Linear programming analysis of VA/Q distributions: average distribution

The defining equations of the multiple inert gas elimination technique are underdetermined, and an infinite number of VA/Q ratio distributions exists that fit the same inert gas data. Conventional least-squares analysis with enforced smoothing chooses a single member of this infinite family whose features are assumed to be representative of the family as a whole. To test this assumption, the average of all ventilation-perfusion ratio (VA/Q) distributions that are compatible with given data was calculated using a linear program. The average distribution so obtained was then compared with that recovered using enforced smoothing. Six typical sets of inert gas data were studied. In all sets but one, the distribution recovered with conventional enforced smoothing closely matched the structure of the average distribution. The single exception was associated with the broad log-normal VA/Q distribution, which is rarely observed using the technique. We conclude that the VA/Q distribution conventionally recovered approximates a simple average of all compatible distributions. It therefore displays average features and only that degree of fine structural detail that is typical of the family as a whole.     

Spectral vs. compartmental averaging of VA/Q distributions: confidence limits

We have investigated the method of statistical averaging as a nonparametric approach to obtain a representative ventilation-perfusion (VA/Q) distribution that exemplifies the family of compatible solutions for multiple inert gas elimination data. The variability of the compatible solutions was examined by determining the standard deviation of the statistical average. For six inert gases, it can be predicted that a distribution with up to seven contiguous nonzero VA/Q compartments can be uniquely recovered, whereas the compatible family becomes more diverse, the broader the distribution. For a given compatible family consisting of multimodal distributions with various phase relationships, the average distribution was found to display an uncharacteristically unimodal shape as a result of modal smoothing. To avoid this possible artifact, an alternative approach was adopted in which statistical averaging was performed in the frequency domain. For both deterministic and empirical data, the energy spectra of all feasible VA/Q distributions displayed a well-defined low-frequency band that was invariant within the compatible family and with a bandwidth that approximated the predicted sampling cutoff frequency. The nonuniqueness of the result was ascribable to a variable high-frequency band that was due to an aliasing effect. For a wide range of clinical data, the representative distributions resulting from compartmental and spectral averaging were indistinguishable from each other and had little variability both in the VA/Q and frequency domains. For these cases, therefore, the resolving power of the recovery algorithm was not critical. Finally, an efficient method of finding the average distribution was proposed.     

Ventilation-perfusion inhomogeneity increases gas uptake: theoretical modeling of gas exchange.

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on gas exchange in the presence of inspired mixtures of two soluble gases using a two-compartment computer model. Theoretical studies involving a mixture of hypothetical gases with equal solubility in blood showed that the effect of increasing inhomogeneity of distributions of either ventilation or blood flow is to paradoxically increase uptake of the gas with the lowest overall uptake in relation to its inspired concentration. This phenomenon is explained by the concentrating effects that uptake of soluble gases exert on each other in low VA/Q compartments. Repeating this analysis for inspired mixtures of 30% O(2) and 70% nitrous oxide (N(2)O) confirmed that, during "steady-state" N(2)O anesthesia, uptake of N(2)O is predicted to paradoxically increase in the presence of worsening VA/Q inhomogeneity.     

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.     

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.     

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.     

