
drops out of the mass balance equation for
CO2
|
(5) |
CO2
is the CO2 content of mixed venous
blood. Introducing the term
I/
results in three unknown variables for the two equations. To solve
Eqs. 4 and 5, the mass balance of N2 and the summation of partial
pressures must also be considered
|
(6) |
|
(7) |
N2 is
the blood-gas partition coefficient (defined as
k × the solubility of
N2, 0.0017 ml/100 ml blood);
PecN2is the
partial pressure of N2 in the
end-capillary blood;
N2
is the partial pressure of N2 in
mixed venous blood; PB is the
barometric pressure; and
PH2O is the
partial pressure of water in fully saturated gas at the given
temperature. Because N2 does
not interact with Hb, partial pressure is directly proportional to
content by the solubility of N2.
Furthermore, because there is no net exchange of
N2 between the environment and the
blood,
N2
may be assumed to equal
PIN2.
Assuming no diffusion limitation of the respiratory gases, the end-capillary tension of gas X is equal to its alveolar tension. Thus CecO2 and CecCO2 are related to PAO2 and PACO2 by the O2-Hb and CO2-Hb dissociation curves.
The solution of Eqs. 4-7 may be
simplified by solving Eq. 4 for
I/,
substituting this into Eq. 6, and
solving for
PAN2. Finally, this may be substituted into Eq.
7 and, with some rearrangement, yield
|
|
(8) |
A/
by using Eqs. 5 and 8.
Because PecO2 and PecCO2 are interdependent as determined by the Bohr and Haldane effects, the solution of these equations requires an iterative process. The algorithm utilized is fully described by Olszowka and Wagner (15). Briefly, two initial estimates are made of end-capillary pH (pHec) and PecO2, and these are used to calculate PecCO2, CecO2, and CecCO2. If the results do not satisfy Eqs. 5 and 8 within preset tolerance limits, the results from the first two estimates are used to make a third estimate of pHec and PecO2. This process is iterated until Eqs. 5 and 8 are satisfied within preset tolerances. If the software does not converge on a satisfactory solution after 50 iterations, then that piece is excluded from further analysis and the program moves to the next piece.
The subroutines used to calculate PecCO2, CecO2, and CecCO2 for a given pHec and PecO2 were developed by Olszowka and Farhi (14) to describe whole lung gas exchange. We apply them to determine gas exchange for each piece of lung tissue, resulting in 551-845 compartments of gas exchange. These compartments may be perfusion or ventilation weighted and averaged to yield whole lung gas exchange. Briefly, O2 content is calculated by first describing a "virtual" PecO2 or what the actual PecO2 would be on a normal, human O2-Hg dissociation curve at a pH of 7.4 and a PecCO2 of 40 Torr. This is done assuming the shape of the dissociation curve is similar under different physiological conditions and between species and then calculating the shift caused by temperature, base excess, and species-specific P50 (the PecO2 at standard conditions and 50% Hb saturation). For these experiments using pigs, the P50, temperature coefficient, and fixed-acid Bohr coefficient used are 35.7 Torr, 0.016, and 0.441, respectively (26). The virtual PecO2 is used to calculate an Hb saturation by using a formula described by Severinghaus (21). The saturation is used in the calculation of PecCO2 at 37°C, which is used to calculate CO2 content. Finally, PecCO2 is calculated at the given temperature, assuming a constant CO2 content.
Data for the gas-analysis computations are entered into a simple
template in an Excel 5.0 workbook. The required inputs for solving the
arterial gas contents are the regional ventilations and perfusions
(ml/min), species type, barometric pressure, Hb, body temperature,
inspired oxygen fraction, mixed venous pH, oxygen tension, and carbon
dioxide tension. A specific P50
value may be entered if measured. If inert gas retentions are desired,
then the solubilities must be entered. The output consists of regional and mixed arterial gas contents, a brief statistical summary of the
A/
distribution, and several graphical displays corresponding to Figs.
4-6. The software will run on Macintosh OS and Windows 95 operating systems and is available from the author on request.
| |
FOOTNOTES |
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests: W. A. Altemeier, Div. of Pulmonary and Critical Care Medicine, BB-1253 Health Sciences Bldg., Box 356522, Seattle, WA 98195-6522 (E-mail: billa{at}u.washington.edu).
Received 17 March 1998; accepted in final form 26 August 1998.
| |
REFERENCES |
|---|
|
Top
Abstract
Introduction
Methods
Results
Discussion
Appendix
References
|
|---|
1.
