Ventilation–Perfusion Relationships

7 Ventilation- Perfusion Relationships Peter D. Wagner and John B. West

I. Introduction II. Analysis Using P , PQOZ, and P 02 N2 A. Oxygen-Carbon Dioxide Diagram B. Riley Method C. Alveolar-Arterial P Differences N2 D. Triple Gradient III. Analysis Following Gas Washout A. Compartmental Analysis B. Continuous Distributions C. Limitations of These Methods IV. Use of Foreign (Inert) Gases A. Introduction B. Principles of Inert Gas Elimination C. Information Content of the Multiple Inert Gas Elimination Method V. Ventilation-Perfusion Inequality in Disease A. Specific Disease States B. General Conclusions References

I.

219 221 221 222 223 224 225 225 226 228 229 229 230 233 246 246 255 259

INTRODUCTION

It would b e natural to s u p p o s e t h a t if a lung w e r e supplied with ade­ quate a m o u n t s of fresh gas and mixed v e n o u s blood, and if complete equi­ libration o c c u r r e d b e t w e e n alveolar gas and p u l m o n a r y capillary blood in every lung unit, then normal p u l m o n a r y gas e x c h a n g e would be a s s u r e d . As is well k n o w n , h o w e v e r , this is not the c a s e . U n l e s s the proportion of the total ventilation and blood flow going to e a c h gas-exchanging unit is the s a m e , overall gas exchange b e c o m e s inefficient a n d , other things being equal, the arterial P02 falls and the PC02 rises. A full understanding of h o w mismatching of ventilation and blood flow

P U L YM SO GN A EA X ,R CV H . O AILN G E Copyright © 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-744501-3

9

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Peter D. Wagner and John B. West

within the lung affects gas e x c h a n g e remains o n e of the most challenging problems in the whole area of p u l m o n a r y gas e x c h a n g e . T w o factors A uthis Nn problem. A N n C of u n First, the way in which greatly increase the complexity , P O > * ^N i Y l 8 ^ change as the ventilation the P02 2 C2 perfusion ratio is altered d e p e n d s on the shapes and positions of the ox­ ygen and c a r b o n dioxide dissociation c u r v e s . T h e s e are not only non­ linear but also interdependent. A s a c o n s e q u e n c e , closed-form solutions are not possible, and indeed until recently, only graphical solutions w e r e possible. S e c o n d , any realistic a p p r o a c h must consider the gas exchange behavior of a series of lung units with some type of distribution of ventilation-perfusion ratios. T h e resultant complexity necessitates nu­ merical analysis, and indeed the introduction of digital computing has rev­ olutionized this area of research (see this v o l u m e , C h a p t e r 8). It is w o r t h noting that p u l m o n a r y physiology seems to be well ahead of other areas of physiology in this regard. T h e r e is every r e a s o n to believe that functional inhomogeneity within other organs impairs their overall function. F o r e x a m p l e , in peripheral tissues such as skeletal muscle, in­ equalities in the ratio of blood flow to o x y g e n u p t a k e must r e d u c e the efficiency of oxygen transfer. In the kidney, inequalities in the ratio of glomerular filtration rate to p l a s m a flow a m o n g different n e p h r o n s pre­ sumably affect renal function. H o w e v e r , relatively little interest has b e e n directed t o w a r d the c o n s e q u e n c e s of these types of functional inhomogeneity. By contrast, the sequelae of v e n t i l a t i o n - p e r f u s i o n in­ equality in the lung d e m a n d attention b e c a u s e this is the c o m m o n e s t mech­ anism of arterial h y p o x e m i a and hypercarbia. In this chapter w e first review w a y s of analyzing ventilation-perfusion inequality b a s e d on the m e a s u r e m e n t of partial p r e s s u r e s of the three nat­ urally occurring respiratory gases: o x y g e n , carbon dioxide, and nitrogen, as they exist u n d e r steady state conditions. This is the simplest a p p r o a c h , w a s historically the first, and is still employed extensively in the clinical setting. N e x t we turn to m e t h o d s b a s e d on simple interventions such as the wash-out of nitrogen from the lung. Both c o m p a r t m e n t a l and continu­ ous distributions of v e n t i l a t i o n - p e r f u s i o n ratios h a v e been obtained in this w a y . Finally, analyses b a s e d on the infusion of multiple infused inert gases are examined. H e r e we exploit the gas exchange behavior of spe­ cially c h o s e n gases rather than rely on the respiratory gases that h a p p e n to be p r e s e n t . This is the m o s t complex but the most informative ap­ p r o a c h available to d a t e . T h e e m p h a s i s of the chapter is on general princi­ ples of gas e x c h a n g e in the p r e s e n c e of ventilation-perfusion inequality rather than the patterns that o c c u r in particular physiological conditions or specific disease states. Studies on both normal and abnormal lungs are included.

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7. Ventilation-Perfusion Relationships II. ANALYSIS USING P^Pco*,

AND P Na

Since v e n t i l a t i o n - p e r f u s i o n inequality usually c a u s e s profound changes in the partial p r e s s u r e s of P02 , PC02 , and PN2in arterial blood and expired g a s , t h e s e constitute the simplest w a y of assessing the inequality. H o w e v e r , although this a p p r o a c h has a d v a n t a g e s , t h e r e are also d r a w ­ b a c k s . T h e main advantage is that the gases are always available and that the m e a s u r e m e n t s can be m a d e relatively easily. A serious disadvantage is that the a m o u n t of resulting information is severely limited. T h e n u m b e r of available m e a s u r e m e n t s is small a n d , furthermore, the c o m m o n respi­ ratory gases d o not h a v e properties that are a n y w h e r e n e a r ideal for this p u r p o s e . N e v e r t h e l e s s , for clinical p u r p o s e s , this a p p r o a c h as originally formulated o v e r 30 years ago by Riley and C o u r n a n d (1949) is still exten­ sively u s e d . A. O x y g e n - C a r b o n Dioxide Diagram T h e o x y g e n - c a r b o n dioxide diagram is the key to understanding h o w mismatching of ventilation and blood flow affect the arterial P02 , PC o2> and P N , 2a n d h o w m e a s u r e m e n t s of t h e s e gases c a n t h r o w light on the t y p e of v e n t i l a t i o n - p e r f u s i o n inequality that must exist. S o m e discussion of the 0 2- C 0 2 diagram c a n be found in C h a p t e r s 2 a n d 3 of this v o l u m e , w h e r e its historical b a c k g r o u n d is c o n s i d e r e d , and a full description w a s given by R a h n and F e n n (1955). Figure 1 s h o w s an 0 2- C 0 2 diagram with the points representing the c o m p o s i t i o n s of inspired gas (/) and mixed

Fig. 1. Oxygen-carbon dioxide diagram showing the ventilation-perfusion ratio line joining the mixed venous (v) to the inspired gas (/) point. Ideal (/), arterial (a), and alveolar (A) points are also shown. Lines of equal PN2have a slope of - 1.

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v e n o u s blood (v). T h e c u r v e d line joining these indicates the alveolar gas composition of lung units having increasing ventilation-perfusion ratios from zero at point v to infinity at point / . N o other alveolar gas composi­ tion in h o m o g e n e o u s lung units can exist in this lung. If w e a s s u m e equili­ bration b e t w e e n alveolar gas and end-capillary blood in every lung unit, the line (called the v e n t i l a t i o n - p e r f u s i o n ratio line) also denotes the par­ tial p r e s s u r e s of end-capillary blood. T h e diagram also shows typical examples of the composition of mixed alveolar gas (A) and mixed arterial blood (a). T h e s e points lie on the gas and blood R lines corresponding to the respiratory e x c h a n g e ratio of the whole lung. In a lung with n o ventilation-perfusion inequality, the points would be superimposed at point /, k n o w n as the ideal point. With increas­ ing ventilation-perfusion inequality they diverge further and further a w a y . T h e corresponding a l v e o l a r - a r t e r i a l P02 and PC02 differences can be read off the diagram. Figure 1 also s h o w s h o w the isopleths (lines of equal partial pressure) for nitrogen cut across the diagram at an angle of 45°. Inspection will show that as the ventilation-perfusion ratio is increased from zero to s o m e w h a t a b o v e normal (that is, b e y o n d point /), the PN2d e c r e a s e s . With further rise in the ventilation-perfusion ratio the PN2 increases again. Also note that while the PN2 of mixed arterial blood rises steadily as the degree of ventilation-perfusion inequality is increased, the change in PN2of mixed alveolar gas is m u c h less and will d e p e n d critically on the slope of the gas R line. I n d e e d w h e n the gas R is 1.0, the alveolar P Nz is constant irrespec­ tive of the degree of v e n t i l a t i o n - p e r f u s i o n inequality p r e s e n t in the lung. It is clear that the partial p r e s s u r e differences for all three g a s e s — oxygen, c a r b o n dioxide, and n i t r o g e n — c o n t a i n information about the amount of ventilation-perfusion inequality. M o r e o v e r , these differences give some information about the type of inequality p r e s e n t . F o r e x a m p l e , a lung with large a m o u n t s of blood flow to regions with low ventilation-perfusion ratios will substantially r e d u c e the arterial P02 and also raise the arterial P N . 2By c o n t r a s t , the p r e s e n c e of areas of high ventilation-perfusion ratios will h a v e m u c h less influence on the mixed alveolar P02 and almost none o n the P N . 2Although the information value of these respiratory gases is limited, they have been extensively studied b e c a u s e no further interventions are necessary to get the information. B . Riley Method In this m e t h o d (Riley and C o u r n a n d , 1949) the P02 and PC02of arterial blood and mixed expired gas are u s e d to construct a t h r e e - c o m p a r t m e n t model of the lung, as s h o w n in Fig. 2. O n e c o m p a r t m e n t (physiologic

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7. Ventilation-Perfusion Relationships 1.0

x

IDEAL COMPARTMENT 0.8

fx

< 3 DEAD SPACE

oo

VENT L IAT O IN P-ERFUS O IN RAT O I

Fig. 2. Analysis of Riley and Cournand. The lung is represented as three compartments. One is perfused but not ventilated (physiologic shunt). Another is ventilated but not per­ fused (physiologic deadspace). The third (ideal) receives the remainder of the ventilation and blood flow. shunt) is c o n s i d e r e d to be perfused but unventilated (point v on Fig. 1), a n o t h e r (physiologic dead space) ventilated but unperfused (point I on Fig. 1), a n d the third c o m p a r t m e n t (ideal) contains the r e m a i n d e r of the ventilation and blood flow (point i on Fig. 1). In p r a c t i c e , the gas composition of the ideal c o m p a r t m e n t is first deter­ mined using the alveolar gas e q u a t i o n and taking the arterial PC02to repre­ sent the ideal value. This is a r e a s o n a b l e approximation in m o s t instances b e c a u s e the blood R line is so nearly horizontal (Fig. 1). O n c e this h a s b e e n d o n e , t h e blood flow to the shunt c o m p a r t m e n t is calculated from the familiar shunt e q u a t i o n , while the ventilation to the physiologic d e a d space is derived from the B o h r d e a d space equation. Details can be found in C h a p t e r 3 of this v o l u m e , which also describes t h e historical develop­ m e n t of this a p p r o a c h . C . Alveolar- Arterial P Nz Differences As s h o w n in Fig. 1, lung units with different v e n t i l a t i o n - p e r f u s i o n ratios generally h a v e a different P N2 (Canfield and R a h n , 1957). T h e r e f o r e , in a lung with v e n t i l a t i o n - p e r f u s i o n inequality, the mixed alveolar P N2 is a ventilation-weighted average

rE «-

_

2PA VA 2VA

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while the arterial P N2 is a blood-flow-weighted average =

s/yg

T h e result is an a l v e o l a r - a r t e r i a l difference for P N , 2the arterial value being higher b e c a u s e poorly ventilated well-perfused units h a v e a high PN2 (Fig. 1). A valuable feature of the a l v e o l a r - a r t e r i a l P N2 difference is that it is un­ affected by direct shunts through unventilated lung b e c a u s e the P N2 of arterial and mixed v e n o u s blood are the s a m e . This p r o p e r t y can therefore be used to distinguish b e t w e e n such shunts and blood flow through fi­ nitely but very poorly ventilated units. F o r e x a m p l e , by comparing the a l v e o l a r - a r t e r i a l differences for P02 and P N , 2Corbet and co-workers (1974) concluded that the h y p o x e m i a of infants with hyaline m e m b r a n e disease w a s caused almost exclusively by blood flow to unventilated regions. By contrast, in a group of patients with cystis fibrosis, the mecha­ nism w a s blood flow through units with low but finite v e n t i l a t i o n perfusion ratios (Corbet et al., 1975). A n o t h e r theoretically useful p r o p e r t y of the a l v e o l a r - a r t e r i a l PN2 dif­ ference is that it is unaffected by diffusion impairment within the lung, which can raise the P02 difference. This is b e c a u s e nitrogen and all the o t h e r inert gases (those which o b e y H e n r y ' s law) equilibrate very rapidly b e t w e e n alveolar gas and p u l m o n a r y capillary blood (Wagner, 1977b). It should b e emphasized that the m e a s u r e m e n t of the P N2 in blood is technically a very arduous p r o c e d u r e . T h e analysis is generally d6ne by gas c h r o m a t o g r a p h y (Lenfant and A u c u t t , 1966) but the value is very sen­ sitive to the t e m p e r a t u r e of the p u l m o n a r y blood, and nitrogen contami­ nation from air leaks is difficult to avoid. B e c a u s e of these difficulties, relatively little practical use has b e e n m a d e of the a l v e o l a r - a r t e r i a l P N2 difference. D. Triple Gradient A few investigators have combined m e a s u r e m e n t s of the alveolar and arterial differences for P02 , PC02 , and PN2(the so-called triple gradient) to derive information about the p a t t e r n of ventilation-perfusion inequality in the lung. F o r example Lenfant (1963) studied a series of normal subjects at various inspired oxygen concentrations and by comparing the behavior of the three a l v e o l a r - a r t e r i a l differences he concluded that the lungs had a significant n u m b e r of units with very low and indeterminable v e n t i l a t i o n perfusion ratios. In a further study (Lenfant, 1964) m a d e u n d e r hyperberic conditions (2.6 atm) the data w e r e r e p o r t e d to be consistent with a bi-

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modal distribution of v e n t i l a t i o n - p e r f u s i o n ratios c o m p o s e d of a large group of well-ventilated units and a n o t h e r small g r o u p having a very low but finite v e n t i l a t i o n - p e r f u s i o n ratio. T h e m o s t sophisticated analysis of the distribution compatible with m e a s u r e d P02 , PC02 , and P N2 d a t a w a s p r e s e n t e d by Markello and col­ leagues (1973). T h e s e investigators u s e d t e c h n i q u e s of numerical analysis to find t h r e e - c o m p a r t m e n t m o d e l s that would fit the lungs of patients fol­ lowing induction with halothane a n e s t h e s i a . T h e c o m p a r t m e n t s consisted of o n e with a high v e n t i l a t i o n - p e r f u s i o n ratio, one with a low ratio, and a direct left-to-right shunt. N o c o n s i s t e n t p a t t e r n w a s found; in s o m e pa­ tients a shunt w a s the p r e d o m i n a n t c a u s e of impaired gas e x c h a n g e , while in o t h e r s v e n t i l a t i o n - p e r f u s i o n inequality w a s m a r k e d . T h e m e t h o d w a s also used to investigate p u l m o n a r y gas e x c h a n g e of patients in the inten­ sive care setting (Markello et al., 1972).

