The anatomical basis for the sloping N2 plateau

Respirat&n Physiology (1981) 44, 325-337 Elsevier/North-Holland Biomedical Press

THE ANATOMICAL BASIS FOR THE SLOPING Nz PLATEAU*

M. PAIVA and L. A. ENGEL lnstitut de Recherche lnterdisciplinaire, School of Medicine, Free University of Brussels, Belgium, and Department of Medicine, WestmeadHospital, Sydney, A ustralia

Abstract. We examined the influence of asymmetry on the interaction of convection and gas-phase diffusion within the acinus of the lung. Single breaths of 02 were simulated by solving a differential equation for gas transport in two trumpet shaped units which were joined at a branch point and whose relative lengths and volumes were made to vary. Despite synchronous bulk flow to and from the units, in proportion to their relative volumes, the shorter unit always reached a higher 02 concentration (Fo2) at end inspiration. Interdependence of gas transport at the branch point resulted in a falling Fo2 within the shorter unit during expiration. The Fo2 at the exit of the model therefore decreased progressively throughout expiration, simulating a sloping alveolar plateau. The simulations suggest that despite the relatively short distances separating parallel intra-acinar pathways, convective-diffusive interactions in the presence of asymmetry may produce substantial inhomogeneity in alveolar gas concentrations. Furthermore, the slope of the N 2 plateau in the normal mammalian lung is explicable on the basis of the asymmetrical airway anatomy and well defined physical processes. Model analysis Ventilation inhomogeneity

Airway asymmetry Convection and diffusion Gas transport

After a breath of inert gas the concentration at the mouth changes as a function of expired volume, a fact known for over 100 years. Fowler (1949) was the first to measure the expired N 2 concentration after a breath of 02 continuously, and to describe the sloping alveolar plateau. Sampling of gas from small airways of dog lungs showed that a major portion of the slope is generated distal to 2 mm airways (Engel et al., 1974). Because of the difficulty of obtaining experimental data about gas mixing within the lung periphery, analysis of models of gas transport has provided most of the recent information on the subject. During the past 10 years several groups of investigators independently developed sophisticated computer AcceptedJbr publication 5 March 1981 * This research was supported partly by a contract of the Ministbre Beige de la Politique Scientifique (Actions Concert6es).

0034-5687/81/0000-0000/$02.50 © Elsevier/North-Holland Biomedical Press 325

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models simulating simultaneous convection and diffusion in the distal part of the lung. All of these dealt with lung anatomy by assuming a symmetrical trumpet-like geometry with identical gas transport in all bronchial paths. For details the reader is referred to a recent review by Scheid and Piiper (1980). Recently, we used a two trumpet model to simulate parallel inhomogeneity of volume flows (Paiva and Engel, 1979) demonstrating an interdependence of gas transport among parallel pathways. This development opened the way to systematically examine the effects on gas mixing of parallel inhomogeneity in flows, volumes, axial lengths and airway cross-sections. In this paper we examine the effect of airway asymmetry at the alveolar duct level on gas mixing both during inspiration and expiration. Our results show that large intra-acinar concentration differences may be achieved at end inspiration, and that interaction of convection and diffusion between parallel pathways during expiration may result in a sloping alveolar plateau without sequential changes in bulk flow. Recently, Luijendijk et al. (1980) reached the same conclusions using a model analysis similar to the above (See Discussion).

Theory and methods The basis for the analysis presented here is a model of gas transport in the series spaces of the human lung (Paiva, 1972, 1973). It consists of simultaneous diffusion and convection within a solid geometrical structure based on the morphometric observations of Weibel (1963), modified according to the data of Hansen and Ampaya (1975). Results within the single symmetrical model are obtained by solving a transport equation whose solution with appropriate boundary conditions gives the gas concentrations in a 'trumpet' model of the lung, where convection and diffusion take place simultaneously. Implicit in the solution are the following assumptions: (1) Flow is of the piston type with no radial velocity gradients; (2) Radial diffusion is instantaneous so that there are no radial concentration gradients; (3) Only binary gas mixtures (O2/N~) are considered and the molecular diffusion coefficient is constant. Cardiogenic mixing is not considered; (4) There is no diffusion across alveolar walls; (5) The dimensions of the model are independent of time, i.e. it is not expansile. The above model has been used in a number of studies (Paiva, 1972, 1973; Lacquet et al., 1975; Paiva et al., 1976; Engel et al., 1979) and the interested reader is referred to these for further details and justification of assumptions used. Recently, the model has been extended to simulate parallel inhomogeneity by taking two such trumpets in parallel with a common airway down to the bifurcation or branch point (Paiva and Engel, 1979). Then S~, S2, and s~, s_~ represent the respective cross-sectional areas of all conducting airways with and without alveoli, respectively, in the two trumpets peripheral to the branch point (fig. 1). In each parallel unit reflexive conditions are assumed at the terminal boundary where the concentration gradient is always zero. This corresponds to x = o in one of the

