Increasing pulmonary arterial (Ppa) and wedge (Pw) pressures at high flow (Q) during exercise could distend the thin-walled vessels. A mechanical descriptor of vascular distension, the distensibility (α, fractional diameter change/mmHg pressure), has been reported to be ∼0.02 for isolated large and small arteries, i.e., a 2% change in diameter per millimeter mercury pressure. In this review we used a pulmonary hemodynamic model to estimate α for data from exercising humans to determine whether interpretable results might be obtained. In 59 normal sea level subjects having published measurements of Ppa and Pw over a range of Q, we found values of α (0.02 ± 0.002) giving calculated Ppa, which matched measured Ppa to within 1.3 ± 0.1 (SE) mmHg. When subjects were exposed to chronic hypoxia (n = 6, in Operation Everest II), α decreased (0.022 ± 0.002 vs. 0.008 ± 0.001, P < 0.05), but when subjects were exposed to acute hypoxia (Duke chamber study, n = 8), α did not decrease (0.014 ± 0.002 vs. 0.012 ± 0.002, P = not significant). Values of α tended to decrease with age in men >60 yr. Thus at rest and during exercise, normal values of α in young persons were similar to those measured in vitro, and the values decreased in chronic hypoxia and with aging where vascular remodeling or vascular wall stiffening was expected. We propose that the estimation of pulmonary vascular distensibility in humans may be a useful descriptor of pulmonary hemodynamics.
- pulmonary arterial pressure
- wedge pressure
- blood flow
in the normal adult lung circulation, the vessels are thin walled and distensible (for reviews see Refs. 4, 5, 15, 16). In vitro measurements have indicated that the distensibility (α, fractional diameter change/mmHg pressure) of pulmonary vessels of several mammalian species, including humans, is ∼0.02 and is reasonably independent of the size or location of the vessel (16). Over the linear portion of the pressure-diameter curve, normal pulmonary arteries distend ∼2% of their initial diameter for each millimeter mercury increase in transmural pressure (Fig. 1). However, α, a mechanical property of the vasculature, has not been generally used to describe hemodynamic measurements in vivo. Rather, pulmonary circulatory behaviors in intact humans and animals have been characterized by calculations of vascular resistance or, when available, by stylized features of pressure-flow data (20), but neither approach considers the impact of vascular α on hemodynamics. In some normal young and old men, exercise has been shown to increase wedge pressures (Pw) by >20 mmHg (9, 10, 22–24). Such a large increase in outflow pressure could dilate the lung vascular bed by 40% if in vitro measurements are assumed applicable to intact humans and the pressure-diameter relationship is linear over the range of the pressure change. Because α is a mechanical property of the lung vasculature and because exercise may induce large increases in pulmonary arterial transmural pressures, it could be useful to estimate the vascular response to the distending pressures.
Recently, Linehan et al. (18) developed a distensible vessel hemodynamic model to interpret pressure-flow curves in the isolated perfused dog lung. α is one of the parameters of the model. For a series of blood flows and over a range of hematocrits, the authors demonstrated that the distensible vessel model had certain advantages in interpreting pressure-flow data over ohmic-Starling resistor models. For instance, the distensible vessel model was considered superior in providing a critical opening pressure, which was independent of hematocrit. In addition, the estimate of α was also independent of hematocrit (18) and was in the range reported for isolated canine vessels (16).
The model had several features that suggested it might usefully be applied to normal humans. 1) It was derived from hemodynamic principles. 2) It was shown to be valid in the perfused dog lung. 3) For the perfused dog lung, the calculated values of α agreed with published values for α in isolated vessels. 4) The required parameters, pulmonary blood flow, inflow pressure [pulmonary arterial pressure (Ppa)], and outflow pressure (Pw), were all clinically available measurements. 5) The requirement for a range of blood flows might be satisfied in humans having measurements at rest and at several levels of exercise intensity.