III. ANALYSIS FOLLOWING GAS WASHOUT U p to this point w e h a v e b e e n considering analyses of v e n t i l a t i o n perfusion relationships b a s e d solely o n the steady state partial p r e s s u r e s of the naturally occurring respiratory g a s e s — o x y g e n , c a r b o n dioxide, and nitrogen. W h e n these d a t a are c o m b i n e d with m e a s u r e m e n t s of the wash-out of nitrogen during o x y g e n breathing (or wash-in or w a s h - o u t of o t h e r insoluble inert gases) additional information about the v e n t i l a t i o n - p e r f u s i o n inequality c a n be obtained. A. C o m p a r t m e n t a l Analysis Briscoe and colleagues (Briscoe, 1959; Briscoe et al., 1960; King and Briscoe, 1967; King et al., 1973) h a v e b e e n the m o s t consistent p r o p o ­ nents of this t y p e of analysis o v e r a period of m a n y y e a r s . C h a p t e r 8 in V o l u m e II of this treatise is d e v o t e d mainly to this subject; a s u m m a r y is included h e r e to show h o w the m e t h o d relates to o t h e r w a y s of measuring v e n t i l a t i o n - p e r f u s i o n inequality. W h e n an almost insoluble gas such as helium or nitrogen is w a s h e d out from the lungs, the pattern of end-tidal or mixed expired gas c o n c e n t r a ­ tions can b e treated as if the lung consisted of t w o populations of lung units, one well ventilated and the o t h e r poorly ventilated. If these data are c o m b i n e d with m e a s u r e m e n t s of arterial oxygen saturation (Briscoe, 1959) the resultant t w o - c o m p a r t m e n t model gives the ventilation, blood flow, and lung v o l u m e of e a c h population of lung units consistent with all the d a t a . F o r e x a m p l e , it has b e e n s h o w n that an e m p h y s e m a t o u s lung

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m a y b e h a v e as if nine-tenths of t h e total ventilation a n d one-half of t h e total blood flow go t o o n e - q u a r t e r of t h e volume of t h e lung (the fast space), w h e r e a s t h e o t h e r t h r e e - q u a r t e r s of the v o l u m e receive only one-tenth of t h e ventilation a n d t h e o t h e r half of the blood flow (the slow space). A n extension of this m e t h o d of analysis allows t h e diffusion properties 44 e a c h c o m p a r t m e n t to be e s t i m a t e d . This is d o n e using the notion of of B o h r integral i s o p l e t h s , " which give t h e rate of rise of P02 along t h e pul­ m o n a r y capillary for different values of diffusing capacity p e r unit blood flow. A s an example of t h e application of this m e t h o d , A r n d t et al. (1970) reported that in 10 patients with interstitial lung disease the lung units in the fast space h a d a n a l v e o l a r - e n d - c a p i l l a r y P02 difference of 10 m m H g , and t h e value of this difference in t h e slow space w a s 56 m m H g . T h e con­ clusion w a s that e v e n at rest a substantial a m o u n t of t h e arterial hypox­ emia of t h e s e patients w a s attributable to diffusion impairment. It might be noted that this conclusion is at variance with that of W a g n e r et al. (1976), w h o found that all t h e h y p o x e m i a in a group of patients with inter­ stitial lung disease w a s caused b y v e n t i l a t i o n - p e r f u s i o n inequality at rest, although a c o m p o n e n t w a s c a u s e d by diffusion impairment o n exercise.

B. Continuous Distributions Although c o m p a r t m e n t a l analysis is a convenient a n d simple w a y of looking at t h e relations b e t w e e n p u l m o n a r y ventilation, blood flow a n d gas e x c h a n g e , it h a s b e e n recognized for m a n y y e a r s that t h e real lung m u s t consist of some kind of distribution of v e n t i l a t i o n - p e r f u s i o n ratios. R a h n (1949) h a s t h e distinction of being t h e first t o suggest that a logarithmic normal distribution might b e p r e s e n t and he a s s u m e d this for some theoretical studies, later e x t e n d e d b y Farhi a n d R a h n (1955). O t h e r investigators h a v e e x a m i n e d d a t a o n gas e x c h a n g e in t h e light of t h e pre­ dicted behavior of distributions of v e n t i l a t i o n - p e r f u s i o n ratios. F o r ex­ a m p l e , as mentioned earlier, Lenfant (1964) m e a s u r e d t h e a l v e o l a r arterial difference for P02 , PC02 , a n d PN2in subjects breathing 7 5 % oxygen at s e a level a n d again at an increased p r e s s u r e of 2.6 a t m and c o m p a r e d the results with those e x p e c t e d from bimodal distributions of v e n t i l a t i o n - p e r f u s i o n ratios. H o w e v e r , t h e first e x p e r i m e n t designed spe­ cifically to r e c o v e r distributions w a s that by Lenfant a n d O k u b o (1968). T h e s e investigators m e a s u r e d t h e arterial P02 a n d PC02 while t h e sub­ j e c t s b r e a t h e d 100% oxygen a n d t h u s w a s h e d t h e nitrogen o u t of their lungs over a period of approximately 10 min. T h e time c o u r s e of the calcu­ lated arterial oxygen c o n t e n t w a s t h e n analyzed using L a p l a c e transform t e c h n i q u e s . A serious m a t h e m a t i c a l difficulty w a s p o s e d by the nonlin-

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earity of the oxygen dissociation c u r v e but this w a s o v e r c o m e by using an empirical exponential fit for the time c o u r s e of oxygen b o u n d to hemoglo­ bin. Figure 3 shows some of their results; subjects 1-5 w e r e normal, w h e r e a s subjects 6 - 1 0 had chronic obstructive lung disease. T h e plots show b o t h blood flow and lung volume plotted against v e n t i l a t i o n perfusion ratio, the latter on a log scale from 0.1 to 10. N o t e that the

1

1.0

10

0.1

1.0

10

Fig. 3. Distributions of blood flow (Q) and lung volume (V) against ventilation-perfusion ratio reported by Lenfant and Okubo (1968). Note that the normal subjects (1-5) had rela­ tively narrow distributions, whereas the patients with chronic ^obstructive lung disease (6-10) had broader and sometimes bizarre distributions. (From Lenfant and Okubo, 1969, reproduced by permission.)

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normal patients (subjects 1-4) s h o w e d relatively n a r r o w distributions /Q side of t h e although subject 3 h a d a well-defined shoulder on t h e low VA distribution. In t h e patients with lung disease (subjects 5 - 1 0 ) t h e distribu­ tions w e r e generally m u c h b r o a d e r a n d s o m e bizarre p a t t e r n s w e r e seen (for example, patient 9). It is worth noting here that the range of v e n t i l a t i o n perfusion ratios s h o w n in Fig. 3 is considerably less t h a n that studied b y the multiple inert gas elimination t e c h n i q u e (see below). C. Limitations of These Methods T h e gas w a s h - o u t m e t h o d s t o study v e n t i l a t i o n - p e r f u s i o n relationships are e x a m p l e s of t h e u s e of forcing functions t o elucidate t h e gas e x c h a n g e b e h a v i o r of t h e lung. W e c a n imagine t h e lung as a black b o x that, w h e n p e r t u r b e d b y a k n o w n disturbing factor, r e s p o n d s in a w a y which d e p e n d s on its v e n t i l a t i o n - p e r f u s i o n ratio distribution. A basic assumption of such a m e t h o d is that t h e forcing function itself d o e s n o t alter the distribution. H o w e v e r , t h e r e is every r e a s o n t o believe that increasing t h e inspired P02 will alter t h e distribution of v e n t i l a t i o n - p e r f u s i o n ratios in s o m e circum­ stances as pointed out b y Lenfant (1965). F o r e x a m p l e , there m a y b e hy­ poxic vasoconstriction in s o m e regions, which will b e relieved w h e n t h e local alveolar P02is increased. Again direct m e a s u r e m e n t s of distributions of v e n t i l a t i o n - p e r f u s i o n ratios in patients with blood flow to very poorly ventilated regions have s h o w n t h a t t h e ventilation to t h e s e units m a y b e abolished during high oxygen breathing ( D a n t z k e r et al., 1975). Clearly a technique that alters t h e distribution in an unpredictable w a y c a n n o t re­ liably b e u s e d to m e a s u r e t h e distribution. A n o t h e r objection to the m e t h o d of Lenfant a n d O k u b o (1968) w a s raised b y Peslin et al. (1971). T h e y pointed o u t that t h e P o s t - W i d d e r equation, which w a s u s e d b y Lenfant a n d O k u b o to obtain an approxi­ mate inversion of the L a p l a c e integral, gave results that w e r e highly sensi­ tive to experimental error. I n d e e d , they argued that with t h e usual experi­ mental a c c u r a c y , t h e data carried little information a b o u t t h e shape of the distribution function. This is an i m p o r t a n t question a b o u t a n y underdetermined system a n d it h a s b e e n extensively investigated for t h e multiple inert gas elimination m e t h o d (see later). A further reservation applies t o t h e c o m p a r t m e n t a l analysis of Briscoe and colleagues. A s indicated a b o v e , t h e first step is to divide t h e lung into fast a n d slowly ventilatory s p a c e s b y m e a n s of a g a s wash-out. T h e blood flow is then apportioned to t h e s e c o m p a r t m e n t s o n t h e assumption that the blood flow within e a c h c o m p a r t m e n t is uniform. In a final step the dif­ fusion properties of e a c h c o m p a r t m e n t a r e c o m p u t e d , again assuming that each c o m p a r t m e n t is h o m o g e n e o u s with r e s p e c t t o diffusion.

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H o w e v e r , t h e s e a r e w e a k a s s u m p t i o n s . T h e r e is n o r e a s o n w h y t h e blood flow a n d diffusion p r o p e r t i e s of a lung unit should always b e m a t c h e d t o its ventilation. It is possible that a lung might h a v e s o m e poorly perfused units that are well ventilated as well as o t h e r s which a r e poorly ventilated. T h e s a m e applies t o t h e diffusion characteristics of t h e units. It therefore s e e m s u n w a r r a n t e d (as t h e a u t h o r s claim) to argue that b e c a u s e t h e h y p o x e m i a of a given patient with interstitial lung disease is m o r e s e v e r e than c a n be a c c o u n t e d for b y t h e v e n t i l a t i o n - p e r f u s i o n inequality of a t w o - c o m p a r t m e n t m o d e l , an additional c a u s e of h y p o x ­ emia m a y b e p r e s e n t (Arndt et al., 1970). A n alternative view is that t h e model with its limited n u m b e r of c o m p a r t m e n t s a n d severe a s s u m p t i o n s is inadequate.

IV. USE OF FOREIGN (INERT) GASES A . Introduction Although t h e naturally occurring respiratory g a s e s — o x y g e n , c a r b o n dioxide, a n d n i t r o g e n — a r e always affected by v e n t i l a t i o n - p e r f u s i o n inequality, t h e r e is n o intrinsic r e a s o n w h y these should b e t h e preferred gases for determining t h e distribution of v e n t i l a t i o n - p e r f u s i o n ratios. In­ d e e d , they h a v e obvious limitations. First, with only three gases avail­ able, t h e a m o u n t of information is severely limited. S e c o n d , it c a n b e s h o w n that t h e gas e x c h a n g e b e h a v i o r of a gas in t h e p r e s e n c e of v e n t i l a t i o n - p e r f u s i o n inequality is d o m i n a t e d by t h e slope of its dissocia­ tion c u r v e in blood, that is, its physiologic " s o l u b i l i t y " (West, 1969-1970). Although c a r b o n dioxide h a s a steeper slope than oxygen in m o s t physiological c i r c u m s t a n c e s , t h e range of solubilities provided by these gases is very small. T h e solubility of nitrogen is irrelevant b e c a u s e the b e h a v i o r of this gas is essentially d e t e r m i n e d by t h e o t h e r t w o . F o r t h e s e r e a s o n s t h e pattern of u p t a k e o r elimination of a series of foreign gases b y t h e lung potentially contains far m o r e information a b o u t any v e n t i l a t i o n - p e r f u s i o n inequality that m a y be p r e s e n t than any p o s ­ sible m e a s u r e m e n t s of o x y g e n , c a r b o n dioxide, a n d nitrogen. M o r e o v e r , these gases h a v e t h e following a d v a n t a g e s . First, since they generally o b e y H e n r y ' s law of solubility, t h e complicating effects of a nonlinear dis­ sociation c u r v e on gas e x c h a n g e a r e a v o i d e d . (Traditionally these gases h a v e b e e n called " i n e r t " by physiologists b e c a u s e they d o not c o m b i n e with hemoglobin. T h e term is a p o o r o n e b e c a u s e several of the gases a r e anesthetic in high c o n c e n t r a t i o n s a n d therefore a r e n o t always physiolog­ ically inert. H o w e v e r , w e shall follow this usage.) A second advantage is

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5 that an e n o r m o u s range of solubilities is available, for e x a m p l e , a factor of approximately 10 b e t w e e n the solubilities of a c e t o n e and sulfur hexafluoride in blood. T h e first m e a s u r e m e n t s of inert gas exchange to derive information about ventilation-perfusion inequality were m a d e by Y o k o y a m a and Farhi (1967). T h e y allowed anesthetized dogs to b r e a t h e a mixture of m e t h a n e , e t h a n e , and nitrous oxide with oxygen for 20 min and then fol­ lowed the wash-out of these gases in expired g a s , and arterial and mixed v e n o u s blood. T h e y interpreted the data in t e r m s of a t w o - c o m p a r t m e n t model b a s e d on simple mixing e q u a t i o n s , which took a c c o u n t of the m a s s conservation that must be p r e s e n t (Farhi and Y o k o y a m a , 1967). T h e y found that the lungs b e h a v e d as if there w a s o n e c o m p a r t m e n t with a nearly normal ventilation-perfusion ratio and a n o t h e r with a low ratio of less than 0 . 1 , which received 1 0 - 2 9 % of the total bloodflow. H o w e v e r , the potential of inert gases for elucidating the pattern of ventilation-perfusion inequality goes far b e y o n d deriving a t w o c o m p a r t m e n t model. T h e r e m a i n d e r of this c h a p t e r is devoted to a m e t h o d based on multiple inert gas elimination, which has n o w been used extensively for obtaining basic physiologic information and also for study­ ing various t y p e s of lung disease. W e review b o t h the theoretical and experimental aspects of the m e t h o d , indicating the quality and quantity of information that can be potentially obtained, and the information that h a s , in fact, b e e n gathered recently in the study of patients with a s t h m a on the o n e h a n d , and patients undergoing general anesthesia on the other. B. Principles of Inert Gas Elimination T h e inert gas elimination m e t h o d rests on the m a s s balance principle, which relates alveolar p r e s s u r e s of inert gases in the lung to the solubility of the gas and the ventilation-perfusion ratio of the area of lung u n d e r consideration. This expression has b e e n derived and described m a n y times in the past ( K e t y , 1951; F a r h i , 1967) and has b e e n further treated in C h a p t e r 8 of this volume and C h a p t e r 1 of Volume II. Specifically, in a small area of lung of h o m o g e n e o u s alveolar partial p r e s s u r e , the relation­ ship b e t w e e n alveolar (PA) and end-capillary (Pc,) and mixed v e n o u s Pd partial p r e s s u r e s of an inert gas and the blood gas partition coefficient (X) and ventilation-perfusion ratio (VJQ) is given by Pc' _ P_A _ \ (\ \ P$ PvA + VJQ B e c a u s e m u c h of the material to follow centers on the interpretation of results obtained with the inert gas elimination t e c h n i q u e , it is important to