SLOPE OF ALVEOLAR PLATEAU

327

V1

Fig. 1. Two trumpet model representing asymmetry of branching where each branch is represented by a symmetricaltrumpet, with common stem joining at the branch point, s, sI and s2 refer to cross-sections of conducting portions only; S, SI and S2 represent total cross-sectional area including alveoli. V1 refers to the volume of the trumpet with the longer pathway; V2 is the volume of the trumpet extending from the branch point to the dashed line whose position is made to vary. units (Vj). In the other, the terminal boundary is placed at different values of x, simulating a variable degree of asymmetry (fig. 1). This is quantitatively expressed as the ratio V2/V~, where V~, is the volume of the unit with the longer pathlength, and is kept constant. For any given position of the branch point V2/V j can vary from unity to zero, both limits in fact constituting a single symmetrical trumpet. One consequence o f this approach is that lung volume (Vj + V2 = F R C ) changes. In order to maintain the same overall turn over ratio (VT/FRC) for different degrees of asymmetry, the simulated tidal volume (VT) was varied appropriately. In terms o f gas transport this adjustment is equivalent to an effectively constant VT and F R C . The only difference is that the total number o f asymmetrical two trumpet units is greater the greater the degree of asymmetry. However, since gas transport in each such unit is identical this does not influence the simulated results. The entrance to the model is at generation 14 and the volume o f the more proximal airways introduces a delay in the time of transit to and from generation 14. Taylor-type phenomena make little difference to this assumption (Engel and Macklem, 1977; Lacquet et al., 1975; Pack et al., 1977; Paiva et al., 1976) and we have ignored the delay in these simulations. If not stated otherwise, we simulate a 1-1itre inspiration and expiration at 1 I/sec in a lung with an F R C o f 3.55 1. An 02 concentration of zero is arbitrarily assigned to residual gas prior to the inspiration of 02 whose fractional concentration is 1.0. The diffusion coefficient chosen is 0.225 cm2/sec, corresponding to that of O2-N2. The simulated volume flow into each trumpet is in proportion to its volume and synchronous. There is no sequential filling or emptying.

328

M. PAIVA A N D L. A. E N G E L

Results In the symmetrical two trumpet model, gas transport is identical to that in a single solid geometry figure (Paiva, 1973; Paiva and Engel, 1979). At end inspiration axial concentration gradients are the same in the two units with a stationary interface within the alveolated zone of the lung. This interface may be thought of as a balance between mouthward diffusion and peripheral convection of N 2 during inspiration of 02 at a constant flow rate (Engel et aI., 1973). On expiration the concentration gradient is rapidly abolished and during the second half of the expiratory phase gas concentrations within the lung model are constant. This is reflected in a horizontal alveolar plateau in the washout recorded at the exit of the model. In the asymmetrical two trumpet model the alveolar 02 concentration (Fo2) in the shorter unit at end inspiration is invariably higher than in the longer unit (figs. 2 and 3). The magnitude of this difference depends on the degree of asym-

F(x,t) ~.04

EXPIRED

0-

0.6

VOLUME(I)

0

6 j

l

J

0./.-

1

7 B 9

10

0.2 - ~

t

i

I

t

i

I

0

2

L.

6

8

10

-x(mm)

I

ALVEOLAR

RESPIRATORY

DUCTS

BRONCHIOLES

Fig. 2. Pattern o f 0 2 concentration (F) during expiration after l-I inspiration of 0 2 at 1 1/see into an asymmetrical two trumpet model (V2/V 1 = 0.12). Dashed lines - shorter unit, V2; solid l i n e s - longer unit, Vl, and c o m m o n pathway. Branch point is at x = 2.7 m m . N u m b e r s 5 to 10 represent concentration at 0.2 sec intervals as a function o f distance (x) from the terminal surface. Inset: 0 2 concentration at exit o f model (generation 13/14) plotted against volume expired. Note that in the shorter unit alveolar concentrations are relatively greater and fall during expiration when the gradients are reversed. This results in a changing concentration in the c o m m o n airway and a sloping alveolar plateau.

