Abstract
Ventilationperfusion (V˙a/Q˙) inhomogeneity was modeled to measure its effect on arterial oxygenation during maintenancephase anesthesia involving an inspired mixture of 30% O_{2} and either N_{2}O or N_{2}. A multialveolar compartment computer model was constructed based on a log normal distribution ofV˙a/Q˙ inhomogeneity. Increasing the log SD of the distribution of blood flow from 0 to 1.75 produced a progressive fall in arterial Po _{2} (Pa_{O2}). The fall was less steep in the presence of N_{2}O than when N_{2} was present instead. This was due mainly to the concentrating effect of N_{2}O uptake on alveolar Po _{2} in moderately lowV˙a/Q˙ compartments. The improvement in Pa_{O2} when N_{2}O was present instead of N_{2} was greatest when the degree ofV˙a/Q˙ inhomogeneity was in the range typically seen in anesthetized patients. Models based on distributions of expired and inspired alveolar ventilation give quantitatively different results for Pa_{O2}. In the presence ofV˙a/Q˙ inhomogeneity, secondgas and concentrating effects may have clinically significant effects on arterial oxygenation even at “steadystate” levels of N_{2}O uptake.
 alveolararterial difference
 oxygen uptake
the concentrating and secondgas effects of rapid nitrous oxide (N_{2}O) uptake (V˙n _{2} o) early in an inhalational anesthetic and its effect on alveolar O_{2}concentration were described by Stoelting and Eger (4,21). It is generally assumed that, after the immediate postinduction phase of anesthesia, maintenancephase levels ofV˙n _{2} o by the lungs do not produce a significant “concentrating effect” on other alveolar gases and, therefore, do not increase O_{2} uptake (V˙o _{2}) or improve arterial oxygenation.
However, in a series of studies by Nunn and coworkers (15, 16,24), it was demonstrated that arterial oxygenation was unimpaired or improved in patients who were undergoing inhalational anesthesia, breathing O_{2} with N_{2}O for >0.5 h, compared with a group breathing O_{2} with nitrogen (N_{2}). This result was surprising in view of the expected tendency of a soluble gas such as N_{2}O to hasten absorption atelectasis and worsen shunt (24).
Farhi and Olzowska (5) calculated the effects of differing inspired concentrations of N_{2}O on the relationship between the Po _{2} and Pco _{2} values and ventilationtoperfusion ratio (V˙a/Q˙). They demonstrated that the shape of the curve on the O_{2}CO_{2} diagram was changed, with a significantly elevated Po _{2} predicted in the presence of a moderately low V˙a/Q˙ and high inspired N_{2}O. The implications for overall gas exchange in the lung were not explored further by these authors at the time.
More recently, Korman and Mapleson (11) have offered an expanded description of the mechanism of the concentrating and secondgas effects. Their treatment distinguishes “constant outflow” and “constant inflow” models based on predetermined values for expired (V˙ae) and inspired alveolar ventilation (V˙a; V˙ai), respectively, within a single lung compartment. These different models may be expected to give different results when applied to the calculation of overall gas exchange in the lung.
The application of a multicompartment analysis of log normal distributions of V˙ae and blood flow (Q˙) in the lung has been used by previous workers investigating the causes of reduced efficiency of gas exchange under worsening inhomogeneity ofV˙a/Q˙ throughout the lung. This was demonstrated by West (25, 26) and Kelman (10) to result in a widening of the predicted alveolararterial difference for all gases. However, these early models did not take into account the interdependent nature of exchange of multiple soluble alveolar gases. More sophisticated models have since been applied to scenarios representing multiple gas exchange during inhalational anesthesia. These include a variant based on a log normal distribution ofV˙ai, which serves to demonstrate that lung units with very low V˙a/Q˙ may suffer collapse when gas uptake exceeds V˙ai and that this process is accelerated by the presence of N_{2}O (2).
The present authors have sought to investigate further the relationship between concentrating and secondgas effects and distributions ofV˙a/Q˙ and their effect on overall O_{2}exchange. We have constructed a multialveolar compartment computer model of alveolarcapillary exchange of multiple gases (O_{2}and CO_{2} and any combination of inert gases such as N_{2}O or N_{2}). This was used to predict the effects of differing degrees of V˙a/Q˙inhomogeneity on V˙o _{2} and arterial Po _{2} (Pa_{O2}) in scenarios related to inhalational anesthesia. Results were sought from two models based on log normal distributions of V˙ae andV˙ai. These were considered to represent constant outflow and constant inflow principles of ventilation, respectively, applied to multiple compartments.