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state the specific a s s u m p t i o n s that go into this relationship. T h e s e as­ sumptions c a n b e listed as follows: 1. E a c h h o m o g e n e o u s lung unit is in a steady state of gas e x c h a n g e such that the net rate of transfer of gas from capillary blood to alveolar gas exactly equals the net rate of elimination through expiration. T h u s , the a m o u n t of inert gas stored in the lung (in blood, lung tissue, and alveolar gas) is c o n s t a n t . 2. Both ventilation and blood flow are t a k e n to be continuous pro­ c e s s e s . T h u s , the tidal nature of ventilation and the pulsatile nature of per­ fusion are specifically not taken into a c c o u n t . 3. T h e lung is treated as a collection of separate " l u n g u n i t s , " e a c h of which is h o m o g e n e o u s . E a c h unit receives ventilation and blood flow, and the ratio of ventilation to blood flow in the various lung units (that m a k e up the entire lung) varies from unit to unit. 4. Diffusion equilibration is a s s u m e d to b e c o m p l e t e . This assumption applies both to diffusion b e t w e e n capillary blood and alveolar g a s , re­ sulting in the assumption that alveolar and end-capillary partial p r e s s u r e s of inert gas are the s a m e , and to diffusion within the gas p h a s e , resulting in the a s s u m p t i o n of uniform partial p r e s s u r e e v e r y w h e r e within the lung unit. This also implies that gases of different molecular weight d o not be­ have differently other than through differences in their solubility. 5. All such lung units receive blood of the same hematocrit. 6. All lung units within the lung are arranged in parallel with o n e an­ other so that they each receive inspired gas that t r a v e r s e s only their o w n conducting airway dead s p a c e . T h u s , there is no transfer of gas either during inspiration or expiration b e t w e e n physically adjacent lung units. T h e s e a s s u m p t i o n s are precisely the ones that are m a d e in all steady state gas e x c h a n g e techniques in which a t t e m p t s are m a d e to quantitate the a m o u n t of v e n t i l a t i o n - b l o o d flow mismatching and shunt. It is gener­ ally held that if a patient or experimental animal is in a steady state as evi­ denced by c o n s t a n t tidal volume and frequency of respiration, c o n s t a n c y of heart rate and blood p r e s s u r e , and c o n s t a n c y of end-tidal P02 and PC02 partial p r e s s u r e s , all of these a s s u m p t i o n s are entirely r e a s o n a b l e . In other w o r d s , real data obtained u n d e r such conditions can be closely fitted by models that are b a s e d on the a b o v e a s s u m p t i o n s . F u r t h e r com­ m e n t s on the a p p r o p r i a t e n e s s of t h e s e a s s u m p t i o n s are m a d e below in re­ viewing the information content of the inert gas elimination m e t h o d . Given single lung units exchanging inert gas u n d e r the a b o v e a s s u m p ­ tions, the behavior of a lung that is m a d e u p of m a n y lung units of different ventilation-perfusion ratio can b e studied mathematically in a straightfor­ ward m a n n e r by employing traditional mixing e q u a t i o n s . O n c e again,

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these equations are statements of m a s s b a l a n c e . T h e total a m o u n t of gas delivered from each unit is a p r o d u c t of the concentration of the gas and the ventilation of the unit (expired gas) or the blood flow of the unit (arte­ rial blood). T h e sum of these quantities over all such units must be equiva­ lent to the total a m o u n t s t r a n s p o r t e d respectively in mixed expired gas and mixed arterial blood. This in turn is equal to the corresponding con­ centration of the gas multiplied by total ventilation (VE ) and total blood flow (QT). T h e s e c o n c e p t s lead to the following equations for mixed ex­ pired gas [Eq. (2)] and mixed arterial blood [Eq. (3)]:

j=l

PaQr

J

3

= fPc;QJ

<>

In these equations the left-hand side reflects measurable quantities that form the experimental data b a s e for the ensuing calculations. T h e righthand side, consisting of the sum of m a n y (N) t e r m s , contains b o t h the calculated alveolar gas and end-capillary partial p r e s s u r e s [Eq. (1)], multiplying the u n k n o w n ventilations (VAj ) [Eq. (2)] and perfusions {Q{) [Eq. (3)] of the various lung units. E q u a t i o n s (2) and (3) e m b o d y t w o dif­ ferent relationships. T h e first is that b e t w e e n expired (or mixed arterial) partial p r e s s u r e s and blood gas partial coefficient (excretion-solubility or r e t e n t i o n - s o l u b i l i t y curves). T h e second is the distribution of ventilation and blood flow. By distribution of ventilation we m e a n the plot, lung unit by lung unit, of ventilation on the ordinate against ventilation-perfusion ratio on the abscissa. By distribution of blood flow we m e a n the plot, lung unit by lung unit, of blood flow on the ordinate against v e n t i l a t i o n perfusion ratio on the abscissa. E q u a t i o n s (2) and (3) tie these t w o rela­ tionships to each other. It can be seen intuitively then that m e a s u r e d retention and e x c r e t i o n - s o l u b i l i t y c u r v e s are a reflection of the distributions of ventila­ tion and blood flow with respect to VA/Q. T h e multiple inert gas elimina­ tion technique exploits these principles by extracting information about the distribution of ventilation and blood flow from the retention solubility curves in a m a n n e r described in detail in C h a p t e r 8 of this volume. It is important to realize b o t h the advantages and the limitations of the inert gas a p p r o a c h , and the results to follow that pertain to disease states have been interpreted in the light of these limitations, as discussed more fully in C h a p t e r 8 of this v o l u m e . Currently used c o m p u t e r algorithms for performing the fitting proce­ dures for obtaining least-squares estimates of the distribution with en-

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forced smoothing are available in the central d e p o s i t o r y , as indicated in C h a p t e r 8 of this v o l u m e . C. Information Content of the Multiple Inert Gas Elimination Method T h e primary objective of the inert gas elimination technique is to esti­ mate the qualitative and quantitative features of the distribution of v e n t i l a t i o n - p e r f u s i o n ratios in various normal and diseased s t a t e s . T h u s , w h e n the t e c h n i q u e is u s e d in a particular setting, a s m o o t h distribution is obtained and the appropriate interpretation is m a d e . This section discusses the various forms of information that c a n be obtained from application of the inert gas t e c h n i q u e . M u c h m o r e can be learned a b o u t jgas e x c h a n g e in the lung than j u s t a description of the VA /Q distribution. This is n o w illustrated. /.

The Residual Sum of Squares: Fitting the Model

In any m a t h e m a t i c a l a p p r o a c h in which d a t a are fitted by s o m e model by using a least-squares criterion, the residual s u m of s q u a r e s b e t w e e n the closest fit by the model and the d a t a t h e m s e l v e s can provide useful infor­ mation a b o u t the acceptability of t h e model. F o r e x a m p l e , if the model is a c c u r a t e a n d t h e r e is n o experimental e r r o r in the m e a s u r e m e n t , the residual sum of squares would be z e r o . T h u s , in the a b s e n c e of experi­ mental e r r o r , a n o n z e r o sum of s q u a r e s would indicate that s o m e feature of t h e m o d e l is u n a c c e p t a b l e . W h i c h a s p e c t could be determined by appropriate modifications of the c o m p o n e n t s of the model in a systematic fashion, until a z e r o sum of s q u a r e s could be obtained. E v e n t h e n , it would be d a n g e r o u s to claim that the particular model is the only o n e compatible with the data. Historically, h o w e v e r , m o s t w o r k e r s h a v e b e e n c o n t e n t to find e v e n o n e model that c a n fit d a t a (Riley and C o u r n a n d , 1951; Briscoe et al.y 1960; Y o k o y a m a and F a r h i , 1967).

In the experimental setting, e v e n w h e n the model is a c c u r a t e , the resid­ ual sum of s q u a r e s will n e v e r be z e r o (that is, the fit to the d a t a will not be perfect) e x c e p t by c h a n c e , and t h e n only u n d e r t w o c i r c u m s t a n c e s . T h e first is if e a c h of the m e a s u r e d d a t a points in the specific c a s e contains no e r r o r (even t h o u g h this rarely, if e v e r , o c c u r s ) . T h e s e c o n d is w h e n the errors are of appropriate magnitude and direction such that the data still lie within the province of the m o d e l . T o illustrate t h e s e c o n c e p t s , consider the calculation of v e n o u s a d m i x t u r e given a m e a s u r e d value of arterial ox­ ygen saturation. If the true o x y g e n saturation w e r e 9 5 % and the m e a s u r e d value w e r e r e p o r t e d as 9 5 % , the calculated v e n o u s a d m i x t u r e would b e c o r r e c t . If, h o w e v e r , the m e a s u r e d arterial o x y g e n saturation w e r e re-

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ported as 94% rather than the correct value of 9 5 % , the model (venous ad­ mixture) would still yield a physiologically reasonable answer, but the value obtained would be in error. In this setting, w h e t h e r the arterial ox­ ygen saturation is correct or in error, an exact (and reasonable) model can be found that fits the data. If, h o w e v e r , the m e a s u r e d arterial oxygen satu­ ration w e r e reported as 103%, the calculated v e n o u s admixture would be negative and physiologically meaningless b e c a u s e oxygen saturation c a n n o t e x c e e d 100%. T h e smallest v e n o u s admixture that could be re­ ported from a m e a s u r e d oxygen saturation of 103% would therefore be z e r o , and there would be a difference b e t w e e n the m e a s u r e d data (103%) and the nearest fit to the data (100% saturation). T h e s e c o n c e p t s can be applied to the multiple inert gas technique in ex­ actly the same m a n n e r . If the inert gas data are error free and the model is correct, a sum of squares of zero will result w h e n the least-squares analy­ sis is performed (Chapter 8, this volume). If the inert gas data contain error, but still lie within the b o u n d s of the m o d e l , it may be possible to fit the data and still have a residual sum of squares of z e r o . Although in the a b o v e e x a m p l e a reported arterial oxygen saturation of 103% would be most unusual, the corresponding result w h e n using the inert gas technique is by no m e a n s u n u s u a l — i n fact, it is the rule. In other w o r d s , it is quite likely that in gathering inert gas elimination data in the p r e s e n c e of experimental error, the sum of squares will not be zero even if this model is correct. T h e r e a s o n lies in E q s . (2) and (3), which d e c r e e a very tight relationship b e t w e e n the retention values for gases of different solubility. This has been described previously (Wagner et al., 1974c). This lengthy introduction is n e c e s s a r y to illustrate the potential com­ plexity of interpreting a sum of squares in a least-fitting p r o c e s s . If the sum of squares is n o n z e r o , as is the rule in most analyses of real data, t w o independent factors may contribute. T h e first is experimental error, and the second is inaccuracy in the m o d e l . T h e differentiation b e t w e e n these t w o c a u s e s for failure to fit the model will n o w be discussed b e c a u s e of its importance in the interpretation of real data. T h e basis for understanding the c a u s e of a n o n z e r o sum of squares is in the knowledge of the coefficient of variation in the inert gas elimination data. If the coefficient of variation of retention and excretion is k n o w n , then the range of sum of squares to be e x p e c t e d from such a degree of r a n d o m error can be determined either numerically (by generating such data repeatedly and attempting to fit t h e m with the least-squares proce­ dure) or m o r e directly by consulting appropriate statistical tables. In our a p p r o a c h to the inert gas elimination technique (Evans and Wagner, 1977), w e use the coefficient of variation for the m e a s u r e m e n t of retention of each gas to weight E q s . (2) and (3) for each gas. In other w o r d s , t h e s e

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equations are multiplied throughout by a weighting factor that m a k e s the weighted retention values h a v e unit v a r i a n c e . If w e use six2g a s e s , w e h a v e that m a n y degrees of freedom and can examine the x table for that n u m b e r . W h e n this is d o n e , it is seen that the normalized sum of squares (that e x p e c t e d w h e n fitting six i n d e p e n d e n t d a t a points w h o s e variance is each 1.0) w o u l d e x c e e d 5.348 5 0 % of t h e time. T h e s u m of s q u a r e s would exceed 10.645 only 10% of the time and 16.812 only 1% of the time on the basis of r a n d o m error. T h u s , it is seen that knowledge of the error of the m e t h o d together with the appropriate calculation allows an interpretation of the residual sum of squares that gives information on h o w well the model fits the data. In o u r e x p e r i e n c e , a residual sum of s q u a r e s greater than 20 is exceedingly r a r e , and usual values are in the range of 2 - 1 0 . In this w a y , taking a c c o u n t of experimental error in real inert gas data (obtained from both h u m a n and animal studies involving both normal and diseased lungs) reveals compati­ bility with the steady state model referred to a b o v e [Eq. ( l ) - ( 3 ) ] . Specifi­ cally, this compatibility implies that n o n e of the a s s u m p t i o n s used are suf­ ficiently u n r e a s o n a b l e that they p r e v e n t an a d e q u a t e analysis of the data. W e h a v e recently used such an analysis in the study of m e c h a n i s m s of gas e x c h a n g e in different experimental animals (Powell and W a g n e r , 1979). All of o u r previous w o r k had b e e n d o n e in mammalian lungs and is based on E q . (1), which describes gas exchange in a mammalian alveolar lung unit. H o w e v e r , it has long b e e n suspected that the appropriate model for gas exchange in most bird lungs is not the alveolar model, but r a t h e r a model involving c r o s s c u r r e n t gas e x c h a n g e (Powell and Wagner, 1979). Support of this c o n c e p t c o m e s from both anatomical studies of the a r r a n g e m e n t of the bird lung and functional studies in which it has b e e n d e m o n s t r a t e d that expired P C 2 0c a n e x c e e d that in the arterial blood by more than c a n be explained on the basis of mammalian lung structure. We h a v e used the inert gas elimination technique in the lungs of normal geese and obtained retention and excretion d a t a that h a v e b e e n fitted with b o t h the standard alveolar least-squares analysis based on E q . (1), and also a modified a p p r o a c h (also by least-squares criteria) in which E q . (1) has been replaced by the appropriate equations for c r o s s c u r r e n t gas e x c h a n g e (Scheid and Piiper, 1970; Powell and W a g n e r , 1979). W e have found con­ sistently that the normalized sum of squares obtained with the alveolar model is of the o r d e r of 4 0 - 1 0 0 , w h e r e a s those obtained with the cross­ current model have in all cases b e e n considerably less than 10. While this result d o e s not p r o v e that c r o s s c u r r e n t gas e x c h a n g e is the only pos­ sible m e c h a n i s m operating in the g o o s e , it supports the hypothesis of c r o s s c u r r e n t gas e x c h a n g e , and certainly rules out a mammalian alveolar arrangement as being responsible for gas e x c h a n g e in the g o o s e .

