Structural Adaptation of Vascular Networks
Role of the Pressure Response
Axel R. Pries, Bettina Reglin, Timothy W. Secomb
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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. (Hypertension. 2001;38:1476-1479.)
Key Words: angioadaptation 䡲 microvessels 䡲 pressure 䡲 model simulation 䡲 shear stress
A
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.
sustained increase in peripheral resistance is a hallmark
of established hypertension. Previous studies1,2 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 ␴⫽[P⫻(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
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,
Received April 28, 2001; first decision June 18, 2001; revision accepted September 24, 2001.
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
[email protected]
© 2001 American Heart Association, Inc.
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Pries et al
Adaptation of Microvascular Networks
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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
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The theoretical model13 allows the prediction of volume flow rate,
pressure, shear stress, and PO2 (assuming that each vessel supplies a
tissue region 200 ␮M wide and 20 ␮M 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
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.
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.
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 pressuresensitivity 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.
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 con-
Figure 2. Pressure versus inner vessel diameter
for arterial (䡩) 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).
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December 2001
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.
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forms 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.
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.
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.
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
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⫽2.917⫻diameter0.624.
Pries et al
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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.
References
1. Folkow B. Structural factor in primary and secondary hypertension.
Hypertension. 1990;16:89 –101.
2. Pries AR, Secomb TW, Gaehtgens P. Structural autoregulation of
terminal vascular beds: vascular adaptation and development of hypertension. Hypertension. 1999;33:153–161.
3. Patel KD, Nollert MU, McEver RP. P-selectin must extend a sufficient
length from the plasma membrane to mediate rolling of neutrophils. J Cell
Biol. 1995;131:1893–1902.
4. Dobrin PB. Mechanical factors associated with the development of
intimal and medial thickening in vein grafts subjected to arterial pressure:
a model of arteries exposed to hypertension. Hypertension. 1995;26:
38 – 43.
Adaptation of Microvascular Networks
1479
5. Fath SW, Burkhart HM, Miller SC, Dalsing MC, Unthank JL. Wall
remodeling after wall shear rate normalization in rat mesenteric arterial
collaterals. J Vasc Res. 1998;35:257–264.
6. Laurant P, Touyz RM, Schiffrin EL. Effect of pressurization on
mechanical properties of mesenteric small arteries from spontaneously
hypertensive rats. J Vasc Res. 1997;34:117–125.
7. Intengan HD, Deng LY, Li JS, Schiffrin EL. Mechanics and composition
of human subcutaneous resistance arteries in essential hypertension.
Hypertension. 1999;33:569 –574.
8. Smiesko V, Johnson PC. The arterial lumen is controlled by flow-related
shear stress. NIPS. 1993;8:34 –38.
9. Brownlee RD, Langille BL. Arterial adaptations to altered blood flow.
Can J Physiol Pharmacol. 1991;69:978 –983.
10. Kamiya A, Togawa T. Adaptive regulation of wall shear stress to flow
change in the canine carotid artery. Am J Physiol. 1980;239:H14 –H21.
11. Rodbard S. Vascular caliber. Cardiology. 1975;60:4 – 49.
12. Pries AR, Secomb TW, Gaehtgens P. Structural adaptation and stability
of microvascular networks: theory and simulations. Am J Physiol. 1998;
275:H349 –H360.
13. Pries AR, Reglin B, Secomb TW. Structural adaptation of microvascular
networks: functional roles of adaptive responses. Am J Physiol. 2001;
281:H1015–H1025.
14. Pries AR, Secomb TW, Gaehtgens P. Design principles of vascular beds.
Circ Res. 1995;77:1017–1023.
15. Pries AR, Secomb TW, Gessner T, Sperandio MB, Gross JF, Gaehtgens
P. Resistance to blood flow in microvessels in vivo. Circ Res. 1994;75:
904 –915.
16. Pries AR, Secomb TW, Gaehtgens P, Gross JF. Blood flow in microvascular networks - experiments and simulation. Circ Res. 1990;67:
826 – 834.
17. Folkow B. Structural autoregulation: the local adaptation of vascular beds
to chronic changes in pressure. In: Ciba Foundation Symposium 100:
Development of the Vascular System. London: Pitman Books; 1983:
56 –79.
18. Conway J. Hemodynamic aspects of essential hypertension in humans.
Physiol Rev. 1984;64:617– 660.
19. Ferrario CM. Contribution of cardiac output and peripheral resistance to
experimental renal hypertension. Am J Physiol. 1974;226:711–717.
20. Coleman TG, Guyton AC. Hypertension caused by salt loading in the
dog, III: onset transients of cardiac output and other circulatory variables.
Circ Res. 1969;25:153–160.
21. Lee RMKW, Garfield RE, Forrest JB, Daniel EE. Morphometric study of
structural changes in the mesenteric blood vessels of spontaneously
hypertensive rats. Blood Vessels. 1983;20:57–71.
22. Rakusan K, Wicker P. Morphometry of the small arteries and arterioles in
the rat heart: effects of chronic hypertension and exercise. Cardiovasc
Res. 1990;24:278 –284.
23. Harper SL, Bohlen HG. Microvascular adaptation in the cerebral cortex
of adult spontaneously hypertensive rats. Hypertension. 1984;6:408 – 419.
24. Bohlen HG, Niggl BA. Adult microvascular disturbances as a result of
juvenile onset diabetes in Db/Db mice. Blood Vessels. 1979;16:269 –276.
25. Tomanek RJ, Palmer PJ, Peiffer GL, Schreiber KL, Eastham CL, Marcus
ML. Morphometry of canine coronary arteries, arterioles, and capillaries
during hypertension and left ventricular hypertrophy. Circ Res. 1986;58:
38 – 46.
26. Lang DJ, Johns BL. Rat venule mechanical characteristics during venous
pressure elevation. Am J Physiol. 1987;252:H704 –H713.
27. Rhodin JAG. Ultrastructure of mammalian venous capillaries, venules,
and small collecting veins. J Ultrastruct Res. 1968;25:452–500.
28. Gore RW. Pressures in cat mesenteric arterioles and capillaries during
changes in systemic arterial blood pressure. Circ Res. 1974;34:581–591.
29. Mulvany MJ. Vascular remodelling of resistance vessels: can we define
this? Cardiovasc Res. 1999;41:9 –13.
30. Greene AS, Tonellato PJ, Lui J, Lombard JH, Cowley AW Jr. Microvascular rarefaction and tissue vascular resistance in hypertension. Am J
Physiol. 1989;256:H126 –H131.
Structural Adaptation of Vascular Networks: Role of the Pressure Response
Axel R. Pries, Bettina Reglin and Timothy W. Secomb
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Hypertension. 2001;38:1476-1479
doi: 10.1161/hy1201.100592
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