Hyatt, max flows Thesis JAP 80

Prediction of maximal expiratory in excised human lungs flow ROBERT E. HYATT, THEODORE A. WILSON, AND EPHRAIM BAR-YISHAY Division of Thoracic Diseases and Internal Medicine, Muyo Clinic, Rochester 55901; and Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, h4innesota 55455 HYATT, ROBERT El., THEODORE A. WILSON, AND EPHRAIM BAR-YISHAY. Prediction of maximal expiratory flow in excised human lungs. J. Appl. Physiol.: Respirat. Environ. Exercise Physiol. 48(6): 991-998, 1980.-The predictions of the wavespeed theory of flow limitation were tested against measured values of maximal expiratory flow (Tj,,,) in nine normal excised human lungs. We obtained static pressure-volume curves and deflation pressure-area (PA) curves of the first three to four airway generations. The pressure drop from the alveolus to the flow-limitation site was assumed to consist of a peripheral frictional loss (estimated from a catheter upstream from the flow-limitation site) and a convective acceleration pressure drop. Predicted v,,, was determined graphically by finding the lowest flow for which the Bernoulli PA curve was tangent to one of the bronchial PA curves. At the point of tangency, local flow speed equals local wave speed. At low lung volumes a point of tangency with the PA curves of the first few generations did not exist, and the flow-limitation site was assumed to be the minimal bronchial area at zero transpulmonary pressure. There was good agreement between measured and predicted %,,,, Measured &,a, was not different from v,,, predicted from normal living man. The wave-speed theory predicted flow over much of the vital capacity, but other mechanisms may limit flow at low lung volumes. bronchial pressure-area behavior; model of flow limitation; peripheral frictional head loss; site of flow limitation; wave-speed theory of expiratory flow limitation was described by Fry and associates in 1954 (8). In 1958 Hyatt et al, (12) described the maximal expiratory flow-volume curve. Since then there have been a number of studies analyzing the flow-limiting phenomenon. Mead and associates (20) and Pride et al. (25) have presented useful descriptive approaches to analyzing maximal expiratory flow f&,,,), but neither analysis defines explicitly the mechanisms leading to flow limitation. THE PHENOMENON BACKGROUND AND THEORY Fry in 1958 (6) outlined a mathematical model for expiratory flow limitation. He pointed out that if 1) the total cross-sectional area of the bronchial tree (A) could be defined as a function of transpulmonary pressure (P) and position along the tree (x) A = f(P, x) 0161-7567/8O/oooO-0$01.25 Copyright (1) 0 1980 the American Physiological and 2) the pressure gradient (dP/dx) in the airways could be described as a function of airway area, position, and flow (V) dP (2) then, for a given flow, this coupled set of equations could, in principle, be integrated from the alveoli, where x = 0 and P = Pst (static lung recoil pressure), to the trachea. Fry (7) later showed that for some airway area-pressure curves, there is a maximum value of expiratory flow, maxt for which a solution of these equations exists. Unfortunately, detailed information about the airway properties and pressure losses required for Eqs, 1 and 2 is not available. Therefore, simplified models that focus on local mechanisms of flow limitation have been proposed. Pardaens et al. (23) and Lambert and Wilson (18) postulated that most of the frictional head loss (APf) occurred peripherally and that the pressure drop associated with convective acceleration occurred predominantly in the central airways. With the above assumption, the position variable (x) can be suppressed and the integral of Eq. 2 to a point in the central airways has 1he form l v 1 pV 3) where p is the gas density. If APf can be determined, P as described by Eq. 3, can be plotted as a function Oi airway area for various values of v. Because on the same graph one can plot airway area vs. pressure (Eq; 1) for each generation of the central airways, it is possible to obtain the simultaneous solution of the two equations graphically. Such curves are shown in Fig. 1. Area-pressure plots of three central airway generations are shown by the solid lines. The dashed line is the plot of Eq. 3 for v = 5.4 l/s at a Pst of 8 cmHz0 and a APf of 3.2 cmHn0. The simultaneous solution of Eqs. 1 and 3 is given by the intersection of the airway area-pressure curves (solid lines) and the flow area-pressure curve (dashed line). The value of v for which the curve of Eq. 3 is tangent to one of the airway area-pressure curves is v,,,. For larger values of v, an intersection of the curves and, hence, a simultaneous solution of the equations would not exist. Dawson and Elliott (3) have identified vm,, as the flow Society 991 992 HYATT, 2.8 m \i=5.4 l/s I I:’ I !