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Peter D. Wagner and John B. West

Lungs

While the sum of squares can be used to j u d g e t h e ability of the model to fit the data even in the p r e s e n c e of experimental e r r o r , it is possible that other models of gas exchange will fit a set of data equally as well as the basic parallel alveolar model described in E q s . ( l ) - ( 3 ) . A likely e x a m p l e in clinical respiratory disease is that of series ventila­ tion. Although the standard inert gas elimination analysis is formulated on the basis of lung units ventilated only in parallel with o n e another, it may be that in certain disease states s o m e lung units receive their inspiration " s e c o n d - h a n d " from their neighboring units through the p r o c e s s of series or collateral ventilation. A n important consideration is that of interpreting insert gas elimination data should such series or collateral ventilation be present. This question has b e e n a d d r e s s e d on t w o levels. T h e first relates to bulk series or collateral ventilation in which gases m o v e b e t w e e n lung units by bulk flow in a m a n n e r not d e p e n d e n t on diffusion p r o c e s s e s and therefore independently of molecular weight (Wagner and E v a n s , 1977). H o w e v e r , it is possible that a s e c o n d form of series ventilation exists. This is sometimes referred to as stratification (Chapter 5 of this volume) and from the functional standpoint it can b e described as the existence of partial p r e s s u r e differences d u e to incomplete diffusive gas mixing, an ef­ fect that would be d e p e n d e n t on molecular weight. T h u s , gases of high molecular weight would be m o r e vulnerable than gases of low molecular weight. T h e interpretation of elimination data w h e n series bulk ventilation is present has b e e n addressed at s o m e length (Wagner and E v a n s , 1977). It has b e e n found that for every individual quantitative arrangement of series ventilated lung units, t h e r e exists a purely parallel equivalent arrangement such that inert gas e x c h a n g e for all gases is identical. This re­ sult has t w o major implications: (1) series bulk ventilation in the steady state c a n n o t b e identified by using the multiple inert gas elimination tech­ nique, and (2) by the same t o k e n , if such series inequality exists it can be interpreted as if it w e r e a parallel p r o b l e m . In other w o r d s , even if series ventilation is p r e s e n t , a purely parallel model will fit the data j u s t as well and the resultant v e n t i l a t i o n - p e r f u s i o n inequality can be interpreted as if it w e r e occurring on a parallel r a t h e r than series basis. T w o o t h e r physiologically r e a s o n a b l e d e p a r t u r e s from the basic parallel model have b e e n examined in the s a m e w a y . First, it is k n o w n that the an­ atomic dead space acts as a mixing c h a m b e r for the last expired gas in each b r e a t h . T h u s , on each inspiration, the first inspired gas to each lung unit contains some mixture of gas expired from all lung units. This notion of shared or " c o m m o n " dead s p a c e will clearly change the a m o u n t of gas that is transferred in each lung unit from that which would o c c u r in the ab­ sence of c o m m o n dead s p a c e . This problem w a s first addressed for the respiratory gases O z and C 0 2 by R o s s and Farhi (1960) and m o r e recently

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and generally by F o r t u n e and W a g n e r (1979) and Petrini and co-workers (1979). A s with the series ventilation analysis, u n d e r m o s t all conditions it w a s found that the p r e s e n c e of shared or c o m m o n d e a d space d o e s alter gas e x c h a n g e , b u t that the p e r t u r b a t i o n s that result can still be interpreted as if they w e r e taking place in a lung with purely parallel p a t h w a y s and n o sharing of dead space. B o t h the analysis of R o s s and Farhi and of F o r t u n e and W a g n e r show that the p r e s e n c e of shared dead space improves gas exchange u n d e r most conditions. T h e latter study has s h o w n that the changes in inert gas transfer that are likely to result from sharing of dead space a r e , h o w e v e r , minor and d o not change the overall interpretation of patterns of v e n t i l a t i o n - b l o o d flow mismatching d e t e r m i n e d from the inert gas elimination t e c h n i q u e , which ignores c o m m o n d e a d s p a c e . Finally, variation in hematocrit a m o n g different regions of the lung will affect gas e x c h a n g e to some e x t e n t , as first suggested by Briscoe (1959). This is b e c a u s e the solubility of gases in red cells is different from that in p l a s m a (Young and Wagner, 1979). W e h a v e studied the potential effects of maldistribution of hematocrit acting in addition to v e n t i l a t i o n perfusion mismatching and found that the possible effects are reasonably small. T h e perturbations p r o d u c e d result in slightly altered inert gas ten­ sions, which c a n still b e fitted by the fundamental parallel m o d e l , which ignores hematocrit inequality. T h e distributions of ventilation-perfu­ sion ratios r e c o v e r e d u n d e r such conditions by the standard leastsquares a p p r o a c h d o not differ significantly through the added effect of hematocrit inequality. T h u s , in s u m m a r y , we h a v e found that the parallel alveolar model of v e n t i l a t i o n - p e r f u s i o n mismatching adequately fits o b s e r v e d inert gas elimination d a t a u n d e r a wide variety of conditions in both m a n and experimental m a m m a l s . This s u p p o r t s the u s e of the parallel model as a framework for interpreting abnormalities in gas e x c h a n g e . H o w e v e r , sev­ eral e x t e n s i o n s of this relatively simple model may well o c c u r , particularily in disease states. T h e three m o s t likely of t h e s e , n a m e l y , series ven­ tilation, sharing anatomic dead s p a c e , and existence of hematocrit varia­ tions within the lung, will all p e r t u r b inert (and respiratory) gas e x c h a n g e . T h e s e perturbations are generally small, but in all c a s e s theoretical analy­ sis s h o w s that data obtained u n d e r such conditions can still be adequately fitted using the simple parallel alveolar model. 3. Resolution of Lung Units of Different Ventilation-Perfusion Ratio As explained in the early sections of this c h a p t e r , m u c h effort has b e e n invested o v e r the y e a r s in devising m e t h o d s for quantitating the a m o u n t of v e n t i l a t i o n - p e r f u s i o n mismatching. Most such m e t h o d s are limited in their resolution. Specifically, the separation of areas of low VA /Q from

Peter D. Wagner and John B. West

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7. Ventilation-Perfusion Relationships

239

areas of z e r o VA /Q (shunt) on the o n e h a n d , and the separation of areas of high VA /Q from areas of infinitely high VA /Q (unperfused lung or dead space) has long b e e n a problem. T h e multiple inert gas elimination tech­ nique w a s devised with the primary intention of improving the resolu­ tion at the e n d s of the VA /Q s p e c t r u m as stated a b o v e . Although it is clear from C h a p t e r 8 of this volume that n o c u r r e n t m e t h o d has perfect resolu­ tion, the multiple inert gas technique is able to resolve these p r o b l e m s considerably b e t t e r than previous a p p r o a c h e s . T h e r e a s o n for this im­ p r o v e d resolution is straightforward and resides in the utilization of sev­ eral gases of appropriate solubilities. This can be u n d e r s t o o d in t e r m s of E q . (1) in the following e x a m p l e . Figure 4A s h o w s the r e t e n t i o n solubility c u r v e s (Wagner et al., 1974c) of t w o lungs, o n e of which con­ tains 2 5 % shunt and the o t h e r of which contains 2 5 % of the blood flow as­ sociated with the m o d e of low v e n t i l a t i o n - p e r f u s i o n ratio, VA /Q = 0.05. T h e remaining 7 5 % of the blood flow in e a c h case is associated with lung units of n o r m a l v e n t i l a t i o n - p e r f u s i o n ratio, and the total ventilation and blood flow for the t w o lungs is the s a m e . Although fof gases of partition coefficient greater than about 1, the difference in the retention c u r v e s for the t w o lungs is not great, there is a m a r k e d difference b e t w e e n the reten­ tion c u r v e s of gases of low solubility. This is b e c a u s e no m a t t e r h o w insol­ uble a gas, if there is no ventilation (shunt), that gas c a n n o t e s c a p e from the blood into the gas p h a s e . O n the o t h e r h a n d , for an extremely insolu­ ble gas, e v e n if the v e n t i l a t i o n - p e r f u s i o n ratio is as low as 0.05 as in this e x a m p l e , most of the gas does e s c a p e into alveolar gas and is eliminated. B e c a u s e the r e t e n t i o n - s o l u b i l i t y c u r v e s are so different u n d e r these t w o conditions, it should be clear h o w it is possible to resolve b e t w e e n the p r e s e n c e of low VA /Q areas or shunt in t h e s e e x a m p l e s . In Fig. 4 B , ex­ actly the s a m e c o n c e p t is illustrated at the other end of the VA /Q spec­ t r u m , w h e r e excretion c u r v e s are illustrated for t w o lungs, o n e having Fig. 4. Retention (arterial/mixed venous partial pressure ratio) and excretion (mixed ex­ pired/mixed venous partial pressure ratio) curves for different lungs. (A) The retention curve for a homogeneous lung is shown and compared with the retention curves of two ab­ normal lungs. In one, there is a 25% shunt, and in the other 25% of the cardiac output per­ fuses units of low V /Q ratio. Notice the large differences in SF and ethane retention in A 6 each case. (B) Excretion curves are shown for a homogeneous lung, a lung with 25% of the ventilation associated with units of high ventilation-perfusion ratio, and a lung with a deadspace. Notice the separation of the curves for gases of high solubility. (C) The retention curve is shown for a lung containing both low V /Q units and shunt with a homogeneous curve for A comparison. Although the solid line to the left of the SF retention point is correct, it is pos­ 6 sible that the retention curve could fall away more steeply, as shown by the dashed line. Un­ certainty in the retention curve leads to uncertainty in the distribution of ventilationperfusion ratios that would be recovered from such a curve, as described more fully in the text.

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2 5 % of the ventilation associated with completely unperfused units (dead space), the other having the same fraction of ventilation associated with units of high VJQ (VJQ = 30.0). While for gases of low solubility the excretion c u r v e s are very similar to o n e a n o t h e r , for gases of high solubil­ ity the excretion curves separate considerably according to w h e t h e r the abnormal units are completely unperfused (dead space) or are units of high VJQ. With the gases that are currently used in the multiple inert gas elimina­ tion technique (see Fig. 4A), a good resolution can be obtained in areas of VJQ such as those illustrated, and m a n y clinical examples are found to c o r r e s p o n d to j u s t these values of VJQ (Wagner et al., 1977b, 1978a). F o r e x a m p l e , some patients with a s t h m a w h o a p p e a r to have a m o d e of low VJQ units, but no shunts are found to have r e t e n t i o n - s o l u b i l i t y curves approaching zero for insoluble gases. We can be quite confident about the resolution in such c a s e s . S o m e patients with chronic obstruc­ tive lung disease have areas of high V JQ and their excretion c u r v e s look like those in Fig. 4B of the lung with 2 5 % ventilation in unit of VJQ = 30. S o m e difficulty in resolution does arise in s o m e instances, h o w e v e r . If areas of low and zero v e n t i l a t i o n - p e r f u s i o n ratio coexist, then a retention solubility curve as shown in Fig. 4C will be found. N o t i c e that here the re­ tention of the least soluble gas u s e d , S F 6, is quite high, a n d , as is illus­ trated, it is not clear as to the fate of the retention c u r v e to the left of this point. T h u s , the c u r v e could continue d o w n w a r d and eventually r e a c h the abscissa at a sufficiently low solubility or the c u r v e might flatten out and b e c o m e horizontal well a b o v e the abscissa. In both c a s e s , resolution would greatly improve if a gas 10 or 100 times less soluble than S F 6 could be used (but such a gas is not currently available). It would then be pos­ sible to differentiate b e t w e e n low VJQ units and shunt with considerable reliability, even w h e n both are present. Given that the least-soluble gas currently available is S F 6, the precise resolution b e t w e e n poorly venti­ lated and unventilated lung units w h e n both exist together will be incom­ plete. T h e s e situations are recognizable by having a high retention for the least soluble gas and a high slope for the retention solubility curve passing through the retention value of that gas. T h e t e c h n i q u e s outlined in Chapter 8 of this volume (particularly those of linear programming) can be used to define quantitatively j u s t how m u c h resolution is present in a given situation. 4. Modality of

Distributions

Closely tied to the issue of resolution b e t w e e n different regions of the VJQ spectrum, is the issue of modality of the distribution obtained from

7. Ventilation-Perfusion Relationships

241

the multiple inert gas t e c h n i q u e . O n e of the m o s t important findings in a variety of these disease states to date has b e e n that of bimodal and in s o m e cases trimodal VA /Q distributions (as o p p o s e d to w h a t could have b e e n found, n a m e l y , the existence of b r o a d unimodal distributions). It is clearly of major importance to k n o w with certainty that a distribution in­ dicated as bimodal by the inert gas analysis is, in fact, a bimodal distribu­ tion and not erroneously interpreted as bimodal b e c a u s e of limitations in the analysis. T h e use of enforced smoothing in the least-squares analysis as p r o p o s e d by E v a n s and Wagner (1977) has b e e n found to reflect modal­ ity quite reliably. T h u s , while rigorous interpretation d e p e n d s u p o n tech­ niques such as linear programming described by O l s z o w k a and W a g n e r in Chapter 8 of this v o l u m e , w e have found repeatedly that such t e c h n i q u e s have always confirmed the impression given w h e n enforced smoothing is used. T h e reliability of the enforced smoothing technique in defining mo­ dality c o m e s from the w a y in which smoothing is utilized. As described by O l s z o w k a and W a g n e r , part of the t e r m to be minimized in the leastsquares a p p r o a c h contains the sum of squares of c o m p a r t m e n t a l perfu­ sions. Minimization of this c o m p o n e n t will always be accomplished best by unimodal rather than bimodal (and particularly trimodal) distributions, so that p r e s e n c e of m o r e than o n e m o d e in the results is very likely to be a real finding. Generally, distributions obtained with the inert gas m e t h o d that do con­ tain m o r e than one m o d e show the m o d e s as smoothly c o n t o u r e d and often separated b y a region of the VA /Q s p e c t r u m devoid of ventilation and blood flow. It is important to interpret t h e s e p a t t e r n s in the correct m a n n e r . The linear programming technique of O l s z o w k a and W a g n e r can be used to m a k e s o m e generalizations regarding p r o p e r interpretation. First, the region b e t w e e n any pair of m o d e s m a y b e devoid of ventilation and blood flow as s h o w n , but not necessarily in every c a s e . H o w e v e r , w h e n e v e r a clearly separated bimodal or trimodal p a t t e r n results, t h e r e can n e v e r be sufficient ventilation or blood flow b e t w e e n the m o d e s to allow a unimodal c u r v e to fit the d a t a the adequately. H o w e v e r , bimodal distributions in which the m o d e s are not completely separated c a n n o t always be resolved as such. W h e n intermodal distance is of the o r d e r of one d e c a d e of v e n t i l a t i o n - p e r f u s i o n ratios (or m o r e ) , bimodal definition is generally possible, but if the t w o m o d e s are separated by less than a dec­ ade of VA /Q, then they may merge and not be separately identifiable using the current inert gas t e c h n i q u e . It would t a k e m o r e inert gases and less experimental error to achieve the separation of m o d e s u n d e r t h o s e condi­ tions. In addition t o p r o p e r interpretation of the region b e t w e e n m o d e s , the shape of the m o d e requires s o m e discussion. T h e r e is generally insuf­ ficient information from the inert gas technique to m a k e precise state-

