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(Hypertension. 2001;38:1476.)
© 2001 American Heart Association, Inc.

Fourth Workshop on Structure and Function of Large Arteries: Part III

Structural Adaptation of Vascular Networks

Role of the Pressure Response

Axel R. Pries; Bettina Reglin; Timothy W. Secomb

From the Department of Physiology, Freie Universität Berlin (A.R.P., B.R.), Berlin, Germany; Deutsches Herzzentrum Berlin (A.R.P.), Berlin, Germany; and Department of Physiology, University of Arizona (T.W.S.), Tucson.

Correspondence to A.R. Pries, MD, Freie Universität Berlin, Department of Physiology, Arnimallee 22, D-14195 Berlin, Germany. E-mail pries{at}zedat.fu-berlin.de

Abstract

Structural reductions in vessel luminal diameters in response to elevated pressure may play a role in the elevation of peripheral resistance generally observed in hypertension. In the present study, a theoretical model is used to simulate the effect of increased driving pressure on flow resistance in microvascular networks. The angioarchitecture (lengths and diameters of all segments, topology) of microvascular networks (n=6) in the rat mesentery was recorded by intravital microscopy. The model simulation of vascular adaptation in response to local wall shear stress, transmural pressure, and tissue PO₂ was used to predict changes in network pressure drop and flow resistance for a given change of driving pressure (P). For P increasing from 15% to 190% of the normotensive value, a 3.3-fold increase in flow resistance was observed (structural autoregulation). If vascular reactivity to pressure was suppressed, the resistance increase was abolished. Suppressing pressure sensitivity also led to a rise in mean capillary pressure at normal driving pressure from 23.8±7.3 mm Hg to 34±6.9 mm Hg. These results indicate that low capillary pressure levels as well as structural autoregulation depend on vascular responses to circumferential wall stress (corresponding to pressure). This tendency of peripheral vascular beds to increase flow resistance for a given increase of bulk flow or driving pressure may amplify and stabilize blood pressure elevation in the development of hypertension.

Key Words: angioadaptation • microvessels • pressure • model simulation • shear stress

A sustained increase in peripheral resistance is a hallmark of established hypertension. Previous studies^1,2 have suggested that structural reduction in vessel diameters resulting from vascular responses to elevated pressure is an important factor in this increase in resistance. The average circumferential stress in vessel walls depends on intravascular pressure, being approximately =[Px(r/w)], where P is the transmural pressure, r is the vessel radius, and w is the wall thickness. Increased intravascular pressure is observed to lead to structural reduction of luminal diameter and increase in vessel wall thickness, both tending to counteract the initial increase in circumferential wall stress.^3–7 However, increased pressure also increases the pressure gradient driving blood flow. This tends to increase the fluid shear stress at the endothelial surface, which causes luminal diameter to increase.^8–11 The net change in resistance in a vascular bed resulting from an increase in arterial pressure depends on the interaction between these adaptive responses.

Theoretical models provide a framework for simulating the interaction of structural responses to pressure, shear stress, and other stimuli in the context of network hemodynamics. A network model for structural diameter changes in the microcirculation, including structural responses to intravascular pressure and wall shear stress, was developed by Pries et al.¹² The model showed that formation of stable, realistic network structures requires, in addition to the hemodynamic responses, sensitivity to the metabolic status of distal branches and propagation of this information to more proximal vessels. Recently, this model has been further developed to simulate structural diameter adaptation of microvascular networks assuming that each vascular segment responds to the local partial pressure of oxygen (PO₂), and that upstream and downstream information transfer are achieved by conducted responses in vessel walls and by convective metabolite transport, respectively.¹³

The goal of the present study is to use the recent model¹³ to simulate the effect of increased arterial pressure on peripheral flow vascular resistance and to examine the role of the structural response to pressure in this effect, by varying the sensitivity of the response. The simulation is based on morphological and topological data obtained in rat mesenteric networks. A further objective is to examine the relationship between intravascular pressure and circumferential stress in vessel walls and to consider the implications for the structural response to intravascular pressure.

