Factors determining temporal pattern of isobaric supersaturation

It is possible to produce a transient supersaturation or undersaturation in tissues and blood by sequentially breathing gases with different equilibration rates. If the ambient gas pressure is sufficiently high, the induced supersaturation can produce vascular bubbles. By means of the classical perfusion-dependent model of inert gas elimination, which assumes that the effects of diffusion are minimal, the magnitude of the total inert gas pressure can be predicted. If, however, the effects of diffusion cannot be ignored, the supersaturation could be substantially larger. This paper estimates the effects of diffusion in a Krogh cylinder on the supersaturation produced by suddenly changing the inert gas partial pressure in the blood. The results of these estimates indicate that diffusion plays a role in this transient supersaturation only in long Krogh cylinders with high blood flows. The effects of diffusion are further reduced by the finite time necessary to switch the inert gases in arterial blood. The conclusions are supported by experiments that measure vascular bubble production after a switch of the inert portion of the inspired gas. These experiments further show that the formation of vascular bubbles after such a switch cannot be entirely explained by the different diffusion constants of the gases used.     

Stratified Pulmonary Blood Flow: Some Consequences in Emphysema and Pulmonary Embolism

Both ventilation and blood flow in the secondary lobule of the lung are stratified; each unit of lung tissue in the proximal portion of the lobule receives up to four times the blood flow of units in the peripheral portion. Questions of the limiting role of gas diffusion within the small airways become virtually irrelevant in the face of this stratification of function.The central portion of the lobule, with its high ventilation, blood flow, and gas exchange, is very vulnerable; small lesions at this site will produce disproportionately large disturbances of gas exchange and of pulmonary vascular resistance. This may well account for some of the phenomena of conditions such as centrilobular emphysema and pulmonary microembolism.     

Inert gas diffusion in heterogeneous tissue II: With perfusion

In this paper, a tractable mathematical model is proposed to describe transient inert gas diffusion in heterogeneous tissue with perfusion controlling gas input to the cellular region. The corresponding solution of overall mass uptake of the inert gas is derived exactly and should be useful in interpreting washout curves from particular tissue zones, whether there is any interaction with cellular diffusion or not. It is shown that the solution contains effectively nearly all models hitherto proposed to describe gas uptake in tissue. However some indication is given of a possible situation where perfusion, extra-cellular and cellular diffusion will need to be treated separately.     

How well mixed is inert gas in tissues?

The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.     

Conducting airway gas exchange: diffusion-related differences in inert gas elimination.

We studied CO2 and inert gas elimination in the isolated in situ trachea as a model of conducting airway gas exchange. Six inert gases with various solubilities and molecular weights (MW) were infused into the left atria of six pentobarbital-anesthetized dogs (group 1). The unidirectionally ventilated trachea behaved as a high ventilation-perfusion unit (ratio = 60) with no appreciable dead space. Excretion of higher-MW gases appeared to be depressed, suggesting a MW dependence to inert gas exchange. This was further explored in another six dogs (group 2) with three gases of nearly equal solubility but widely divergent MWs (acetylene, 26; Freon-22, 86.5; isoflurane, 184.5). Isoflurane and Freon-22 excretions were depressed 47 and 30%, respectively, relative to acetylene. In a theoretical model of airway gas exchange, neither a tissue nor a gas phase diffusion resistance predicted our results better than the standard equation for steady-state alveolar inert gas elimination. However, addition of a simple ln (MW) term reduced the remaining residual sum of squares by 40% in group 1 and by 83% in group 2. Despite this significant MW influence on tracheal gas exchange, we calculate that the quantitative gas exchange capacity of the conducting airways in total can account for less than or equal to 16% of any MW-dependent differences observed in pulmonary inert gas elimination.     

The interaction of diffusion and perfusion in homogeneous tissue

A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.     

The Diffusion of Oxygen, Carbon Dioxide, and Inert Gas in Flowing Blood

Measurements were made of exchange rates of oxygen, carbon dioxide, and krypton-85 with blood at 37.5°C. Gas transfer took place across a 1 mil silicone rubber membrane. The blood was in a rotating disk boundary layer flow, and the controlling resistance to transfer was the concentration boundary layer. Measured rates were compared with rates predicted from the equation of convective diffusion using velocities derived from the Navier-Stokes equations and diffusivities calculated from the theory for conduction in a heterogeneous medium. The measured absorption rate of krypton-85 was closely predicted by this model. Significant deposition of material onto the membrane surface, resulting in an increased transfer resistance, occurred in one experiment with blood previously used in a nonmembrane type artificial lung. The desorption rate of oxygen from blood at low P_o2¹ was up to four times the corresponding transfer rate of inert gas. This effect is described somewhat conservatively by a local equilibrium form of the convective diffusion equation. The carbon dioxide transfer rate in blood near venous conditions was about twice that of inert gas, a rate significantly greater than predicted by the local equilibrium theory. It should be possible to apply these theoretical methods to predict exchange rates with blood flowing in systems of other geometries.     