SLOPE OF ALVEOLAR

329

PLATEAU

F (x,t) 1.0-

0.8 -

0.6 -

0.4 -

0

!

I

I

,

I

I

0

2

I4

6

8

10

w(rnrnl

b&fCETOSLAR RESPIRATORY BRONCHIOLES

Fig. 3. Gas concentrations later onset and smaller

in asymmetrical

slope of alveolar

lung model with V,/V,

plateau

despite greater

= 0.03. See legend

asymmetry.

See Results

to fig. 2. Note and Discussion

for details.

metry. It is greater in fig. 3 where VI/V, = 0.03 than in fig. 2 where VJV, = 0.12. During expiration the alveolar concentration in the longer unit is essentially unchanged with rapid equilibration in most of the unit volume. A small axial gradient persists near the branch point due to back diffusion and is discussed below. In cantrast, the alveolar FoZ in the shorter unit falls during expiration, the rate of fall depending both on degree of asymmetry and the magnitude of the volumes subtended at the branch point. Furthermore, equilibration of gas concentrations does not occur and a reversed concentration gradient is apparent even near the terminal boundary (despite a gradient of zero at the boundary). The above results are a consequence of the interdependence of gas transport among parallel pathways. During inspiration convective flow into the smaller unit is less than that into the larger unit (in proportion to the relative volumes). At the branch point this corresponds to a difference of velocity in the same proportion. The lower convective velocity into the smaller unit, together with its shorter diffusive pathlength, contribute to a more proximally situated stationary interface during inspiration. Stated differently, inspired gas reaches the terminal alveoli of the smaller unit more rapidly by diffusion, resulting in higher concentrations than in the larger unit. Thus the smaller unit is ‘better ventilated’ despite equivalent inspiratory flow per unit volume to the two units.

330

M. PAIVAAND L.A. ENGEL

During expiration there is also an interdependence of gas transport between the two paths at the branch point. The relatively poorly ventilated larger unit has a higher N2 concentration (FN2) or lower Fo,~, at the onset of expiration. The relatively large convective velocity ensures rapid equilibration of gas concentration within the unit. At the branch point, gas with a high Fo, is convected at a relatively low velocity from the shorter unit. The gradient of Fo2 at the branch point favors diffusive flux of 02 out of (N2 into) the smaller unit, and because of its small volume and short diffusion pathlength, the flux is sufficient to progressively lower Fo, even in the terminal divisions. The presence of an O~/N2 concentration gradient at the branch point causes some diffusion of 02 back into the larger unit, explaining the curvilinearity of the concentration curve near the branch point dm-ing expiration (fig. 2). However this back diffusion of O2 is opposed by a relatively large convective flow, resulting in a quasi stationary concentration gradient and no significant change in the alveolar Fo, within the unit. Since during expiration the gas concentration at the branch point and downstream is determined by the concentrations leaving the two units, the decreasing alveolar Fo: in the shorter unit necessarily causes a progressive decrease in the expired 02 concentration as expiration proceeds. The magnitude and pattern of this fall depend both on the degree of asymmetry, and the relative volumes of the asymmetrical units. Thus, for example, when the branch point is 2.7 mm from the terminal boundary of the larger unit, corresponding roughly to generation 19/20, a large degree of asymmetry (VSV J = 0.03) with a relatively small short unit (fig. 3) results in a slope of 1.7~o/1 on the expired concentration vs. volume curve. A smaller degree of asymmetry (V2/V1 = 0.12) but with a relatively larger short unit results in a slope of 7~o/1 (fig. 2). The 2 degrees of asymmetry illustrated in figs. 2 and 3 represent single points on curve 3 in fig. 4. This describes the slope of phase III on the expired concentration vs. volume curve (at end expiration) for any degree of asymmetry (V2/Vl = 0 -~ 1.0) computed at 5 different branch points. Curve 1 corresponds to a branch point position roughly at the beginning of the acinus. In a bronchial tree corresponding to the Hansen and Ampaya lung model, where the longest pathway has 26 generations, curves 1 to 5 represent branch points at generations 15/16, 17/18, 19/20, 20/21 and 21/22, respectively. It is apparent that curve 3 predicts the greatest slopes of the alveolar plateau for the widest range of volume inequality. It therefore suggests that in a single breath N2 test performed with a VT of 1 1 at 1 1/sec the slope of the alveolar plateau is most sensitive to asymmetry distal to generation 19/20 i.e, well within the gas exchanging zone. When flow is reduced the interface penetrates less deeply into the lung and there is more time for diffusion. The curves describing the influence of asymmetry on slope of the alveolar plateau are shifted to the right (fig. 5). This indicates that asymmetrical pathways subtended by a more proximally situated branch point contribute more to the slope of the plateau. Thus asymmetry within 3 mm from the terminal unit (distal to approx, generation 19/20) has less effect (Curve 3A).