Methods

Intravital Microscopy
Male Wistar rats (n=6; body weight, 300 to 450 g) were prepared for intravital microscopy by anesthesia (atropine 0.1 mg/kg, pentobarbital 20 mg/kg, and ketamine 100 mg/kg); cannulation of trachea, jugular vein, and carotid artery; and exteriorization of the small bowel through an abdominal midline incision. All procedures were approved by the local and state authorities for animal welfare. Microvascular networks in the mesentery were scanned and recorded. The volume flow rate through the networks varied between 500 and 1200 nL/min with a mean (±SD) of 727±302 nL/min. The topological structure of the networks and diameter, length, and flow velocity (for n=3 networks) for all vessel segments (n, 432±102) were determined from video recordings. Details of the animal preparation and intravital microscopy setup have been given elsewhere.^14–16

Model Simulation
The theoretical model¹³ allows the prediction of volume flow rate, pressure, shear stress, and PO₂ (assuming that each vessel supplies a tissue region 200 µM wide and 20 µM thick) for all vessel segments of a given network architecture. These quantities are used to estimate a net stimulus for an incremental diameter change in each segment. Shear stress was assumed to stimulate diameter increase according to the experimental evidence discussed above. Pressure was assumed to lead to a reduction in inner vessel diameter, similar to a sustained myogenic response. A metabolic signal was calculated from the PO₂ in each segment and was assumed to be conducted upstream and convected downstream. Values for parameters used in the simulated adaptation describing the sensitivity to pressure, shear stress, and metabolic stimuli were optimized for the control state by comparing velocity distributions measured directly with those predicted by the simulations. Simulations were performed for driving pressures ranging from 4% to 195% of the normotensive value. Before adaptive changes of vessel diameters, bulk rates throughout the network increase in proportion to driving pressure. Adaptive responses to the changed conditions then lead to redistribution of flow resistance within the network.

Results

Effects of altered driving pressure on bulk flow and flow resistance following structural adaptation are shown in Figure 1 and are similar to those found using the earlier model.² In simulations with standard pressure-sensitivity ("standard"), the increase in flow in response to increased pressure is blunted, especially at pressures close to the normal value (upper panel). This structural autoregulation results from a strong increase in flow resistance (lower panel). If pressure-sensitivity is reduced ("intermediate"), flow resistance varies less. Abolition of pressure response ("none") leads to the opposite variation of flow resistance with pressure, reflecting vascular responses to shear stress.

View larger version (20K): [in this window] [in a new window]   Figure 1. Bulk flow through microvascular networks (top) and network flow resistance (bottom) after complete adaptation, as a function of driving pressure. Results represent mean values of simulations for 6 networks, with experimentally determined geometry for standard, intermediate, and abolished vascular sensitivity to transmural pressure. All data are normalized with respect to values obtained for the reference driving pressure and blood flow as measured in vivo.

For normotensive conditions, Figure 2 shows how the distribution of intravascular pressures through the network depends on pressure-sensitivity of the adaptive response. The profile predicted with the standard pressure sensitivity conforms with typical experimental data. It shows a steep pressure drop on the arterial side, capillary pressures 20 mm Hg, and a very low venous pressure decline. In contrast, abolition of pressure sensitivity leads to a nearly linear pressure decline and a capillary pressure level of 33 mm Hg.

View larger version (21K): [in this window] [in a new window]   Figure 2. Pressure versus inner vessel diameter for arterial () and venous () segments and mean±SD capillary pressure (•) for a microvascular network in the rat mesentery. Results for standard level of pressure sensitivity (left) correspond quantitatively to experimental values and earlier model predictions (see Pries et al14). In contrast, complete suppression of pressure sensitivity (right) leads to a more linear pressure decline and a significant increase of mean capillary pressure (33.6±6.9 mm Hg vs 19.1±4.2 mm Hg).

Discussion

The structural response of vessels to intravascular pressure plays a crucial role in the circulatory system by ensuring that flow resistance is concentrated on the arterial side of the system and that capillary pressure is thereby maintained at a low level (Figure 2).¹⁴ However, a further consequence of this response is that increased systemic pressure results in increased peripheral resistance, because vascular diameters are decreased throughout the network. Increased pressure also leads initially to elevated wall shear stress levels, which would tend to increase vessel diameters, but the response to pressure dominates the response to wall shear stress, as shown in Figure 1.

This structural response tends to reduce changes in perfusion accompanying changes in driving pressure and may thus be called structural autoregulation.^1,2,17 Because it leads to persistent increases in peripheral resistance, it is likely to be important in the development of high blood pressure triggered by a mildly elevated cardiac output as seen, for example, in young and borderline hypertensive patients¹⁸ and transiently in some experimental forms of hypertension.^19,20 If the vascular reaction to pressure (long-term myogenic response) is enhanced during development of hypertension, this would lead to even stronger increases of flow resistance and pressure.