Lobar contribution to VA/Q inequality during constant-flow ventilation

Previous studies have shown that normal arterial PCO2 can be maintained during apnea in anesthetized dogs by delivering a continuous stream of inspired ventilation through cannulas aimed down the main stem bronchi, although this constant-flow ventilation (CFV) was also associated with a significant increase in ventilation-perfusion (VA/Q) inequality, compared with conventional mechanical ventilation (IPPV). Conceivably, this VA/Q inequality might result from differences in VA/Q ratios among lobes caused by nonuniform distribution of ventilation, even though individual lobes are relatively homogeneous. Alternatively, the VA/Q inequality may occur at a lobar level if those factors causing the VA/Q mismatch also existed within lobes. We compared the efficiency of gas exchange simultaneously in whole lung and left lower lobe by use of the multiple inert gas elimination technique in nine anesthetized open-chest dogs. Measurements of whole lung and left lower lobe gas exchange allowed comparison of the degree of VA/Q inequality within vs. among lobes. During IPPV with positive end-expiratory pressure, arterial PO2 and PCO2 (183 +/- 41 and 34.3 +/- 3.1 Torr, respectively) were similar to lobar venous PO2 and PCO2 (172 +/- 64 and 35.7 +/- 4.1 Torr, respectively; inspired O2 fraction = 0.44 +/- 0.02). Switching to CFV (3 l.kg-1.min-1) decreased arterial PO2 (112 +/- 26 Torr, P less than 0.001) and lobar venous PO2 (120 +/- 27 Torr, P less than 0.01) but did not change the shunt measured with inert gases (P greater than 0.5).(ABSTRACT TRUNCATED AT 250 WORDS)     

Effect of ventilation-perfusion inhomogeneity and N(2)O on oxygenation: physiological modeling of gas exchange.

Ventilation-perfusion (VA/Q) inhomogeneity was modeled to measure its effect on arterial oxygenation during maintenance-phase 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 of VA/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(O(2))). 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 low VA/Q compartments. The improvement in Pa(O(2)) when N(2)O was present instead of N(2) was greatest when the degree of VA/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(O(2)). In the presence of VA/Q inhomogeneity, second-gas and concentrating effects may have clinically significant effects on arterial oxygenation even at "steady-state" levels of N(2)O uptake.     

Operation Everest II: pulmonary gas exchange during a simulated ascent of Mt. Everest

Eight normal subjects were decompressed to barometric pressure (PB) = 240 Torr over 40 days. The ventilation-perfusion (VA/Q) distribution was estimated at rest and during exercise [up to 80-90% maximal O2 uptake (VO2 max)] by the multiple inert gas elimination technique at sea level and PB = 428, 347, 282, and 240 Torr. The dispersion of the blood flow distribution increased by 64% from rest to 281 W, at both sea level and at PB = 428 Torr (heaviest exercise 215 W). At PB = 347 Torr, the increase was 79% (rest to 159 W); at PB = 282 Torr, the increase was 112% (108 W); and at PB = 240 Torr, the increase was 9% (60 W). There was no significant correlation between the dispersion and cardiac output, ventilation, or pulmonary arterial wedge pressure, but there was a correlation between the dispersion and mean pulmonary arterial pressure (r = 0.49, P = 0.02). When abnormal, the VA/Q pattern generally had perfusion in lung units of zero or near zero VA/Q combined with units of normal VA/Q. Alveolar-end-capillary diffusion limitation of O2 uptake (VO2) was observed at VO2 greater than 3 l/min at sea level, greater than 1-2 l/min VO2 at PB = 428 and 347 Torr, and at higher altitudes, at VO2 less than or equal to 1 l/min. These results show variable but increasing VA/Q mismatch with long-term exposure to both altitude and exercise. The VA/Q pattern and relationship to pulmonary arterial pressure are both compatible with alveolar interstitial edema as the primary cause of inequality.     

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)     

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.     

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.     

Ventilation-perfusion inequality during constant-flow ventilation

Previous work by Lehnert et al. (J. Appl. Physiol. 53:483-489, 1982) has demonstrated that adequate alveolar ventilation can be maintained during apnea in anesthetized dogs by delivering a continuous stream of inspired ventilation through cannulas aimed down the main-stem bronchi. Because an asymmetric distribution of ventilation might introduce ventilation-perfusion (VA/Q) inequality, we compared gas exchange efficiency in nine anesthetized and paralyzed dogs during constant-flow ventilation (CFV) and conventional ventilation (intermittent positive-pressure ventilation, IPPV). Gas exchange was assessed using the multiple inert gas elimination technique. During CFV at 3 l X kg-1 X min-1, lung volume, retention-excretion differences (R-E*) for low- and medium-solubility gases, and the log standard deviation of blood flow (log SD Q) increased, compared with the findings during IPPV. Reducing CFV flow rate to 1 l X kg-1 X min-1 at constant lung volume improved R-E* and log SD Q, but significant VA/Q inequality compared with that at IPPV remained and arterial PCO2 rose. Comparison of IPPV and CFV at the same mean lung volume showed a similar reversible deterioration in gas exchange efficiency during CFV. We conclude that CFV causes significant VA/Q inequality which may be due to nonuniform ventilation distribution and a redistribution of pulmonary blood flow.     

