Abstract
Numerical methods for determining endcapillary gas contents for ventilationtoperfusion ratios were first developed in the late 1960s. In the 1970s these methods were applied to validate distributions of ventilationtoperfusion ratios measured by the multiple inertgaselimination technique. We combined numerical gas analysis and fluorescentmicrosphere measurements of ventilation and perfusion to predict gas exchange at a resolution of ∼2.0cm^{3} lung volume in pigs. Oxygen, carbon dioxide, and inert gas exchange were calculated in 551–845 compartments/animal before and after pulmonary embolization with 780μm beads. Whole lung gas exchange was estimated from the perfusion and ventilationweighted endcapillary gas contents. Before lung injury, no significant difference existed between microsphereestimated 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 lowsolubility inert gas retentions suggests underestimation of areas with low ventilationtoperfusion 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
 ventilationperfusion matching
 aerosol
 fluorescent microspheres
the primary determinant of gas exchange efficiency in the lung is the matching of alveolar ventilation (V˙a) and blood flow (Q˙) (5, 16). Ventilationperfusion (V˙a/Q˙) matching can be assessed by determining ventilation and perfusionweightedV˙a/Q˙distributions in the lung by using the multiple inertgaselimination technique (MIGET) (24). This method is useful for determining the amount of perfusion through lowV˙a/Q˙areas and therefore the impact ofV˙a/Q˙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 gasexchanging unit.
Highresolution 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 coworkers (17) reported highspatialresolution measurements of regional ventilation by using aerosolized 1μm 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 relevantV˙a/Q˙distributions were measured.
To evaluate aerosolized 1μmmicrosphere deposition as a measurement of regional ventilation, we measuredV˙a/Q˙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 endcapillary tensions of both respiratory and inert gases of varying solubility in multiple compartments of ∼2cm^{3} volume. Whole lung gas exchange is determined from mean perfusion and ventilationweighted endcapillary gas contents.
METHODS
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 1μm microspheres and injected 15μm fluorescent microspheres. Measurements were repeated after vascular embolization with 780μm 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 ofV˙a/Q˙Distributions from Microsphere Data
Fluorescent signals in each lung piece are linearly proportional to alveolar ventilation and perfusion to that piece and are converted to milliliters per minute by multiplying the fraction of the total lung fluorescence in the piece by the total alveolar ventilation or cardiac output, respectively. Total alveolar ventilation is calculated by subtracting the anatomic deadspace volume from the measured expired tidal volume and multiplying by the respiratory rate. In the first three animals, the inertgas dead space of acetone from the initial set of MIGET data was used to estimate anatomic dead space (11). In the final two animals, anatomic dead space was graphically determined from the singlebreath washout of CO_{2}. Before embolization, exhaled CO_{2}concentration measured with an infrared CO_{2} detector (model 1260, Novametrix Medical Systems, Wallingford, CT) was digitally sampled at 200 Hz. Exhaled flow measured with a pneumotach was simultaneously sampled at 200 Hz and integrated to provide volume. CO_{2} concentration was plotted against expired volume and dead space estimated by Fowler’s method (6,28). The dead space estimated from three consecutive breaths was averaged.
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 theV˙a/Q˙distribution and its effect on respiratory and inert gas exchange. The data may also be manipulated to allow comparison with the 50compartment model ofV˙a/Q˙distribution provided by MIGET software.
Alveolar tensions of O_{2} and CO_{2}(
PAO2
and
PACO2
, respectively) and endcapillary O_{2} and CO_{2} contents (C
ecO2
and C
ecCO2
, respectively) for each lung piece are determined by solving mass balance equations for each gas, given that piece’sV˙a/Q˙(Fig. 1). A full discussion of the calculations may be found in the
.
Fig. 1.
Calculation of whole lung gas exchange by perfusion and ventilationweighted averages of arterial and alveolar gas composition of individual lung pieces. Given an individual lung piece’s perfusion and ventilation plus data on mixed venous blood composition, Hb, temperature (temp), barometric pressure, and individual P_{50}, endcapillary gas composition is calculated by developed software. Flowweighted average of all pieces will give arterial gas composition; the ventilationweighted average gives mixed alveolar gas composition.
, alveolar
;V˙a, alveolar ventilation; Q˙, blood flow;
and
, arterial O_{2} and CO_{2} content respectively; P
and P
, endcapillary
and
, respectively; C
and C
, endcapillary O_{2} and CO_{2} content, respectively; pH_{
v̅
},
, and
: mixed venous pH,
, and
, respectively; Pb, barometric pressure; subscript 1, 2, n, andi: piece 1, piece 2, total no. of pieces, and piece i, respectively.
