INTRODUCTION

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THE EFFECT ON GAS EXCHANGE of inhomogeneity of ventilation-to-perfusion ratios (A/) in the lung has been explored by previous authors (1). Analysis of log normal distributions of expired alveolar ventilation (A; AE) and blood flow () by West (17, 18) and Kelman (8) predicted reduced gas exchange for any gas species. For the sake of simplicity, this early modeling assumed the presence of no soluble accompanying gases in the inspired mixture.

However, two-compartment modeling of the effect of increasing inhomogeneity of ventilation and predicted a paradoxical increase in the uptake of one gas when mixtures of two soluble gases are administered, such as is the case during inhalational anesthesia with oxygen and nitrous oxide (N₂O). These findings are presented in the accompanying paper (12).

To determine the clinical relevance of these findings, we have extended this study using a computer model of physiological distributions of ventilation and to investigate the predicted effects of differing degrees of A/ inhomogeneity on gas exchange in the presence of a typical inspired mixture of O₂ and N₂O. The model first employed theoretical log normal distributions. Because distributions of AE and inspired A (AI) may produce different effects, results based on each were compared. In addition, measured distributions of AE and published previously by other authors using the multiple inert-gas elimination technique (6) were modeled to see whether the patterns of widening of distributions measured in patients are expected to produce the same effects on gas exchange as widening of the smooth theoretical distributions.

	METHODS

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A computer model was used to calculate the exchange of multiple gases across the alveolar-capillary membrane according to principles of mass balance for each gas. The model assumes that, within a compartment, arterial and alveolar partial pressures for each gas species are identical. The independent variables for the calculation of alveolar partial pressures and gas exchange for each gas are its inspired fractional concentration, the mixed venous content [or partial pressure and Ostwald solubility coefficient ()], and AE or AI and for that compartment. The structure and data flow of this model are outlined in more detail in the accompanying papers (12, 13). The distributions of ventilation and given to the model were obtained as follows.

Theoretical Log Normal Distributions

When a log normal distribution of AI was nominated, the effect of absorption atelectasis was modeled as follows. No inspired ventilation was distributed to compartments where AI/ was below a critical value at which AE was calculated to be less than zero. This is based on similar assumptions to those made by Dantzker et al. (5) that such compartments would suffer collapse. Given that steady-state gas exchange was being modeled, it was assumed that perfusion of such compartments was shunt, with an end-capillary gas content identical to that of mixed venous blood. Both AE and 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 total AI to its nominated value. Modifications incorporated by Dantzker et al. to simulate the effect of hypoxic pulmonary vasoconstriction on the distribution of were included. Once again, perfusion of all compartments was scaled so that total remained at the nominated value. An iterative approach is required for these modifications so that final distributions obtained were consistent with all of the input variables.

West (17) 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 AI/ was incorporated, 50 compartments were required to avoid noticeable quantization error because of inclusion or exclusion of compartments with AI/ values near the critical value.

Measured Distributions

View this table: [in this window] [in a new window]   Table 1.   Results of modeling changes in N2O when moving from narrower to wider distributions measured using the multiple inert-gas elimination technique

Analysis Performed

Theoretical log normal distributions. A scenario typical of the maintenance phase of an inhalational anesthetic was modeled involving administration of an inspired mixture of 30% O₂ and 70% N₂O. For purposes of comparison, regardless of whether a distribution of AE or AI was nominated, overall AE was held at 4.1 l/min and was 4.8 l/min. Parameters examined in the primary analysis were uptakes of O₂ (O₂), CO₂ (CO₂), and N₂O (N₂O) on a global basis and by compartment. Analyses were performed with either specified mixed venous partial pressures or specified gas uptakes (or combinations of these for different gases). Where specified, O₂ and CO₂ were set at 250 and 200 ml/min, respectively.

Measured distributions. The analysis was repeated using the three pairs of measured distributions. Gas exchange was calculated and compared for each pair of distributions using the input variables listed above. For purposes of standardization, the distributions were scaled so that overall AE and (including shunt and dead space), inspired concentrations, and O₂ and CO₂ were set at the values given above. The mixed venous N₂O partial pressure (P_N2O) was set at a value giving an N₂O of 100 ml/min for the narrower distribution of each pair.