A mathematical model for breath gas analysis of volatile organic compounds with special emphasis on acetone

Recommended standardized procedures for determining exhaled lower respiratory nitric oxide and nasal nitric oxide (NO) have been developed by task forces of the European Respiratory Society and the American Thoracic Society. These recommendations have paved the way for the measurement of nitric oxide to become a diagnostic tool for specific clinical applications. It would be desirable to develop similar guidelines for the sampling of other trace gases in exhaled breath, especially volatile organic compounds (VOCs) which may reflect ongoing metabolism. The concentrations of water-soluble, blood-borne substances in exhaled breath are influenced by: (i) breathing patterns affecting gas exchange in the conducting airways, (ii) the concentrations in the tracheo-bronchial lining fluid, (iii) the alveolar and systemic concentrations of the compound. The classical Farhi equation takes only the alveolar concentrations into account. Real-time measurements of acetone in end-tidal breath under an ergometer challenge show characteristics which cannot be explained within the Farhi setting. Here we develop a compartment model that reliably captures these profiles and is capable of relating breath to the systemic concentrations of acetone. By comparison with experimental data it is inferred that the major part of variability in breath acetone concentrations (e.g., in response to moderate exercise or altered breathing patterns) can be attributed to airway gas exchange, with minimal changes of the underlying blood and tissue concentrations. Moreover, the model illuminates the discrepancies between observed and theoretically predicted blood-breath ratios of acetone during resting conditions, i.e., in steady state. Particularly, the current formulation includes the classical Farhi and the Scheid series inhomogeneity model as special limiting cases and thus is expected to have general relevance for a wider range of blood-borne inert gases. The chief intention of the present modeling study is to provide mechanistic relationships for further investigating the exhalation kinetics of acetone and other water-soluble species. This quantitative approach is a first step towards new guidelines for breath gas analyses of volatile organic compounds, similar to those for nitric oxide.     

High-frequency ventilation of ducks and geese

We studied gas exchange in anesthetized ducks and geese artificially ventilated at normal tidal volumes (VT) and respiratory frequencies (fR) with a Harvard respirator (control ventilation, CV) or at low VT-high fR using an oscillating pump across a bias flow with mean airway opening pressure regulated at 0 cmH2O (high-frequency ventilation, HFV). VT was normalized to anatomic plus instrument dead space (VT/VD) for analysis. Arterial PCO2 was maintained at or below CV levels by HFV with VT/VD less than 0.5 and fR = 9 and 12 s-1 but not at fR = 6 s-1. For 0.4 less than or equal to VT/VD less than or equal to 0.85 and 3 s-1. less than or equal to fR less than or equal to 12 s-1, increased VT/VD was twice as effective as increased fR at decreasing arterial PCO2, consistent with oscillatory dispersion in a branching network being an important gas transport mechanism in birds on HFV. Ventilation of proximal exchange units with fresh gas due to laminar flow is not the necessary mechanism supporting gas exchange in HFV, since exchange could be maintained with VT/VD less than 0.5. Interclavicular and posterior thoracic air sac ventilation measured by helium washout did not change as much as expired minute ventilation during HFV. PCO2 was equal in both air sacs during HFV. These results could be explained by alterations in aerodynamic valving and flow patterns with HFV. Ventilation-perfusion distributions measured by the multiple inert gas elimination technique show increased inhomogeneity with HFV. Elimination of soluble gases was also enhanced in HFV as reported for mammals.(ABSTRACT TRUNCATED AT 250 WORDS)     

Effects of crocetin on pulmonary gas exchange in foxhounds during hypoxic exercise.

The carotenoid compound crocetin has been hypothesized to enhance the diffusion of O(2) through plasma, and observations in the rat and rabbit have revealed improvement in arterial PO(2) when crocetin is given. To determine whether crocetin enhances diffusion of O(2) between alveolar gas and the red blood cell in the pulmonary capillary in vivo, five foxhounds, two previously subjected to sham and three to actual lobectomy or pneumonectomy, were studied while breathing 14% O(2) at rest and during moderate and heavy exercise before and within 10 min after injection of a single dose of crocetin as the trans isomer of sodium crocetinate (TSC) at 100 microg/kg iv. This dose is equivalent to that used in previous studies and would yield an initial plasma concentration of 0.7-1.0 microg/ml. Ventilation-perfusion inequality and pulmonary diffusion limitation were assessed by the multiple inert gas elimination technique in concert with conventional measurements of arterial and mixed venous O(2) and CO(2). TSC had no effect on ventilation, cardiac output, O(2) consumption, arterial PO(2)/saturation, or pulmonary O(2) diffusing capacity. There were minor reductions in ventilation-perfusion mismatching (logarithm of the standard deviation of perfusion fell from 0.48 to 0.43, P = 0.001) and in CO(2) output and respiratory exchange ratio (P = 0.05), which may have been due to TSC or to persisting effects of the first exercise bout. Spectrophotometry revealed that TSC disappeared from plasma with a half time of approximately 10 min. We conclude that, in this model of extensive pulmonary O(2) diffusion limitation, TSC as given has no effect on O(2) exchange or transport. Whether the original hypothesis is invalid, the dose of TSC was too low, or plasma diffusion of O(2) is not rate limiting without TSC cannot be discerned from the present study.     