METHODS
A computer model was designed to represent the exchange of multiple gases across the alveolarcapillary membrane. Log normal distributions of Q˙ and ventilation were generated with log_{e} SDs varying between 0 (homogeneous lung) and 1.75. West (25, 26) showed that, for any given mode and log SD, identical results are obtained with a primary distribution of either Q˙ or ventilation. The structure and data flow of this model are outlined in more detail in the .
Either V˙ae or V˙ai can be nominated for the distribution to be generated. Where V˙ai was nominated, the effect of absorption atelectasis in compartments whereV˙ae/Q˙ was less than zero was modeled. This is based on similar assumptions as those made by Dantzker et al. (2), who assumed that compartments with negative calculated V˙ae would suffer collapse. Given that steadystate gas exchange was being modeled, it was assumed that perfusion of such compartments was shunt, with an endcapillary gas content identical to that of mixed venous blood. Both V˙aeand V˙ai for these compartments was made zero, and the inspired ventilation from them was redistributed to the remaining compartments by multiplying each by a scaling factor to restore total V˙ai to its nominated value.
Modifications incorporated by Dantzker et al. (2) to simulate the effect of hypoxic pulmonary vasoconstriction (HPV) on the distribution of Q˙ were included. Once again, perfusion of all compartments was scaled so that total Q˙ remained at the nominated value. An iterative approach is required for these processes, where the scaling of ventilation and perfusion progressively reduces, so that final distributions obtained for each are consistent with nominated target values for exchange of each gas.
West (25) demonstrated that 10 compartments are adequate to obtain maximal precision of results for output variables from such a model. It was found, however, that when collapse of compartments with critically low V˙ai/Q˙ was incorporated, 50 compartments were required to avoid noticeable quantization error because of inclusion or exclusion of compartments withV˙ai/Q˙ values near the critical value.
Analysis performed.
A scenario typical of the maintenance phase of an inhalational anesthetic was modeled involving administration of an inspired mixture of 30% O_{2} and 70% N_{2}O. This was contrasted with a parallel situation involving 70% N_{2} instead. Regardless of what type of distribution of V˙a was nominated (expired vs. inspired, with or without collapse of lowV˙ai/Q˙ units), overall V˙ae was kept at 4.1 l/min. Overall Q˙ was maintained at 4.8 l/min, regardless of whether the effect of HPV was incorporated. Analyses were performed with constant gas uptakes (V˙o _{2}: 250 ml/min; CO_{2} uptake: 200 ml/min;V˙n _{2} o: 100 ml/min). Output variables in the primary analysis were uptakes of individual gas species and alveolar and arterial partial pressures, on a global basis or by compartment. For the sake of simplicity in analysis of the data, there was no other soluble anesthetic agent in the inspired mixture.
The effects on Pa_{O2} of N_{2}O washout, such as occurs at the end of an inhalational anesthetic, were also investigated and contrasted with the situation in the presence of N_{2} instead. The scenarios modeled utilized the algorithm described above applying a constantoutflow principle and with arterial Pco _{2} held constant (rather thanV˙ae). This was done on the assumption that, in the spontaneously breathing patient, maintenance of constant arterial Pco _{2} rather than V˙ae is more physiologically realistic, given that V˙ae will vary with net gas elimination. The inspired concentration of N_{2}O was set at zero. Two different rates of N_{2}O elimination (400 and 100 ml/min) were examined, with theV˙n _{2} o fixed at these values.
RESULTS
In the presence of V˙n _{2} oof 100 ml/min, Pa_{O2} decreased progressively as the log SD of the distribution of Q˙ increased, reflecting worseningV˙a/Q˙ inhomogeneity. However, where a log normal distribution of V˙ae or constant outflow model was employed, the fall was significantly less steep in the presence of N_{2}O than when N_{2} was present instead.