Once C
ecO2
and C
ecCO2
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 alveolararterial O_{2} difference (aaDo
_{2}) is calculated by summing each piece’s ventilationweighted
PAO2
and dividing by the total alveolar ventilation. Assuming complete equilibration between the alveolar gas and endcapillary blood, this givesPAO2=∑i=1n V˙i⋅PecO2∑i=1n V˙i
Equation 1whereV˙_{i}is the alveolar ventilation to piecei, nis the number of pieces analyzed from the lung, and P
ecO2
is the endcapillary O_{2} tension. The microsphereestimatedaaDo
_{2}(aaDo
_{2 MS}) is compared with theaaDo
_{2}calculated with the alveolar gas equation (3), the measured arterial gas tensions, and the measured respiratory quotient (aaDo
_{2 ABG}). TheaaDo
_{2 MS}includes only gas exchange abnormalities fromV˙a/Q˙heterogeneity, as opposed to theaaDo
_{2 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 (
Pv¯
)] of the six inert gases were estimated from the measuredV˙a/Q˙distribution. Because an inert gas does not interact with components of blood, its endcapillary retention [endcapillary pressure (Pec)/
Pv¯
] depends only on the gas solubility in plasma (λ) and theV˙a/Q˙of that particular lung compartment (18)PecPv¯=λλ+V˙AQ˙
Equation 2The arterial retention for each inert gas was calculated by summing the perfusionweighted endcapillary retentionsPaPv¯=∑i=1n Q˙i⋅PecPv¯CO
Equation 3whereQ˙_{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 ttests 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
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 endcapillary 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 aV˙a/Q˙> 200; therefore, the impact on estimates of mixed arterial contents was negligible.
In the normal lungs, the mean microsphereestimated
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 betweenaaDo
_{2 MS}andaaDo
_{2 ABG}of 0.36 was not significant (Table 1). MIGET consistently underestimated the
PaO2
(Fig. 2) and overestimated
PaCO2
in the normal lungs.
Table 1.
AaD
o
_{2}
estimated by microspheres and calculated from measured arterial gases and the respiratory exchange ratio
In the abnormal lungs, microspheremeasured 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). TheaaDo
_{2 MS}differed from theaaDo
_{2 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).
MicrospheremeasuredV˙a/Q˙distributions predicted arterial retentions of inert gases of varying solubilities with high precision. Grouping all animals and conditions together, the correlation of microspherepredicted retentions for six inert gases with measured retentions is 0.992 (Fig.3
A). When only preembolization data are evaluated, the correlation between microsphereestimated 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.3
B) reveals a consistent bias to underestimate the arterial retention of lowsolubility gases, suggesting an underestimation of lowV˙a/Q˙units by the microsphere method. This bias increases when gas exchange has been impaired.
Fig. 3.
Microsphereestimated inert gas exchange. Open symbols, baseline measurements; solid symbols, postembolization measurements.A: microspheremeasured inert gas retentions are highly correlated with measured values about a line of unity. B: systematic underestimation of retentions for lowsolubility gases sulfur hexafluoride and ethane after embolization suggest underestimation of lowV˙a/Q˙regions.
Highresolution measurements of ventilation and perfusion allow the effect ofV˙a/Q˙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 constantV˙a/Q˙, permitting evaluation of the contribution of individual pieces to overall gas exchange (Fig. 4). For example, a piece with high perfusion located along a lowV˙a/Q˙isopleth will affect
PaO2
more than a piece with similarV˙a/Q˙but lower perfusion. Pieces may also be grouped by C
ecO2
to construct a flowweighted histogram (Fig.5). Finally,V˙a/Q˙data may be grouped into any number of perfusion or ventilationweighted bins and plotted as a frequency polygon (Fig.6). Using 50 compartments allows direct comparison withV˙a/Q˙measurements from MIGET.
Fig. 4.
Scattergram of regional ventilation and blood flow.A: in normal lungs, there is significantV˙a/Q˙heterogeneity as demonstrated by range over which ventilation and perfusion are distributed, yet correlation between ventilation and perfusion is 0.89, resulting in efficient gas exchange.B: after embolization, range over which ventilation and perfusion are distributed is not significantly changed; however, correlation between ventilation and perfusion has decreased to 0.72, resulting in decreased efficiency of gas exchange.
Fig. 6.
Ventilation and perfusionweighted distributions ofV˙a/Q˙. In these graphs, ventilation or perfusionweighted log(V˙a/Q˙) distributions have been binned into 48 compartments between log(0.005) and log(100) plus shunt and dead space to emulate data presentation from MIGET software. A: in normal lungs, microspheregenerated 50compartment distributions had SDs significantly lower than typical MIGETmeasured distributions. Enforced smoothing algorithms in MIGET limit resolving capabilities to SDs of 0.35–0.4. B: after embolization, SDs of both ventilation and perfusionweighted distributions increase, accompanied by a decrease in mean of distributions.