For the above reasons, we wondered whether a model that utilized Ppa and Pw over a range of flow (Q) could estimate α in exercising humans. Our approach was to investigate whether, for a range of pulmonary blood flows in each normal subject, a single value for α would yield calculated Ppa, which predicted measured arterial pressures. Confidence in the model would be enhanced if normal values for α in vivo were similar to values reported in vitro and in the perfused dog lung. Our approach also compared changes in α within one group of volunteers exposed to chronic hypoxia versus changes in another group exposed to acute hypoxia. Confidence in the model would be enhanced if α decreased more when arterial remodeling was likely present (i.e., in chronic hypoxia) than when remodeling was not expected (i.e., in acute hypoxia). In addition, our approach compared α in groups of younger vs. older volunteers. Confidence in the model would be enhanced if values for α were less in older subjects, for whom pulmonary arterial compliance was expected to be lower (13). Because vascular α is a mechanical property of the lung vasculature, we felt it important to ascertain whether it could be estimated in intact humans.
THE α MODEL
In the present review we analyzed human data using the distensible vessel model (18). The derivation is too long to include herein. Basically, the model assumed that the local pressure drop was directly proportional to both local vascular resistance and Q. The vascular resistance was assumed to be directly proportional to blood viscosity and a local geometrical factor, which was a function of the fourth power of vessel diameter. The mechanical property, α, is the slope of the linear portion of the diameter-pressure relationship and was assumed to be independent of vessel diameter (18). Assuming constant hematocrit, we integrated the equation over the entire vascular volume from pulmonary artery to pulmonary vein to give (1) where Ppa was mean pulmonary artery pressure (mmHg), Pw was pulmonary venous or wedge pressure (mmHg), Q was mean pulmonary flow (l/min), and Ro was total pulmonary resistance (Ppa/Q at rest).
The usefulness of the distensible vessel model in interpreting pressure-flow data obtained from isolated dog lungs perfused with blood of different hematocrits was evaluated by Linehan et al. (18). In applying Eq. 1 to interpret data from human subjects, we assumed that Ro was equal to the total pulmonary resistance (Ppa/Q) at rest, where the transmural pressure of the pulmonary arterial bed is minimal. We solved Eq. 1 for α using the method of successive iterations. That is, given values for Ro and the measured values for Pw and Q at rest and during exercise, we varied α until we found the value that gave the minimal average difference and standard deviation between measured and calculated Ppa over the whole range of available Q.
Rest and Exercise in Normoxia and Chronic Hypoxia: Operation Everest II
Pulmonary hemodynamics at sea level were measured in eight normal volunteers at heart catheterization while at rest sitting on a cycle ergometer and during serial cycle exercises over a large range of Q (10, 23) (Table 1). For six of the subjects, shown in Fig. 2A, averaged values of Ppa and Pw progressively increased with increasing Q, but the pressure gradient (Ppa-Pw) increased relatively little. However, averaged data obscured variability for pressures within and between the subjects. For example, in the subject illustrated in Fig. 3A, the Pw and the pressure gradient (Ppa-Pw) varied unpredictably with increasing flow. For the subject shown in Fig. 3B, the Pw and Ppa showed nearly parallel increases with increasing Q, so that the pressure gradient was approximately constant. In the subject shown in Fig. 3C, the Pw changed little with increasing Q, such that Ppa and the pressure gradient both increased. Thus the Pw response to exercise varied markedly from one individual to the next, and pressure-flow lines through the data would not take account of how varying Pw influenced Ppa. Estimation of α using Eq. 1 appeared to take account of varying Pw. In the Operation Everest (OE) II subject of Fig. 3A, for example, despite variation in pulmonary and wedge pressures with increasing Q, a single value for α (0.019) was found, which gave Ppa differences (calculated − measured) ranging from +2.6 to −2.2 mmHg (mean = 0 mmHg) for seven measurements of Q from rest to near maximal exercise. Without regard to algebraic sign, the absolute difference between calculated and measured pressures averaged 1.3 ± 0.3 (SE) mmHg (Table 1). For all eight subjects, a value for α was found where calculated Ppa showed reasonable agreement with measured values (Table 1). The individual values for α ranged from 0.013 to 0.032, which were within the range of in vitro measurements for normal humans and other mammals, as shown in Fig. 1.