The difference in predicted Pa_{O2} in the presence of N_{2}O compared with N_{2} was smallest at lower SDs of Q˙ (more homogeneous lungs) and greatest (an increase of ∼50%) at more severe levels of V˙a/Q˙inhomogeneity (Fig. 1).
The constant inflow (V˙ai based) model produced quantitatively different results, predicting a much smaller increase in Pa_{O2} when N_{2}O replaces N_{2} than that predicted by the V˙aebased model, even where total gas uptakes were constrained to the same values.
In the N_{2}O washout scenarios, a lower Pa_{O2}was predicted in the presence of N_{2}O compared with N_{2} at all degrees of V˙a/Q˙inhomogeneity (Fig. 2). The effect was relatively greatest at mild degrees of V˙ae/Q˙spread, where Pa_{O2} is reduced significantly in the presence of rapid N_{2}O elimination (400 ml/min), although much more modestly at low rates of N_{2}O excretion (100 ml/min).
DISCUSSION
Pa_{O2} steadily declined as the log SD of the distribution of Q˙ increased. This is consistent with previously held assumptions regarding the effect of V˙a/Q˙inhomogeneity on gas uptake (10, 25, 26). However, the results of this modeling suggest that substituting N_{2} with N_{2}O can produce significant increases in arterial oxygenation, even at a low rate ofV˙n _{2} o by the lung, and that this effect is a direct result of the presence ofV˙a/Q˙ inhomogeneity. Improvement in oxygenation of this degree is not expected in a homogeneous lung (indicated by a log_{e} SD of zero in Fig. 1), where a minor rise in Pa_{O2} of only ∼4 Torr is predicted.
Importantly, improved oxygenation is not predicted by a traditional threecompartment model of V˙a/Q˙ scatter, where only shunt, dead space, and a uniform compartment are considered. If the homogeneous lung just mentioned is considered, the effect of a superimposed true shunt fraction will only be to reduce further the minor increase in Pa_{O2} induced by the alveolar concentrating effects ofV˙n _{2} o.
The level of V˙n _{2} o applied to these calculations, using the formula of Severinghaus (19), is consistent with the situation well into the maintenance phase of anesthesia, where essentially steadystate kinetics of gas exchange can be considered to be present. At this stage, the concentrating and secondgas effects of the phase of rapid V˙n _{2} o early in the course of the anesthetic are customarily considered to have passed.
A number of authors (1, 3, 6, 12, 13) studying distributions of V˙ae and Q˙ using the multiple inertgas elimination technique (MIGET) in subjects under N_{2}O anesthesia have demonstrated an increase in the spread of V˙ae/Q˙ throughout the lung (as indexed by the log SD of the distributions) after induction of anesthesia. Dueck et al. (3) suggested thatV˙n _{2} o from lowV˙ae/Q˙ lung units may increase alveolar Po _{2} and Pa_{O2} and that this might continue for some time after induction of anesthesia, although the mechanism for this was not explored in detail.
The explanation for this phenomenon lies in the increased concentration of alveolar O_{2} produced byV˙n _{2} o, operating in lung compartments with moderately low V˙a/Q˙. The effect of this is to increase Pa_{O2} andV˙o _{2} within that compartment. Figure3 shows that the increase inV˙o _{2} in the presence of N_{2}O compared with N_{2} is greatest in those compartments with moderately low V˙a/Q˙. These compartments obtain a high proportion of total Q˙ and not surprisingly have a predominant effect on the composition of mixed blood leaving the lung. It should be noted that, according to Farhi and Olzowska (5), significant increases in alveolar Po _{2} in moderately lowV˙ae/Q˙ lung units are not expected if the inspired N_{2}O concentration fraction is less than ∼50%. Thus the effect of N_{2}O on arterial oxygenation would not be expected to be as significant at a low inspired fraction of N_{2}O concentration.
Two phenomena of interest emerge from these results. These are, first, the significant secondgas and concentrating effects occurring in moderately low V˙a/Q˙ compartments where N_{2}O is present in sufficient concentration and, second, the quantitatively different predictions of models based on generated distributions of inspired and expired ventilation.
