Teaching the effects of gravity and intravascular and alveolar pressures on the distribution of pulmonary blood flow using a classic paper by West et al

"Distribution of blood flow in isolated lung; relation to vascular and alveolar pressures" by J. B. West, C. T. Dollery, and A. Naimark (J Appl Physiol 19: 713-724, 1964) is a classic paper, although it has not yet been included in the Essays on the American Physiological Society Classic Papers Project (http://www.the-aps.org/publications/classics/). This is the paper that originally described the "zones of the lung." The final figure in the paper, which synthesizes the results and discussion, is now seen in most textbooks of physiology or respiratory physiology. The paper is also a model of clear, concise writing. The paper and its final figure can be used to teach or review a number of physiological concepts. These include the effects of gravity on pulmonary blood flow and pulmonary vascular resistance; recruitment and distention of pulmonary vessels; the importance of the transmural pressure on the diameter of collapsible distensible vessels; the Starling resistor; the interplay of the pulmonary artery, pulmonary vein, and alveolar pressures; and the vascular waterfall. In addition, the figure can be used to generate discovery learning and discussion of several physiological or pathophysiological effects on pulmonary vascular resistance and the distribution of pulmonary blood flow.     

Recruitment in networks of pulmonary capillaries.

To improve our understanding of the pressure-flow characteristics of pulmonary capillaries, we analyzed by means of computer stimulation a theoretical model composed of 50 interconnected nonlinear elements. Each element required a critical pressure across it before flow occurred and there was a subsequent linear pressure-flow region whose slope, or resistance, could be related to the transmural pressure of the element ("distensibility"). The critical pressures and resistances of each element of the network were randomly chosen from distributions. We found that recruitment (i.e., onset of flow) occurred over a large range of network upstream or "arterial" pressures, and that relatively high arterial pressures were required before all elements had no distensibility. Intermittent and reverse flow were commonly seen in some elements as the arterial pressure was raised in steps. These flow reversals were particularly common when the critical pressures and resistances of the elements were inversely related. The critical pressures required for such behavior in the capillary segments of the pulmonary microcirculation were calculated to be extremely small, of the order of 0.02 cmH2O. Pressures of this magnitude might result from sticking of red cells to capillary walls or to each other. The properties of such a network may explain the patchiness of flow in the pulmonary microcirculation and the large range of arterial pressures over which recruitment is observed to occur.     

Perinatal history of hypoxia leads to lower vascular pressures and hyporeactivity to angiotensin II in isolated lungs of adult rats

The most dramatic changes in pulmonary circulation occur at the time of birth. We hypothesized that some of the effects of perinatal hypoxia on pulmonary vessels are permanent. We studied the consequences of perinatal exposure to hypoxia (12 % O2 one week before and one week after birth) in isolated lungs of adult male rats (approximately 12 weeks old) perfused with homologous blood. Perfusion pressure-flow relationship was tilted towards lower pressures in the perinatally hypoxic as compared to the control, perinatally normoxic rats. A non-linear, distensible vessel model analysis revealed that this was due to increased vascular distensibility in perinatally hypoxic rats (4.1 +/- 0.6 %/mm Hg vs. 2.3 +/- 0.4 %/mm Hg in controls, P = 0.03). Vascular occlusion techniques showed that lungs of the perinatally hypoxic rats had lower pressures at both the pre-capillary and post-capillary level. To assess its role, basal vascular tone was eliminated by a high dose of sodium nitroprusside (20 microM). This reduced perfusion pressures only in the lungs of rats born in hypoxia, indicating that perinatal hypoxia leads to a permanent increase in the basal tone of the pulmonary vessels. Pulmonary vasoconstrictor reactivity to angiotensin II (0.1-0.5 microg) was reduced in rats with the history of perinatal-hypoxia. These data show that perinatal hypoxia has permanent effects on the pulmonary circulation that may be beneficial and perhaps serve to offset the previously described adverse consequences.     