	RESULTS

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Theoretical Log Normal Distributions

Paradoxical augmentation of steady-state N₂O. A P_N2O of 468 Torr was nominated, giving a N₂O for a homogeneous lung (0 log SD) of 100 ml/min. Increasing the log SD of the distribution of (increasing inhomogeneity of A/ matching) produced an increased arterial partial pressure of N₂O (Pa_N2O) and N₂O. This occurred in the presence of either fixed O₂ and CO₂ exchange or fixed mixed venous partial pressures of these gases. The predicted N₂O at a log SD of 1.75 was more than twice the value predicted at 0 log SD.

View larger version (22K): [in this window] [in a new window]   Fig. 1.   Predicted N2O uptake (N2O) with increasing ventilation-to-perfusion ratio (A/) inhomogeneity as indexed by the log SD of the distribution of blood flow () for a constant mixed venous partial pressure of N2O (PN2O) (468 Torr). O2 uptake (O2) (and respiratory quotient) was held constant. Predictions from a model based on a log normal distribution of expired alveolar ventilation (AE), a model based on a log normal distribution of inspired alveolar ventilation (AI), are shown. The constant inflow model was also modified to incorporate the effects of alveolar collapse of compartments with critically low AI/ and also with the effect of hypoxic pulmonary vasoconstriction (HPV).

Rising P_N2O. The effect of the P_N2O on this phenomenon was investigated by repeating the study (Fig. 2) at different values of P_N2O between 0 and 600 Torr (where it exceeds Pa_N2O and net N₂O elimination is expected to occur in the homogeneous lung). Mixed venous partial pressures of O₂ and CO₂ were held constant. At low P_N2O where high N₂O was simulated, Pa_N2O and N₂O fell progressively with increasing A/ inhomogeneity. This fall became less steep as P_N2O rose to a threshold (P_N2O of ~300 Torr in this scenario), where the slope reversed and N₂O increased with worsening inhomogeneity. At a P_N2O of 300 Torr, paradoxical augmentation of N₂O occurs.

View larger version (21K): [in this window] [in a new window]   Fig. 2.   Effect of rising PN2O on the relationship of N2O to the severity of A/ inhomogeneity. In the scenario modeled, with an inspired fraction of N2O of 0.7 and constant mixed venous partial pressures of O2 and CO2, the threshold for paradoxical augmentation of N2O was a PN2O of 300 Torr.

O₂ exchange. O₂ was calculated simultaneously with N₂O at increasing P_N2O (Fig. 3). It was found that paradoxical augmentation of O₂ [and thus arterial O₂ partial pressure (Pa_O2)] occurred as the log SD of the distribution of perfusion was increased from 0 to 1.75. The augmentation effect was similar in nature but reciprocal to that found for N₂O, in that it diminished as P_N2O rose and ceased around the same threshold P_N2O, where augmentation of the inert-gas uptake commenced. At higher values of P_N2O (lower N₂O), O₂ and Pa_O2 fell with worsening A/ inhomogeneity, as is normally expected, and was demonstrated in the accompanying paper (13) modeling a low "maintenance-phase" level of N₂O.

View larger version (22K): [in this window] [in a new window]   Fig. 3.   Effect of rising PN2O on the relationship of O2 to the severity of A/ inhomogeneity. In an identical scenario to that modeled in Fig. 2, the threshold PN2O for paradoxical augmentation of O2 is the same (300 Torr), but the direction of the effect of rising PN2O is opposite.