Distribution of ventilation-perfusion ratios in dogs with normal and abnormal lungs.

We have recently described a new method for measuring distributions of ventilation-perfusion ratios (VA/Q) based on inert gas elimination. Here we report the initial application of the method in normal dogs and in dogs with pulmonary embolism, pulmonary edema, and pneumonia. Characteristic distributions appropriate to the known effects of each lesion were observed. Comparison with traditional indices of gas exchange revealed that the arterial PO2 calculated from the distributions agreed well with measured values, as did the shunts indicated by the method and by the arterial PO2 while breathing 100 per cent 02. Also the Bohr dead space closely matched the dispersion of ventilation in realtion to VA/Q. Assumptions made in the method were critically evaluated and appear justified. These include the existence of a steady state of gas exchange, an alveolar-end-capillary diffusion equilibration, and the fact that all of the observered VA/Q inequality occurs between gas exchange units in parallel. However, theoretical analysis suggests that the method can detect failure of diffusion equilbration across the blood-gas barrier should it exist. These results suggest that the method is well-suited to clinical investigation of patients with pulmonary disease.     

Multiple inert gas elimination technique

The understanding of pulmonary gas exchange has undergone several major advances since the early 1900's. One of the most significant was the development of the multiple inert gas elimination technique for assessing the ventilation-perfusion (VA/Q) distribution in the lung. By measuring the mixed venous, arterial, and mixed expired concentrations of six infused inert gases, it is possible to distinguish shunt, dead space, and the general pattern of VA/Q distribution. As with all mathematical models of complex biological phenomena, there are limitations that can result in errors of interpretation if the technique is applied uncritically. In addition, methodological limitations also can lead to both experimental error and errors of interpretation. Despite these limitations, the multiple inert gas elimination technique remains the most powerful tool developed to date to analyze pulmonary gas exchange.     

Effect of inert gas switching at depth on decompression outcome in rats

The present investigation was performed to determine whether inert gas sequencing at depth would affect decompression outcome in rats via the phenomenon of counterdiffusion. Unanesthetized rats (Rattus norvegicus) were subjected to simulated dives in either air, 79% He-21% O2, or 79% Ar-21% O2; depths ranged from 125 to 175 feet of seawater (4.8-6.3 atmospheres absolute). After 1 h at depth, the dive chamber was vented (with depth held constant) over a 5-min period with the same gas as in the chamber (controls) or one of the other two inert gas-O2 mixtures. After the gas switch, a 5- to 35-min period was allowed for gas exchange between the animals and chamber atmosphere before rapid decompression to the surface. Substantial changes in the risk of decompression sickness (DCS) were observed after the gas switch because of differences in potencies (He less than N2 less than Ar) for causing DCS and gas exchange rates (He greater than Ar greater than N2) among the three gases. Based on the predicted gas exchange rates, transient increases or decreases in total inert gas pressure would be expected to occur during these experimental conditions. Because of differences in gas potencies, DCS risk may not directly follow the changes in total inert gas pressure. In fact, a decline in predicted DCS risk may occur even as total inert gas pressure in increasing.     

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.     

Analysis of acetylene reduction rates of soybean nodules at low acetylene concentrations

It has been previously proposed that acetylene reduction data at subsaturating acetylene concentrations could be interpreted by use of the Michaelis-Menten equation, based on the acetylene concentration external to the nodules. One difficulty of this view is that the assumption that the system is not diffusion limited is violated when studying intact nodules. The presence of a gas diffusion barrier in the nodule cortex leads to an alternate expression for the gas exchange rates at subsaturating gas concentrations. A theoretical comparison of the `apparent' Michaelis-Menten model and diffusion model illustrated the difficulties observed in the former model of overestimating the Michaelis-Menten coefficient and yielding a correlation between the Michaelis-Menten coefficient and the maximum rate. On the other hand, use of a diffusion model resulted in (a) estimates of the Michaelis-Menten coefficient consistent with enzyme studies, (b) stability of the estimates of the Michaelis-Menten coefficient independent of treatment, and (c) a sensitivity of the diffusion barrier conductance to plant drought stress. It was concluded that all studies of nodule gas exchange need to consider possible effects caused by the presence of a diffusion barrier.     