In OE II (10, 23), six of the eight subjects studied at sea level were exposed to increasing altitude over 3 wk and then had pulmonary hemodynamic measurements at 6,100 m (barometric pressure = 347 mmHg), and exercise PaO2 = 34 mmHg. Comparisons of the mean pressure-flow plots for the group indicated that for a given Q during exercise, Ppa increased more during chronic hypoxia than at sea level (Fig. 2A). However, during chronic hypoxia, Pw did not increase with exercise. Thus in these subjects, the Ppa-Pw gradient and calculated pulmonary vascular resistances were greater during chronic altitude exposure than at sea level.
Compared with sea level, during chronic hypoxia, the resting Ro increased in the six subjects, and values for α fell by more than half (Table 1). During chronic hypoxia and with the obtained values of α for each subject, the calculated Ppa showed reasonable agreement with the measured values (Table 1), compatible with the concepts that α described the lung circulatory response to exercise in these subjects and with the notion that the lung circulation had become less distensible.
Rest and Exercise in Normoxia and Acute Hypoxia: the Duke University Chamber Study
The Duke University chamber study (Moon RE, personal communication; Ref. 26) measured pulmonary hemodynamics in subjects at sea level and during acute hypoxia on the same day. Thus hypoxia was present, but the pulmonary vascular bed would not have had time to remodel. In eight normal volunteers (six male, two female), the sea level measurements at heart catheterization were with the subject sitting on a cycle ergometer, at rest, and during serial exercises. As in OE II, hemodynamic measurements at sea level in the Duke study showed that Ppa and Pw rose progressively with increasing exercise intensity, and the Ppa-Pw pressure gradient was little changed (Fig. 2B). The subjects in the Duke University study had repeat measurements when the chamber had been acutely decompressed to 523 mmHg (10,000 ft, 3,050 m) and to 429 mmHg (15,000 ft, 4,570 m). For the group, arterial values of Po2 during exercise averaged 48 mmHg at 10,000 ft and fell to 33 mmHg at 15,000 ft. During acute exposure to simulated altitude, values of Ppa and Pw for a given cardiac output were similar to pressures measured in these subjects at sea level (Fig. 2B), findings that contrasted with those during chronic hypoxia in OE II (Fig. 2A).
Estimation of α using Eq. 1 indicates that, at sea level, values for α averaged 0.014 (Table 1), which, although less than in the OE II study, are within the range of reported in vitro values. During acute exposure to 3,050 m, seven subjects with adequate data had values for Ro that were not different from sea level (Table 1). Estimated values for α were also not different from sea level, no matter whether the Ro used in Eq. 1 was that from sea level (Table 1) or from 3,050 m. During acute exposure to 4,570 m, five subjects with adequate data had values for Ro (2.26 ± 0.20) and α (0.01 ± 0.001) that were not different from the sea level values.
Rest and Exercise in Normoxia in Younger vs. Older Subjects
Comparison was made between younger (2, 3, 14) and older (9) normal subjects, all of whom were studied supine, at rest, and during exercise at sea level at the Karolinska Institute (Stockholm, Sweden). In the 16 younger subjects ranging in age from 16 to 40 yr, Pw rose with flow as exercise intensity increased, but there was relatively little increase in the pressure gradient, Ppa-Pw (Fig. 4, top). Measurements in 14 older men ranging in age from 61 to 83 yr showed larger increases in Pw with increasing Q than occurred in younger men (Fig. 4, top). However, the pressure gradient, Ppa-Pw, was similar in younger and older men. The hemodynamic differences between the younger and older subjects were primarily lower lung blood flows for a given oxygen uptake and higher Ppa and Pw in the latter (9).
Reports indicate that pulmonary vascular resistance increases (6) and extensibility of the main pulmonary artery decreases (13) with advancing age. In subjects aged 16–40 yr, values of α averaged 0.021 and 0.020 (Table 2). In the 14 subjects aged 61–83 yr from the Karolinska laboratory, values of α were slightly less (P < 0.05) than in the younger subjects studied in the same laboratory (Table 2). Although α tended to decrease with age after 60 yr, the trend was not statistically significant (Fig. 4, bottom).