Measured Distributions

	DISCUSSION

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Paradoxical Increase in Inert-gas Uptake

At first glance, this increase in gas uptake seems somewhat counterintuitive, given that it has been well demonstrated by computer modeling by previous authors (8, 17, 18) that the expected result of increasing inhomogeneity in A/ matching is a reduction in gas exchange for all gas species. Modeling of gas elimination showed that this reduction is maximal for gases with an Ostwald blood-gas partition coefficient  equal to the overall AE/ of the lung (4). In the presence of an overall AE/ of 0.86, exchange of a gas such as N₂O with a  of 0.47 would be expected to be significantly reduced by A/ inhomogeneity. Where gas uptake was modeled (18), this value of  was higher, but inert-gas exchange was still predicted to be decreased at any level of inhomogeneity compared with that in a perfectly homogeneous lung.

The important limitation of some of these early studies was that they assumed an insoluble vehicle gas as the balance of the inspired mixture. More physiologically realistic models have since been applied that allow for the interdependent exchange of multiple alveolar gases, including N₂O. Dantzker et al. (5) applied a modified form of such a computer model, involving a log normal distribution of AI to demonstrate that lung units with very low A/ may suffer collapse where gas uptake exceeds AI. These later models of multiple gas exchange (5, 6), which looked at O₂-N₂O mixtures, did not explore the relationship of global gas exchange to A/ inhomogeneity.

Examination of the exchange of individual gas species on a compartment-by-compartment basis provides some insight into the mechanism for paradoxical augmentation. Figure 4 plots the distribution of exchange of individual gas species in a heterogeneous lung. For simplicity, the exchange of O₂ and CO₂ is shown as a single plot representing net respiratory gas exchange (O₂-CO₂), where O₂ predominates in the lower A/ compartments and CO₂ in the better ventilated areas. It shows that O₂ and N₂O occur predominantly within low A/ compartments and largely follow the distribution of . This is consistent with the perfusion-limited nature of uptake of these gases.

View larger version (29K): [in this window] [in a new window]   Fig. 4.   Predicted gas exchange by lung compartment for a lung with log SD for of 1.75. AE/ increases from left to right. N2O is plotted along with , AE, and the balance of O2 and CO2 uptake for that compartment.

Uptake of one gas within the lung will raise the concentration of other gases in the alveolar gas mixture. The net exchange of O₂ and CO₂ governs the magnitude of the concentrating effects on alveolar N₂O within each compartment. N₂O exchange will also exert similar effects on O₂ and CO₂. The asymmetric nature of respiratory gas exchange across the distribution of A/ shown in Fig. 4 results in an asymmetric concentrating effect on alveolar N₂O. This is demonstrated by Fig. 5, which shows the different distributions of N₂O partial pressures in two lungs of differing degrees of inhomogeneity. In the moderately low A/ compartments, substantial O₂ concentrates N₂O in the alveolus and drives N₂O there. These compartments have the greatest , and here the concentrating effect on alveolar N₂O is most powerful. Lung units with moderately low A/ receive a substantial proportion of total pulmonary and thus would be expected to have a dominating influence on the content of these perfusion-limited gases in arterial blood and thus on total exchange of these gases.

View larger version (19K): [in this window] [in a new window]   Fig. 5.   Distributions of end-capillary N2O partial pressure (Pc'N2O) across 10 compartments with 2 distributions of with low and high degrees of inhomogeneity (log SD of 0.5 and 2.0, respectively).

Figure 6 demonstrates quantitatively the process of paradoxical augmentation by comparing two lungs of differing A/ homogeneity. For both the more uniform and the more inhomogeneous lung, the area under the N₂O curve is the overall N₂O. As the SD of the distribution increases, there is redistribution of a greater proportion of total to lower A/ areas. N₂O increases markedly in these compartments as this occurs, and this increase outweighs the reduced uptake in higher A/ lung units that occurs as their is reduced. Figure 6 shows that, for the overall lung, the concentrating effects of O₂ on alveolar N₂O are magnified by greater inhomogeneity.

View larger version (34K): [in this window] [in a new window]   Fig. 6.   Distributions of N2O and across the 10 compartments with 2 distributions of with low and high degrees of inhomogeneity (log SD of 0.25 and 1.75, respectively). The higher N2O and high perfusion in the moderately low A/ compartments are obvious in the more severely inhomogeneous distribution.

