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(Hypertension. 1995;26:38-43.)
© 1995 American Heart Association, Inc.
Articles |
From the Department of Surgery, Loyola University Medical Center, Maywood, and Hines Veterans Affairs Hospital, Hines, Ill.
Correspondence to Philip B. Dobrin, MD, PhD, Department of Surgery, Loyola University Medical Center, 2160 South First Ave, Maywood, IL 60153.
| Abstract |
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Key Words: deformation stress shear stress circumferential stress longitudinal stress radial directons
| Introduction |
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An interesting indirect model of the responses of arteries to hypertension may be found in the histological responses of autogenous veins when they are used as arterial bypass grafts. After exposure to arterial pressures, these vessels undergo intimal hyperplasia and medial thickening. However, it is unlikely that arterial pressure itself elicits these responses. It is more likely that pressure and flow produce deformations and stresses in the vessel wall and that these act internally as stimuli. One may specify nine mechanical factors that occur in the wall of pressurized vein that might act as stimuli.9 There are three static deformations: increased circumference (Fig 1, factor 1), increased length (Fig 1, factor 3), and increased radial deformation (ie, decreased wall thickness; Fig 1, factor 5). In opposition to these deformations, the vessel wall generates increased stress in the circumferential direction (Fig 1, factor 2), in the longitudinal direction (Fig 1, factor 4), and in the radial direction (Fig 1, factor 6). Stresses in the circumferential and longitudinal directions are tensile, whereas stress in the radial direction is compressive. In addition, vein grafts subjected to elevated pressure may undergo pulsatile deformations and increased pulsatile stresses (Fig 1, factors 7 and 8). Finally, blood driven by arterial pressure produces flows at different velocities. This is important because velocity is directly related to the blood-intima shear stress (Fig 1, factor 9). Shear stress may be computed as
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![]() | (1) |
where TW is the shear stress, µ is the viscosity of blood (0.035 poise), Q is the velocity of blood flow (in milliliters per second), and r is the inner radius of the vessel. Shear stress cannot be meaningfully calculated unless flow is well ordered and stable. The mathematical methods used to compute each of the mechanical factors listed above are given elsewhere.10
Several investigators have reported that intimal hyperplasia developing in vein grafts correlates with low flow velocity.11 12 13 Others have correlated it with circumferential deformation,14 circumferential wall tension,14 or circumferential stress.15 16 However, all of the nine factors illustrated in Fig 1 occur simultaneously, and morphological changes may occur in response to any or all of them. Because of this simultaneity, an algorithm was developed to experimentally separate the nine mechanical factors shown in Fig 1 as possible stimuli for the development of intimal hyperplasia and medial thickening in autogenous vein grafts. The experimental algorithm is shown in Fig 2.17
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| Methods |
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Step 1 Experiments
In 14 dogs, the femoral arteries were bypassed bilaterally using
autogenous femoral vein grafts as illustrated in Figs 3 and 4. The artery on one side was ligated;
this caused all femoral flow on that side to pass through the graft at
high velocity. The artery on the opposite side was left patent; this
permitted flow to be divided between the vein graft and the native
artery. As a result, flow velocity through the vein graft on the side
where the artery was not ligated was lower than on the side where the
artery had been ligated. No thrill was palpable over the grafts at the
time of surgery, indicating that there was not frank turbulence.
However, minor degrees of flow disturbance may have been
present at and beyond the anastomosis and at the flow dividers.
Flows were measured with an electromagnetic flowmeter at the time of
vein graft implantation. These measurements indicated that total
femoral flows on the two sides were equal and that flow through the
vein grafts was approximately doubled on the side in which the femoral
artery was ligated. However, flow measurements were discontinued when
it was found that it was not possible to obtain flow measurements with
the electromagnetic flowmeter when the grafts were excised, as this
would require extensive dissection through scar with possible injury to
the grafts.