Summary of Data Relating to α
Including 27 normal young subjects during supine cycle exercise as reported from Bern, Switzerland (11) (Table 2), there were 59 normal young subjects studied at sea level. For all of them combined, the value of α averaged 0.02 ± 0.006 (SD), no matter whether the subjects were supine or upright (Tables 1 and 2). For this population, the values of α ranged from 0.006 to 0.035, with a coefficient of variation (SD/mean) of 0.3. When all 73 subjects presented in this review are considered, the 267 paired comparisons of calculated with measured Ppa showed good agreement between measurements with a slight trend for the calculated values to underestimate measured values at the higher pressures (Fig. 5). For mean pressures ranging between 10 and nearly 50 mmHg, the SD (1.6 mmHg) and SE (0.1 mmHg) of the difference between measured and calculated pressures were considered acceptable given the assumptions in the model.
The focus of the present review is to suggest that a distensible vessel hemodynamic model used to interpret pressure-flow curves and estimate pulmonary vascular α in the isolated perfused dog lung (18) can also be useful in interpreting Ppa in normal humans during exercise. In applying the distensible vessel model to the clinical setting, we should emphasize certain assumptions. 1) The model is based on the assumption that lung vessel α is independent of vessel diameter. As shown in Fig. 1, in vitro data do indicate that α is relatively independent of diameter over nearly a four-log increase in diameter, but the relationship is not exact. The model does not address slight differences in α between one small artery and another, or the well-known spatial heterogeneity in microcirculatory pulmonary blood flow (1, 7, 8, 25). Rather, the model acts primarily to link resistance to α. It is likely that this model, which employs but few parameters, provides an overall description of the lung vasculature because much of normal resistance is in the pulmonary arterioles and α is the most important variable affecting these vessels. 2) The model assumed a linear diameter-pressure relationship for the pulmonary arterial bed, which might not occur at the higher pressures. However, pressure limitations are ambiguous, because the upper limit of the pressure range for diameter-pressure linearity is not established for normal humans. 3) We assumed that Ro in our resting subjects reflected a transmural arterial pressure that was minimal. 4) The model does not differentiate between α of perfused vessels with exercise and the recruitment of previously closed vessels, including capillaries (12). Because it is likely in humans that recruitment becomes maximal with mild exercise (24), we have assumed for the analysis that distension is the dominant effect. Given the assumptions underlying the model used to calculate α and the potential for the model to be too simple a descriptor of pulmonary hemodynamics, it is perhaps encouraging that for >260 measurements in 73 individual subjects, the calculated values of Ppa closely approximated the measured values.
However, the key issue was whether calculated values of α gave information physiologically relevant for humans. In exercising, normal, young humans, 80–90% of the variation in the Ppa during exercise can be explained by the changes in Pw (24). But the exercise Pw is greatly variable among individual subjects, some of whom show little change, some show large increments, and others show erratic values depending on the exercise intensity, as illustrated (Fig. 3). These changes in Pw variably affect Ppa. Simply drawing pressure-flow lines through these data obscures the physiology. The variable effect of Pw on Ppa has largely been missed because analyses have been in grouped data, which minimize individual variations. In the elderly subjects during exercise, pressure-flow lines showed the large increments in Pw but provided no insight into the increased lung vessel stiffness, a property indicated by the calculation of α. The present analysis suggests for both young and old normal subjects that increasing Pw during exercise dilates the lung circulation, the extent of which depends on properties of the vascular walls. Therefore the model used to calculate α includes the effects of vascular α to account for variable pressure responses during exercise.