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Peter D. Wagner and John B. West

merits about the height, width, and shape of a m o d e . This is not surprising since there are only six gases forming the d a t a b a s e . T h e potential varia­ tion in height and shape of a m o d e can be explored with the linear pro­ gramming technique of O l s z o w k a and Wagner. H o w e v e r , the total a m o u n t of ventilation and blood flow in a m o d e and its m e a n position along the VJQ axis can be determined with considerable a c c u r a c y . In s u m m a r y , u p to three m o d e s of a VJQ distribution can in theory be defined by the current inert gas elimination technique using six different inert g a s e s . T h e least-squares a p p r o a c h using enforced smoothing ( E v a n s and Wagner, 1977) reliably indicates the p r e s e n c e , location, and magni­ tude of such m o d e s w h e n they exist. This is supported by independent linear programming t e c h n i q u e s , as discussed by O l s z o w k a and Wagner. Although the existence and magnitude of such m o d e s can generally be de­ fined, there are some limitations regarding the a m o u n t of information that is available, particularly pertaining to the precise height and width of a m o d e on the o n e hand, and the p r e s e n c e or a b s e n c e of ventilation and blood flow in the region b e t w e e n the m o d e s on the other. M o d e s sepa­ rated by less than about one d e c a d e of VJQ may not be separable with the current t e c h n i q u e . 5. Gas Diffusion: The Effects of Molecular

Weight

Still further information can be obtained from application of the inert gas elimination technique. Recall that r e t e n t i o n - s o l u b i l i t y c u r v e s are in­ terpreted on the assumption that inert gases are transferred in a c c o r d a n c e with solubility and ventilation/perfusion ratio alone [Eq. (1)]. T o the ex­ tent that diffusion p r o c e s s e s are incomplete for inert g a s e s , t h o s e gases of high molecular weight ( S F 6 M W , 146, and halothane, M W , 197.5) will be retained to a relatively greater degree than would be e x p e c t e d on the basis of solubility alone as c o m p a r e d to the remaining four gases, w h o s e molecular weights range from 30 (ethane) to 74 (ether). This concept can be exploited in the analysis of retention and excretion data, particularly using the gas halothane since it is b r a c k e t e d (in t e r m s of solubility) by t w o gases on each side, all of which h a v e reasonably low molecular weights by comparison. T h u s , the next gases of higher solubility are ether and ace­ t o n e , of molecular weights 74 and 58, respectively, w h e r e a s the gases of lower solubility are ethane and c y c l o p r o p a n e , of molecular weights 30 and 42, respectively. With this particular arrangement of solubilities and molecular weights, the least-squares analysis would result in a p o o r fit (to retention data) that would be directionally opposite for halothane c o m p a r e d to the four surrounding gases (if halothane were sufficiently influenced by diffusion p r o c e s s e s ) . This would be evident in examination of the sum of squares and the sign of the differences (or residuals) for

7. Ventilation-Perfusion Relationships

243

each gas. T h u s , the analysis of the residual sum of squares referred to earlier in this c h a p t e r is e x t e n d e d here to subdivide the c o m p o n e n t s of the sum of s q u a r e s , gas by g a s , a particular pattern being e x p e c t e d if molecu­ lar weight is an important factor determining the elimination of the g a s . Preferential interference to the e x c h a n g e of high molecular weight gases has n e v e r b e e n o b s e r v e d in our h a n d s , in m a n or animals in normal or dis­ eased states, including patients with chronic obstructive lung disease in w h o m p a r e n c h y m a l destruction leading to large gas spaces may well re­ sult in incompleteness of diffusive gas mixing. A d a r o and Farhi (1971) re­ ported in an abstract that a small reduction in elimination of freon 12 ( M W , 86.5) o c c u r r e d c o m p a r e d to acetylene ( M W , 26) in a dog prepara­ tion. Molecular weight d e p e n d e n c y of gas exchange can also b e explored graphically using retention or excretion data as follows. While the rela­ tionship b e t w e e n retention and solubility [Eq. (1)] is hyperbolic on a linear scale, the inverse relationship (that is, the plot of the reciprocal of retention against the reciprocal of solubility) is, in a h o m o g e n e o u s lung, a linear relationship [Eq. (1)]. E v e n in lungs with some degree of ventilation blood flow mismatching, o n e or o t h e r of the retention and excretion c u r v e s usually results in a fairly linear inverse relationship. Such a linear transformation is simply a c o n v e n i e n t tool for comparing the retention and excretion values for different g a s e s . H a l o t h a n e would again b e the appropriate gas to study and would lie below the straight line connecting a c e t a n e , ether, c y c l o p r o p a n e , and e t h a n e . In this graphical m a n n e r , the behavior reflected by the a b o v e sum of squares analysis would be evident. 6. Diffusion of Gases between Alveolar Gas and Capillary Blood While c o m p a r i s o n of the inert gases o n e to the o t h e r gives information about diffusion in the gas p h a s e , c o m p a r i s o n of the inert gases as a group with o x y g e n gives information a b o u t the c o m p l e t e n e s s of diffusion equili­ bration a c r o s s the b l o o d - g a s barrier b e t w e e n capillary blood and alveolar gas. Although experimental verification is currently infeasible, calcula­ tions of the rate of attainment of partial p r e s s u r e equilibrium for inert gases (Forster, 1957; Wagner, 1977b) suggest that all inert gases equili­ brate very rapidly. A s blood e n t e r s the gas e x c h a n g e vessels from the mixed v e n o u s blood, all of the inert gas transfer t a k e s place within the first few h u n d r e d t h s of a second and the remaining time spent in the gas exchange region does not result in further gas e x c h a n g e . T h e rate of equil­ ibration is independent of the b l o o d - g a s partition coefficient, but does d e p e n d on molecular weight. F o r a hypothetical inert gas of molecular weight 32, 9 9 % of the gas e x c h a n g e t a k e s place within 0.04 sec (assuming

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Peter D. Wagner and John B. West

a normal diffusing capacity). Similar calculations for oxygen reveal an approximately tenfold greater time required for the same degree of equili­ bration. T h e fundamental reason for this difference in behavior is that the diffusion of oxygen from alveolar gas to capillary blood d e p e n d s u p o n the very low solubility of oxygen in the blood gas barrier, a solubility approxi­ mately equal to that in saline, n a m e l y , 0.0031 m l / 1 0 0 m l / m m H g . On the o t h e r h a n d , the rate of rise of partial p r e s s u r e of oxygen in the blood de­ p e n d s to a large extent on the p r e s e n c e of hemoglobin. A s oxygen r e a c h e s the blood, it diffuses into the red cell and c o m b i n e s rapidly with hemoglo­ bin. This delays its rise in partial p r e s s u r e . Variations in the rate of diffu­ sion equilibration of inert gases (over the range of molecular weights en­ c o m p a s s e d in inert gas technique) are m u c h smaller than the order of mag­ nitude difference b e t w e e n o x y g e n and any such inert gas (Forster, 1957; Wagner, 1977b). This fundamental difference in the rate of diffusion equilibration for inert gases on the one h a n d , and o x y g e n on the other, affords the potential for evaluating the role of a l v e o l a r - c a p i l l a r y diffusion impairment in 0 2 exchange in diseased lungs. This has in the past b e e n an essentially im­ possible task b e c a u s e the same pathological changes that lead to diffusion impairment p r o d u c e v e n t i l a t i o n - p e r f u s i o n d i s t u r b a n c e s , and the t w o c a n n o t usually be separated by traditional m e t h o d s . In a lung with v e n t i l a t i o n - b l o o d flow inequality, but no diffusion im­ /Q distribution recovered from pairment for inert gases or o x y g e n , the VA the inert gas data can be used to calculate an e x p e c t e d value for arterial P02 . Such a calculation uses directly m e a s u r e d mixed v e n o u s P02 and PC02 values together with information concerning hemoglobin concentration, t e m p e r a t u r e , and a c i d - b a s e b a l a n c e . Such a calculation should statisti­ cally agree with directly m e a s u r e d values for arterial P02 since, after allowances are m a d e for the nonlinear nature of the oxyhemoglobin disso­ ciation c u r v e , the rules of gas e x c h a n g e are similar for inert gases and ox­ ygen. H o w e v e r , w h e n diffusion impairment b e c o m e s evident, oxygen will b e affected to a m u c h greater extent than inert gases a n d , in fact, most w o r k e r s believe that situations in which diffusion impairment interferes with inert gas transfer would not be compatible with life. In a setting w h e r e oxygen is diffusion limited but inert gases are not, the m e a s u r e d arterial P02 will be lower than that calculated from the inert gas data since the calculation expressly a s s u m e s complete diffusion equilibration for all gases in the s y s t e m . While small degrees of diffusion impairment may not b e detectable b e c a u s e of the p r e s e n c e of r a n d o m experimental error, if a significant fraction of the total a l v e o l a r - a r t e r i a l P02 difference is c a u s e d by diffusion impairment, it will be detectable by this indirect comparison

245

7. Ventilation-Perfusion Relationships

b e t w e e n inert gases and o x y g e n . Illustrations of this c o m p a r i s o n will follow in the review of v e n t i l a t i o n - p e r f u s i o n inequality in disease states. A question that might be raised is w h e t h e r any o t h e r physiological phe­ n o m e n o n could cause a similar internal inconsistency b e t w e e n inert gas and oxygen transfer. A theoretical possibility is the contribution of w h a t are k n o w n generally as p o s t p u l m o n a r y s h u n t s . Bronchial veins and thebe­ sian veins carrying desaturated blood m a y e m p t y into the arterial side of the circulation and thereby c a u s e a depression of arterial P02 . Such a shunt, h o w e v e r , will not affect arterial inert gas levels since passage of inert gases through the bronchial and thebesian circulations d o e s not re­ sult in modification of their c o n c e n t r a t i o n s . O n e way to resolve the uncer­ tainty concerning these t w o possible m e c h a n i s m s for inconsistency b e t w e e n inert gas and oxygen transfer is to c o m p a r e t h e m during both air breathing and oxygen breathing. If the inconsistency w e r e p r o d u c e d by diffusion impairment, the breathing of 100% oxygen would abolish (or at least considerably reduce) the difference b e t w e e n inert gas and 0 2 ex­ c h a n g e . If, h o w e v e r , bronchial or thebesian v e n o u s shunts w e r e responsi­ ble, the discrepancy b e t w e e n inert gas and oxygen e x c h a n g e should in­ c r e a s e u p o n oxygen breathing. F a c t o r s such as series inequality of ventilation, intrapulmonary varia­ tion in hematocrit, and the reinspiration of shared d e a d s p a c e are not p o ­ tential c a u s e s of such inconsistency. A s discussed earlier, t h e s e exten­ sions of the basic parallel model all p r o d u c e p e r t u r b a t i o n s of inert gas ex­ change that can b e interpreted on a parallel-model basis. W e h a v e found consistently that these parallel-model extensions and their " a s if" parallel equivalents p r o d u c e the same arterial P02 and PC02 as well. 7. Intrapulmonary

and Extrapulmonary

Factors in

Hypoxemia

/Q distribu­ O n e of the m o s t helpful analyses that can b e m a d e using VA tions obtained from inert gas d a t a is to partition the c a u s e s of h y p o x e m i a into intra- and e x t r a p u l m o n a r y factors. This is of considerable clinical im­ p o r t a n c e since understanding of a disease state in which both intra- and e x t r a p u l m o n a r y factors play a role is essential for making rational thera­ peutic decisions. This is particularly likely to be the case in t h e intensive care setting, w h e r e intrapulmonary factors such as the distribution of v e n t i l a t i o n - p e r f u s i o n ratios, shunting, and dead space may rapidly c h a n g e , while at the same time e x t r a p u l m o n a r y factors such as cardiac output, total ventilation, hemoglobin c o n c e n t r a t i o n , and a c i d - b a s e status m a y also change frequently. U n d e r s t a n d i n g the net change in arterial P02 w h e n several such variables are simultaneously altered is possible using the results of the inert gas a p p r o a c h . (This c o n c e p t will also be illustrated

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in the discussion to follow concerning findings m a d e using the m e t h o d in patients with different c a r d i o p u l m o n a r y diseases.) T h e actual data (inert gas d a t a , mixed v e n o u s P02 , cardiac o u t p u t , hemoglobin, a c i d - b a s e status, and so on) can be used to calculate the ex­ pected arterial P02 \ this is d o n e by using the principles enunciated in C h a p t e r 8 of this volume. It is then a straightforward matter using the digital c o m p u t e r to change any o n e of the input variables such as cardiac o u t p u t , hemoglobin, or a c i d - b a s e status and to recalculate the e x p e c t e d . In this w a y , the net effect of any single-variable change can arterial P02 be estimated, leaving other variables at their real levels. Such an analysis adds considerably to insight into the m e c h a n i s m s of h y p o x e m i a , and par­ ticularly into the relative i m p o r t a n c e of intra- and e x t r a p u l m o n a r y factors, the determination of which will often affect therapeutic decisions.