The historical development of our understanding of the mechanism of the effect of uptake of one gas on that of other inspired gases is somewhat confused. The term “secondgas effect” was originally applied to the observed increase in the rate of rise of the alveolar concentration of volatile agent when N_{2}O was administered. The mechanism was postulated to be that further fresh gas was indrawn to replace the volume of N_{2}O taken up. The term concentrating effect was coined by Stoelting and Eger (21) when they demonstrated an increase in alveolar concentration of volatile anesthetic agent above the fresh gas concentration and is a result of contraction of alveolar volume during rapidV˙n _{2} o.
Korman and Mapleson (11) recently provided a more complete description of these processes that distinguishes constant outflow and constant inflow models based on predetermined values forV˙ae and V˙ai, respectively. Unlike the earlier classic description (21), their treatment predicts final alveolar concentrations that agree with those calculated by equations based on principles of mass balance applied to the relationship of V˙a to gas uptake. The constant outflow principle assumes a predetermined expired alveolar volume for a lung compartment. Net uptake of alveolar gas causes further fresh gas to be passively drawn into the alveolus, evoking the secondgas effect. When a constant inflow principle applies, inspired alveolar volume is predetermined for the compartment, and net gas uptake causes shrinkage in alveolar volume, producing a concentrating effect and a lower expired volume. When the terms secondgas effect and concentrating effect are used in the present study, it is to refer to the effects of these two distinct but often concurrent mechanisms relatingV˙a to gas exchange.
The difference between these two principles for a single compartment is illustrated diagramatically by Korman and Mapleson (11), and Fig. 4 is adapted from their diagram. Constant inflow before and after equilibration of alveolar gas and blood is represented by columns A and B, respectively. Constant outflow before and after equilibration is represented by columns C and D. Figure 4 is based on a simplified analysis like theirs in which no net exchange of vehicle gas takes place. If, for the sake of simplicity, we assume a respiratory exchange ratio of 1.0 for the compartment, we can consider the accompanying respiratory gases (here labeled as O_{2}) to function as the insoluble vehicle gas. The V˙a/Q˙of the compartment has been adjusted so that onehalf of the N_{2}O in the inspired gas mixture is taken up. The diagram illustrates that, regardless of whether a constant outflow or constant inflow principle is applied, the final gas concentrations at equilibrium will be the same, dictated by theV˙a/Q˙ and inspired concentration. However, the volumes of gas inspired, taken up, and expired are very different.
These principles can be applied to multiple compartments and, substituting ventilation rates over time for static volumes, have been applied to the computer modeling performed here. WhenV˙ae is nominated for each lung compartment according to a specified distribution, the model can be considered analogous to a constant outflow model. Changes in gas exchange due, for example, to changes in fractional inspired or mixed venous gas content will alter the calculated V˙ai for that compartment, butV˙ae is predetermined. When a distribution ofV˙ai is nominated instead, the model performs as a constant inflow model, and V˙ae is the dependent variable.
In our modeling, the constant inflow (V˙ai based) model produced quantitatively different results for overall gas exchange, predicting a much smaller increase in Pa_{O2}with N_{2}O than that predicted by theV˙aebased model, even when total gas uptakes and total V˙ai and V˙ae were constrained to the same values. The reason for this lies in the different shapes of the distributions produced for ventilation (Fig.5). In the constant inflow model, the relatively high proportion of inspired ventilation taken up produces very low or even negative values for V˙ae in lowV˙ai/Q˙ compartments. In these compartments, when net gas uptake occurs, V˙ai is necessarily higher in the constant outflow model than in the constant inflow model, with greater V˙o _{2} andV˙n _{2} o for a given combination of alveolar and mixed venous partial pressures. The different performance of the two distributions is accentuated in a situation of relatively low overall inertgas uptake, in which perfusiondrivenV˙o _{2} forces down alveolar Po _{2} and mixed venous Po _{2}, whereas further concentrating retained inert gas in the poorly ventilated alveolus. The steepness of the HbO_{2} dissociation curve at lower Po _{2} values depresses the overall Pa_{O2} when endcapillary blood from these lowV˙ai/Q˙ lung units mixes with the smaller volume of blood from better ventilated regions.
Clinical implications.
It is notable that the predicted increment in Pa_{O2}produced by the substitution of inspired N_{2} with N_{2}O (especially as calculated using a constant outflow model) is maximal in the range of V˙a/Q˙inhomogeneity commonly seen in healthy, anesthetized patients. This corresponds with SDs of the distribution of Q˙ used in these lung models of 1.0–1.5 (1, 3, 6, 12, 13). This has possible clinical implications, and, whereas the mechanism of the effect has been outlined above, the theoretical factors modulating this effect as well as existing clinical data were also examined.