Pulmonary vascular distensibility of arterial, middle, and venous regions in newborn lambs

The pulmonary circulation in the adult is characterized by being relatively distensible, but whether the newborn lung shares this feature is less certain. We perfused isolated lungs treated with indomethacin from lambs of four ages (less than 1, 2-4, 12-14, and 30-32 days) to determine the effects of increasing left atrial pressure on the pulmonary vascular pressures measured by vascular inflow and outflow occlusion. An index of pulmonary vascular distensibility was assessed by comparing the slope of the pulmonary vascular pressure at the upstream end of a region as a function of the pressure at the downstream end of the region. A vascular distensibility index (VDI) of 1 indicates a rigid nondistensible system, whereas a VDI less than 1 indicates some degree of distensibility. During normoxia, lungs from all age groups were relatively indistensible as determined by VDI for the total vasculature (VDItotal) as well as for the different regions based on occlusion pressures (VDIarterial, VDImiddle, and VDIvenous). There were significant effects of age on the VDItotal, with decreases in the normoxic values occurring over the first 12-14 days of age, indicating an increase in pulmonary vascular distensibility. Only the VDIvenous was similarly affected by increasing neonatal age. Hypoxia significantly reduced the VDItotal in these same age groups. In addition, hypoxia, which increased the pressure gradients of the arterial and middle regions, significantly increased the VDIarterial in the youngest and oldest age groups but significantly decreased the VDImiddle at all ages by approximately 50%. In summary, we observed age-related changes in the vascular distensibility of the pulmonary circulation, with the VDItotal decreasing with increasing postnatal age.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pulmonary pressure-flow relationships in the fetal lamb during in utero ventilation

Pressure-flow relationships in the ventilated lung have not been previously determined in undelivered fetal sheep. Therefore we studied 11 late-gestation chronically prepared fetal sheep during positive-pressure ventilation with different gas mixtures to determine the roles of mechanical distension and blood gas tensions on pressure-flow relationships in the lung. Ventilation with 3% O2-7% CO2 produced a substantial fall in pulmonary vascular resistance even though arterial blood gases were not changed. Increases in pulmonary arterial PO2 during ventilation were associated with falls in pulmonary vascular resistance beyond that measured during mechanical distension. Decreases in pulmonary arterial PCO2 and associated increases in pH were also associated with falls in pulmonary vascular resistance. Pulmonary blood flow ceased at a pulmonary arterial pressure that exceeded left atrial pressure, indicating that left atrial pressure does not represent the true downstream component of driving pressure through the pulmonary vascular bed. The slope of the driving pressure-flow relationship in the normal mature fetal lamb was therefore different from the ratio of pulmonary arterial pressure to pulmonary arterial flow. We conclude that mechanical ventilation, increased PO2 and decreased PCO2, and/or increased pH has an important influence on the fall in pulmonary vascular resistance elicited by positive pressure in utero ventilation of the fetal lamb and that the downstream driving pressure for pulmonary blood flow exceeds left atrial pressure.     

Dynamic viscous flow in distensible vessels of skeletal muscle microcirculation: application to pressure and flow transients

Blood flow in the microcirculation of the rat skeletal muscle during transient changes of arterial pressure is analyzed theoretically. Although flow in such small vessels is quasi-steady and has a very low Reynolds number, time-dependent nonuniform flows along the length of the blood vessels can be observed due to vessel distensibility. The governing equations for a single microvessel are derived using previously measured microvessel elasticity, and several solutions to different inflow and outflow pressures and flow conditions are investigated. The results indicate that when such distensible microvessels are subjected to a step increase of arterial pressure, the arterial flow shows a rapid overshoot followed by a progressive decay to steady-state. An arterial step flow induces a different response which takes the form of a monotonically increasing pressure. Pressure and flows are nonuniform along the vessel length during such transients. In-vitro whole organ pressure-flow data are presented in the dilated rat gracilis muscle which qualitatively agree with the theoretical predictions.     

Distensibility of small arteries of the dog lung.

To obtain in situ measurements of the distensibility of small (100- to 1,000-microns-diam) pulmonary arterial vessels of the dog lung, X-ray angiograms were obtained from isolated lung lobes with the vascular pressure adjusted to various levels. The in situ diameter-pressure relationships were compared with the diameter-pressure relationships for small arteries that were dissected free from the lungs and cannulated with small glass pipettes for the measurement of diameter and transmural pressure. The diameter-vascular or diameter-transmural pressure curves from both in situ and cannulated vessels were sufficiently linear in the pressure range studied (0-30 Torr) that they could be characterized by linear regression to obtain estimates of D0, the diameter at zero vascular pressure, and beta, the change in diameter (micron) per Torr change in pressure. The vessel distensibility coefficient (alpha) was defined as alpha = beta/D0. The mean values of alpha were approximately 2.0 +/- 0.8%/Torr (SD) for the in situ vessels and 1.7 +/- 0.6%/Torr for the cannulated vessels, with no statistically significant difference between the two methods. The influence of vasoconstriction elicited by serotonin was evaluated in the in situ vessels. Serotonin-induced vasoconstriction caused a decrease in D0 and little change in alpha.     