V. VENTILATION-PERFUSION INEQUALITY IN DISEASE

A. Specific Disease States Previously published findings are briefly summarized and m o r e recent data are p r e s e n t e d in light of the preceding discussion concerning the quantity and quality of information that can be obtained by application of the inert gas p r o c e d u r e . While it is recognized that the n u m b e r of patients studied is relatively small, and in particular that most patients studied w e r e in a d v a n c e d stages of their illness, analysis of individual results in the disease states to follow has provided considerably insight into the factors that determine abnormal gas e x c h a n g e . /. Chronic Obstructive Pulmonary Disease

(COPD)

W e have applied the inert gas t e c h n i q u e to 23 patients with various clin­ ical presentations of chronic obstructive p u l m o n a r y disease (Wagner et al., 1977b). All w e r e in a d v a n c e d stages of the disease with grossly re­ d u c e d air-flow r a t e s . W e m a d e an a t t e m p t to select t w o groups of patients. O n e exhibited the clinical characteristics of hyperinflation, chest X-ray changes showing attenuation of vascular markings, flattening of dia­ p h r a g m , and normal or smaller than normal cardiac silhouettes. T h e s e pa­ tients had little or no sputum p r o d u c t i o n and had relatively mild hypox­ emia with essentially no h y p e r c a p n i a . T h o s e patients w h o fit the clinical criteria of B u r r o w s and c o - w o r k e r s (1966) for type A can be contrasted with the second group (type B variety), w h o in general had moderately severe h y p o x e m i a often with C 0 2 retention and had evidence of p r e s e n t

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or past right heart failure, and w h o s e chest X-ray findings did not reveal the a t t e n u a t e d vascular markings and hyperinflation characteristic of the type A patient. In type A patients, an almost uniform finding w a s that, in addition to units of normal v e n t i l a t i o n - p e r f u s i o n ratio, a population of lung units of very high v e n t i l a t i o n - p e r f u s i o n ratio w a s p r e s e n t . In contrast there w a s rarely any shunt and no areas of extremely low v e n t i l a t i o n - p e r f u s i o n ratio (VA /Q < 0.1). T h e r e a s o n for h y p o x e m i a in t h e s e patients w a s that the m o d e of lung units that received m o s t of the perfusion had a s o m e w h a t lower than normal average value of VA /Q (about 0.6 c o m p a r e d to the normal of 0 . 8 - 1 . 0 ) . Statistical analysis confirmed bimodality of distribu­ tions, strongly supporting the conclusion that the units of relatively normal VA /Q and those of high VA /Q w e r e not part of a continuous spec­ t r u m . T h e behavior of the high molecular weight gases w a s not found to be different from that of the low molecular weight g a s e s , supporting the conclusion that gaseous diffusion p r o c e s s e s w e r e not a contributing factor to h y p o x e m i a . This is thought to be an important result since it is j u s t this group of patients that would be e x p e c t e d on anatomical grounds to be vul­ nerable to such a problem b e c a u s e of the d e v e l o p m e n t of large air spaces in the destructive e m p h y s e m a t o u s p r o c e s s . M e a s u r e d arterial P02 values w e r e statistically not different from those calculated on the basis of c o m ­ plete a l v e o l a r - c a p i l l a r y diffusion equilibration according to the rationale a d v a n c e d earlier in this chapter. T h u s , all of the h y p o x e m i a w a s explained by the o b s e r v e d pattern of v e n t i l a t i o n - p e r f u s i o n mismatching, and diffu­ sion impairment across the blood gas barrier d o e s not a p p e a r to be detect­ able as a m e c h a n i s m of h y p o x e m i a in t h e s e patients. A n important finding w a s the r e s p o n s e t o 100% oxygen breathing. T h e s e patients (even after 30 min of 100% o x y g e n breathing) rarely had an arterial P02 a b o v e 500 torr, which would suggest by classical analysis a reasonably large shunt (unventilated units). H o w e v e r , inert gas d a t a w e r e rarely compatible with m o r e than 1 or 2 % shunt since the retention of the least soluble gas u s e d , sulfahexafluoride, rarely e x c e e d e d t h e s e values. This a p p a r e n t inconsis­ tency is probably best explained by the slow nitrogen w a s h - o u t of poorly ventilated lung units in this disease state. E v e n after 30 min of o x y g e n breathing, poorly ventilated lung units still have high alveolar nitrogen partial p r e s s u r e s and consequently fairly low alveolar o x y g e n partial pres­ sures. Such units will contribute to the relatively low arterial P02 that w a s found. O n e x e r c i s e , t h e s e patients generally d r o p p e d their arterial P02 . The three most likely physiological m e c h a n i s m s to explain such a d r o p in arte­ rial PQ2 o n exercise are (1) worsening of v e n t i l a t i o n - p e r f u s i o n relation­ ships, (2) a fall in mixed v e n o u s P02 (because o x y g e n u p t a k e increases

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relatively m o r e than cardiac o u t p u t ) , and (3) the d e v e l o p m e n t of a l v e o l a r - e n d - c a p i l l a r y partial p r e s s u r e differences b e c a u s e of incomplete diffusion equilibration across the b l o o d - g a s barrier. T h e third m e c h a n i s m w a s ruled out in these patients since, as w a s found at rest, the arterial P02 calculated from the o b s e r v e d distributions m e a s u r e d during exercise agreed closely with directly m e a s u r e d P02 values. T h e first m e c h a n i s m w a s also ruled out since the o b s e r v e d distributions during exercise w e r e statistically n o different from t h o s e seen during rest. This finding must b e interpreted in light of the a d v a n c e d stages of disease in these patients since they w e r e not capable of increasing oxygen uptake to m o r e than a b o u t 750 m l / m i n . In o t h e r w o r d s , patients able to perform higher levels of exercise, raising their cardiac o u t p u t and minute ventilation to greater levels, might show changes in the distribution of ventilation and blood flow. T h e operative m e c h a n i s m w a s , in fact, the fall in mixed v e n o u s P02 .

T h e type B patients s h o w e d m u c h m o r e variation in their VJQ distri­ butions. S o m e had patterns similar to those of type A , some had areas of low ventilation-perfusion ratio without areas of high v e n t i l a t i o n perfusion ratio, and s o m e s h o w e d b o t h patterns simultaneously (areas of low, normal, and high VJQ). This variability is difficult to interpret, but it is tempting to speculate that high VJQ areas in type B patients still reflect " e m p h e s y m a t o u s c h a n g e s " as in the type A patients. It is well k n o w n that such changes are difficult to detect in patients of predominantly type B clinical presentation. It is also tempting to speculate that areas of low VJQ o b s e r v e d in these patients are due to airway obstruction and inade­ quate ventilation of lung units probably b e c a u s e of retention of m u c u s in the smaller a i r w a y s . This is certainly compatible with the results seen in patients with a s t h m a (to be described later). All of the other analyses re­ ferred to a b o v e reveal the same operative m e c h a n i s m s as in type A pa­ tients. T h u s , there w a s no evidence of diffusion impairment either at rest or during e x e r c i s e , and the apparently p o o r r e s p o n s e to 100% oxygen breathing w a s again seen to b e d u e to the failure of nitrogen wash-out from poorly ventilated lung units in the allotted period, and not to the p r e s e n c e of shunt. T h e fall in arterial P02 on exercise again w a s ascribed to the fall in mixed v e n o u s P02 r a t h e r than changes in the VJQ distribu­ tion or to the d e v e l o p m e n t of a l v e o l a r - e n d - c a p i l l a r y differences due to diffusion impairment. 2 . Interstitial Lung

Disease

A total of ten patients with a d v a n c e d interstitial lung disease of various etiologies w e r e studied, both at rest and during exercise, as well as while breathing 100% oxygen. At rest, m o s t of the lung is operating in the range

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of normal VA/Q, b u t , in general, b e t w e e n 10 and 2 0 % of the cardiac out­ put is associated with essentially unventilated or completely unventilated units (Wagner et al., 1976). T h u s , in t h e s e patients there w e r e n o areas of moderately r e d u c e d v e n t i l a t i o n - p e r f u s i o n ratios; units w e r e either normal or essentially unventilated. A surprisingly small fraction of the cardiac o u t p u t w a s associated with t h e s e shuntlike areas in view of the large alveolar arterial gradient for o x y g e n . H o w e v e r , it w a s repeatedly found that inert gas and oxygen e x c h a n g e w e r e internally consistent, such that the o b s e r v e d shunt and VA/Q inequality completely a c c o u n t e d for the h y p o x e m i a . T h e r e a s o n for the moderately severe h y p o x e m i a in the face of relatively m o d e s t VA/Q inequality w a s the low value of the mixed v e n o u s P02 , which w a s uniformly 30 m m H g or less e v e n at rest. This is consistent with the pulmonary vascular involvement characteristically seen in a d v a n c e d stages of interstitial lung disease, a n d , indeed, p u l m o ­ nary vascular resistance w a s elevated in these patients. T h u s , a s o m e w h a t lower than normal cardiac o u t p u t resulted in a lower than n o r m a l v e n o u s P^, which, w h e n combined with only m o d e s t degrees of ventilation blood flow inequality, led to large a l v e o l a r - a r t e r i a l P02 differences. A s in the patients with chronic obstructive lung d i s e a s e , t h e r e w a s n o evidence that failure of diffusion equilibration b e t w e e n alveolar gas and end-capillary blood played any role in the m e c h a n i s m of h y p o x e m i a . O n exercise, t h e r e w a s a uniform d e c r e a s e in arterial P02 in all patients. W e again investigated the m e c h a n i s m of this fall and found that changes in the VA/Q distribution w e r e minor and could not a c c o u n t for the a d d e d h y p o x ­ emia. H o w e v e r , even though the mixed v e n o u s P02 fell and a c c o u n t e d for a considerable portion of the fall in arterial P02 on e x e r c i s e , not all of the o b s e r v e d h y p o x e m i a could be explained on this basis. A b o u t half of the d r o p in P02 could not be explained o n the basis of inert gas e x c h a n g e , suggesting a contribution by diffusion impairment. It is w o r t h stressing that this is the only clinical state o b s e r v e d in which diffusion impairment a p p e a r s to play a detectable role. E v e n t h e n , it is only u p o n exercise in a d v a n c e d disease and the a m o u n t of h y p o x e m i a attributable to diffusion impairment is small. T h u s , on the a v e r a g e , only a b o u t 15% of the total al­ veolar arterial PQ2 difference on exercise is attributable to this mecha­ nism. A s with the patients with chronic obstructive lung disease, n o dif­ ference w a s o b s e r v e d in the b e h a v i o r of low and high molecular weight inert g a s e s . U p o n oxygen breathing, t h e r e w a s no c h a n g e in distribution of v e n t i l a t i o n - p e r f u s i o n ratios, a n d , in particular, t h o s e areas appearing as very poorly ventilated o n r o o m air remained poorly ventilated during oxygen breathing. This finding is in c o n t r a s t with the findings m a d e u n d e r other clinical conditions (Wagner et al., 1974a,b) in which conversion of

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low VJQ units into shunt (unventilated units) w a s seen to a c c o m p a n y the breathing of oxygen. 3.

Asthma

T h e inert gas elimination t e c h n i q u e has recently b e e n used in patients with a s t h m a . T h e initial study involved a small group of a s y m p t o m a t i c pa­ tients w h o by most clinical criteria would be j u d g e d to b e essentially, but not completely in remission (Wagner et al., 1978a). T h u s , t h e s e patients, in addition to being a s y m p t o m a t i c , had no d y s p n e a , no wheezing, no s p u t u m p r o d u c t i o n , and on p u l m o n a r y function testing had mild (or no) reduction in air flow r a t e s . C h e s t X rays w e r e n o r m a l . Arterial P02 w a s generally 80 or m o r e with a normal arterial PQO2' In spite of these normal or nearly normal findings, a consistent observa­ tion in the VJQ distributions r e c o v e r e d from inert gas data w a s the pres­ ence of a m o d e of lung units of very low ventilation-perfusion ratios /Q = 0.07) ( W a g n e r e t al., 1978a). Equally consistently, n o shunt (mean VA w a s found. T h e m o d e of low VJQ ratios received on the average about 20% of the cardiac output and less than 1% of the ventilation, the re­ mainder of the ventilation and blood flow being associated with units in the normal range of VJQ. T h e r e w a s generally a clear-cut separation b e t w e e n these t w o populations of units, and statistical testing confirmed with a high degree of probability the existence of t w o m o d e s in the distri­ bution. T h e s e patients w e r e all given aerosolized isoproterenol and thereafter the distributions were m e a s u r e d at 5-min intervals for 20 min. A c u t e changes at 5 min w e r e remarkably consistent and consisted of a doubling of the perfusion of the lung units of low VJQ. T h e distributions were oth­ erwise little changed. By 10 min after bronchodilator therapy, the distri­ butions had returned to their baseline configurations and remained so for the rest of the observation period without further c h a n g e . Air flow rates uniformly improved after bronchodilator therapy and remained well a b o v e the baseline values t h r o u g h o u t the 20-min observation period. Finally, four of the patients w e r e given 100% oxygen to b r e a t h e and no change w a s found in their VJQ distribution. T h e m o d e of low VJQ units present while breathing r o o m air lay within the VJQ range k n o w n to be susceptible to oxygen-induced atelectasis (Dantzker et al., 1975), yet there w a s no conversion of t h e s e areas into shunt on oxygen breathing. W h e n all of these results are taken together, the following picture emerges. 1. T h e r e is a surprising a m o u n t of VJQ inequality present in some a s y m p t o m a t i c asthmatics despite relatively normal results obtained by other t e c h n i q u e s .

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2. T h e r e a s o n for the nearly normal arterial P02 in the face of a m o d e s t a m o u n t of VJQ inequality w a s the high mixed v e n o u s P02 o b s e r v e d in these patients. This can be seen to be the r e v e r s e of the situation o b s e r v e d in patients with interstitial lung disease described earlier. T h e mixed v e n o u s point w a s in turn due to high values for cardiac o u t p u t , which in turn are explained by the anxiety of the experimental situation, and p o s ­ sibly by residual bronchodilator effects from earlier t h e r a p y . 3. T h e consistently bimodal p a t t e r n t a k e n together with the a b s e n c e of shunt strongly suggests that collateral ventilation plays an important role in this disease state. T h e low VA /Q units w e r e u n d o u b t e d l y c a u s e d by o b ­ struction of distal airways [by b r o n c h o c o n s t r i c t i o n , m u c u s , or e d e m a (see below)], but it is hard to imagine diffuse obstruction of distal airways by any such m e a n s resulting in such a clear-cut m o d e of low VA /Q units without shunt. This is b e c a u s e o n e would e x p e c t complete obstruction of at least some distal airways and resulting shunt d e v e l o p m e n t , and a greater range of VA /Q values in the distribution. Ventilation of completely obstructed units by collateral p a t h w a y s is an attractive explanation for the a b s e n c e of shunt and for bimodality, and is m o r e reasonable than postu­ lating " a l m o s t , but not quite c o m p l e t e " obstruction in such a uniform m a n n e r . T h e r e is good anatomic evidence ( L a m b e r t , 1955; Loosli, 1937; Macklin, 1936; Martin, 1966) and physiological evidence to support the existence of collateral p a t h w a y s in the peripheral regions of the lung. 4. T h e acute r e s p o n s e to bronchodilator t h e r a p y , namely, the wor­ sening of v e n t i l a t i o n - p e r f u s i o n relationships as manifested by the in­ crease in perfusion of poorly ventilated lung units, explains the fall in arte­ rial P02 seen not only in our p a t i e n t s , but also quite frequently in o t h e r pa­ tients with a s t h m a (Chick et al., 1973; Ingram et al., 1970; K n u d s o n and C o n s t a n t i n e , 1967; Tai and R e a d , 1967). As v e n t i l a t i o n - p e r f u s i o n relationships w o r s e n e d acutely, cardiac output w a s also o b s e r v e d to increase by a b o u t 5 0 % . T h e m e c h a n i s m for wor­ sening of VA /Q relationships m a y b e in part (a) the rise in cardiac o u t p u t itself altering the distribution of perfusion, and (b) preferential vasodila­ tation of the blood vessels associated with the poorly ventilated units. (Such units may h a v e b e e n subject to excessive vasoconstriction prior to therapy on the basis of either alveolar h y p o x i a or the effect of some medi­ ator that was part of the asthmatic p r o c e s s . ) B e c a u s e the changes after bronchodilator involve an increase in perfusion of poorly ventilated units, the results are not compatible with the alternative theory of deterioration following bronchodilator t h e r a p y , namely, poorly ventilated lung units losing e v e n m o r e of their ventilation w h e n the b e t t e r ventilated p a t h w a y s are dilated by the isoproterenol ( K n u d s o n and C o n s t a n t i n e , 1967). 5. T h e failure of the VA /Q inequality to disappear after bronchodilator

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therapy in the face of continued i m p r o v e m e n t in air flow rates suggests that the physical basis of r e d u c e d ventilation in these low VJQ units is not bronchoconstriction, but r a t h e r the p r e s e n c e of m u c u s a n d / o r e d e m a in the appropriate airways. Although it could be argued that the low VJQ units receive very little bronchodilator w h e n delivered by aerosol, subse­ quent studies described below support the notion that the low VJQ units are created by m u c u s and e d e m a in the airways rather than b r o n c h o c o n ­ striction. 6. Finally, the failure of units with low VJQ areas to collapse during 100% oxygen breathing further supports the notion of collateral ventila­ tion in that collateral p a t h w a y s m a y h a v e provided the m e a n s for lung units of low VJQ to e s c a p e atelectasis by increasing their inspired venti­ lation. Following this initial study, a n u m b e r of relatively well-controlled asth­ matics completely free of s y m p t o m s and with normal or nearly normal air flow rates w e r e challenged with either methacholine or an antigen (to which they w e r e naturally sensitive, as determined by prior challenging procedures). W e then m e a s u r e d VJQ distributions before and after inha­ lation challenge sufficient to r e d u c e air flow rates by at least 30%, and in some cases as m u c h as 8 0 % . In s o m e patients, w e followed the time course of changes without further intervention, and in some w e used bronchodilator therapy (either isoproterenol or metaproterenol) (Wagner etal., 1977a, 1978b). T h e findings can be s u m m a r i z e d as follows. Prior to challenge, most of the patients had essentially n o r m a l distributions of VJQ. Challenge with methacholine generally p r o d u c e d m o d e s t widening of the VJQ distribu­ tion, but did not p r o d u c e a bimodal pattern in any way similar to that de­ scribed above for the s p o n t a n e o u s asthmatic g r o u p . This is despite rela­ tively greater reduction in air flow rates than seen in the s p o n t a n e o u s asthmatics. T h u s , in comparing the initial patients with those challenged with methacholine, less v e n t i l a t i o n - p e r f u s i o n inequality w a s seen despite more air flow obstruction, as j u d g e d by flow r a t e s . W e take this ap­ parently paradoxical finding as further evidence that acute b r o n c h o c o n ­ striction is not sufficient to p r o d u c e a population of lung units of very low VJQ as seen in s p o n t a n e o u s a s t h m a t i c s . Administration of bronchodi­ lator rapidly reversed the relatively minor increases in VJQ inequality seen with methacholine and any arterial h y p o x e m i a that followed chal­ lenge w a s also abolished. Challenge with antigenic substances by inhala­ tion p r o d u c e d generally similar results as seen with metacholine. T h e r e was a t e n d e n c y , h o w e v e r , for slightly m o r e severe VJQ disturbances to develop at a given degree of air flow rate reduction, but still antigenic challenge did not p r o d u c e distinct population of low VJQ units in the acute setting.