DISCUSSION
The primary finding of this study is that measurement of regional ventilation with aerosolized 1μm 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, highresolution measurements of ventilation and perfusion by microspheres accurately predict
PaO2
and
PaCO2
. Because arterial blood is fully saturated in normal lungs, small differences in O_{2} content are associated with large differences in
PaO2
due to the low solubility of O_{2} 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 meanV˙a/Q˙distribution. MIGET algorithms described a bimodal ventilation distribution with a highV˙a/Q˙component in the majority of animals studied. Given a fixed total minute ventilation, this causes the perfusionweighted distribution to shift to a lower meanV˙a/Q˙and an underestimation of gas exchange. This erroneous identification by MIGET of a highV˙a/Q˙mode may be caused by airway excretion of highly soluble gases, particularly acetone (7, 22, 23).
The microspheremeasuredV˙a/Q˙distributions significantly underestimate gasexchange impairment after vascular embolization. Predicted Pa_{O2} values all decreased after embolization but were consistently overestimated. There are three possible explanations for this systematic error. First, the degree ofV˙a/Q˙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 underestimatesV˙a/Q˙heterogeneity within that tissue cube (Fig.7
A). 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 P
ecO2
and
PAO2
. If flow redistribution increases transit time sufficiently for some capillaries, this assumption may be invalid (Fig.7
B). 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 endcapillaryalveolar equilibrium of gas tensions and that the microsphereestimated
PaO2
is consistently greater than MIGETestimated
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 righttoleft shunt. The microsphere technique measures intrapulmonary shunt (V˙a/Q˙= 0) only if the entire lung region examined receives no ventilation. Shunt occurring below this resolution would decrease the cube’s microspheremeasuredV˙a/Q˙but causes an overestimation of the cube’s C
ecO2
. 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 lungpiece size and does measure intracardiac shunt. MIGET does not measure postpulmonary shunt caused by the bronchial circulation or the Thebesian veins; however, gasexchange abnormalities due to postpulmonary shunt will be equally underestimated by MIGET and cannot explain the disparity between the microsphere and MIGETestimated
PaO2
.
Fig. 7.
Possible mechanisms for underestimation of arterial
after lung injury by microsphere method. A: after embolization,V˙a/Q˙heterogeneity developed because of redistribution of regional perfusion. Measurements of perfusion and ventilation in a 2.0cm^{3} tissue cube that is supplied by 2 different vessels will underestimateV˙a/Q˙heterogeneity if magnitude of flows in 2 vessels change in different directions, resulting in an averaging of high and lowV˙a/Q˙regions. B: transit time in pulmonary capillaries has been estimated at 0.75 s, whereas time estimated for equilibration between endcapillary blood and alveolar gas is 0.25 s. If flow through a pulmonary capillary increases more than 3fold after embolization, a functional diffusion limitation may occur.
Gas exchange may also be evaluated by theaaDo
_{2}. An increase inaaDo
_{2}is caused byV˙a/Q˙heterogeneity, shunt, or a diffusion limitation.V˙a/Q˙heterogeneity increases theaaDo
_{2}because
PAO2
is calculated by a ventilationweighted average of the equilibrated oxygen tension in each piece, whereas
PaO2
is calculated by a flowweighted average of oxygen tension in each piece. Thus pieces with highV˙a/Q˙that have higher P
ecO2
contribute more to the
PAO2
, and pieces with a lowV˙a/Q˙that have lower P
ecO2
contribute more to
PaO2
. Although a significant difference does not exist between theaaDo
_{2 ABG}and theaaDo
_{2 MS}in the normal lungs, the individual data provide interesting insights. First, in five of the nine preembolization measurements, theaaDo
_{2 MS}was lower than theaaDo
_{2 ABG}. Because diffusion limitation is not believed to occur in the normal lung, the difference can only be explained by underestimation of lowV˙a/Q˙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 ofaaDo
_{2}by microspheres raises the possibility thatV˙a/Q˙heterogeneity is being underestimated. Of note, three of the nineaaDo
_{2 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. TheaaDo
_{2 MS}increased postembolization in all five animals, consistent with the increasedV˙a/Q˙heterogeneity seen with both microsphere and MIGET methods. However, theaaDo
_{2 MS}was consistently less than theaaDo
_{2 ABG}, most likely resulting from unmeasuredV˙a/Q˙heterogeneity below the scale of resolution for this method.
Predicting inert gas exchange for a givenV˙a/Q˙distribution has several advantages over respiratory gas exchange. First, inert gases do not interact with blood components or each other; therefore, gasexchange 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. Figure3
B 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 lowV˙a/Q˙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 highsolubility gas (e.g., acetone) due to unmeasured highV˙a/Q˙units. Figure 3
B suggests that the microsphere method tends to overestimate acetone retention.