-! Pst =8 2.6 2.4 1I I -5 (solid further 1, Area-pressure lines) for subject discussion. 2nd generation l 3rd generation 0 4th generation I 1 I 0 5 10 Transmural FIG. 0 pressure, plots of 77. Dashed three line p km H20) central airway generations is plot of Eq. 3. See text for at which the gas velocity equals the tube wave speed at some point in the bronchial tree, the choke point. If aA/ ax0 at this critical point, flow is independent of downstream pressure once &,, has been achieved. In the graphic solution shown in Fig. 1, the tangency point is equivalent to the choke point. This result follows from recalling that at the tangency point the slopes (dA/dP) of the airway and flew area-pressure plots are equal. Substituting V,,, for V in Eq. 3 and differentiating with respect to A yields l V max = A )I “’ (4 which is identical to the expression for Vm,, from the wave-speed theory. Elliott and Dawson (4) tested their formulation of the flow-limiting mechanism in dog tracheas and physical models and found’that Vm,, and the pressure distribution through the system were consistent with their predictions. Furthermore, Jones et al. (14), in intact dog lungs, obtained measurements of peripheral head loss, maximum flow, and minimum airway area which are consistent with Eq. 3. In this paper we report the results of our test of this model on excised human lungs. The static pressure-volume curve of the lung, the area-pressure behavior of the central airways, and direct estimates of peripheral head loss at maximum flow were obtained, The graphic method described above was used to predict individual flow-volume curves, which were then compared with measured flow-volume curves. METHODS Human lungs were obtained at autopsy. The lungs WILSON, AND BAR-YISHAY were studied 6-24 h after death. Normality of the lungs was assessedby the postmortem forced expiratory volume at I s (FE&) as percent of the forced vital capacity (FVC), FE&%, being greater than 65% (24) and by gross and histological examination of the Formalinfixed lungs. In addition, for the material to be included in the study, the postmortem ratio of residual volume (RV) to total lung capacity (TLC) had to be less than 3O%, slow and forced vital capacities had to agree within lo%, and static pressure-volume curves had to be reproducible. Of 24 lungs studied, only 9 were acceptable by these criteria. Data on these lungs are given in Table 1. Single lungs were studied except for subject 65, in which case both lungs were available. Despite the borderline FEV1%, the lung of subject 68 was normal in all other respects. For all subjects the mean FE&% was 77%, and the mean slope of the flow-volume curve from 50 to 25% vital capacity of 2.2 s-l was within the normal range for man (2); low slopes indicate obstructive disease. The main-stem bronchus (trachea in subj 65) was cannulated, and 20-40 ml of a 0,5% solution of is’oproterenol was placed in the airways fur 20 min; the solution was then drained from the airways and the lung was degassedin a vacuum jar. Two static deflation pressurevolume curves were obtained and averaged. Absolute gas volumes at RV were estimated by measuring the water displaced by the lung, weighing the lung, calculating the tissue volume (assuming a tissue density of 1.065) and subtracting tissue volume from displaced volume to obtain gas volume, Pressure-volume curves were repeated periodically during the study. The major airways were outlined with powdered tantalum, the lungs were suspended by the cannula, and orthogonal radiographs were taken during stepwise deflation at transpulmonary pressures of 25, 15, 9, 7, 5, 3, 2, 1, 0, and -5 cmHz0. In several cases,pressures of -10 and -30 cmHz0 were employed. We made no correction for an estimated magnification of 3%. The airways remained circular to pressures of -5 cmHz0. The mean of the two diameter measurements was used to compute airway area. All measurements were checked by a second observer. The areas of all bronchi in a given generation were summed to construct area-pressure plots (Fig. 1). The main-stem bronchus was defined as generation 1. It was possible to measure three generations in four lungs and four generations in