331

SLOPE OF ALVEOLAR PLATEAU dF (Xt,V) xlOt dV 7.5.

5.0.

2.5.

0

o

a'2

oZ

6.6

or8

i v2/v,

Fig. 4. Slope of the alveolar plateau (dF/dv) at end expiration, plotted as a function of degree of asymmetry (V2/V0, following 1-1 breaths at 1 l/sec. Curves 1 to 5 represent branch point positions at 6, 4.3, 2.7, 2.1 and 1.5 mrn from the terminal surface of the larger unit, respectively. See Results and Discussion for further details.

dF (Xt,V) x]O0 dV

/x

?.5-

5.0_

2.5.

B q

/{\\ o

%x 0.2

o~,

0.6

0.8

i

~- v J v •,

Fig. 5. Effect of flow rate on relationship between asymmetry and slope of the alveolar plateau at different branch points. Curves 1, 2 and 3 are the same as in fig. 4. Curves IA, 2A and 3A simulate slopes at corresponding branch points, but at flows of 0.5 1/sec. See Results and Discussion for further details.

H o w e v e r , a s y m m e t r i c a l p a t h s s u b t e n d e d b y the p r o x i m a l r e s p i r a t o r y b r o n c h i o l e s ( a p p r o x . g e n e r a t i o n 17/18) h a v e a n i n c r e a s e d i n f l u e n c e ( C u r v e 2A). C u r v e l p r e d i c t s t h a t at 1 1/sec a s y m m e t r i c a l u n i t s s u b t e n d e d b y t e r m i n a l b r o n c h i o l e s h a v e to s h o w large v o l u m e i n e q u a l i t y (V2/V , < 0.15) to c o n t r i b u t e s i g n i f i c a n t l y to the slope o f the p l a t e a u . A t the l o w e r flow rates a n o t i c e a b l e effect is a p p a r e n t at s m a l l e r v o l u m e inequalities.

332

M. PA1VA A N D L. A. E N G E L

20/J~

-

-

V3 23/X

4 x _ _ _ m _ / / X

D

2~

Fig. 6. Diagrammatic representation of branching distal to generation 19 (after Parker et al., 1971). to V are gas transport paths of different lengths. A to E are branch points subtending units with

differing volumes. At each branch point the degree of asymmetry and the subtended volumes determine the slope of the alveolar plateau, that in generation 19 being due to a cumulative effect. See table 1 and Discussion for details. TABLE 1

Slope of N 2 plateau (SN2) calculated for asymmetrical branching structure shown in fig. 6 BP

Distance of BP* from x = o (mm)

A B C D E

2.83 2.28 1.79 1.35 0.97

Curve in

V2/V I

fig. 4 3 3 4 4-5 5

0.35/1.01 0.27/0.63 0.19/0.35 0.14/0.14 0.01/0.09

= = = = =

0.35 0.43 0.55 1.0 0,11

SN2 (To/l)

Volume subtended at BP (ram 3)

2.0 1.3 0.2 0 0

1.367 0.906 0.538 0.288 0.103

Total SN, (at A) = (2 × 1.367) + (1.3 × 0.906) + (0.2 x 0.538) = 2.9o/(/l -

1.367

*BP: Branch point in fig. 6; V2/VI : ratio of volumes subtended by the 2 daughter branches at each BP.

The above simulations examine the effect of asymmetry at a single branch point. However, asymmetry of branching is apparent along the whole length of the bronchial tree. Therefore on expiration the changing gas concentrations must be additive such that in successively more proximal branch points, the different sloping alveolar plateaus are averaged, weighted by the volume flows in the respective daughter branches. This is illustrated for the asymmetrical geometry shown in fig. 6, by the calculations in table 1. The volumes were calculated using dimensions given by Hansen and Ampaya (1975, fig. 1). For a VT = 1 1 and a flow of 1 l/see the SN2 in generation 19 (distal respiratory bronchiole) was 2.9~/1. When flow was reduced to 0.5 1/see the computed SN2 fell to 2.3~o/1, whereas when flow was 1.5 1/see SN, rose to 3.0~o/1.