The calculated inert gas retentions support the hypothesis that unmeasuredV˙a/Q˙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, 2.0cm^{3} lung pieces from a 14kg pig has >10 acini, suggesting that measured regional ventilation heterogeneity could increase at smaller resolutions. BecauseV˙a/Q˙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), resolutiondependent 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 2.0cm^{3} 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 resolutiondependent 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.
Footnotes

Address for reprint requests: W. A. Altemeier, Div. of Pulmonary and Critical Care Medicine, BB1253 Health Sciences Bldg., Box 356522, Seattle, WA 981956522 (Email: billa{at}u.washington.edu).

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.
 Copyright © 1998 the American Physiological Society
Appendix
Numerical Gas Analysis
The mass balance equation for O_{2}isV˙IQ˙ PIO2−V˙AQ˙ PAO2=k (CecO2−Cv¯O2)
Equation 4whereV˙i is the inspired regional ventilation,V˙a is the expired regional ventilation,
Cv¯
O2
is the O_{2} content of mixed venous blood, and k is a temperaturedependent factor that converts betweenstpd andbtps units. Because the inspired partial pressure of CO_{2} is ∼0, the termV˙i/Q˙drops out of the mass balance equation for CO_{2}
V˙AQ˙ PACO2=k (Cv¯CO2−CecCO2)
Equation 5where
Cv¯
CO2
is the CO_{2} content of mixed venous blood. Introducing the termV˙i/Q˙results in three unknown variables for the two equations. To solveEqs. 4
and
5
, the mass balance of N_{2} and the summation of partial pressures must also be consideredV˙IQ˙ PIN2−V˙AQ˙ PAN2=λN2 (PecN2−Pv¯N2)
Equation 6
PAO2+PACO2+PAN2=PB−PH2O
Equation 7where
PIN2
is the partial pressure of N_{2} in the inspired gas;
PAN2
is the partial pressure of N_{2} in the alveolar gas; λN_{2} is the bloodgas partition coefficient (defined ask × the solubility of N_{2}, 0.0017 ml/100 ml blood); P
ecN2
is the partial pressure of N_{2} in the endcapillary blood;
Pv¯
N2
is the partial pressure of N_{2} in mixed venous blood; Pb is the barometric pressure; and Ph
_{2}O is the partial pressure of water in fully saturated gas at the given temperature. Because N_{2} does not interact with Hb, partial pressure is directly proportional to content by the solubility of N_{2}. Furthermore, because there is no net exchange of N_{2} between the environment and the blood,
Pv¯
N2
may be assumed to equal
PIN2
.
Assuming no diffusion limitation of the respiratory gases, the endcapillary tension of gas X is equal to its alveolar tension. Thus C
ecO2
and C
ecCO2
are related to
PAO2
and
PACO2
by the O_{2}Hb and CO_{2}Hb dissociation curves.
The solution of Eqs. 47
may be simplified by solving Eq. 4
forV˙i/Q˙, substituting this into Eq. 6
, and solving for
PAN2
. Finally, this may be substituted into Eq.
7
and, with some rearrangement, yieldV˙A/Q˙+λN2PIN2/PIO2 (PB−PH2O−PAO2−PACO2)
−V˙A/Q˙⋅PAO2−λN2⋅PIO2=k (CecO2−Cv¯O2)
Equation 8C
ecO2
and C
ecCO2
may now be solved for any givenV˙a/Q˙by using Eqs. 5
and
8
.
Because P
ecO2
and P
ecCO2
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 endcapillary pH (pH_{ec}) and P
ecO2
, and these are used to calculate P
ecCO2
, C
ecO2
, and C
ecCO2
. 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 pH_{ec} and P
ecO2
. 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 P
ecCO2
, C
ecO2
, and C
ecCO2
for a given pH_{ec} and P
ecO2
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, O_{2} content is calculated by first describing a “virtual” P
ecO2
or what the actual P
ecO2
would be on a normal, human O_{2}Hg dissociation curve at a pH of 7.4 and a P
ecCO2
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 speciesspecific P_{50} (the P
ecO2
at standard conditions and 50% Hb saturation). For these experiments using pigs, the P_{50}, temperature coefficient, and fixedacid Bohr coefficient used are 35.7 Torr, 0.016, and 0.441, respectively (26). The virtual P
ecO2
is used to calculate an Hb saturation by using a formula described by Severinghaus (21). The saturation is used in the calculation of P
ecCO2
at 37°C, which is used to calculate CO_{2} content. Finally, P
ecCO2
is calculated at the given temperature, assuming a constant CO_{2} content.
Data for the gasanalysis 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 P_{50}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 theV˙a/Q˙distribution, and several graphical displays corresponding to Figs.46. The software will run on Macintosh OS and Windows 95 operating systems and is available from the author on request.