Sequential V(A)/Q distributions in the normal rabbit by micropore membrane inlet mass spectrometry.

We developed micropore membrane inlet mass spectrometer (MMIMS) probes to rapidly measure inert-gas partial pressures in small blood samples. The mass spectrometer output was linearly related to inert-gas partial pressure (r(2) of 0.996-1.000) and was nearly independent of large variations in inert-gas solubility in liquid samples. We infused six inert gases into five pentobarbital-anesthetized New Zealand rabbits and used the MMIMS system to measure inert-gas partial pressures in systemic and pulmonary arterial blood and in mixed expired gas samples. The retention and excretion data were transformed into distributions of ventilation-to-perfusion ratios (V(A)/Q) with the use of linear regression techniques. Distributions of V(A)/Q were unimodal and broad, consistent with prior reports in the normal rabbit. Total blood sample volume for each VA/Q distribution was 4 ml, and analysis time was 8 min. MMIMS provides a convenient method to perform the multiple inert-gas elimination technique rapidly and with small blood sample volumes.     

Meclofenamate enhances blood oxygenation in acute oleic acid lung injury

To assess the role of vasoactive prostanoids in acute lung injury, we studied 16 dogs after intravenous injection of oleic acid (OA; 0.08 ml/kg). Animals were ventilated with 100% O2 and zero end-expiratory pressure. Base-line hemodynamic and blood gas observations were obtained 90-120 min following OA. Observations were repeated 30 min after infusion of meclofenamate (2 mg/kg; n = 10), or after saline (n = 6). Resistance to pulmonary blood flow was assessed using the difference between pulmonary arterial diastolic and left atrial pressures (PDG). Ventilation-perfusion (VA/Q) distributions were derived with the multiple inert gas technique. Prior to infusion, there were no significant differences between the two groups. PDG was elevated mildly above normal levels, and shunt flow was the principal gas exchange disturbance. Saline induced no significant changes in hemodynamics or gas exchange. Meclofenamate enhanced PDG to a small, significant degree and effected a 32% reduction in shunt flow (P less than 0.01). Perfusion was redistributed to normal VA/Q units with little change in low VA/Q perfusion or in overall flow. Arterial PO2 rose from 75 +/- 36 to 184 +/- 143 Torr (P less than 0.05). At autopsy, there were no significant differences in wet to dry lung weights. Prostaglandin inhibition redistributes perfusion from shunt to normal VA/Q units, thereby improving arterial PO2, without altering lung water acutely.     

Effect of local pulmonary blood flow control on gas exchange: theory

The effect of local pulmonary blood flow control by local alveolar O2 tension on steady-state pulmonary gas exchange is analyzed with techniques derived from control theory. In a single homogeneous lung unit with normal inspired and mixed venous blood gas composition, the homeostatic effect on local ventilation-perfusion ratios (VA/Q) regulation occurs over a restricted range of VA/Q. The homeostatic effect is maximal at a moderately low VA/Q (about 0.4) due to the slope of the O2 dissociation curve. In a multicompartment lung with a lognormal distribution of VA/Q, regulation of arterial O2 tension varies with the extent of inhomogeneity. At mild degrees of inhomogeneity where local pulmonary blood flow (Q) control acts predominantly on the lower VA/Q of the Q distribution, the regulatory effect is best. At severe degrees of inhomogeneity where local Q control acts mainly on the higher VA/Q of the Q distribution, the regulatory effect is worse, and positive-feedback behavior may occur. Local Q control has the potential of reducing the deleterious effects of lung disease on pulmonary gas exchange particularly when it operates in association with other regulatory mechanisms.     