O₂ and N₂O produce competing concentrating effects, predominantly in these low A/ compartments, the balance of which is determined by their solubilities, inspired concentration, and mixed venous content. The mutual enhancement of uptake that O₂ and N₂O possess is limited only by the approach of their alveolar partial pressures to the mixed venous for each gas within these compartments and to a lesser extent by dilution of alveolar gas by CO₂.

An interesting manifestation of paradoxical augmentation is that when Pa_N2O is very close to P_N2O, such that net inert-gas exchange is calculated to be negative for the homogeneous lung, it is still positive for the lung with significant A/ inhomogeneity, despite identical inspired and mixed venous gas content. Examination of gas exchange in such an inhomogeneous lung on a compartment-by-compartment basis shows that N₂O is being taken up by low AE/ units and eliminated by high AE/ units, with the balance determining the direction of global gas exchange. This "flow through" of gas within the lungs has been predicted to occur for N₂ in the presence of A/ inhomogeneity, and raised urinary N₂ has been used as a test for the severity of chronic pulmonary obstructive disease (1, 9). It can be seen for other inert gases at particular ranges of inspired and mixed venous partial pressures. At high degrees of inhomogeneity, N₂O in low A/ units is magnified to a considerably greater extent than N₂O exchange in other compartments (Fig. 7).

View larger version (24K): [in this window] [in a new window]   Fig. 7.   Distributions of N2O across the lung compartments at a high PN2O plotted at 3 different levels of inhomogeneity of AE/. In the less inhomogeneous lung, N2O is eliminated by all lung units, whereas, at higher degrees of inhomogeneity, concentrating effects in low AE/ compartments predominate, making net N2O exchange positive.

Dueck et al. (6) measured N₂O in their subjects during maintenance-phase anesthesia. However, there is no data available in the literature measuring N₂O and changes in A/ distributions simultaneously. Most studies employing the multiple inert-gas elimination technique in anesthetized patients have measured distributions before and after induction of anesthesia to generate widening of these distributions. There are obvious difficulties in directly measuring changes in N₂O exchange that occur in patients who are not receiving anesthesia when the first distribution is taken. For this reason, we have used computer modeling to simulate gas exchange with given A/ distributions. Where this was applied to Dueck's published distributions, the predictions of modeling of both two-compartment (12) and theoretical log normal distributions were confirmed; widening inhomogeneity of A/ increases N₂O where maintenance-phase levels of inert-gas exchange are modeled. This also casts some light on the physiological factors that will limit paradoxical augmentation. These measured distributions were collected from patients with significant chronic lung disease and also incorporate varying degrees of true shunt and dead space ventilation. The calculated increase in N₂O was greatest for the distributions of subject 7, where there was no significant change in true shunt or dead space moving from the narrower to the wider distribution. Using the distributions of subject 8, an increase in N₂O was still predicted, despite a large increase in dead space ventilation i.e., a doubling of the amount of ventilation that was effectively wasted. The greater uptake by perfused lung units still overcame the effects of reduced A to them. Similarly, the distributions of subject 6 predicted only a small reduction in N₂O, despite the superimposition of a large proportion of true shunt accompanying the wider distribution. Thus augmentation of N₂O in ventilated lung units largely compensated for the reduction in effective pulmonary capillary imposed by the increased shunt.

It is of interest that, in the study by Dueck et al. (6), the measured N₂O was highest (325 ml/min uptake after 85 min of N₂O anesthesia) in subject 7, who demonstrated the most severe degree of inhomogeneity of pulmonary . Examination of the distributions measured for this subject show that there was a significant proportion of lung units with low AE/ at the time of the measurement. We have shown that it is in these compartments that the most powerful concentrating effects occur, which drive the paradoxical increase in inert-gas exchange.

At higher levels of N₂O, augmentation of O₂ with increasing A/ inhomogeneity is predicted (Fig. 3). This may produce clinically significant increases in Pa_O2 compared with the homogeneous lung. The corresponding clinical scenario is the immediate postinduction phase. The concentrating and second gas effects of rapid N₂O early in an inhalational anesthetic were described by Stoelting and Eger (16). They demonstrated that high N₂O raises the alveolar concentration of accompanying gases, including O₂, by contraction of alveolar volume with or without indrawing of further inspired gas to replace the lost volume. However, Fig. 3 shows that a more pronounced postinduction increase in Pa_O2 is expected at more severe levels of A/ inhomogeneity.

