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.     

Spectral analysis of inert gas elimination data: resolution limits

A new method of analyzing inert gas data for recovery of the pulmonary ventilation-perfusion ration (VA/Q) distribution is proposed. It is shown that the conventional inert gas elimination equation takes the form of a convolution integral, and the relationship between VA/Q distribution and inert gas elimination resembles that of a noncausal low-pass filter with infinite zero-frequency gain. With the use of this formulation, characteristic features of VA/Q distribution may be represented in the frequency domain in terms of the corresponding energy spectrum. It is shown that the lack of resolution associated with finite data samples and measurement error is caused by distortions in the high-frequency contents of the resulting VA/Q distribution. With six inert gases, the technique cannot resolve a log SD less than 0.21 decade and a modal separation less than 0.87 decade. In the presence of measurement error, the degree of resolution is even less. It is suggested that for maximum resolution the number of discrete and duplicate data samples should be chosen so that the resulting noise and sampling cutoff frequencies are approximately equal.     

Reproducibility of the multiple inert gas elimination technique

Although measurement errors in the multiple inert gas elimination technique have a coefficient of variation of approximately 3%, small biological fluctuations in ventilation, blood flow, or other variables must contribute additional variance to this method of assessing ventilation-perfusion (VA/Q) mismatch. To determine overall variance of computed indices of VA/Q mismatch, an analysis of variance was carried out using a total of 400 duplicate pairs of inert gas samples obtained from canine (N = 118) and human (N = 282) studies in the past 2 years. In both sets VA/Q mismatch ranged from minimal (2nd moment of ventilation and blood flow distributions, log SDV and log SDQ, respectively approximately equal to 0.3 each) to severe (log SDV and log SDQ approximately equal to 2.0). Differences between duplicate log SD values were computed and found to be a constant fraction of the mean log SD of each duplicate pair, averaging 13% for both canine and human ventilation and blood flow data. The resultant coefficient of variation for a single measurement of log SD about its mean averaged 8.6% for all data combined. This analysis demonstrates excellent reproducibility of these dispersion indices over a wide range of conditions, and if the mean of duplicate values is used, thus reducing variability by square root 2 to 6.1%, log SD can be estimated with an approximately 95% confidence limit of +/- 12%.     

Information content of multiple inert gas elimination measurements

The multiple inert gas elimination technique provides a fundamental assessment of the distribution of ventilation-perfusion (VA/Q) ratios in the lung. The resolution of the finer structure of this distribution is limited however. This study examines the theoretical basis of this limitation and presents an objective method for evaluating the independence of inert gas measurements. It demonstrates the linear dependence of the inert gas kernels and their filtering characteristics to be the factors most limiting information content. The limited number of gases available for measurement and experimental error are lesser limitations. At usual levels of experimental error, no more than seven different inert gases having partition coefficients between those of SF6 and acetone will provide independent information, and information content will be maximized by choosing gases with partition coefficients spaced equally on a logarithmic scale. A fivefold reduction in experimental error will not significantly alter the information content of the measurements. The analysis applies equally to other methods of multiple inert gas elimination data interpretation.     

Diffusion-related differences in elimination of inert gases from the lung

Partial pressures of intravenously infused acetylene, Freon 22, and isoflurane (gases with similar solubilities in blood but differing molecular weights) were compared in arterial and mixed venous blood and mixed expired gas of 13 anesthetized mongrel dogs to determine whether gas molecular weight influenced gas exchange. Analysis of covariance was used to account for the variables of ventilation-perfusion ratio, partition coefficient, and experimental run before individual gas effects were sought. A gas effect difference was observed such that the arterial fractional retention of isoflurane (mol wt 184.5) would be 12% higher than that of acetylene (mol wt 26) if the two gases had identical partition coefficients. This effect was neither significantly increased by positive end-expiratory pressure nor decreased by high-frequency oscillatory ventilation. To test whether the individual gas effect was greater with gases with disparate erythrocyte and plasma partition coefficients, the exchange of ethyl iodide (erythrocyte-to-plasma solubility ratio 8.1) and diethyl ether (solubility ratio 0.95) was compared in five dogs. A larger difference between the elimination of the two gases was observed than predicted from the differences in molecular weight. The observed individual gas effect appears to be diffusion related, influenced both by the molecular weight of a gas and its erythrocyte-plasma partition coefficient ratio.     

A tidal breathing model for the multiple inert gas elimination technique.

The tidal breathing lung model described for the sine-wave technique (D. J. Gavaghan and C. E. W. Hahn. Respir. Physiol. 106: 209-221, 1996) is generalized to continuous ventilation-perfusion and ventilation-volume distributions. This tidal breathing model is then applied to the multiple inert gas elimination technique (P. D. Wagner, H. A. Saltzman, and J. B. West. J. Appl. Physiol. 36: 588-599, 1974). The conservation of mass equations are solved, and it is shown that 1) retentions vary considerably over the course of a breath, 2) the retentions are dependent on alveolar volume, and 3) the retentions depend only weakly on the width of the ventilation-volume distribution. Simulated experimental data with a unimodal ventilation-perfusion distribution are inserted into the parameter recovery model for a lung with 1 or 2 alveolar compartments and for a lung with 50 compartments. The parameters recovered using both models are dependent on the time interval over which the blood sample is taken. For best results, the blood sample should be drawn over several breath cycles.     