Altemeier, W. A.,
M. M.,
S. E. McKinney,
H. T. Robertson,
and
R. W. Glenny.
Regional ventilation has fractal properties that are posture dependent (Abstract).
Am. J. Respir. Crit. Care Med.
157:
A370,
1998.
2.
Altemeier, W. A.,
H. T. Robertson,
S. E. McKinney,
and
R. W. Glenny.
Pulmonary embolization causes hypoxemia by redistributing blood flow without changing ventilation.
J. Appl. Physiol.
85:
2337-2343,
1998
3.
Anthonisen, N. R.,
and
J. A. Fleetham.
Ventilation: total, alveolar, and dead space.
In: Handbook of Physiology. The Respiratory System. Gas Exhange. Bethesda, MD: Am. Physiol. Soc., 1987, sect. 3, vol. IV, chapt. 7, p. 113-130.
4.
Dantzker, D. R.,
P. D. Wagner,
V. W. Tornabene,
N. P. Alazraki,
and
J. B. West.
Gas exchange after pulmonary thromboembolism in dogs.
Circ. Res.
42:
92-102,
1978
5.
Fenn, W. O.,
H. Rahn,
and
A. B. Otis.
A theoretical study of the composition of the alveolar air at altitude.
Am. J. Physiol.
146:
637-653,
1946.
6.
Fowler, W. S.
Lung function studies II. The respiratory dead space.
Am. J. Physiol.
154:
405-416,
1948.
7.
George, S. C.,
J. E. Souders,
A. L. Babb,
and
M. P. Hlastala.
Modeling steady-state inert gas exchange in the canine trachea.
J. Appl. Physiol.
79:
929-940,
1995
8.
Glenny, R. W.,
and
H. T. Robertson.
Fractal properties of pulmonary blood flow: characterization of spatial heterogeneity.
J. Appl. Physiol.
69:
532-545,
1990
9.
Hakim, T. S.,
R. Lisbona,
and
G. W. Dean.
Gravity-independent inequality in pulmonary blood flow in humans.
J. Appl. Physiol.
63:
1114-1121,
1987
10.
Hansen, J. E.,
and
A. E. P.
Human air space shapes, sizes, areas, and volumes.
J. Appl. Physiol.
38:
990-995,
1975
11.
Hlastala, M. P.,
and
H. T. Robertson.
Inert gas elimination characteristics of the normal and abnormal lung.
J. Appl. Physiol.
44:
258-266,
1978
12.
Hubmayr, R. D.,
B. J. Walters,
P. A. Chevalier,
J. R. Rodarte,
and
L. E. Olson.
Topographical distribution of regional lung volume in anesthetized dogs.
J. Appl. Physiol.
54:
1048-1056,
1983
13.
Nicolaysen, G.,
J. Shepard,
M. Onizuka,
T. Tanita,
R. S. Hattner,
and
N. C. Staub.
No gravity-independent gradient of blood flow in the lung.
J. Appl. Physiol.
63:
540-545,
1987
14.
Olszowka, A. J.,
and
L. E. Farhi.
A system of digital computer subroutines for blood gas calculations.
Respir. Physiol.
4:
270-280,
1968[Medline].
15.
Olszowka, A. J.,
and
P. D. Wagner.
Numerical analysis of gas exchange.
In: Pulmonary Gas Exchange, edited by J. B. West. New York: Academic, 1980, p. 263-306.
16.
Riley, R. L.,
and
A. Cournand.
"Ideal" alveolar air and the analysis of ventilation-perfusion relationships in the lungs.
J. Appl. Physiol.
1:
825-847,
1949
17.
Robertson, H. T.,
R. W. Glenny,
D. Stanford,
L. M. McInnes,
D. L. Luchtel,
and
D. Covert.
High-resolution maps of regional ventilation utilizing inhaled fluorescent microspheres.
J. Appl. Physiol.
82:
943-953,
1997
18.
Roca, J.,
and
P. D. Wagner.
Principles and information content of the multiple inert gas elimination technique.
Thorax
49:
815-824,
1993[Abstract].
19.
Rodarte, J. R.,
M. Chaniotakis,
and
T. A. Wilson.
Variability of parenchymal expansion measured by computed tomography.
J. Appl. Physiol.
67:
226-231,
1989
20.
Santolicandro, A.,
R. Prediletto,
E. Fornai,
B. Formichi,
E. Begliomini,
A. Giannella-Neto,
and
C. Giuntini.
Mechanisms of hypoxemia and hypocapnia in pulmonary embolism.