Regional ventilation-perfusion distribution is more uniform in the prone position.

The arterial blood PO(2) is increased in the prone position in animals and humans because of an improvement in ventilation (VA) and perfusion (Q) matching. However, the mechanism of improved VA/Q is unknown. This experiment measured regional VA/Q heterogeneity and the correlation between VA and Q in supine and prone positions in pigs. Eight ketamine-diazepam-anesthetized, mechanically ventilated pigs were studied in supine and prone positions in random order. Regional VA and Q were measured using fluorescent-labeled aerosols and radioactive-labeled microspheres, respectively. The lungs were dried at total lung capacity and cubed into 603-967 small ( approximately 1.7-cm(3)) pieces. In the prone position the homogeneity of the ventilation distribution increased (P = 0.030) and the correlation between VA and Q increased (correlation coefficient = 0.72 +/- 0.08 and 0.82 +/- 0.06 in supine and prone positions, respectively, P = 0.03). The homogeneity of the VA/Q distribution increased in the prone position (P = 0.028). We conclude that the improvement in VA/Q matching in the prone position is secondary to increased homogeneity of the VA distribution and increased correlation of regional VA and Q.     

Determination of the distribution of ventilation-perfusion ratios: technic of elimination of multiple inert gases

The multiple inert gas elimination technique (MIGT) facilitates the estimation of the distributions of ventilation-perfusion (VA/Q) ratios in the experimental and clinical setting. The most relevant technical aspects and equipment and operational requirements needed to measure a mixture of inert gases in both the gas phase and the blood phase using gas chromatography are overviewed with detail. Results obtained in 3 dogs and 4 syringe-homogeneous lung models were entirely consistent with data formerly reported in the literature. Particular attention is paid to the linearity of the gas chromatograph detectors, reproducibility of inert gases sampling, and analysis of brands of heparin to detect acetone content. The errors of measurement (coefficients of variation) in blood were: 1.4 for sulfur hexafluoride; 1.8% for ethane; 2% for cyclopropane and halothane, each; 2.4% for diethyl ether; and, 3.6% for acetone. Important practical points are also emphasized in order to draw attention to potential problems and issues that should be concentrated upon to minimize the error in the measurements. It is concluded that the setting up of the MIGT is well established and validated.     

Contributions of ventilation and perfusion inhomogeneities to the VA/Q distribution.

The anatomic distributions of ventilation (VA) and perfusion (Q) in prone and supine dogs have been described in the literature. These data also provide frequency distributions, i.e., the distribution of lung units as a function of VA or Q. A comprehensive distribution that encompasses these two distributions is described, and the properties of the comprehensive distribution that determine the width of the VA/Q distribution are identified. Using data on the VA and Q distributions taken from various sources in the literature, we estimated the widths of the VA/Q distributions. The widths estimated from the independent data on the VA and Q distributions agree well with the widths obtained from gas exchange data. The analysis provides information about the relative contributions of the VA and Q distributions to the width of the VA/Q distribution. In the prone dog, the VA and Q distributions, as described by the available data, have different length scales, and we argue that these distributions are therefore not highly correlated. As a result, the variance of the VA/Q distributions is approximately the sum of the variances of the VA and Q distributions. Two-thirds of the variance in VA/Q is a result of nonuniform Q, and one-third is a result of nonuniform VA. In the supine dog, the variance of VA is larger than in the prone dog because of a vertical gradient and the variance of Q is larger, in part, because of a vertical gradient. Because the magnitudes of the vertical gradients of VA and Q are about equal, the vertical gradient of VA/Q is small, and these components of the VA and Q inhomogeneities contribute little to the width of the VA/Q distribution. The other components of Q inhomogeneity cause the additional variance of VA/Q in the supine dog.     

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)