The effect of changing the gaseous diffusion coefficient on the mass loss pattern of Hyalophora cecropia pupae

The importance of gas phase diffusion in insect gas exchange remains unclear. The role of diffusion in gas exchange of developing Hyalophora cecropia pupae was examined by altering the gaseous diffusion coefficient in the breathing mixture. Gaseous diffusion coefficients were manipulated by substituting helium or sulfur hexafluoride for the nitrogen usually present in air. Sensitive mass loss recordings were employed to monitor gas exchange activity. Mass loss recordings showed a two-phase cycle, open and closed-flutter. Mass loss rates during the open and closed-flutter periods were not altered in proportion to the changes induced in the rate of diffusion. Open-phase duration was inversely and proportionally related to the diffusion coefficient. These results are consistent with changes in spiracle resistance or convective flow during the open period in response to a change in the diffusion coefficient. In addition, they indicate a significant gas phase diffusive resistance within the pupal tracheal system. This previously unreported gas phase resistance appears to be a major determinant of the duration of the open period and thus of overall water loss rates in these pupae.     

Modeling and analysis of diffusion and reaction in legume nodules

Diffusion of gases through legume nodules is important for nitrogen fixation. A mathematical model is presented for diffusion and enzymatic reaction for legume nodules with a reactive core and an inert shell. The transient model is solved numerically for spherical geometry for acetylene reduction by nitrogenase enzyme. The results are used to estimate the diffusivities of acetylene and ethylene in the nodules by comparing predicted and experimental lag times. The experimental results are also analyzed using an effectiveness factor plot for spherical nodules with inert shells and reactive cores. The results show that the diffusivities are slightly higher than those for acetylene and ethylene in water because of some contribution of gas phase diffusion. Applications to oxygen diffusion through nodule tissue are suggested.     

Validation of measurements of ventilation-to-perfusion ratio inequality in the lung from expired gas.

The analysis of the gas in a single expirate has long been used to estimate the degree of ventilation-perfusion (Va/Q) inequality in the lung. To further validate this estimate, we examined three measures of Va/Q inhomogeneity calculated from a single full exhalation in nine anesthetized mongrel dogs under control conditions and after exposure to aerosolized methacholine. These measurements were then compared with arterial blood gases and with measurements of Va/Q inhomogeneity obtained using the multiple inert gas elimination technique. The slope of the instantaneous respiratory exchange ratio (R slope) vs. expired volume was poorly correlated with independent measures, probably because of the curvilinear nature of the relationship due to continuing gas exchange. When R was converted to the intrabreath Va/Q (iV/Q), the best index was the slope of iV/Q vs. volume over phase III (iV/Q slope). This was strongly correlated with independent measures, especially those relating to inhomogeneity of perfusion. The correlations for iV/Q slope and R slope considerably improved when only the first half of phase III was considered. We conclude that a useful noninvasive measurement of Va/Q inhomogeneity can be derived from the intrabreath respiratory exchange ratio.     

Diffusion limitation in normal humans during exercise at sea level and simulated altitude

The relative roles of ventilation-perfusion (VA/Q) inequality, alveolar-capillary diffusion resistance, postpulmonary shunt, and gas phase diffusion limitation in determining arterial PO2 (PaO2) were assessed in nine normal unacclimatized men at rest and during bicycle exercise at sea level and three simulated altitudes (5,000, 10,000, and 15,000 ft; barometric pressures = 632, 523, and 429 Torr). We measured mixed expired and arterial inert and respiratory gases, minute ventilation, and cardiac output. Using the multiple inert gas elimination technique, PaO2 and the arterial O2 concentration expected from VA/Q inequality alone were compared with actual values, lower measured PaO2 indicating alveolar-capillary diffusion disequilibrium for O2. At sea level, alveolar-arterial PO2 differences were approximately 10 Torr at rest, increasing to approximately 20 Torr at a metabolic consumption of O2 (VO2) of 3 l/min. There was no evidence for diffusion disequilibrium, similar results being obtained at 5,000 ft. At 10 and 15,000 ft, resting alveolar-arterial PO2 difference was less than at sea level with no diffusion disequilibrium. During exercise, alveolar-arterial PO2 difference increased considerably more than expected from VA/Q mismatch alone. For example, at VO2 of 2.5 l/min at 10,000 ft, total alveolar-arterial PO2 difference was 30 Torr and that due to VA/Q mismatch alone was 15 Torr. At 15,000 ft and VO2 of 1.5 l/min, these values were 25 and 10 Torr, respectively. Expected and actual PaO2 agreed during 100% O2 breathing at 15,000 ft, excluding postpulmonary shunt as a cause of the larger alveolar-arterial O2 difference than accountable by inert gas exchange.(ABSTRACT TRUNCATED AT 250 WORDS)