Pulsatile pressure and flow in the skeletal muscle microcirculation

Although blood flow in the microcirculation of the rat skeletal muscle has negligible inertia forces with very low Reynolds number and Womersley parameter, time-dependent pressure and flow variations can be observed. Such phenomena include, for example, arterial flow overshoot following a step arterial pressure, a gradual arterial pressure reduction for a step flow, or hysteresis between pressure and flow when a pulsatile pressure is applied. Arterial and venous flows do not follow the same time course during such transients. A theoretical analysis is presented for these phenomena using a microvessel with distensible viscoelastic walls and purely viscous flow subject to time variant arterial pressures. The results indicate that the vessel distensibility plays an important role in such time-dependent microvascular flow and the effects are of central physiological importance during normal muscle perfusion. In-vivo whole organ pressure-flow data in the dilated rat gracilis muscle agree in the time course with the theoretical predictions. Hemodynamic impedances of the skeletal muscle microcirculation are investigated for small arterial and venous pressure amplitudes superimposed on an initial steady flow and pressure drop along the vessel.     

Vessel distensibility and flow distribution in vascular trees

 In a class of model vascular trees having distensible blood vessels, we prove that flow partitioning throughout the tree remains constant, independent of the nonzero driving flow (or nonzero inlet to terminal outlet pressure difference). Underlying assumptions are: (1) every vessel in the tree exhibits the same distensibility relationship given by $D/D_0 = f(P)$ where $D$ is the diameter which results from distending pressure $P$ and $D_0$ is the diameter of the individual vessel at zero pressure (each vessel may have its own individual $D_0$). The choice of $f(P)$ includes distensibilities often used in vessel biomechanics modeling, e.g., $f(P) = 1 + \alpha P$ or $f(P) = b + (1-b) \exp(-c P)$, as well as $f(P)$ which exhibit autoregulatory behavior. (2) Every terminal vessel in the tree is subjected to the same terminal outlet pressure. (3) Bernoulli effects are ignored. (4) Flow is nonpulsatile. (5) Blood viscosity within any individual vessel is constant. The results imply that for a vascular tree consistent with assumptions 2–5, the flow distribution calculations based on a rigid geometry, e.g., $D=D_0$, also gives the flow distribution when assuming the common distensibility relationships. Received: 30 October 2001 / Published online: 14 March 2002     

Heterogeneous mechanics of the mouse pulmonary arterial network

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure–radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.     

Microfocal X-ray CT imaging and pulmonary arterial distensibility in excised rat lungs

The objective of this study was to develop an X-ray computed tomographic method for measuring pulmonary arterial dimensions and locations within the intact rat lung. Lungs were removed from rats and their pulmonary arterial trees were filled with perfluorooctyl bromide to enhance X-ray absorbance. The lungs were rotated within the cone of the X-ray beam projected from a microfocal X-ray source onto an image intensifier, and 360 images were obtained at 1 degrees increments. The three-dimensional image volumes were reconstructed with isotropic resolution using a cone beam reconstruction algorithm. The vessel diameters were obtained by fitting a functional form to the image of the vessel circular cross section. The functional form was chosen to take into account the point spread function of the image acquisition and reconstruction system. The diameter measurements obtained over a range of vascular pressures were used to characterize the distensibility of the rat pulmonary arteries. The distensibility coefficient alpha [defined by D(P) = D(0)(1 + alphaP), where D(P) is the diameter at intravascular pressure (P)] was approximately 2.8% mmHg and independent of vessel diameter in the diameter range (about 100 to 2,000 mm) studied.     

Effect of hepatic venous sphincter contraction on transmission of central venous pressure to lobar and portal pressure