five lungs. TABLE 1. Data on subjects studied $ubj No. Age, yr Sex FW, % RV/TLC, %I 57 58 13 40 M F 76 82 15 59 14 65 68 23 79 9 19 F M F 77 65 12 15 70 77 23 65 M M 71 73 10 81 83 16 43 M F 81 87 10 FEVI, capacity; forced expiratory volume RV, residual volume; TLC, 11 16 24 Cause of Death Gunshot, head Ovarian carcinoma Skull injury Electrocution Subarachnoid hemorrhage Hanging Cerebral hemorrhage Car accident GI hemorrhage Lung Left Left Left Both Left Left Right Left Left at 1 s as percent of forced total lung capacity. vital PREDICTED MAXIMAL FLOW IN 993 MAN Next the lungs were placed in a pressure-corrected integrated-flow plethysmograph with an adequate amplitude and a phase response to 15 Hz. The lungs were inflated to a pressure of 25 cmHz0, and expirations were produced by exposing the airway to a drum evacuated to -50 to -150 cmHs0. In this manner we defined the minimal negative pressure producing the maximal expiratory flow-volume curve. A PE-160 catheter (external diameter of 1.6 mm) with multiple lateral pressure taps 10 diameters from the sealed radiopaque end was then positioned at various sites in the airway during maximal expiration. The catheter-transducer system had an amplitude response of t5% and a phase lag of 9” at 16 Hz. The catheter was continuously perfused with air from a high-pressure source through a small orifice to maintain patency. With the use of the catheter, a point slightly downstream of the flow-limiting site was identified. At this point, airway pressure fell to very negative values during maximal expiration. The catheter was then moved approximately 3 cm further upstream (toward the alveoli) to a point at which lateral pressure remained positive throughout most of the expiration. The pressure drop from the alveolus to the catheter in this position was taken as the peripheral head loss (APf) during maximal flow. With the catheter so positioned, three reproducible flow-volume curves were obtained. The movement of the catheter during forced expiration was determined by radiographs taken at distending pressures of 25 and 0 cmH20. On the average, the catheter moved 2 cm during the flow-volume maneuver. In one study a videofluoroscopy system was used during the forced maneuvers, and the images were transferred from videotape to a stop-action video disk. We examined the catheter motion, and no detectable yaw was noted. If at any time during the study there was evidence of gas trappingnamely, a progressive decrease in vital capacity-the lung was disconnected from the plethysmograph and degassed. ANALYSIS The area-pressure behavior of the first three to four generations was graphed as shown in Fig. 1. The assumptions relative to equating transpulmonary and transmural pressure are considered in the Discussion. Next, values of % (pv2/A2) (the last term of Eq. 3) were calculated for fixed values of v, with A varying from 0.25 to 5.5 cm2 and p = 1.14 g/l. Isoflow plots of these values for flows from 0.4 to 10 l/s, at intervals of 0.2 l/s, were plotted against P and placed on a transparent grid. The dashed line in Fig. 1 is one such plot. Since at a given lung volume we knew both Pst and APf, the grid could be placed at the correct position along the pressure axis and the point of tangency of the area-pressure curves of the airway and the flow curve could be identified by inspection. In Fig. I, for example, the zero pressure of the grid was placed at P = 4.8 cmHz0 (Pst of 8 cmH20 minus APf of 3.2 cmH20), and the curve of v = 5.4 l/s was found to be tangent to generation 3 at an area of 2.1 cm* and a pressure of 1 cmH20. Frequently, at low lung volumes no tangency points existed. In this situation we assumed that the flow-limiting site was the minimum bronchial area at zero transmural pressure. The isoflow curve pass- ing through this point was taken as irm,, for that volume. For a given lung we were restricted in our analysis to the volume range over which the lateral catheter recorded positive pressures. Within this volume range we arbitrarily chose points for analysis at approximately lo15% increments of the vital capacity, starting at maximal inflation. RESULTS Table 2 summarizes pertinent data related to the flowlimiting site as identified by our analysis. The number of volumes at which V max was predicted in a given lung ranged from 2 to 4. In 16 of the 29 values of vm,, predicted, tangency points were identified. The tangency points were agreed upon by two observers, The pressure (P*) at the tangency points averaged -0.4 t 1.65 (SD) cmH20. Tangency choke points generally occurred in generations l-3. The area (A*) at the tangency point for single lungs averaged 1.08 t 0.6 (SD) cm’ and correlated positively with lung size. The value of the peripheral frictional resistance (Rf) varied considerably among lungs and showed no systematic trend with lung volume. However, in six of the nine lungs Rf was highest at the largest lung volume. Mean Rf for all lungs was 1.39 t 0.83 (SD) cmH20 l s. Mean Rf at approximately 55% l 2. Parameters excised human lungs measured TABLE Subj No. Volume, %I VC Pst, Observed cmHn0 ir,,,, P*, cmH?O from A”, cm” l/s 57 58 59 65 68 70 77 81 83 87 75 62 49 85 71 56 42 82 65 82 64 87 73 60 46 85 70 55 40 83 65 48 78 56 33 80 60 40 16.2 12,O 9.0 6.3 10.9 6.5 4s 2.5 12.9 7.8 12.2 6.8 12.3 8.2 5*9 4.1 14.6 10.9 7.9 5.6 8.0 3.9 2.0 11.8 6.5 3.8 7.7 4.5 2.4 3.6 3*1 2.4 1.6 2.3 1.9 1.6 1.2 3.0 2.5 7.3 5.9 2.5 2.0 1.6 1.2 4.3 3.4 2.6 1.7 5.8 3.2 2.0 3.9 2,7 1.5 2.5 2.1 1.1 0 -0.9 0.4 -1.9 -3.1 -5.0 1.2 I.3 0 0 1.0 0.4 0.1 0.3 0.3 0.6 0.82 0.8 (0.82) (0.82) 0.42 0.38 0.35 0.34 0.6 (0.58) (2.64) (2.64) 0.84 (0.69) (0.69) (0.69) 1.61 1.61 (1.61) (1.61) 2.1 1.9 1.65 1.38 1.38 (1.27) 1.08 (1.01) (1.01) Generation No. of FL Site-t 3 3 (31 (31 1 1 1 1 1 (1) (4) (4) 3 (3) (31 (3) 3 3 (3) (3) 3 3 4 3 3 (21 3 (3) (3) Rf, cmH?O. 1-l .S 2.1 1.6 2.5 3.1 1.6 1.2 1.0 1*7 0.8 0.2 0.7 0.3 3.1 2.7 2.2 2.0 1.0 1*2 0.7 2.3 0.6 0.3 0.5 1.9 1.0 1.2 1.1 0.8 0.9 VC, vital capacity; Pst, static lung recoil pressure; ir,,,, maximal expiratory flow; P *, transmural pressure at tangency point (no entry indicates no tangency point); A*, airway area at tangency point; Rf, t No. of generation at which tangency point frictional resistance, occurred (FL, flow limitation); parentheses indicate that minimum area at zero transmural pressure for this generation was used to predict v max. HYATT, 1 st gerleratlon 0 2 nd generation l 3rd generatlon O’L----JJ 5 5 BAR-YISHAY l I 0 4th generatron r AND vital capacity was 1.08 t 0.9 (SD) cmHz0 1-l s. It should be emphasized that we have no data on the linearity of the peripheral pressure-flow relations. Airway area-pressure plots (Fig. 2) in seven of the nine cases showed that the curves of the various generations converged to nearly the same area at zero pressure. The trend was also for the &ea at high transmural pressures to be greater in the higher-numbered (more distal from mainstem) generations, although, as can be seen from Fig. 2, this was not always the case. Indeed, we were impressed with the variability of the generation areapressure plots at higher pressures. Figure 3 presents the measured flow-volume curves for each lung (solid line) and our predictions for v,,, (solid circles from tangency points, open circles by using mini- %57 6.0 WILSON, 15 25 4.0 965 #70 r #66 3.5 3.0 2.5 t l / 0 / / / / 0 #81 l %83 // 01 -5 5 15 I -5 25 I I 5 I I 15 I 1 -5 I 25 1 1 5 I I 15 1 I 25 Pressure I cm H20) FIG. 2. Airway area-pressure plots for all subjects. Symbols identify generations l-4. Note different area and pressure scales used for subject 0 FIG. values, 65. 4. Measured Data obtained 2 values from 4 Measured of maximal Fig. 3 with 4 // / / 6 / /- / 8 10 i II/s) flow plotted against same symbols. predicted 83 2 ? 0 77 8- FIG. 3. Measured flow-volume curves for each subject indicated by solid Lines. Solid cirdes are predicted values of maximal flow from tangency points; open. circles are predicted by using minimum area at zero transmural pressure. 4I O4 124- - J 3 2 1 0 6 4 2 I 0 84- 2 1 I 04 3 2 1 08 0’ PREDICTED MAXIMAL FLOW IN 995 MAN mum area at zero transmural pressure). Except for subjects 58 and 70, there was quite close agreement between observation and prediction. Paired t test anaIysis revealed no significant difference between the observed and the predicted flow (P > 0.05). vmax was equally well predicted by the tangency points (closed circles) or by the minimum area (open circles). Figure 4 plots flow predicted by our analysis against measured flow. In general, most points scatter about the line of identity. The points prominently above the line of identity are from lungs 65 and 70. There was no obvious explanation for these deviations. We also compared our measured flows with those obtained from normal nonsmoking subjects. We were able to make this comparison in eight subjects by using the data reported by Knudson et al. (15). When we had only a single lung, we used 53% of the ir,,, predicted from the Knudson group’s data for right lungs and 47% for