Am. J. Respir. Crit. Care Med.
152:
336-347,
1995[Abstract].
21.
Severinghaus, J. W.
Simple, accurate equations for human blood O2 dissociation computations.
J. Appl. Physiol.
46:
599-602,
1979
22.
Souders, J. E.,
S. C. George,
N. L. Polissar,
E. R. Swenson,
and
M. P. Hlastala.
Tracheal gas exchange: perfusion-related differences in inert gas elimination.
J. Appl. Physiol.
79:
918-928,
1995
23.
Swenson, E. R.,
H. T. Robertson,
N. L. Polissar,
M. E. Middaugh,
and
M. P. Hlastala.
Conducting airway gas exchange: diffusion-related differences in inert gas elimination.
J. Appl. Physiol.
72:
1581-1588,
1992
24.
Wagner, P. D.,
H. A. Saltzman,
and
J. B. West.
Measurement of continuous distributions of ventilation-perfusion ratios: theory.
J. Appl. Physiol.
36:
588-599,
1974
25.
Wagner, P. D.,
and
J. B. West.
Pulmonary gas exchange.
In: Bioengineering Aspects of the Lung, edited by J. B. West. New York: Dekker, 1977, vol. 3, p. 361-457. (Lung Biol. Health Dis. Ser.)
26.
Willford, D. C.,
and
E. P. Hill.
Modest effect of temperature on the porcine oxygen dissociation curve.
Respir. Physiol.
64:
113-123,
1986[Medline].
27.
Wilson, T. A.,
and
K. C. Beck.
Contributions of ventilation and perfusion inhomogeneities to the A/ distribution.
J. Appl. Physiol.
72:
229-304,
1992.
28.
Young, A. C.
Dead space at rest and during excercise.
J. Appl. Physiol.
8:
91-94,
1955
This article has been cited by other articles:
|
|
 |
|
  A. I. Batchinsky, W. B. Weiss, B. S. Jordan, E. J. Dick Jr., D. A. Cancelada, and L. C. Cancio Ventilation-perfusion relationships following experimental pulmonary contusion J Appl Physiol, September 1, 2007; 103(3): 895 - 902. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 H. T. Robertson, B. Neradilek, N. L. Polissar, and R. W. Glenny Sporadic coordinated shifts of regional ventilation and perfusion in juvenile pigs with normal gas exchange J. Physiol., September 1, 2007; 583(2): 743 - 752. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. J. Emery, R. L. Eveland, S. S. Kim, J. Hildebrandt, and E. R. Swenson CO2 relaxes parenchyma in the liquid-filled rat lung J Appl Physiol, August 1, 2007; 103(2): 710 - 716. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
H. T. Robertson and M. P. Hlastala Microsphere maps of regional blood flow and regional ventilation J Appl Physiol, March 1, 2007; 102(3): 1265 - 1272. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
J. Y. C. Tsang, W. J. E. Lamm, B. Neradilek, N. L. Polissar, and M. P. Hlastala Endothelin receptor blockade does not improve hypoxemia following acute pulmonary thromboembolism J Appl Physiol, February 1, 2007; 102(2): 762 - 771. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
I. R. Starr, W. J. E. Lamm, B. Neradilek, N. Polissar, R. W. Glenny, and M. P. Hlastala Regional hypoxic pulmonary vasoconstriction in prone pigs J Appl Physiol, July 1, 2005; 99(1): 363 - 370. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
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]
|
|
|
|
|
|
M. P. Hlastala, W. J. E. Lamm, A. Karp, N. L. Polissar, I. R. Starr, and R. W. Glenny Spatial distribution of hypoxic pulmonary vasoconstriction in the supine pig J Appl Physiol, May 1, 2004; 96(5): 1589 - 1599. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
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]
|
|
|
|
|
|
H. Chang, S. J. Lai-Fook, K. B. Domino, C. Schimmel, J. Hildebrandt, H. T. Robertson, R. W. Glenny, and M. P. Hlastala Spatial distribution of ventilation and perfusion in anesthetized dogs in lateral postures J Appl Physiol, February 1, 2002; 92(2): 745 - 762. [Abstract] [Full Text] [PDF]
|
|
,
, and
: mixed venous pH,
PO2, and
PCO2, respectively;
PB, barometric pressure;
subscript 1, 2, n, and
i: piece
1, piece 2, total no.
of pieces, and piece i,
respectively.