Nunn and coworkers (15, 16, 24) measured Pa_{O2} in a series of 50 patients who had undergone an average of 36–45 min of general anesthesia with either spontaneous or controlled ventilation breathing O_{2} in either 70% N_{2} or N_{2}O. They were unable to find any evidence of poorer arterial oxygenation in the N_{2}O group. In fact, after their findings were adjusted for the slightly different inspired fraction of O_{2} of the groups, Pa_{O2} was the same in the presence of N_{2}and N_{2}O in the controlled ventilation groups. This surprised the authors, who were unable to explain the findings. Moreover, analysis of their figures (using Fisher's test andztest) shows that, for the spontaneous ventilation groups, Pa_{O2} was clinically and statistically significantly higher (107 vs. 81 Torr, P < 0.01) in the presence of N_{2}O than in the presence of N_{2}.
They did not explore the possibility of a concentrating effect as an explanation of higher alveolar Po _{2} values, presumably because of the assumption that, at expected rates ofV˙n _{2} o, this would be trivial. With the use of their data, the expected improvement in Pa_{O2} in the presence of N_{2}O would be expected to be only ∼5%, assuming no inhomogeneity ofV˙ae/Q˙, (even less if the effect of a typical shunt of ∼10–15% is incorporated). However, with the assumption of a typical degree of V˙a/Q˙ inhomogeneity of an essentially log normal pattern among their anesthetized subjects, improvements in arterial oxygenation in the presence of N_{2}O are entirely explained by our model.
Alveolar collapse and absorption atelectasis.
The clinical phenomenon and theoretical basis of absorption atelectasis have been well described, and the kinetics of reduction of gas volume in a homogeneous segment of lung due toV˙o _{2}, where conducting airways are obstructed, has been quantified by previous authors (2, 7,24). Compared with the situation prevailing when pure O_{2} is inhaled, it can be shown that the speed and magnitude of the effect is greater when N_{2}O is present and markedly reduced when N_{2} is present instead. Dantzker et al. (2) applied a computer model involving a log normal distribution of V˙ai to demonstrate that lung units with very low V˙a/Q˙ may suffer collapse when gas uptake exceeds V˙ai. This threshold level ofV˙ai/Q˙ was higher in the presence of soluble gases, such as N_{2}O, and at higher inspired O_{2}concentrations.
These authors pointed out that the fate of these segments is not clear. They may remain open and receive collateral ventilation from adjacent areas or even further fresh gas from the anatomic dead space or may suffer a loss of alveolar volume, leading to collapse. In the latter case, any continuing perfusion of these collapsed units would be effectively shunt, and the effect of this can be predicted to be a reduction of Pa_{O2}. Because steadystate gas exchange consistent with maintenancephase anesthesia was examined, the effect of alveolar collapse in the presence of critically lowV˙ai/Q˙ was incorporated in all cases examined in the present study, with the associated Q˙ considered to be shunt. Dantzker et al. (2) showed that the threshold value ofV˙ai/Q˙ for alveolar collapse when N_{2}O is present is considerably higher. This predictably produced a much greater number of low V˙ai/Q˙compartments suffering collapse and a higher proportion of totalQ˙ becoming shunt in all scenarios modeled by us with N_{2}O. However, at no point was Pa_{O2}predicted in our modeling to be lower in the presence of N_{2}O, despite the larger proportion of total Q˙perfusing nonventilated lung compartments. Therefore, the concentrating effects of V˙n _{2} o on alveolar Po _{2} in moderately lowV˙ai/Q˙ compartments consistently outweighed the effect of the increased proportion of Q˙ involved in shunting.
Relationship of ventilation to gas exchange.