The accompanying paper (12) shows that competing concentrating effects of uptake of one gas on the other are inevitably present in any lung compartment where two gases are being taken up. Logically, the net concentrating effect can only be in one direction at any given time. The position of balance of these processes and the direction of the net concentrating effect are determined by the relative inspired concentrations and uptakes of the two gases. In the more complex physiological model presented here, the point of balance is complicated by a number of factors not encompassed in the simplified treatment given by the accompanying paper (12). These are the presence of alveolar CO₂ exchange, the differing solubilities of the gases involved, and the alinear nature of the dissociation curve for O₂, which cause these gases to be taken up unequally in lung compartments of different A/.

As shown by Figs. 2 and 3, the direction of the overall concentrating effect changes at a certain P_N2O and N₂O. Inhomogeneity simply magnifies these existing concentrating effects, and thus paradoxical augmentation can only be seen for one gas or the other at any time.

Clinical Considerations: Inert-gas Exchange

It can be seen from Fig. 2 that the phenomenon of paradoxical augmentation of gas uptake only commences when the mixed venous partial pressure has risen above a certain threshold (in this scenario 300 Torr). Thus it is a product of a relatively low inspired-to-mixed venous partial pressure gradient and commences when uptake of the gas has declined below a certain value. Consideration of changing gas exchange over time shows that this threshold P_N2O is reached after only a short time after induction of anesthesia. Figure 2 shows that, in our scenario, the threshold for paradoxical augmentation of N₂O is at ~550 ml/min. Severinghaus (15) states that the N₂O (ml/min) at time t (min) after introduction of an inspired N₂O concentration of 70% is given by
Thus we can expect to reach this point after several minutes in a typical patient, and for the remainder of time under anesthesia N₂O is predicted to increase with worsening A/ inhomogeneity.

One of the physiological factors that might be expected to minimize paradoxical augmentation of O₂ and N₂O is incomplete denitrogenation of the body. This is due to accumulation of the poorly soluble N₂ in low AE/ lung compartments as shown by Dantzker et al. (5), where its presence dilutes the most potent concentrating effects of O₂ and N₂O. The effect of this was examined by repeating the analysis of Fig. 1, superimposing an excretion of N₂ of 10 ml/min from the lungs. This level of N₂ elimination is consistent with the findings of Beatty et al. (2) for patients during maintenance-phase anesthesia. Figure 8 shows that N₂O is reduced in the presence of N₂ elimination to a greater extent at higher levels of A/ inhomogeneity, but that paradoxical augmentation still clearly occurs for N₂O despite this.

View larger version (17K): [in this window] [in a new window]   Fig. 8.   Effect of N2 elimination of 10 ml/min from the lungs on paradoxical augmentation of N2O with increasing A/ inhomogeneity, compared with a lung with no N2 elimination. Mixed venous partial pressures of O2 and CO2 were held constant.

The lack of effect of N₂ retention on paradoxical augmentation of N₂O may not hold true for O₂, however. Paradoxical augmentation of O₂, if it is a clinical reality, occurs during the early postinduction phase of rapid N₂O, when incomplete denitrogenation of the alveolar volume is likely. The presence of significant levels of retained alveolar N₂ throughout the lung is likely to ablate much of the early concentrating effect on alveolar O₂.

Conclusion

At higher levels of N₂O, such as are seen in the early phases after anesthetic induction (and in the absence of retained alveolar N₂), paradoxical augmentation of O₂ with worsening A/ inhomogeneity is seen instead. The effect on O₂ is not seen concurrently with that for N₂O. This is because the effect of inhomogeneity is to magnify the existing concentrating effects of uptake one gas on the other. These can only operate in one direction or the other at a time, depending on the relative uptakes and inspired concentrations of the gases.