left lungs (1). We also corrected both sets of data to atmospheric temperature, pressure saturated (ATPS). The results are plotted in Fig. 5, which shows a very good agreement between our measured values and those obtained from this large normal population. It should be noted that Knudson’s data tend to be about 23% higher than our measured values. It is possible that we failed to reach the true in vivo total lung capacity in these lungs. This would tend to lead to an overestimation of the volume at which flows were predicted from Knudson et al. and hence an overestimation of flow from their data. DISCUSSION The correspondence between prediction and measurement presented in Figs. 3 and 4 supports the basic modeling used to predict vm,, in these nine excised human lungs. However, it is appropriate to consider in detail certain aspects of this modeling and the measurements employed. A major simplifying assumption was that the frictional head loss occurred predominantly in the periphery and the pressure loss due to convective acceleration predominantly in the central airways. This assumption is sup/ l / / / / - / / l / / / J - / / lb 1’ I 2 I 4 Measured FIG. values, I 6 i I 8 I 1 Ws) 5. Measured values of maximal flow plotted against from data of Knudson et al. (15). See text for details. predicted ported by the report of Jones et al. (14) in dogs, in which they accurately predicted v,,, from measurements of the peripheral head loss and minimum central airway area, A basically similar partitioning of the pressure losses was found in intact dogs by Mink and Wood (21). Although a similar study in excised human lungs by the same investigators (22) initially suggested that central convective losseswere low, further analysis of these data appears to be consistent with our assumption (L. D. H. Wood, personal communication). We estimated the frictional head loss from a lateral pressure catheter placed a few centimeters upstream from the choke point. This assumes that convective losses are minimal at the site. From the airway areapressure plots and the measured lateral pressure, we estimated that the maximum pressure loss caused by convective acceleration averaged 0.8 cmHz0, which would have increased our predicted flow by only 7%. Furthermore, any frictional losses between the catheter and the choke point would offset this effect. Thus our use of the lateral catheter appears reasonable and is further supported by the similarity between our estimates of Rf at 50% vital capacity and those of Mink and Wood (22) and Silvers et al. (28), who used a retrograde catheter in human lungs. In addition, in several preliminary studies, we found close agreement between the estimate used in this study and a more direct measure of the peripheral loss, namely the local stagnation pressure measured with an open-ended catheter. Clearly, precise quantification of the peripheral loss is critical to our analysis; an overestimation of APf would lead to an underprediction of flow, and vice versa. The available evidence suggeststhat our values for APf were reasonably accurate. By treating the airways with isoproterenol, we attempted to maintain the smooth muscle of the airways in a constant relaxed state throughout the study. By obtaining frequent radiographs during the study, we looked for small decreasesin diameter and detected none. By frequent measurements of the static pressure-volume curve of the lung, we attempted to use the pressurevolume curves most appropriate to the flow-volume curves. Furthermore, our analysis assumesthat dynamic and static lung recoil pressures were the same at the volumes studied; this assumption is supported by the study of Webster et al. (31). Clearly, another crucial aspect of our approach was the use of deflation bronchial area-pressure curves to define the tangency point and the minimum area at zero transmural pressure. This approach assumesthat physiological changes in length have no appreciable systematic effect on bronchial area-pressure behavior. This assumption is supported by studies of dog (9, 10) and pig (11) bronchi. The approach also assumesno significant timedependent effects on bronchial area-pressure behavior. Jones et al. (14) found no time-dependent effects in the main-stem bronchi of the dog. Since our choke points generally occurred distal to the main-stem bronchus, that study (14) supports our assumption. On the other hand, Sasaki et al. (27) reported time-dependent effects in dog bronchi undergoing compression at isovolume. However, the