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253

W e feel that these studies are internally consistent with the notion that s y m p t o m s and reduction in expiratory air flow rates go h a n d in h a n d and are related primarily to b r o n c h o c o n s t r i c t i o n (probably predominantly of the large, m o r e central airways). G a s e x c h a n g e d i s t u r b a n c e s , on the o t h e r h a n d , may well o c c u r in a s y m p t o m a t i c patients and are related m o r e to m u c u s retention a n d / o r e d e m a formation in peripheral a i r w a y s , changes not easily identified in m e a s u r e m e n t s of air flow r a t e s . E v i d e n c e collected so far suggests that patients with spontaneously occurring low VJQ areas , given certain b r o n c h o d i l a t o r s , especially iso­ will d r o p their arterial P02 p r o t e r e n o l , w h e r e a s patients with mainly bronchoconstriction will h a v e arterial h y p o x e m i a abolished by bronchodilator t h e r a p y . T h u s , e v e n in those patients in w h o m the arterial P02 is relatively n o r m a l , a fall in arte­ rial P02 following t r e a t m e n t with isoproterenol probably indicates the existence of a fair a m o u n t of v e n t i l a t i o n - b l o o d flow inequality and m a y well indicate the need for m o r e aggressive t h e r a p y aimed at mobilizing se­ cretions.

4. General

Anesthesia

General anesthesia has long b e e n k n o w n to be associated with abnor­ malities in gas e x c h a n g e and m a n y investigators h a v e looked into this problem. T h e c a u s e s are u n d o u b t e d l y m a n y , as stressed by R e h d e r and co-workers (1975) (see also V o l u m e I I , C h a p t e r 4), and a complete expla­ nation of the m e c h a n i s m of gas e x c h a n g e disturbances in patients un­ dergoing anesthesia will probably differ from patient to patient. H o w e v e r , a major stumbling block in the elucidation of such m e c h a n i s m s has b e e n the inability to characterize accurately the gas e x c h a n g e disturbances t h e m s e l v e s , first b e c a u s e elevated levels of inspired P02 are u s e d , a n d , second, soluble gaseous anesthetic agents such as nitrous oxide are com­ monly e m p l o y e d as part of the anesthetic regime. T h e standard tools for quantitating gas e x c h a n g e are related to analyzing the arterial P02 [for ex­ a m p l e , in t e r m s of v e n o u s admixture according to the original c o n c e p t s of Riley and C o u r n a n d (1951)]. H o w e v e r , in the p r e s e n c e of the raised inspired oxygen concentrations and the additional concentrating effect on alveolar P02 of soluble gas u p t a k e (Farhi and O l s z o w k a , 1968), v e n o u s ad­ mixture values m a y variably u n d e r e s t i m a t e the true abnormality p r e s e n t . T h u s , if all of the gas e x c h a n g e abnormality is c o m p r i s e d of unventilated lung (shunt), v e n o u s admixture will accurately reflect the abnormality even u n d e r these conditions, but to the e x t e n t that areas of low VA /Q are p r e s e n t , quite large u n d e r e s t i m a t e s m a y result. Without attempting to elucidate the m e c h a n i s m s of abnormalities of gas exchange at this point, w e h a v e u n d e r t a k e n a pilot study in which 10 pa­ tients with mild abnormalities of gas e x c h a n g e due to chronic obstructive

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Peter D. Wagner and John B. West

lung disease w e r e studied during general a n e s t h e s i a for n o n t h o r a c i c surgical indications ( D u e c k et al., 1979). In e v e r y c a s e , large c h a n g e s in p a t t e r n s of inert g a s elimination w e r e o b s e r v e d during a n e s t h e s i a . T h e s e c h a n g e s c o r r e s p o n d e d t o t h e d e v e l o p m e n t of v a r i o u s c o m b i n a t i o n s of shunt and of a r e a s of low V /Q, often a m o u n t i n g t o 4 0 % of t h e c a r d i a c A output. A n e x a m p l e of t h e m a g n i t u d e of t h e s e c h a n g e s is s h o w n in Fig. 5 w h e r e t h e inert gas r e t e n t i o n s and a s s o c i a t e d V /Q distribution are s h o w n b o t h A before a n d after induction of a n e s t h e s i a . B o d y position a n d total ventila-

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100 oo

VENTILATION / P E R F U S I O N RATIO

Fig. 5. Upper left: Retention and excretion points (•) obtained in a patient with mild chronic obstructive pulmonary disease lying supine prior to anesthesia. Solid lines are the retention and excretion curves of the corresponding homogeneous lung. Upper right: Asso­ ciated V /Q distribution showing areas of low ventilation-perfusion ratio, but no shunt. A Lower left: Retention and excretion data obtained in the same patient in the same position at the same level of ventilation during anesthesia. The retentions of sulfahexafluoride, ethane, and cyclopropane are greatly elevated compared to the awake control values. Lower right: Associated V /Q distribution showing a large increase in the perfusion of units with very A low ventilation-perfusion ratio. This amounts to almost 50% of the cardiac output. Shunt re­ mains very small.

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tion w e r e the same before and after induction, and ventilation w a s as­ sisted without P E E P during anesthesia. Although the m e c h a n i s m of these large changes is not evident from t h e s e m e a s u r e m e n t s , several possibili­ ties arise. T h e concentrating effect of nitrous oxide on alveolar gas ten­ sion and the rapid uptake of nitrous oxide itself could explain through re­ duction in expired ventilation ( D a n t z k e r et al., 1975) some of the eleva­ tion of inert gas retention. C h a n g e s in the mechanical properties of the chest wall, particularly of the diaphragm ( F r o e s e and B r y a n , 1977), could influence the distribution of ventilation and thus the distribution of v e n t i l a t i o n - p e r f u s i o n ratios. H o w e v e r , m e a s u r e m e n t s m a d e with radio­ active gases in normal subjects by L a n d m a r k and c o - w o r k e r s (1977) d o not confirm that the topographical changes are of sufficient magnitude to a c c o u n t for the gas exchange d i s t u r b a n c e s w e o b s e r v e d h e r e . Change in vascular tone b e c a u s e of chemical interference to hypoxic vasoconstric­ tion by the anesthetic agents is a n o t h e r possible factor as yet not evalu­ ated. Reduction in lung volume of s o m e lung units for r e a s o n s that are not yet clear m u s t h a v e occurred (since F R C uniformly fell in these patients) and this may lead to interference with their ventilation. It is clearly the ob­ j e c t of future studies in this setting to attempt to elucidate the relative roles of t h e s e , and possibly o t h e r factors in this important problem.

B. General Conclusions E x p e r i e n c e with the multiple inert gas elimination technique in both experimental and clinical disease states in animals and m a n over the last 6 years leads to s o m e general conclusions a b o u t p a t t e r n s of abnormal gas exchange. 1. The Shape of Distributions

in Lung

Disease

It has b e e n o u r experience that w h e n v e n t i l a t i o n - b l o o d flow inequality o c c u r s in a wide variety of lung diseases (ranging from vascular obstruc­ tion in p u l m o n a r y embolism to airway obstruction in a s t h m a and chronic obstructive lung disease) that the p a t t e r n s of VA /Q maldistribution are multimodal in c h a r a c t e r rather than b r o a d and unimodal. T h e latter would reflect a range of abnormalities continuously from the normal range to complete abolition of either ventilation or blood flow. T o some extent, the clear-cut modality may reflect o u r choice of a d v a n c e d disease states, and it may well b e possible that milder forms of disease are associated with less clearly defined modality of distributions. This question remains to be resolved. It is important to s t r e s s , h o w e v e r , that the findings of multimodality are mathematically reliable. T h e very n a t u r e of enforced smoothing in the m e t h o d tends to favor r e c o v e r y of distributions of unimodal shape

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in an effort to minimize the residual sum of s q u a r e s . T h u s , the direction of error in a mathematical sense would be to r e c o v e r unimodal distributions w h e n , in fact, they are m o r e than o n e m o d e is confirmed by the rigorous p r o c e d u r e of linear programming. It is also important to consider the implications of multimodality as c o m p a r e d to the existence of b r o a d unimodal distribution. W e feel that this is particularly relevant to the discussion of patients with e m p h y s e m a in which a m o d e of high VJQ regions is present (presumably b e c a u s e of alveolar wall and hence alveolar capillary destruction of areas of lung that still remain ventilated). This is also important in the analysis of distribu­ tions in asthmatic subjects w h e r e the clear-cut bimodality seems m o r e compatible with the notion of collateral ventilation than with some range of degrees of airway obstruction without collateral ventilation. It is fortunate that the distributions r e c o v e r e d are in general bimodal in disease states. This is b e c a u s e b r o a d unimodal distributions give rise to inert gas retention data that are subject to m u c h " n o n u n i q u e n e s s , " a no­ tion discussed at length both in C h a p t e r 8 of this volume and in previous publications (Olszowka, 1975; E v a n s and Wagner, 1977; Wagner, 1977a). T h u s , a b r o a d unimodal distribution gives rise to data that could be inter­ preted equally well as consisting of several m o d e s of VJQ. On the other h a n d , a clearly bimodal distribution is not subject to such uncertainty in interpretation and, as stated, w e h a v e examined this question rigorously using the linear programming t e c h n i q u e s of C h a p t e r 8 of this volume. 2 . Collateral

Ventilation

VJQ distributions and p a t t e r n s of inert gas elimination cannot j u s t by the n u m b e r s obtained reveal the existence of collateral ventilation. H o w ­ ever, as discussed for patients with a s t h m a , the VJQ patterns o b s e r v e d d o suggest the p r e s e n c e of collateral ventilation in that disease. Similar arguments apply to patients with chronic obstructive lung disease, and e v e n patients with interstitial lung disease. T h e a b s e n c e of very poorly ventilated units in patients with chronic obstructive lung disease of clin­ ical type A may be due to the free collateral ventilatory channels that are k n o w n to exist in this disease state. T h e failure of low VJQ areas to col­ lapse and b e c o m e transformed into shunt on oxygen breathing, both in pa­ tients with chronic obstructive lung disease having low VJQ areas and in patients with interstitial lung d i s e a s e , suggests the importance of collat­ eral ventilation in stabilizing the gas exchange performance of those af­ fected regions in chronic disease states. In contrast, both normal subjects, and, in particular, patients with acute lung disease from t r a u m a or e d e m a , a p p e a r to be m o r e susceptible to ate­ lectasis as a c o n s e q u e n c e of o x y g e n breathing. This is consistent with the

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idea that fluid in the peripheral airways p r e v e n t s collateral ventilation channels from effectively maintaining ventilation to o b s t r u c t e d lung units. F u r t h e r support of the i m p o r t a n c e of collateral ventilation c o m e s from c o m p a r a t i v e physiological studies of the effects of anesthesia in dogs and s h e e p . Dogs are well k n o w n to h a v e extensive collateral ventilation (Van Allen et al., 1930), but s h e e p , on the o t h e r h a n d , are k n o w n to h a v e very little collateral ventilation. A n e s t h e s i a affects these t w o species some­ w h a t differently in that dogs tolerate general anesthesia very well. T h u s , dogs can be anesthetized and mechanically ventilated for a period of sev­ eral h o u r s without the d e v e l o p m e n t of m u c h shunt, w h e r e a s sheep treated similarly m a y develop severe h y p o x e m i a and considerable atelectasis fairly rapidly (R. D u e c k , personal c o m m u n i c a t i o n ) . Although it is prema­ ture to ascribe t h e s e differences to the p r e s e n c e or a b s e n c e of collateral ventilation, all of these studies t a k e n together certainly offer strong evi­ d e n c e that collateral ventilation is an important m e c h a n i s m for preventing m o r e serious d e v e l o p m e n t of gas e x c h a n g e abnormalities in diseased lungs. T h e severe h y p o x e m i a and p o o r r e s p o n s e to high oxygen concen­ tration breathing frequently seen in the intensive care setting may reflect the inability of collateral ventilation to b e effective w h e n there is fluid in the a i r w a y s . 3. Intrapulmonary the Mechanism

and Extrapulmonary of Hypoxemia

Factors in

M o s t medical students are taught that the four c a u s e s of h y p o x e m i a are hypoventilation, shunt, v e n t i l a t i o n - p e r f u s i o n inequality, and diffusion impairment. E a c h of these c a u s e s u n d o u b t e d l y can p r o d u c e h y p o x e m i a , but o n e of the m o r e important results of studies of gas exchange over the last few years has b e e n experimental verification of the important role played by o t h e r predominantly e x t r a p u l m o n a r y factors in determining the . Studies h a v e b e e n cited earlier in which absolute level of the arterial P02 patients with interstitial lung disease usually h a v e severe h y p o x e m i a , while patients with a s t h m a may have little h y p o x e m i a . W e find that, in fact, patients with a s t h m a may h a v e m o r e v e n t i l a t i o n - b l o o d flow inequal­ ity than patients with interstitial lung disease and yet h a v e less severe hy­ p o x e m i a . It is important to recognize the important role of the mixed v e n o u s P02 , which in turn reflects the cardiac o u t p u t (in relation to ox­ ygen uptake) in explaining these apparently inconsistent results. A n o t h e r setting w h e r e the interaction b e t w e e n intra- and e x t r a p u l m o n a r y factors is important is in the intensive care w a r d . H e r e , in patients with heart failure following myocardial infarction, the level of h y p o x e m i a can be s e v e r e . This is usually due to a very low cardiac o u t p u t c o m b i n e d with mild to m o d e s t v e n t i l a t i o n - b l o o d flow inequality r a t h e r than to severe