Furthermore, during exercise, remodeling of the pulmonary vasculature might be revealed by the calculation of α. Although pulmonary arterioles could not be examined directly in the subjects who had spent 3 wk in a hypoxic environment, their exercise-induced increases in Ppa and in the gradient Ppa-Pw were consistent with narrowing of the lumen in the arteriolar vessels. The observation that the calculated values of α decreased for the subjects, compared with their prior values measured at sea level, was consistent with the concept that chronic hypoxia had induced thickening or increased tone in the walls of the pulmonary arterioles, thereby reducing α. In contrast, subjects who were acutely exposed to a hypoxic environment, as shown in Fig. 2B, had values of Ppa and Pw for a given Q that were not different from sea level values. Acute hypoxia has been reported not to decrease significantly the calculated value of α in the pig lung (20). The findings suggest that the increased transmural pressures, including those occurring during exercise, oppose hypoxic vasoconstriction in unremodeled pulmonary vessels. The value α appeared slightly reduced in older men, particularly those >70 yr of age, as might be expected if, as reported, α of the pulmonary arteries fall in the aged (6). Therefore, estimated values of α were relatively small in chronic hypoxia and old men, where lung vessels might be expected to be remodeled or stiffer than normal, and little changed when remodeling was probably not present, i.e., acute hypoxia.
The horse can achieve very high pulmonary blood flow during exercise (17). For an in vivo comparison of humans with another species, we examined published data in horses at rest and during exercise, where blood flows up to 285 l/min were obtained (17). Over the range of lung blood flows, a single value of α was found (0.01), where the differences between the calculated and measured Ppa were small (Fig. 6). This value for α was at the lower end of the normal range for humans.
From the above, several pieces of evidence indicate that the α model might be a useful descriptor of the pulmonary vasculature. 1) For a given individual at rest and during exercise a value of α could be found from a model that accounts for the influence of Pw on Ppa. 2) Values of α appeared to be independent of whether subjects exercised in the supine or the upright position. 3) The values of α in exercising humans were similar to the values reported for arterial segments in vitro in humans and other mammals. 4) The values of α in exercising humans were similar to the values reported in perfused dog lungs. 5) The values of α decreased in subjects made chronically hypoxic, but not in those made acutely hypoxic. 6) The values of α were lower in old men, particularly after the age of 70 yr. 7) The values of α for exercising horses were within the range of values found in exercising humans. The results support the concept that α is a mechanical property of the normal lung vasculature, with values of α that are widely shared among mammals, including humans.
If so, the current analysis suggests that during exercise in normal persons, increases in pulmonary vascular transmural pressures distend the lung arterioles and thereby substantially contribute to the exercise-related fall in resistance to Q. Because 1) increases in Pw readily distend the lung circulation, 2) large increases in Pw may occur during exercise, and 3) the Pw closely follows left ventricular diastolic pressure, left heart events appear largely to control the normal pulmonary circulation during exercise (24). The present review does not exclude possible chemical or neural influences on the lung circulation during exercise. However, considering that results calculated from the distensible vessel model provided a good description of pulmonary hemodynamics and that left heart pressures induced much of the exercise-related distension, the normal human lung circulation seems to be dominated by mechanical factors during exercise as previously reviewed (24).
In terms of the body’s physiological design, one wonders how the lung circulation dominated by mechanical influences can effectively distribute blood flow to the alveoli under conditions of high pressure and flow. Krenz and Dawson (16) have suggested that, because the α for pulmonary arteries (and veins) is reasonably independent of their diameter, this independence could act to stabilize flow distribution “without requiring an elaborate controlling mechanism.” They speculated that Q maldistribution would result when substantial regional differences in α occur among parallel channels. If so, then α of the pulmonary vasculature becomes important not only for exercise in health but also for diseases affecting the lung vasculature. Future investigations will be required to determine whether measurements of pulmonary vascular α will be useful in identifying early stages of pulmonary circulatory disease.
This work was supported in part by National Heart, Lung, and Blood Institute Grants HL-57144 and HL-14985.
The authors acknowledge the assistance of the late Christopher A. Dawson (deceased 14 June 2003), who was to have been an author of this paper. Drs. Richard E. Moon and Peter D. Wagner provided individual hemodynamic data for the eight subjects in the Duke University chamber study.
↵† Deceased 15 September 2004.
- Copyright © 2005 the American Physiological Society