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A portion of the vein graft on both sides of the animal was restricted
in dimension by placing a Marlex cuff over a portion of the length of
the graft (Figs 3 and 4). The cuff was placed so that when the vessel
was distended by arterial pressure the restricted region of
the vein did not exceed its usual dimensions at normal venous
pressures. The cuff was placed proximally around the vein grafts
bilaterally in odd-numbered animals and distally around the vein grafts
bilaterally in even-numbered animals. The portions of the vein without
cuffs were able to distend without constraint. Experimental data were
used as follows. (1) Since total flow on the two sides of the animal
was equal, flow velocity must by physical principles have been higher
through the restricted region of the graft on the side on which the
artery was ligated, since all flow was required to pass through the
graft. Conversely, flow velocity was lowest through the distended
region of the graft where the native artery was left patent and flow
was divided. In this case, only part of the flow passed through the
vein graft. On both sides, flow velocity was higher through the portion
of the vein where diameter was restricted by the cuff than through the
unrestricted, diameter-distended portion of the graft. These
differences in flow velocity would apply even if there were
turbulence because a given volume of blood was required to pass through
series-connected vessels that were of different diameters. Because
entering and exiting volumes must be equal, the flow velocity must have
been higher through the restricted area than through the wider
restricted area of the grafts (Bernoulli's principle). (2)
Circumferential deformation is measured by increased vessel diameter
and clearly was highest in the dilated, unrestricted areas. (3) Mean
circumferential stress (
) is given by
![]() | (2) |
where PT is transmural pressure,
ri is internal radius, and h is wall thickness.
In the experiments shown in Figs 3 and 4, circumferential deformation
and circumferential stress were largest in the distended portion of the
grafts but were only slightly elevated in the portions of the grafts
where the cuff limited distension. The mesh bore much of the
circumferential load in the restricted regions. (4) Radial deformation
is reflected by narrowing of wall thickness. Narrowing was greatest in
the regions of the graft that were distended. (5) Mean radial
compressive stress (
r) is equal to one half the
transmural pressure, ie,
r=PT/2. Therefore,
radial stress was greatest in the portions of the grafts wrapped by the
cuff. In these regions, the vein grafts were pressurized from within
the lumen and constrained from without by the mesh.
Step 2 Experiments
In 13 dogs, 3- to 5-cm-long segments of vein were implanted
bilaterally as end-to-end interposition grafts replacing a segment of
excised carotid artery (Fig 5). After construction of
the anastomoses, two sterile, rigid, polyethylene rods were placed
parallel to the graft on one side of the animal. The rods were sutured
to the pressurized veins to deliberately overextend the grafts by 10%
to 15%. Greater lengthening caused tearing of the grafts. Actual
measured extension was 12.6±0.8%. This increased the longitudinal
deformation and longitudinal stress in the wall of the graft on the one
side of the animals. Longitudinal deformation is produced by forced
stretching of the vessel. The stretched vessel wall exerts increased
longitudinal stress in response to extension. Longitudinally extending
the vessel also slightly increased radial deformation by causing
thinning of the wall. It also slightly decreased circumferential
deformation and decreased circumferential stress because extension
slightly reduced the radius.
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Step 3 Experiments
Reversed femoral veins were implanted bilaterally as end-to-end
interposition grafts in 11 dogs, replacing a segment of excised carotid
artery (Fig 6). After the anastomoses were constructed,
a 1-cm Marlex band was wrapped around the carotid artery proximal to
the vein graft on one side but not on the other. This Marlex band was
secured to narrow the lumen of the artery sufficiently to decrease
pressure in the vein grafts but maintain diastolic pressure
at at least 50 mm Hg. Measurements were obtained distal to the grafts
during surgery with a fluid-filled, 1-in, 20-gauge needle connected
to a Statham pressure transducer. The Marlex band was used to lower the
pressure slightly in the veins to separate circumferential deformation
from circumferential stress. Veins are extremely distensible at
pressures up to 35 to 50 mm Hg, but they become virtually rigid at
pressures above this range.17 Because
diastolic pressure in the vein graft was maintained above
50 mm Hg, the diameters of the vein grafts on the two sides were equal
(equivalent circumferential deformations). Systolic and
diastolic pressures measured at the time of surgery were
103±6 and 74±6 mm Hg in the graft on the side without the proximal
carotid stenosis and 79±3 and 61±2 mm Hg in the grafts with
the proximal carotid stenosis, respectively. Thus,
diastolic pressure was maintained above 50 mm Hg, although
pulse pressure was reduced on the banded side. In summary, the Marlex
band on the one carotid artery decreased systolic,
diastolic, mean, and pulse pressures in the vein grafts but
maintained diastolic pressures at greater than 50 mm Hg.