This type of computer modeling of gas exchange requires that a distribution of ventilation be nominated. This distribution must be assumed to be a reasonable generalization of the type of distribution seen in the population being modeled. Previous workers (1, 3, 6,12, 13, 18, 22) have demonstrated, using the MIGET, that subjects both awake (spontaneously breathing) and undergoing general anesthesia with controlled ventilation exhibit patterns ofV˙a/Q˙ matching throughout the lung, essentially consistent with a log normal distribution, although variations on this pattern are seen in a variety of physiological and pathological situations. Common variations are seen in patients with normal lungs, such as a “shelf” of low V˙a/Q˙subunits, which can transform into true shunt, typically seen after administration of 100% O_{2}. The SD of the distribution is seen to increase with age and also with anesthesia.
The different predictions of V˙ae (constant outflow) models and V˙ai (constant inflow) models, particularly in relation to calculated Pa_{O2}, pose the question for computer modeling of gas exchange: what ventilatory distribution, when applied to such a model, gives the most physiologically realistic results? Is it inspired ventilation, expired ventilation, or some other ventilatory parameter? The different predicted behavior of the lung in oxygenation of the blood in the presence of a soluble and an insoluble gas, such as N_{2}O and N_{2}, may provide some guidance when correlated with the available clinical data.
Clinical studies carried out in the past using MIGET are based on calculations of the proportion of expired ventilation that is not part of anatomic dead space (19) and thus relate to aV˙aebased or constant outflow principle and computer model. However, the function of many artificial ventilators used in clinical anesthesia practice may be better described by a constant inflow principle (11, 14), where the inspired tidal volume delivered to the patient is set. It has also been suggested that a constant outflow model relates more closely to the situation of spontaneous ventilation. Here the subjects regulate the degree of expansion of the thorax with each breath in response to their respiratory drive. All gas inflow is the result of the negative intrathoracic pressure generated whether actively by chest expansion or passively by uptake of gas across the alveolarcapillary membrane.
The findings of the studies of Nunn and coworkers (15, 16,24) are consistent with these assumptions. A significant difference in Pa_{O2} was seen between their N_{2}O and N_{2} groups when spontaneous ventilation took place, as was predicted by the constant outflow model based on a log normal distribution of V˙ae. However, there was no difference (adjusting their findings for the slightly different inspired fraction of O_{2} concentration of the groups) in the presence of controlled ventilation, as was predicted by the constant inflow model based on a log normal distribution ofV˙ai with collapse of critically lowV˙ai/Q˙ segments. Dueck et al. (3), studying subjects under controlled ventilation with O_{2} and either N_{2} or N_{2}O, also found no difference in arterial oxygenation.
When compared with the predictions of the computer models outlined, these studies provide evidence, on the basis of arterial oxygenation, that each mode of ventilation is characterized by its own predominantV˙a principle (constant inflow or constant outflow).
Diffusion hypoxia and V˙a/Q˙ inhomogeneity.
Not surprisingly, a lower Pa_{O2} was predicted in the presence of N_{2}O compared with N_{2} at all degrees of V˙a/Q˙ inhomogeneity. This is the basis of socalled “diffusion hypoxia.” The effect is relatively most severe at mild degrees of V˙ae/Q˙spread, where Pa_{O2} is reduced significantly in the presence of rapid N_{2}O elimination (400 ml/min), although much more modestly at low rates of N_{2}O excretion (100 ml/min). Whereas this depression of Pa_{O2} is greater the higher the rate of N_{2}O elimination occurring, it can be seen that the major contributor to hypoxemia at severe degrees ofV˙a/Q˙ inhomogeneity is mismatch ofV˙a/Q˙ itself rather than N_{2}O elimination.
For any gas for which the inspired concentration is zero, the predicted effect of increasing V˙a/Q˙ inhomogeneity is to reduce fractional elimination (26). The practical outcome of this in terms of N_{2}O kinetics will be a prolongation of the phase of washout of inert gas from the body. The reduction in Pa_{O2} during N_{2}O washout (as compared with an O_{2}N_{2} mixture) is less in absolute terms at higher levels of inhomogeneity. Furthermore, the N_{2}O elimination rate will be lower with more severe inhomogeneity; therefore, the reduction in Pa_{O2} expected at a given time postanesthesia with N_{2}O compared with N_{2}can be expected to be still less. However, the clinical consequences of any reduction may be considered more severe: when the baseline is low, the duration of the effect is more prolonged.
Conclusion.