effects were essentially negligible when compressing 996 pressures were small, as in our study. We also ignored bronchial-parenchymal interdependence when using our measured airway area-pressure curves to predict vm,,. Interdependence would, of course, make the areas larger than those we used and lead to a prediction of higher flows. However, the analysis of Lai-Fook et al. (17) indicates that interdependence is determined by the shear modulus, and the shear modulus of the lung is low. Calculations based on this shear modulus (11) reveal that at the lung volumes and area changes examined in this study, the interdependence effect is small. This assumption is also supported by the measurements reported by Lai-Fook et al. (16). Clearly, not all bronchi in a given generation were of equal size. But, as a first approximation, it seemed reasonable to sum the areas to obtain an estimate of bronchial compliance. In general, when tangency points existed, they were easily identified. These points occurred in the same generations identified as flow-limiting sites from direct pressure measurements by Ma&em and Wilson (19) in normal man and by Mink and Wood (22) in excised human lungs. However, in 13 of the 29 examples presented, we could not identify a point of tangency. This was particularly true at the lower lung volumes. There are at least two explanations for this. It is possible that the choke point was located at a higher-numbered generation than those measured. Since it is likely that distal generations are more compliant and their area-pressure curves converge toward the same area at zero transmural pressure (seebelow), one might assumethat tangency points could have been identified had we been able 1) to measure the area-pressure behavior past the fourth generation and 2) to estimate APf at low lung volumes. When no tangency points could be defined, we used the minimum area at the equal pressure point (zero transmural pressure) to predict vm,,. This approach appeared satisfactory (Figs. 3 and 4) and was based on the following considerations. Tangency or choke points, when present, occurred on the average very near to zero transmural pressure, and the choke point area was very near the minimum area (Table 2 and Fig. 2). In addition, we measured in eight lungs, in a manner similar to that of Rohrer (26), the airway area at zero transmural pressure for the furst five to seven generations (unpublished observations). On the average, there was no change in total cross-sectional area of the collapsed bronchial tree with distance. This suggests that, had we been able to measure area-pressure curves out to generation 7, tangency points would have occurred very near the minimum area. The tendency of our measured area-pressure plots to converge to the same minimum area has already been noted (Fig. 2). Although these appear tQ be reasonable justifications for the approach used in the analyses, we are aware that Mink and Wood (22) in excised human lungs found that lateral pressure averaged -5.4 cmHz0 at the flow-limiting site. Thus the approximation used by us requires further examination. Our failure to obtain tangency points at low volumes made us wonder whether the wave-speed mechanism is operative at relatively low lung volumes. Indeed, it appears possible that at lower lung volumes some mechanism other than the wave-speed phenomenon limits max- HYATT, WILSON, AND BAR-YISHAY imal flow. We reasoned as follows. Using assumptions regarding A and dP/dA, one can estimate from Egr 4 the lowest ir,,, that would be predicted by the wave-speed theory. If it is assumed that lateral pressure at the choke point is approximately pleural pressure, a reasonable estimate of the minimum values of A is given by the smallest measured area at zero transmural pressure. It seemsunlikely that A decreases in the more distal generations. We then used two estimates of airway compliance. One upper limit of specific airway compliance can be considered to be the specific compliance of the lung. A minimum estimate of dP/dA can thus be obtained from the slope of the lung pressure-volume curve between Pst = 0 and Pst = 1. Using this value of dP/dA and the above minimum estimate of A, we made an estimate from Eg. 4 of the lowest possible value of ir,,, for each subject and identified the corresponding volume from the flow-volume curve. The mean volume-expressed as percent vital capacity remaining-below which the wave speed would not predict X7maxwas 38%. Another estimate of minimal V maxwas made by