As a result, the stenosis on the carotid artery used in the
step 3 experiments provided equal circumferential deformations
bilaterally but unequal circumferential stresses (equation 2).
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All of the dogs were killed 3 months after surgery; the grafts were excised, perfusion-fixed at 100 mm Hg with 10% formaldehyde embedded in paraffin, sectioned, stained with Verhoeff's elastica, and prepared for histological examination. The histological responses of the grafts on the two sides were correlated with the mechanical factors listed in Fig 1. Sections of the midpoint of the vein grafts were studied, not the anastomotic regions. Drawings of these figures were used to determine the cross-sectional areas of the intima and the media with a calibrated grid planimeter. Statistical comparisons were made with paired t tests.
| Results |
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Medial Thickening
Fig 4 gives the cross-sectional area values for the media in each
portion of the graft for the same 14 animals. Comparison of the cuffed
and contiguous noncuffed portions showed that medial thickening was
almost twice as great in the distended regions as in the regions
limited by the cuffs. This was true for the side on which the artery
was ligated (high flow velocity, 1.53 versus 2.91 mm2) as
well as the side on which the artery was left patent (low flow
velocity, 1.79 versus 2.71 mm2). These differences were
statistically significant (P<.05). However, comparison of
the distended regions across the two sides (2.91 versus 2.71
mm2) disclosed no statistically significant differences.
Similarly, comparison of the cuffed regions across the two sides (1.53
versus 1.79 mm2) showed no significant differences.
Therefore, unlike intimal thickening, medial thickening was associated
with graft deformations or static wall stresses, not with flow
velocity. However, it was not possible from those data to identify the
direction of the deformation or stress associated with medial
thickening. To make this identification, step 2 and step 3 experiments
were performed.
Step 2 Experiments: Longitudinal Extension
Intimal Thickening
Step 2 experiments were performed in 13 animals to determine the
effects of deformation and stress in the longitudinal direction. Grafts
were constructed in an end-to-end fashion with the graft on one side
extended longitudinally 12.6±0.8% compared with the pressurized but
unstretched graft on the contralateral side. Extending the vein also
caused thinning of the wall and therefore increased radial deformation
(wall thinning). Longitudinal stretch also produced increased
longitudinal stress. Fig 5 demonstrates that longitudinal
hyperextension did not produce increased intimal thickening. The
cross-sectional areas were 0.76±0.13 mm2 on the stretched
side versus 0.67±0.20 mm2 on the unstretched side. The
difference was not statistically significant. From these data, it may
be concluded that intimal hyperplasia was not associated with increased
longitudinal deformation (increased longitudinal stretch) or increased
radial deformation (wall thinning).
Medial Thickening
Fig 5 provides the cross-sectional areas of the media of
the grafts in the 13 animals. Medial areas were 5.83±0.62
mm2 on the stretched side versus 6.02±0.71 mm2
on the unstretched side. These areas were not significantly different
from one another. Therefore, one may conclude that neither intimal nor
medial thickening was associated with deformation or stress in the
longitudinal direction or deformation in the radial direction. This
suggests that medial thickening is associated with deformation or
stress in the circumferential direction. Further clarification required
step 3 experiments.
Step 3
Experiments: Circumferential Deformation Versus Stress
Intimal Thickening
Step 3 experiments involved reversed femoral veins anastomosed
end-to-end as interposition grafts in the carotid artery (Fig 5). A
calibrated Marlex band was placed proximally around the carotid
arteries on one side of the animals to lower the pressure delivered to
the graft but maintain diastolic pressure at greater than
50 mm Hg. Fig 7 shows pressure-diameter relations from
an earlier study for 30 native dog veins and dog vein
grafts.18 These curves illustrate that both native veins
and vein grafts exhibit marked distensibility at pressures up to 50
mm Hg, with very little distensibility and little change in diameter
at pressures greater than 50 mm Hg. Therefore, the calibrated decrease
in pressure produced by the Marlex band in the step 3 experiments (Fig 6) permitted the vein grafts on the two sides to be at equal diameters,
ie, equal deformations. However, because the pressure was decreased on
the side with the carotid stenosis, the circumferential stress
was decreased on that side. This occurs because stress is dependent on
both pressure and radius (Equation 2). Statistical comparison
demonstrated that intimal thickening for the nine animals in which the
grafts remained patent was not significantly different on the two sides
(1.30±0.34 versus 1.08±0.37 mm2). Therefore, it may be
concluded that intimal hyperplasia was not associated with
circumferential stress. However, as shown in Fig 4, medial thickening
was greatest where circumferential deformation was largest. From these
data and those of previous experiments (Figs 3 and 5), one may conclude
that intimal thickening is best correlated with low flow velocity and
not with increased deformation or static stresses in any direction in
the vessel wall.