SLOPEOF ALVEOLARPLATEAU

333

Discussion

The main result of these simulations is the realization that intra-acinar airway asymmetry may result in significant differences in alveolar gas concentrations among parallel units and may be responsible for the slope of the N2 plateau recorded at the mouth. Previous experimental work has indicated that most of this slope is generated distal to 2 mm diameter airways (Engel et al., 1974). However, symmetrical model simulations suggested that axial equilibration of gas concentrations within the airways occurs so rapidly during expiration that no slope of the alveolar plateau would be seen (Paiva, 1972, 1973; Scherer et al., 1972; Pack et al., 1977). This seemed to be also the case in the presence of parallel inhomogeneity of volume flows (Paiva and Engel, 1979). The present simulations extend our understanding of the complex interaction between convection and diffusion within an asymmetrically branching bronchial tree. Our results confirm and extend those of Mon and Ultman (1976) who simulated gas transport within an airway model composed of branches distal to a 0.5 mm diameter airway, as suggested by Parker et al. (1971). Instead of solving a unidimensional differential equation Mon and Ultman used the Monte Carlo random walk technique to simulate combined bulk flow and molecular diffusion within the asymmetrical model. Despite the different approach these authors also found that geometric asymmetries alone contribute substantially to variations in concentration within the distal airways. Although they focussed on the distribution of inhaled boli of gas, through the use of superposition techniques Mon and Ultman inferred the presence of a sloping alveolar plateau. They speculated that this may be due to the geometrical asymmetries. Recently Luijendijk et al. (1980) applied the concept of gas interdependence at branch points to a solid geometrical model of the lung, examining the effects of asymmetry on the relative slopes of helium and SF 6 alveolar plateaus. Similarly to us, and independently, the authors also arrived at the conclusion that airway asymmetry may result in a sloping alveolar plateau. It is noteworthy that Luijendijk et al. as well as Mon and Ultman, used an expansile model whereas ours was assumed to be rigid. The qualitative agreement between the simulations suggests that this is not a critical assumption, at least for 1-1 breaths simulations. In symmetrical models simulations with an expansile model (Scherer et al., 1972) also do not differ from those with a rigid one (Paiva, 1972, 1973). However, varying diffusion path lengths in an asymmetrical geometry may result in quantitative differences for larger displacements e.g. vital capacity simulations. This deserves further study. Whereas Luijendijk et al. (1980) examined only two degrees of asymmetry at different branch points of the Hansen and Ampaya model, our analysis includes the effects of a full range of volume asymmetry, from V2/V~ = 0 to V2/V~ = 1.0. Furthermore, it is not restricted to any particular pattern of branching. Although the presence of airway asymmetry in the acinus is well documented (Parker et al., 1971; Hansen et al., 1975) there is no concensus on the exact anatomy and no

334

M. PAIVA A N D L A . E N G E L

single complete acinus has ever been studied by the method of serial sections. Although our model, and that of Luijendijk et aL, examines the effect of airway asymmetry at a particular branch point, in a real lung there is a serial distribution of branch points at which the subtended units influence the pattern of expired gas concentrations. The net slope of the alveolar plateau, measured at the mouth, consists of a complex average of these, appropriately weighted by the respective volume flows. A simplified illustration of this for a specific geometry is shown in table 1. The geometrical model chosen was patterned after Parker et al. (1971) who suggested 3 to 9 dichomotous divisions from the distal respiratory bronchiole to the alveolar sacs, with a mean of 6.6. The model (fig. 6) contains 5 transport paths with 25 alveolar sacs, each consisting of 10 alveoli, and 23 alveolar ducts having 16 alveoli each. Figure 5 illustrates the effect of flow which determines the position of the stationary interface. As flows change and the latter penetrates to a different depth into the lung, the region whose asymmetry influences the alveolar plateau changes concomitantly. This is responsible in part for the differences in slope computed at different flows for the specified geometry shown in fig. 6 (See Results). If the degree of asymmetry were identical along the bronchial tree the N2 slope in single breath maneuvers performed at different flows should vary in relation to the time available for diffusion. However, the pattern of branching between lobular branches and distal respiratory bronchioles is approximately symmetrical whereas in the alveolar ducts and sacs the branching is markedly asymmetrical (Parker et al., 1971). Thus the demonstrable flow dependence of the N2 plateau slope after 1-1 breaths of 02 (Bashoff et al., 1967; Kjellmer et al., 1959) could also reflect this difference in bronchial geometry. Our simulations do not offer a simplifying view of gas transport in the lung. Indeed they point to a complex interaction of convection and diffusion both during inspiration and expiration, sensitive to the airway geometry. As previously described {Paiva and Engel, 1979) alveolar gas concentration within terminal units at end inspiration are not necessarily proportional to their relative volume expansions or turnover ratios, even in the absence of phase differences and asynchrony. Volume flow per unit volume (or specific compliance) in two units may be identical, yet alveolar concentration of inspired gas may differ greatly. Furthermore, the pattern of gas concentration throughout the respiratory cycle in the two units may be quite dissimilar. In the past, two conditions have been considered necessary to produce a sloping N 2 plateau. Firstly, units had to be present with differing end-inspiratory Fs 2. Secondly, these units were required to empty sequentially, the better ventilated unit (low FN:) emptying first. The elucidation of an interregional contribution to the alveolar plateau (Anthonisen et al., 1970) supported this thinking. However, the results of our model analysis suggest that the intraregional contribution, which in a 1-1breath plays a dominant role (Engel and Macklem, 1977), may have a different basis. There need not be any sequential filling or emptying in the convective sense