In the present theoretical model, the structural response to pressure is assumed to depend directly on the intravascular pressure, which is approximately equal to the transmural pressure difference because tissue hydrostatic pressure is normally small. However, the dominant stress in the vessel wall induced by transmural pressure is the circumferential stress, and the stimulus for structural response is therefore more likely to be associated with this component of stress. As already noted, the average circumferential stress is proportional to the product of the transmural pressure and the ratio of wall thickness to vessel radius. This ratio is not constant, as shown by a meta-analysis of experimental studies on vessels of terminal vascular beds (Figure 3).^21–28 Both the ratio of wall thickness to radius and the average circumferential stress vary with transmural pressure by about 1 order of magnitude. These results demonstrate that despite structural adaptations of the vascular wall acting to reduce changes in the level of circumferential wall stress,^3–5 wall stress is not regulated to a constant value throughout vascular beds. For both arterial and venous vessels, wall stress levels increase with distance from the capillary region, corresponding to a pressure of 30 mm Hg in Figure 3.

View larger version (16K): [in this window] [in a new window]   Figure 3. Wall thickness relative to inner vessel radius (left) and average wall stress (right) vs intravascular pressure. Data points correspond to a meta-analysis of literature studies.21–28 A relation between microvascular pressure and diameter derived in an earlier study14 was used to estimate intravascular pressure as a function of vessel diameter. Capillary pressure is 30 mm Hg.

The same data are used in Figure 4 to show the variation of average circumferential wall stress with vessel diameter. Interestingly, a close relationship is found, in which wall stress increases as a function of vessel diameter, irrespective of vessel type, transmural pressure, or position along arteriovenous flow pathways. A regression of log wall stress on log diameter yields an exponent of 0.624 and a correlation coefficient (r) of 0.901, indicating that average wall stress increases approximately in proportion to the square root of diameter.

View larger version (24K): [in this window] [in a new window]   Figure 4. Log-log plot of wall stress as a function of vessel diameter for the data points from Figure 4, combined for arteriolar and venular vessels. The parameters of the regression line shown are: wall stress=2.917xdiameter0.624.

The mechanistic basis for this dependence of circumferential stress on diameter is not known at present. However, it presumably results from the combined effect of 2 different modes of structural remodelling²⁹: change in circumference at constant wall mass (eutrophic remodelling) and change in wall mass (hypo- or hypertrophic remodelling). Change in circumference at constant mass is the only mode available for short-term changes of wall geometry in the context of acute changes of smooth muscle tone. It leads to an increase of luminal diameter and to a decrease in wall thickness (or vice versa). With respect to long-term vascular adaptation, experimental data suggest an eutrophic inward remodelling for essential hypertension, whereas other modes have been reported for different pathologies with sustained changes of systemic hemodynamic conditions.²⁹ The resulting changes in diameter and wall thickness in turn influence wall and shear stress, resulting in several negative feedback loops. Further work is needed to understand how these processes lead to the distributions of diameter, wall thickness, and wall stress observed in vascular networks.

Resistance to blood flow in peripheral tissues depends on the number of microvessels as well as on their diameter. Reduction in vessel number, ie, microvascular rarefaction, is observed in hypertension and may play an important role in increasing vascular resistance.³⁰ The assumptions of the present model do not allow for loss of vessels and reduction of vascular density. However, the model could be extended to include this phenomenon by assuming that vessels with diameters that fall below a minimum diameter required for blood flow are effectively lost from the network.

In conclusion, the present theoretical simulations indicate that the structural response of vessels to intravascular pressure has double-edged effects on the function of peripheral vascular beds. On one hand, it results in luminal diameters that are smaller in arterial vessels than in corresponding venous vessels, so that vascular resistance is concentrated on the arterial side. This ensures that capillary pressure is relatively low, so that excessive fluid filtration is avoided. On the other hand, it has the effect that an increase in arterial pressure leads to increased peripheral resistance, such that arterial pressure must then be sustained at a higher level to deliver a given cardiac output. This effect may be important in the development of hypertension.

Received April 28, 2001; first decision June 18, 2001; accepted September 24, 2001.

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