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Medial Thickening
Fig 6 also shows that the cross-sectional area of the media of the
vein grafts was 4.02±0.97 mm2 on the side with the
proximal stenosis compared with 3.85±0.52 mm2 on
the nonstenotic control side. These medial areas were not
significantly different. Therefore, medial thickening was similar in
the presence of equivalent circumferential deformations, despite the
fact that the circumferential stress was decreased on the side with the
stenosis. From these data and those of previous experiments
(Figs 4 and 5), it may be concluded that medial thickening of vein
grafts was best associated with deformation in the circumferential
direction (increased diameter) and not with circumferential stress. Fig 5 shows that medial thickening was not associated with deformation or
stress in the longitudinal direction.
During construction of the stenosis of the proximal carotid artery as shown in Fig 6, the pulse pressure (systolic minus diastolic pressure) was reduced from 29 mm Hg on the nonstenotic side to 18 mm Hg on the side with the carotid band. Measurements made at the time the grafts were harvested showed that the pulse pressure was reduced to a similar extent. It was 24 mm Hg on the unbanded side and 15 mm Hg on the side with the carotid band. Pulse pressures are directly related to pulsatile stresses (Equation 2). Because medial thickening was not significantly different on the two sides, it may be concluded that medial thickening is best associated with mean deformation and not with pulsatile pressures or pulsatile stresses. Conclusions really cannot be drawn regarding the role of pulsatile deformations in vein grafts because the vein wall is virtually nondistensible at pressures above 50 mm Hg (Fig 7). Therefore, little pulsatile motion occurs with or without a proximal band as long as the diastolic pressure remains greater than 50 mm Hg.
| Discussion |
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Several studies have reported that intimal thickening in veins and prosthetic grafts is associated with low blood flow velocity,9 11 12 13 whereas other studies suggest that it is associated with circumferential wall tension14 or wall stress.14 15 16 However, exposing a vein graft or an artery to elevated pressures subjects it simultaneously to deformations and stresses in all three directions. The present study attempted to systematically separate these simultaneous factors. Flow velocity is directly related to low blood-artery shear stress, a factor increasing the probability of platelet adherence to the intima. Low shear stress also alters the mechanical and biochemical environment of the endothelium.19 Shear stress is directly related to blood flow velocity but cannot be computed accurately unless flow is well ordered and has developed stable velocity profiles. For this reason, no attempt was made in the present experiments to actually compute shear stresses in the different regions in the vein graft. However, the relative velocities are predictable through these series-coupled vessel segments, as dictated by Bernoulli's principle.
Medial thickening occurs to the greatest extent in regions of the vessel subjected to increased circumferential deformation, ie, increased diameter. In vitro studies of arterial smooth muscle cells demonstrate that oscillating motion increases the synthesis of connective tissues,8 but it is not clear from those experiments whether the mean stretch around which pulsations oscillate or the pulsatile deformation itself is the effective stimulus. The present experiments suggest that medial thickening is best associated with increased mean deformation in the circumferential direction.
These experiments in vein grafts may be viewed as an indirect model of that which occurs in arteries subjected to hypertension. Studies in hypertensive animals treated with a variety of antihypertensive agents demonstrate that the structural changes that occur in the media of these arteries best correlate with increased pulse pressure.7 This may be explained by an important difference in the compliance characteristics of veins and arteries. Veins are virtually rigid at pressures greater than 50 mm Hg (Fig 7), whereas arteries exhibit gradually decreasing compliance at pressures up to 200 mm Hg.10 As a result, veins subjected to increased arterial pulse pressures experience almost no change in dimensions. Conversely, arteries subjected to increased arterial pulse pressures undergo graded deformations, depending on the mean pressure and diameter and the magnitude of the pressure pulse. This is consistent with the finding that medial thickening in vein grafts depends on deformation in the circumferential direction.
| References |
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