A multicompartment model of a log normal distribution ofV˙a/Q˙ values predicts that concurrent administration of O_{2}N_{2}O mixtures results in clinically significant secondgas and concentrating effects in lowV˙a/Q˙ lung units. The effect of the enrichment of alveolar O_{2} in these compartments is improved arterial oxygenation compared with an O_{2}N_{2} mixture, even in the presence of the very modest rates ofV˙n _{2} o seen well into a prolonged inhalational anesthetic.
The most significant increase in Pa_{O2} produced byV˙n _{2} o is predicted to occur at levels of V˙a/Q˙ inhomogeneity typically seen in anesthetized subjects. The increase is small when a log normal distribution of V˙ai is modeled but is substantial when a log normal distribution of V˙ae is nominated.
Consideration of the mechanics of V˙a in relation to gas uptake suggests that spontaneous ventilation is more consistent with a model characterized by a log normal distribution ofV˙ae (constant outflow principle). Controlled ventilation is consistent with a distribution predominantly ofV˙ai (constant inflow principle). Under this hypothesis, data from this modeling are consistent with previously published clinical measurements of Pa_{O2} under anesthesia.
In the presence of significant V˙a/Q˙inhomogeneity, secondgas and concentrating effects on oxygenation may be clinically significant even at steadystate levels ofV˙n _{2} o.
Footnotes

Address for reprint requests and other correspondence: P. J. Peyton, Dept of Anaesthesia, Austin & Repatriation Medical Centre, Heidelberg 3084, Melbourne, Australia (Email:phil{at}austin.unimelb.edu.au).

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. Section 1734 solely to indicate this fact.
 Copyright © 2001 the American Physiological Society
Appendix
Computer Program: Generation of Log Normal Distributions
Using a routine described by West (25), a frequency distribution of V˙ae per unit volume of lung (V˙ae/vol) or Q˙ per unit volume (Q˙/vol) can be generated. The distribution is Gaussian in shape when the abscissa (V˙ae/vol) is plotted logarithmically. As pointed out by Kelman (10), description of a log normal distribution in terms of a “mean” is unhelpful, and the distribution can best be described in terms of two parameters: the mode (or V˙ae/vol of peak frequency) and the log SD. The position of the first SD with a log normal distribution can be located as that point at which the frequency is 60.65% of the mode frequency on the left of it. This is also the point of maximal negative slope. Second and third and negative SDs will be placed equidistantly along the abscissa. The magnitude of the log SD of the distribution can be varied around a mode, and both can be specified.
The equation used is
A range of values of V˙ae/vol or Q˙/vol spanning 3 log SDs on either side of the mode is taken [although, where the nominated log_{e} of the SD was set at >1.0, a fourth SD is added to the lower end of the range, as suggested by West (25), in view of the presence of appreciable amounts ofQ˙ in the small volume of lung represented by negligible values ofV˙ae/vol]. From this range, the distribution is divided into a number of compartments evenly spaced along the abscissa. The components of the distribution can be evenly scaled so that the total V˙ae of the compartments combined equals any given specified value. If Q˙/vol is given at a constant and equal value for each compartment and scaled similarly up to a given value, the resultant distribution of V˙ae/Q˙ for the compartments will also be log normal. The output of this subroutine is a series of paired values for V˙ae and Q˙ for each compartment, which, when summated, equal the selected totalV˙ae and Q˙, give a desired overallV˙ae/Q˙, and have a predetermined variance.
Either V˙ae or V˙ai can be nominated for the distribution to be generated. By substituting ventilation rates over time for static volumes, where V˙ae is nominated for a lung compartment, the model can be considered analogous to a constant outflow model as defined by Korman and Mapleson (11), i.e., V˙ae remains constant, despite gas exchange within the alveolus, and gas uptake andV˙ai are calculated from the various input parameters. Changes in gas exchange due, for example, to changes in fractional inspired or mixed venous gas content will not changeV˙ae for that compartment. This assumes that net uptake of alveolar gas causes further fresh gas to be passively drawn into the alveolus. Where V˙ai is nominated, a constant inflow principle applies in which V˙ai is constant, and net gas uptake causes shrinkage in alveolar volume and a lowerV˙ae.