using the same minimum area and a bronchial elastance equal to the elastance of a cylindrical hole in the lung parenchyma (17) computed by means of a shear modulus of 0.6 Pst. This yields an even lower value of .dP/dA; yet the wave-speed theory could only predict V,ax down to a value of 26% vital capacity remaining. Obtaining wave-speed predictions of T;rm,xnear residual volume would require values of A or dP/dA much smaller than the above estimates. To the extent that our estimates of A and dP/dA are correct ,we suggest that the wave-speed theory cannot predict flows consistent with th .osemeasured over the lower 25% of the vital capacity a.nd that other mechanisms may plimi .t flow at low lung volumes. Considering the above uncertainties in the modeling and the measurements, we believe that the agreement between measured and predicted vm,x, as shown in Figs. 3 and 4, is very encouraging. These data suggest that our modeling does incorporate the major determinants of . v max. The fact that our measured and predicted flows agree so closely with predictions from living man (15) adds support to this conclusion. This similarity to living man also suggests I) that cannulation of the main-stem bronchus did not alter the flowJimiting process and 2) that in most individuals of the age range we studied the flow-limiting site occurs in, or upstream from, the mainstem bronchus. These conclusions contrast with the fmdings of Smaldone and Bergofsky (29) but are supported by preliminary studies we performed in two cases in which we received both lungs, one being subject 65. A flow-volume curve was first obtained with both lungs, the trachea being cannulated .. Then flow-volume curves were repeated after the lungs were separated and the main-stem bronchus was cannulated. The flow-volume curves were normalized by plotting vma, as vital capacities per second and volume as percent vital capacity. The shapes of the normalized curves were very similar (Fig. 6). There are other interesting implications of this study. One is the importance of the airway area-pressure curves in the prediction of vm,,, a point stressed by Fry (7). Another is that time-dependent airway area-pressure PREDICTED MAXIMAL FLOW Right lung m Left lung 0 Both lungs 0 IN MAN 997 too 80 60 20 0 %vc %vc FIG. 6. A: normalized flow-volume curves for both lungs and for individual lungs separated from trachea in one subject. Flow expressed in vital capacities (VC) per second and volume as percent vital capacity 40 remaining in lung. B: data comparing left lung with that of both lungs from normalized flow-volume another subject. curve of effects appear small. At the volumes studied, it also way areas can be measured radiographically. It is to be appears that the effects of interdependence are minor. hoped that further refinement of the acoustic reflection Our results further suggest that it is reasonable in normal technique (5,13) may provide such data, including airway man to partition the flow-related pressure losses into area-pressure curves as a function of distance. Finally, central and peripheral components as indicated by Eq. 3 some method of estimating peripheral frictional resistand to invoke the wave-speed concept to predict o,,, ance must be developed. Recent work suggests that analover the upper 75% of the vital capacity. Our results also ysis of flow-volume curves obtained with the use of gases tend to support many aspects of the equal pressure-point with different physical properties may provide estimates formulation proposed by Mead et al. (20). However, it is of the peripheral pressure loss (30). of interest that we found that flow limitation could occur The authors thank Drs. J . R. Rodarte and S, J. Lai-Fook for their at positive transmural pressuresadvice in the conduct of this study, our technical staff for their expert for reviewing the manuThe success of the modeling used in this study has assistance, Drs. K. Rehder and R. Lambert potential clinical implications, since it has defined the script, and Dr. J. Ludwig and his colleagues in the Dept. of Pathology and Anatomy for making this study possible. important parameters determining the maximal expiraThis investigation was supported in part by Research Grant HLtory flow-volume curve. The challenge now is to measure 21584 from the National Institutes of Health. Address for reprint requests: R. E. Hyatt, Mayo Clinic, 200 First St. these parameters by relatively noninvasive techniques in man. 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