SLOPE OF ALVEOLAR PLATEAU

335

i.e. all volume changes are synchronous and in constant proportion to each other. The changing expired gas concentration is due to greater diffusive 02 transport out of the shorter unit early in expiration, with a decreased diffusive transport later in expiration (figs. 2 and 3). Seen in terms of N2, some of the N2 expired from the larger unit to the branch point initially diffuses back into the shorter unit as a consequence of a large concentration gradient (e.g. fig. 2). This 'diffusive Pendelluft' results in a relatively lower expired F~2. Later in expiration, as the F~2 rises in the shorter unit, the N2 concentration gradient between it and the branch point decreases, with a consequent reduction in this back diffusion process. Hence more of the N2 convected from the larger unit contribute to the expirate, resulting in a rising N2 plateau. This pattern of expired gas concentration is analogous to a first in-first out pattern of lung filling and emptying without any actual convective sequencing. In disease states, when time constant inequalities become sufficiently large for phase differences in bulk flow to develop, the mechanisms proposed by Otis et al. (1956) may become superimposed on those described here. As a consequence the slope of the N 2 plateau will be steeper. Diffusion during breathholding at end inspiration can be predicted to diminish the alveolar concentration differences. The rate of change will depend on the magnitude of the initial differences, the size of the units, the linear distance between them, and the cross-section at the branch point. It is noteworthy that equalization of alveolar gas concentration during breathholding may not take place as rapidly as during expiration (figs. 2 and 3). In the latter case 02 reaching the branch point from the shorter unit is swept away, so that a sustained concentration gradient enhances the diffusive transport ofOz from the shorter unit whose Fo2 approaches that at the branch point. This in turn may correspond closely to the alveolar Fo~ in the larger unit (e.g. fig. 2). In the absence of convection, gas diffusion results in more rapid flattening of concentration gradients at the branch point with consequent slowing of the mixing process. Furthermore, the linear distance between the terminal divisions of the two units would determine diffusion time and hence the rate of equilibration. The single breath N2 test and the slope of the alveolar plateau have been widely used as indicators of gas mixing. It is for this reason that we have focussed our discussion on the convection/diffusion ofO2/N2, assuming that these behave as inert gases. In reality, of course, 02 is not inert, and strictly speaking our results apply to an inspired foreign inert gas with the same diffusivity a s O z / N 2. However, the assumption that gas exchange does not contribute significantly to the single breath N 2 results is probably true in the absence of breathholding and our computations, appropriately scaled, apply to an airfilled lung. The possible mechanisms to explain the slope of the alveolar plateau have been reviewed recently (Engel and Macklem, 1977). Krogh and Lindhard (1917) first proposed that inspired gas may not have time to diffuse to the periphery of the lung during a respiratory cycle, and that this series or stratified inhomogeneity gives

336

M. PAIVA AND L. A. ENGEL

rise to the slope. Although the present simulations suggest that concentration gradients are present within the acinus throughout the respiratory cycle this should not be confused with the above concept. Indeed, in the shorter pathway the gradient during expiration is reversed, the F,,> at the terminal boundary being greater than at the branch point (figs. 2 and 3). The results of our simulations suggest that neither stratification nor sequential emptying of parallel units is necessary to produce the sloping alveolar plateau.

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simulated

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35: 401-410. by a digital

Gas transport

computer.

in a model

lung. J. Appl. Physiol. 41: 115- 119.

Comput.

derived

from

SLOPE OF ALVEOLAR PLATEAU

337

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