In addition, the effect of absorption atelectasis in compartments whereV˙ae/Q˙ was less than zero was modeled, on the basis of similar assumptions as those made by Dantzker et al. (2) that compartments with negative calculatedV˙ae would suffer collapse. Given that steadystate gas exchange was being modeled, it was assumed that perfusion of such compartments was shunt, with an endcapillary gas content identical to that of mixed venous blood. Both V˙ae andV˙ai for these compartments were made zero, and the inspired ventilation from them was redistributed to the remaining compartments by multiplying each by a scaling factor to restore totalV˙ai to its nominated value. Modifications incorporated by Dantzker et al. to simulate the effect of HPV on the distribution of Q˙ were included. For each compartment, Q˙ is given by
Derivation of a Formula for a Computer Program to Calculate Alveolar Gas Concentrations in the Presence of Multiple Gas Uptake
V˙aebased model.
The system of equations used is based on those described by Olszowska and Wagner (17).
Consider a lung compartment with a given ratio of V˙aeand Q˙, which is ventilated with an inspired mixture of O_{2} and inert gases G, G′, G", etc. The lung compartment takes up these gases in a physiologically realistic manner that is dependent on the gradient between alveolar and mixed venous content of these gases and also eliminates CO_{2}.
For each gas G in the alveolar gas mixture, the equation
If we assume that the lung compartment is an ideal compartment in which Pa
_{G} equals Pc
V˙ai/Q˙ can be defined by transposing Eq.EA1
for O_{2}
Finally, this set of simultaneous equations can be solved using an appropriate iterative technique knowing that
As well as estimating the different acidbase status of mixed venous and pulmonary arterial blood, it is necessary to take into account the acute disturbances in acidbase balance that occur within compartments, particularly in the face of relatively extreme degrees ofV˙a/Q˙ mismatch that are seen in some of these. Widely varying HbO_{2} saturations and Pco
_{2} values are seen across the compartments, and the Bohr and Haldane effects produced vary widely, affecting O_{2} and CO_{2} carriage. For this purpose, the HendersenHasselbalch equation was used to relate Pco
_{2} and pH in conjunction with the following equation relating base excess of the blood to plasma pH and bicarbonate (HCO
It was assumed that, within the time course of pulmonary blood transit, no acute buffering of acidbase changes produced by acute changes in Pco
_{2} occurred other than that of the CO_{2}HCO
Thus it can be seen that, for a lung compartment characterized by a given combination of input values for V˙ae, Q˙, mixed venous partial pressure (or mixed venous content), and inspired partial pressure of a gas, we can solve for alveolar partial pressure of the gas (and fractional endcapillary blood content for that compartment) if we know the alveolar partial pressure of the other gases in the alveolar mixture. Assuming that there is one unique set of alveolar gas concentrations that meets the conditions set by any combination of input values, it is possible to calculate Pa
_{G}, Pa
_{G′}, Pa
_{G"}, etc., and Pa
_{O2} (and Cc
The output variables for the whole lung were partial pressure of each gas species (including CO_{2}) in mixed alveolar gas and mixed endcapillary blood, mixed endcapillary blood content, and uptake of each gas. These were calculated by taking a flowweighted average of the outputs of all of the compartments for both alveolar gas and endcapillary blood and total uptakes obtained by summating the uptakes of all of the compartments. After each of these steps, the acidbase status of the mixed endcapillary or arterial blood was further calculated by using an iterative approach, as described above, to arrive at final values for Pa _{CO2} and Pa _{O2}.
A further iterative process allows nomination of the uptake of any or all of the gases as an input variable. This was performed by varying the mixed venous point for each gas by continuous bisection until the set of mixed venous values is obtained that meets the conditions specified by the inspired fractional concentration,V˙ae/Q˙, and net exchange of each gas species for all of the compartments.
V˙aibased model.
Consider a similar lung compartment with a given ratio ofV˙ai and Q˙.
Equation EA3
above can be transposed to solve forV˙ae/Q˙
An alternative method involves using Eqs. EA1EA5 and solving for V˙ai and then progressively coercing the distribution of V˙ai to be log normal using an iterative method. The resulting solution is identical to that achieved using Eq. EA6 . This method was often found to be faster, as it obviates the need for calculation of paired values for Pa _{CO2} and Cc′_{CO2} consistent with theV˙ae/Q˙ obtained from Eq. EA6 during every iteration in pursuit of the solution for each compartment.