In dogs anesthetized with pentobarbital, central vena caval pressure (CVP), portal venous pressure (PVP), and intrahepatic lobar venous pressure (proximal to the hepatic venous sphincters) were measured. The objective was to determine some characteristics of the intrahepatic vascular resistance sites (proximal and distal to the hepatic venous sphincters) including testing predictions made using a recent mathematical model of distensible hepatic venous resistance. The stimulus used was a brief rise in CVP produced by transient occlusion of the thoracic vena cava in control state and when vascular resistance was elevated by infusions of norepinephrine or histamine, or by nerve stimulation. The percent transmission of the downstream pressure rise to upstream sites past areas of vascular resistance was elevated. Even small increments in CVP are partially transmitted upstream. The data are incompatible with the vascular waterfall phenomenon which predicts that venous pressure increments are not transmitted upstream until a critical pressure is overcome and then further increments would be 100% transmitted. The hepatic sphincters show the following characteristics. First, small rises in CVP are transmitted less than large elevations; as the CVP rises, the sphincters passively distend and allow a greater percent transmission upstream, thus a large rise in CVP is more fully transmitted than a small rise in CVP. Second, the amount of pressure transmission upstream is determined by the vascular resistance across which the pressure is transmitted. As nerves, norepinephrine, or histamine cause the hepatic sphincters to contract, the percent transmission becomes less and the distensibility of the sphincters is reduced. Similar characteristics are shown for the "presinusoidal" vascular resistance and the hepatic venous sphincter resistance.(ABSTRACT TRUNCATED AT 250 WORDS)     

A hemodynamic model representation of the dog lung

The published morphometric data from human, cat, and dog lungs suggest that the power-law relationships between the numbers (Na and Nv) and diameters (Da and Dv) of arteries and veins and between the lengths (La and Lv) and diameters of the arteries and veins could be used as scaling rules for assigning dimensions and numbers to the intrapulmonary vessels of the arterial and venous trees of the dog lung. These rules, along with the dimensions of the extrapulmonary arteries and capillary sheet and the distensibility coefficients of the vessels obtained from the literature, were used to construct a steady-state hemodynamic model of the dog lung vascular bed. The model can be characterized approximately by 15 orders of arteries with Na approximately 2.07 Da-2.58 and 13 orders of veins with Nv approximately 2.53 Dv-2.61. For the intrapulmonary vessels (orders 1-12), La approximately 4.85 Da1.01, and Lv approximately 6.02 Da1.07. The average ratio of the numbers of vessels in consecutive orders is approximately 3.2 for the arteries and veins. These arterial and venous trees are connected by the capillary sheet with an undistended thickness of approximately 3.5 microns and an area of 33 m2. The average distensibility (% increase in diameter over the undistended diameter/Torr increase in transmural pressure) for the model arteries and veins is approximately 2.4%/Torr, and the distensibility of the capillary sheet (% increase in thickness over the undistended thickness/Torr increase in transmural pressure) is approximately 3.6%/Torr. The calculated arterial-capillary-venous volumes and compliances of the model agree well with experimental estimates of these variables in dogs. In addition, the model appears consistent with certain aspects of the pressure-flow relationships measured in dog lungs. The model appears to be a useful summary of some of the available data on pulmonary morphometry and vessel properties. It is anticipated that the model will provide the basis for dynamic modeling of the dog lung in the future.     

Flow and pressure distributions in vascular networks consisting of distensible vessels

We examine the influence of vessel distensibility on the fraction of the total network flow passing through each vessel of a model vascular network. An exact computational methodology is developed yielding an analytic proof. For a class of structurally heterogeneous asymmetric vascular networks, if all the individual vessels share a common distensibility relation when the total network flow is changed, this methodology proves that each vessel will continue to receive the same fraction of the total network flow. This constant flow partitioning occurs despite a redistribution of pressures, which may result in a decrease in the diameter of one and an increase in the diameter of the other of two vessels having a common diameter at a common pressure. This theoretical observation, taken along with published experimental observations on pulmonary vessel distensibilities, suggests that vessel diameter-independent distensibility in the pulmonary vasculature may be an evolutionary adaptation for preserving the spatial distribution of pulmonary blood flow in the face of large variations in cardiac output.     

A theory of blood flow in skeletal muscle

A theoretical analysis of blood flow in the microcirculation of skeletal muscle is provided. The flow in the microvessels of this organ is quasi steady and has a very low Reynolds number. The blood is non-Newtonian and the blood vessels are distensible with viscoelastic properties. A formulation of the problem is provided using a viscoelastic model for the vessel wall which was recently derived from measurements in the rat spinotrapezius muscle (Skalak and Schmid-Sch?nbein, 1986b). Closed form solutions are derived for several physiologically important cases, such as perfusion at steady state, transient and oscillatory flows. The results show that resting skeletal muscle has, over a wide range of perfusion pressures an almost linear pressure-flow curve. At low flow it exhibits nonlinearities. Vessel distensibility and the non-Newtonian properties of blood both have a strong influence on the shape of the pressure-flow curve. During oscillatory flow the muscle exhibits hysteresis. The theoretical results are in qualitative agreement with experimental observations.     