The physiological factors which govern inert gas exchange

The decay constants (k _j ) of the equation of inert gas exchanges are the roots of an algebraic equation of degreen+1, wheren is the number of distinct absorbing tissues. The coefficients of this equation can be obtained numerically by certain independent experiments to measure the tissue parameters. Graphical solution of this equation yields theoretical values of thek _j . Combining these constants with the numerical values for the partial derivatives of thek _j then gives the per cent rate of change of thek _j as any one tissue parameter varies by a given fraction of its normal range. A numerical example of these calculations shows good conformity with experiment, and permits a quantitative estimate of variations in the speed of gas exchange from a knowledge of changes in the physiological state. The opinions expressed in this article are the private ones of the writers, and are not to be construed as reflecting the policies of the Navy Department or the Naval Service at large.     

Effects of acetone in heparin on the multiple inert gas elimination technique

We have detected acetone in several brands of heparin. If uncorrected, this leads to errors in measuring acetone in blood collected in heparinized syringes, as in the multiple inert gas elimination technique for measuring ventilation-perfusion ratio (VA/Q) distributions. Error for acetone retention [R = arterial partial pressure-to-mixed venous partial pressure (P-V) ratio] is usually small, because R is normally near 1.0, and the error is similar in arterial and mixed venous samples. However, acetone excretion [E = mixed expired partial pressure (P-E)-to-P-V ratio] will appear erroneously low, because P-E is accurately measured in dry syringes, but P-V is overestimated. A physical model of a homogeneous alveolar lung at room temperature and without dead space shows: the magnitude of acetone E error depends upon the ratio of blood sample to heparinized saline volumes and acetone partial pressures, without correction, acetone E can be less than that of less soluble gases like ether, a situation incompatible with conventional gas exchange theory, and acetone R and E can be correctly calculated using the principle of mass balance if the acetone partial pressure in heparinized saline is known. Published data from multiple inert gas elimination experiments with acetone-free heparin, in our labs and others, are within the limits of experimental error. Thus the hypothesis that acetone E is anomalously low because of physiological mechanisms involving dead space tissue capacitance for acetone remains to be tested.     

Estimation of ventilation-perfusion inequality by inert gas elimination without arterial sampling

Estimation of ventilation-perfusion (VA/Q) inequality by the multiple inert gas elimination technique requires knowledge of arterial, mixed venous, and mixed expired concentrations of six gases. Until now, arterial concentrations have been directly measured and mixed venous levels either measured or calculated by mass balance if cardiac output was known. Because potential applications of the method involve measurements over several days, we wished to determine whether inert gas levels in peripheral venous blood ever reached those in arterial blood, thus providing an essentially noninvasive approach to measuring VA/Q mismatch that could be frequently repeated. In 10 outpatients with chronic obstructive pulmonary disease, we compared radial artery (Pa) and peripheral vein (Pven) levels of the six gases over a 90-min period of infusion of the gases into a contralateral forearm vein. We found Pven reached 90% of Pa by approximately 50 min and 95% of Pa by 90 min. More importantly, the coefficient of variation at 50 min was approximately 10% and at 90 min 5%, demonstrating acceptable intersubject agreement by 90 min. Since cardiac output is not available without arterial access, we also examined the consequences of assuming values for this variable in calculating mixed venous levels. We conclude that VA/Q features of considerable clinical interest can be reliably identified by this essentially noninvasive approach under resting conditions stable over a period of 1.5 h.     

Calculating the distribution of ventilation-perfusion ratios from inert gas elimination data

It is well known that the major cause of hypoxemia in lung disease is ventilation-perfusion (VA/Q) inequality, but it has been extremely difficult to measure the distribution of ventilation-perfusion ratios except in terms of unrealistically simple (albeit useful) models. The multiple inert gas elimination technique provides considerable information concerning the shape, position, and dispersion of the VA/Q distribution, although it cannot precisely define all features of the distribution. Although there are many techniques for obtaining information about the distribution from inert gas elimination data, we have found the most flexible and useful approach to be a multicomponent analysis with enforced smoothing, sometimes known as ridge regression. This presentation describes in some detail the physiological and mathematical principles principles involved in the transformation of inert gas elimination data into a representative distribution of ventilation-perfusion ratios by enforced smoothing techniques. It is important to realize that with this approach and any other approach aimed at estimating the distribution of ventilation-perfusion ratios, the results must be properly interpreted.     

Low VA/Q areas: arterial-alveolar N2 difference and multiple inert gas elimination technique

In 16 critically ill patients the arterial-alveolar N2 difference and data from the multiple inert gas elimination technique (MIGET) were compared in the evaluation of the contribution of low alveolar ventilation-perfusion ratio (VA/Q) lung regions (0.005 less than VA/Q less than 0.1) to venous admixture (Qva/QT). The arterial-alveolar N2 difference was determined using a manometric technique for the measurement of the arterial N2 partial pressure (PN2). We adopted a two-compartment model of the lung, one compartment having a VA/Q of approximately 1, the other being open, gas filled, unventilated (VA/Q = 0), and in equilibrium with the mixed venous blood. This theoretical single compartment represents all lung regions responsible for the arterial-alveolar N2 difference. The fractional blood flow to this compartment was calculated using an appropriate mixing equation (Q0/QT). There was a weak but significant relationship between Q0/QT and the perfusion fraction to lung regions with low VA/Q (0.005 less than VA/Q less than 0.1) (r = 0.542, P less than 0.05) and a close relationship between Q0/QT and the perfusion fraction to lung regions with VA/Q ratios less than 0.9 (r = 0.862, P less than 0.001) as obtained from MIGET. The difference Qva/QT-Q0/QT yielded a close estimation of the MIGET right-to-left shunt (Qs/QT) (r = 0.962, P less than 0.001). We conclude that the assessment of the arterial-alveolar N2 difference and Q0/QT does not yield a quantitative estimation of the contribution of pathologically low VA/Q areas to QVa/QT because these parameters reflect an unknown combination of pathological and normal (0.1 less than VA/Q less than 0.9) gas exchange units.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.