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v e n t i l a t i o n - b l o o d flow inequality alone. In other situations in the inten­ sive care setting in acute respiratory failure, the cardiac output may be inordinately high so that the degree of h y p o x e m i a d o e s not accurately re­ flect the a m o u n t of v e n t i l a t i o n - b l o o d flow inequality. T h e interpretation of the arterial P02 in t e r m s of its determinants (intrapulmonary versus e x t r a p u l m o n a r y factors) is therefore of major practical importance in the understanding of patients with various cardiopul­ monary diseases. This is particularly so b e c a u s e therapeutic implications are major. In a patient in the intensive care setting it is important to k n o w w h e t h e r alterations in arterial P02 take place b e c a u s e the lungs are getting better (or worse) on the o n e h a n d , or b e c a u s e cardiac output, hemoglobin concentration, a c i d - b a s e s t a t u s , e t c . , are changing, on the other. This knowledge will clearly affect the type of t h e r a p y . 4. The Role of Diffusion Impairment

in

Hypoxemia

In various forms of clinical cardiopulmonary disease, including chronic obstructive pulmonary disease, diffuse interstitial lung disease, a s t h m a , and pulmonary e d e m a of various kinds, w e h a v e found very little evi­ d e n c e that failure of diffusion equilibration b e t w e e n alveolar gas and endcapillary blood contributes significantly to h y p o x e m i a . T h e only condition u n d e r which this may b e a factor in our experience is during exercise in patients with a d v a n c e d interstitial lung disease. Although it appears not to matter w h a t the etiology of the interstitial p r o c e s s is, the quantitative ef­ fect remains relatively small. T h u s , only some 15% of the total a l v e o l a r - a r t e r i a l P02 difference is on the average due to failure of alveolar-end-capillary diffusion equilibration, while the remaining 8 5 % is due to the combination of v e n t i l a t i o n - b l o o d flow mismatching and shunt. M o r e o v e r , w e h a v e n e v e r o b s e r v e d any difference in the degree of elimination of inert gases that c a n be related to differences in molecular weight. In this regard, the range of molecular weights a m o n g the six inert gases is from 30 to 197.5, that is, a sixfold range. This result applies to all of the clinical conditions listed a b o v e and provides strong evidence that diffusion within the gas p h a s e of the lungs is n e v e r sufficiently impaired to contribute measurably to h y p o x e m i a . 5. Changes Induced by Breathing 100%

Oxygen

E v e r since Briscoe first suggested that the breathing of 100% oxygen could induce atelectasis (Briscoe et al.y 1960), there has been interest in w h e t h e r this is likely to be of clinical significance. This has always been a difficult question to a n s w e r since the d e v e l o p m e n t of shunt by 100% ox­ ygen breathing cannot usually b e sorted out using conventional tools (be­ cause shunt is calculated from the m e a s u r e m e n t of arterial P02 breathing

7. Ventilation-Perfusion Relationships

259

100% o x y g e n ) . O u r a c c u m u l a t e d experimental e v i d e n c e in both normal subjects and patients with a variety of c a r d i o p u l m o n a r y diseases suggests that oxygen-induced atelectasis d o e s , in fact, o c c u r . E x p e r i m e n t a l d a t a agree with theoretical predictions that only lung units of VJQ less t h a n a b o u t 0.1 are susceptible to collapse during 100% o x y g e n breathing. M o r e o v e r , w e h a v e found that patients with chronic lung diseases such as interstitial lung d i s e a s e , a s t h m a , a n d chronic obstructive p u l m o n a r y dis­ ease do not a p p e a r to be vulnerable to this p r o c e s s , e v e n w h e n lung units of VA/Q less t h a n 0.1 are p r e s e n t , and w e h a v e tentatively attributed this to the e x i s t e n c e of collateral ventilatory p a t h w a y s in such lungs. Oxygen-induced atelectasis a p p e a r s to o c c u r in n o r m a l subjects w h e n they h a v e such areas of low VJQ (older subjects) (Wagner et al., 1974b), and particularly in the intensive c a r e setting in patients with p o s t t r a u m a t i c respiratory failure ( " a d u l t respiratory distress s y n d r o m e " ) and pulmo­ nary e d e m a . U n d e r t h e s e c o n d i t i o n s , areas of low VJQ that are p r e s e n t breathing r o o m air a p p e a r to b e largely c o n v e r t e d t o unventilated lung u p o n breathing 100% oxygen. T h e s e changes generally a p p e a r to o c c u r within 30 min of oxygen breathing. While w e suspect that such atelectasis could be r e v e r s e d and possibly p r e v e n t e d by j u d i c i o u s use of positive p r e s s u r e ventilation, this remains to be d e m o n s t r a t e d .

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Corbet, A. J. S., Ross, J., Popkin, J., and Beaudry, P. (1975). Relationship of arterial-alveolar nitrogen tension to alveolar-arterial oxygen tension, lung volume, flow measure­ ments, and diffusing capacity in cystic fibrosis. Am. Rev. Respir. Dis. 112, 513-519. Dantzker, D. R., Wagner, P. D., and West, J. B. (1975). Instability of lung units with low V / Q ratios during 0 breathing. J. Appl. Physiol. 38, 886-895. A 2 Dueck, R., Young, I., Clausen, J., and Wagner, P. D. (1980). Altered distribution of pul­ monary ventilation and blood flow in human subjects following induction of inhalation anesthesia. Anesthesiology (in press). Evans, J. W., and Wagner, P. D. (1977). Limits on V / Q distribution from analysis of exper­ A imental inert gas elimination. J. Appl. Physiol. 42, 889-898. Farhi, L. E. (1967). Elimination of inert gas by the lung. Respir. Physiol. 3, 1-11. Farhi, L. E., and Olszowka, J. A. (1968). Analysis of alveolar gas exchange in the presence of soluble inert gases. Respir. Physiol. 5, 53-67. Farhi, L. E., and Rahn, H. (1955). A theoretical analysis of the alveolar-arterial 0 dif­ 2 ference with special reference to the distribution effect. J. Appl. Physiol. 7, 799-703. Farhi, L. E., and Yokoyama, T. (1967). Effects of ventilation-perfusion inequality on elimi­ nation of inert gases. Respir. Physiol. 3, 12-20. Forster, R. E. (1957). Exchange of gases between alveolar air and pulmonary capillary blood: Pulmonary diffusing capacity. Physiol. Rev. 37, 391-452. Fortune, J. B., and Wagner, P. D. (1979). Effects of common deadspace on inert gas ex­ change in mathematical models of the lung. J. Appl. Physiol. 47(4):896-906. Froese, A. B., and Bryan, A. C. (1977). Effects of anesthesia and paralysis on diaphragmatic mechanics in man. Anesthesiology 41, 242-255. Ingram, R. H., Jr., Krumpe, P. E., Duffell, G. M., and Maniscalco, B. (1970). Ventilation-perfusion changes after aerosolized isoproterenol in asthma. Am. Rev. Respir. Dis. 101, 364. Kety, S. (1951). The theory and applications of the exchange of inert gas at the lungs and tissues. Pharmacol. Rev. 3, 1-41. King, T. C , and Briscoe, W. A. (1967). Bohr integral isopleths in the study of blood gas ex­ change in the lung. J. Appl. Physiol. 22, 659-674. King, T. C , Ali, N., and Briscoe, W. A. (1973). Treatment of hypoxia with 24 percent ox­ ygen. Am. Rev. Respir. Dis. 108, 19-29. Knudson, R. J., and Constantine, H. P. (1967). An effect of isoproterenol on ventilationperfusion in asthmatic versus normal subjects. J. Appl. Physiol. 22, 402-403. Lambert, M. W. (1955). Accessory bronchiole-alveolar communications. J. Pathol. Bacteriol. 70, 311-312. Landmark, S. J., Knopp, T. J., Rehder, K., and Sessler, A. D. (1977). Regional pulmonary perfusion and V/Q in awake and anesthetized-paralyzed man. J. Appl. Physiol.: Respir. Environ. Exercise Physiol. 43, 993-1000. Lenfant, C. (1963). Measurement of ventilation-perfusion distribution with alveolararterial differences. J. Appl. Physiol. 18, 1090-1094. Lenfant, C. (1964). Measurement of factors impairing gas exchange in man with hyperbaric pressure. J. Appl. Physiol. 19, 189-194. Lenfant, C. (1965). Effect of high F, of measurement of ventilation-perfusion distribution in man at sea level. Ann. N.Y. Acad. Sci. 21, 797-808. Lenfant, C , and Aucutt, C. (1966). Measurement of blood gases by gas chromatography. Respir. Physiol. 1, 398-407. Lenfant, C , and Okubo, T. (1969). Distribution function of pulmonary blood flow and ventilation-perfusion ratio in man. J. Appl. Physiol. 24, 668-677.

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Loosli, C. G. (1937). Interalveolar communications in normal and pathologic mammalian lungs. Review of literature. Arch. Pathol. 24, 734-744. Macklin, C. C. (1936). Alveolar pores and their significance in the lung. Arch. Pathol. 21, 202-203. Markello, R., Winter, P., and Olszowka, A. (1972). Assessment of ventilation-perfusion inequalities by arterial-alveolar nitrogen differences in intensive-care patients. Anes­ thesiology 37, 4-15. Markello, R., Olszowka, A., Winter, P., and Farhi, L. (1973). An updated method for deter­ mining V / Q inequalities and direct shunt using 0 , C 0 and N . Respir. Physiol. 19, A 2 2 2 221-232. Martin, J. B. (1966). Respiratory bronchioles as the pathway for collateral ventilation. J. Appl. Physiol. 21, 1443-1444. Olszowka, A. J. (1975). Can V / Q distributions in the lung be recovered from inert gas re­ A tention data? Respir. Physiol. 25, 191-198. Peslin, R., Dawson, S., and Mead, J. (1971). Analysis of multicomponent exponential curves by the Post-Widder's equation. J. Appl. Physiol. 30, 462-472. Petrini, M. F., Robertson, H. T., and Hlastala, M. P. (1979). Separation of respiratory deadspace into its series and parallel components. Fed. Proc, Fed. Am. Soc. Exp. Biol. 38, 949. (Abstr.) Powell, F. L., and Wagner, P. D. (1979). Inert gas transfer in the goose. Fed. Proc, Fed. Am. Soc. Exp. Biol. 38, 965. (Abstr.) Rahn, H. (1949). A concept of mean alveolar air and the ventilation-blood flow relationship during pulmonary gas exchange. Am. J. Physiol. 158, 21-30. Rahn, H., and Fenn, W. O. (1955). "A Graphical Analysis of the Respiratory Gas Exchange." Am. Physiol. S o c , Washington, D.C. Rehder, K., Sessler, A. D., and Marsh, H. M. (1975). General anesthesia and the lung. Am. Rev. Respir. Dis. 112, 541-563. Riley, R. L., and Cournand, A. (1949). "Ideal" alveolar air and the analysis of ventilation-perfusion relationships in the lung. J. Appl. Physiol. 1, 825-847. Riley, R. L., and Cournand, A. (1951). Analysis of factors affecting partial pressures of ox­ ygen and carbon dioxide in gas and blood of lungs: Theory. J. Appl. Physiol. 4, 77-101. Ross, B. B., and Farhi, L. E. (1960). Deadspace ventilation as a determinant in the ventilation-perfusion concept. J. Appl. Physiol. 15, 363-371. Scheid, P., and Piiper, J. (1970). Analysis of gas exchange in the avian lung: Theory and experiments in the domestic fowl. Respir. Physiol. 9, 246-262. Tai, E., and Read, J. (1967). Response of blood gas tensions to aminophylline and isoprenaline in patients with asthma. Thorax 22, 543-544. Van Allen, C. M., Lindskog, G. E., and Richter, H. G. (1930). Gaseous interchange between adjacent lung lobules. Yale J. Biol. Med. 2, 297-298. Wagner, P. D. (1977a). A general approach to the evaluation of ventilation-perfusion ratios in normal and abnormal lungs. Physiologist 20, 18-25. Wagner, P. D. (1977b). Diffusion and chemical reaction in pulmonary gas exchange. Physiol. Rev. 57, 257-313. Wagner, P. D., and Evans, J. W. (1977). Conditions for equivalence of gas exchange in series and parallel models of the lung. Respir. Physiol. 31, 117-138. Wagner, P. D., Dantzker, D. R., Dueck, R., Uhl, R. R., Virgilio, R., and West, J. B. (1974a). Continuous distributions of ventilation-perfusion ratios in acute and chronic lung disease. Clin. Res. 22, 134A. (Abstr.)

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Wagner, P. D., Laravuso, R. B., Uhl, R. R., and West, J. B. (1974b). Continuous distribu­ tions of ventilation-perfusion ratios in normal subjects breathing air and 100% O . J. z Clin. Invest. 54, 54-68. Wagner, P. D., Saltzman, H. A., and West, J. B. (1974c). Measurement of continuous distri­ butions of ventilation-perfusion ratios: Theory. J. Appl. Physiol. 36, 588-599. Wagner, P. D., Dantzker, D. R., Dueck, R., dePolo, J. L., Wasserman, K., and West, J. B. (1976). Distribution of ventilation-perfusion ratios in patients with interstitial lung dis­ ease. Chest 69, 256-257. Wagner, P. D., Allen, D. H., Mathison, D. A., Metcalf, J. F., Rubinfeld, A. R. (1977a). Gas exchange following bronchial challenge in patients with extrinsic asthma. Am. Rev. Respir. Dis. 115, 387. (Abstr.) Wagner, P. D., Dantzker, D. R., Dueck, R., Clausen, J. L., and West, J. B. (1977b). Ventilation-perfusion inequality in chronic obstructive pulmonary disease. J. Clin. In­ vest. 59, 203-216. Wagner, P. D., Dantzker, D. R., Iacovoni, V. E., Tomlin, W. C , and West, J. B. (1978a). Ventilation-perfusion inequality in asymptomatic asthma. Am. Rev. Respir. Dis. 118, 511-524. Wagner, P. D., Ramsdell, J. W., Incaudo, G. A., Rubinfeld, A. R., and Young, I. H. (1978b). Gas exchange following bronchial challenge with antigen in patients with ex­ trinsic asthma. Am. Rev. Respir. Dis. Ill, 409. (Abstr.) West, J. B. (1969-1970). Effect of slope and shape of dissociation curve on pulmonary gas exchange. Respir. Physiol. 8, 66-85. Yokoyama, T., and Farhi, L. E. (1967). The study of ventilation-perfusion ratio distribution in the anesthetized dog by multiple inert gas washout. Respir. Physiol. 3, 166-176. Young, I. H., and Wagner, P. D. (1979). Effect of intrapulmonary hematocrit maldistribu­ tion on 0 , CO and inert gas exchange. J. Appl. Physiol. 46, 240-278.

2

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