A continuum model for pressure-flow relationship in human pulmonary circulation

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.     

Carbon monoxide promotes hypoxic pulmonary vascular remodeling

CO is a biologically active gas that produces cellular effects by multiple mechanisms. Because cellular binding of CO by heme proteins is increased in hypoxia, we tested the hypothesis that CO interferes with hypoxic pulmonary vascular remodeling in vivo. Rats were exposed to inspired CO (50 parts/million) at sea level or 18,000 ft of altitude [hypobaric hypoxia (HH)], and changes in vessel morphometry and pulmonary pressure-flow relationships were compared with controls. Vascular cell single strand DNA (ssDNA) and proliferating cell nuclear antigen (PCNA) were assessed, and changes in gene and protein expression of smooth muscle alpha-actin (sm-alpha-actin), beta-actin, and heme oxygenase-1 (HO-1) were evaluated by Western analysis, RT-PCR, and immunohistochemistry. After 21 days of HH, vascular pressure at constant flow and vessel wall thickness increased and lumen diameter of small arteries decreased significantly. The presence of CO, however, further increased both pulmonary vascular resistance (PVR) and the number of small muscular vessels compared with HH alone. CO + HH also increased vascular PCNA and nuclear ssDNA expression compared with hypoxia, suggesting accelerated cell turnover. CO in hypoxia downregulated sm-alpha-actin and strongly upregulated beta-actin. CO also increased lung HO activity and HO-1 mRNA and protein expression in small pulmonary arteries during hypoxia. These data indicate an overall propensity of CO in HH to promote vascular remodeling and increase PVR in vivo.     

Effect of catheter size on pressures recorded in small pulmonary veins in dog lung.

Controversy continues about the contribution of the veins to pulmonary vascular resistance. From data obtained in studies using intravascular catheters, it appears that a major fraction (up to 44%) of the total pulmonary vascular pressure drop resides in larger (greater than 1.0 mm diam) veins, whereas micropuncture data and various models give much less pressure drop. Theoretically, artifactual pressure drops can be obtained if an intravascular catheter partly obstructs the vessel. We made measurements of pressure in the same lung vein with two different-sized catheters (1.2 and 0.6 mm OD, respectively). In paired experiments the larger catheter always measured a higher pressure than the smaller one, except close to the large lobar vein outlet. In some of the experiments we measured the diameter of the vessel containing the indwelling catheter by freezing the lung and then serial-sectioned the frozen lung. From these data we could infer that the range of vein diameter in the which the smaller catheter measured a lower pressure was 1.5-4 mm. We conclude that the larger catheter overestimated the pressure because of greater obstruction. The pressures obtained with the smaller catheter suggest that little (less than 10%) of the total pulmonary vascular resistance resides in veins larger than approximately 1 mm diam under zone 3 baseline conditions.     

Distensibility and pressure-flow relationship of the pulmonary circulation. I. Single-vessel model

To ascertain the relative contributions of vascular distensibility and nonhomogeneous behavior within the pulmonary circulation to the distinctive nonlinear relationship between inflow pressure (Pin) and flow [pressure-flow (P-F) relationship] and between Pin and outflow pressure (Pout) at constant flow (Pin-Pout relationship), we developed a multibranched model in which the elastic behavior of, and forces acting on, individual branches can be varied independently. The response of the multibranched model is described in the companion article (J. Appl. Physiol. 68: 1514-1527, 1990). Here we describe the methods used and the responses of single components of the larger model. Perivascular pressure is modeled as a function of intravascular and transpulmonary pressures (Pv and Ptp, respectively) and vessel length as a function of lung volume. These and the relationship between vascular area (A) and transmural pressure (Ptm) were modeled primarily from the dog data of Smith and Mitzner (J. Appl. Physiol. 48: 450-467, 1980). Vasomotor tone is modeled as a radial collapsing pressure (Pt) in the same plane as Ptm. In view of lack of information about the relationship between Pt and A for a given active state, different patterns were assumed that span a wide range of possible relationships. The P-F and Pin-Pout relationships of single vessels were very similar to those reported for the entire intact circulation. Of note, the slope of the Pin-Pout relationship in the low Pout range (0-5 Torr) was very low (less than 0.25) and increased gradually with Pout toward unity. Vasomotor tone caused an apparent parallel shift in the P-F relationship in the physiological flow range of the dog (2-8 l/min) regardless of the pattern used to model the Pt vs. A relationship; different patterns affected the P-F relationship only over the low flow range before the parallel shift was established.