Mechanics of Normal and Diseased Blood Vessels

Basic science for vascular surgery Section Editor- Bruce L . Gewertz, MD (Chicago, Illinois)

Mechanics of Normal and Diseased Blood Vessels Philip B. Dobrin MD, PhD, Maywood, IIIinois

KEY WORDS: Vascular mechanics; blood vessels.

Vascular mechanics is that body of knowledge which combines physiology, pathophysiology, and mechanical engineering. It is both biological and quantitative, and it provides a unique perspective on the pathophysiology of arterial disease. This paper reviews blood vessel mechanics for the vascular surgeon utilizing a minimum of mathematics and historical information. For the interested reader detailed quantitative analyses and extensive reviews of the literature are presented elsewhere [1-41. After reviewing some fundamental principles of blood vessel mechanics, this paper examines application of these concepts to clinical problems in vascular surgery. These include: changes in the arterial wall with age, hemodynamics, aneurysms, poststenotic dilatation, vascular grafts, active muscular contraction of blood vessels, hypertension, and tortuosity. When pressurized, blood vessels are distended in the circumferential and longitudinal directions; at the same time they undergo radial thinning of the wall. These three deformations occur with little twist or torsion. Therefore this paper is organized to consider the From the Department of Surgery, Loyola University Medical Center, Maywood, Illinois, and Hines Veteran’s Administration Hospital, Hines, Illinois. Reprint requests: Philip B. Dobrin, MD, PhD, Department of Surgery, Loyola University Medical Center, Maywood, IL 60153. 283

mechanics of blood vessels in each of these three orthogonal directions.

CIRCUMFERENTIAL DIRECTION Normal blood vessels

Studies in humans and experimental animals show that arterial pressure causes arteries to distend in the circumferential direction. Vessels are subject to a continuous level of deformation by diastolic pressure, and this is augmented by the systolic-diastolic pressure cycle. During each cardiac cycle in vivo arteries exhibit oscillations in circumference or diameter that closely resemble the configuration of the arterial pressure pulse. In normal subjects both the carotid and femoral arteries oscillate 8-10% in external diameter or 10-14% in internal diameter. The difference between external and internal diameter changes is due merely to geometry and the fact that the vessel wall is incompressible. Indeed, even in a rubber tube, a given change in external circumference is associated with a larger percent change in internal circumference. Thus this difference depends solely on the dimension that is measured. However, the difference between external and internal diameter changes in blood vessels is important when comparing data obtained by arteriographic and

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Equation 5: T = P x r where T is wall tension. It must be emphasized that the Law of Laplace applies to a cylinder at equilibrium where the wall is infinitely thin. Therefore it is not strictly applicable to the arterial wall. At low pressures and small diameters both arteries and veins are extremely compliant (Fig. 1). This is due largely to the mechanical properties of the elastic lamellae in the vessel wall. Elastin is a fibrous protein which behaves mechanically and thermodynamically like a folded chain. It is extremely extensible and, when heated, actually shrinks as the chains assume a Equation I : PT = Pin - Po,, more entropic state. Rubber also exhibits this shrinkwhere P, is transmural pressure, Pi, is the pressure age behavior when heated. When loaded, elastic fibers within the lumen and Po,, is the pressure surrounding can be extended 50 to 70% as the protein chains are the outside of the vessel. Transmural pressure is the unwrinkled and gradually become stiff. Elastin bears a potential energy that holds a vessel open and distends large portion of the circumferential distending force in it. Therefore the periodic intrathoracic pressure swings blood vessel walls, and there is a direct relationship that accompany respiration tend to increase transmu- between the tension required to maintain equilibrium ral pressure. However this does not fully account for and the number of elastic lamellae present in the wall. the increased deformation of the intrathoracic vessels It has been estimated that each individual elastic suggesting increased mechanical compliance of the lamellae bears approximately 250 N/M tension [ 5 ] . thoracic vessels. When stretched, elastin exhibits an elastic modulus of about 4.5 x 10s N/M2. Elastic modulus is an engiThe distending force exerted by transmural pressure may be quantitated as the product of transmural pres- neering measure of stiffness. sure and the area over which that pressure is exerted. At high pressures arteries and veins are greatly distended, and this is associated with increasing stiffness Equation 2: F, = PT x (Di x L) (Fig. 1). This is due to the stretching and stiffening of where F, is the distending force, P, is the transmural the elastic lamella, and the gradual recruitment of colpressure, Di is the internal diameter, and L is an arbi- lagen fibers in the media. Collagen is the second major trary unit length of vessel. The quantity (Di x L) is the fibrous connective tissue in the wall. The structure of area over which transmural pressure is exerted. At collagen is fundamentally different from that of elasequilibrium, i.e., a steady diameter, the vessel exerts a tin as it is composed of closely-wound helical chains. The chains of this protein are tightly cross-linked, retractive force (FR)which is equal and opposite to F,. The retractive force may be quantitated as the product of the stress generated by the stretched wall and the area over which that stress is exerted. ultrasonic techniques with those obtained by measurement of external dimensions. In contrast to the systemic arteries, the intrathoracic aorta and pulmonary arteries exhibit large changes in diameter during each cardiac cycle, usually on the order of 10-18% in external diameter. There is no satisfactory explanation as to why deformations are so large within the chest. One factor may be the periodic negative and positive pressures within the thoracic cavity, for these increase the transmural pressure across the vessel wall. Transmural pressure is given by

Equation 3: F, = 0, x (2 th X L) where FR is the retractive force, a, is the circumferential stress or force per unit area exerted by the wall, 2 th are the two wall thicknesses, and L is the same unit length of vessel used in Equation 2. The quantity (2 th x L) is the area over which the wall stress is exerted. Stress describes force per unit area. Stress is comparable to pressure, but stress is used for solid materials such as the vessel wall, while pressure is used for fluids and gases. Setting Equations 2 and 3 equal and solving for stress gives Equation 4:

0,

= P

x

T ' th

This gives the stress generated by the wall at equilibrium. Note that for a wall of infinite thinness, (ri/th) becomes r, and Equation 4 becomes the well-known Law of Laplace.

4

a

' ' ' o;

;s

do

1;s

do

1;s

do

PRESSURE m m Hg

Fig. 1. Pressure-diametercurves for human and dog blood vessels. Slope of curves is proportional to compliance. Arteries are compliant at low pressures gradually becoming stiffer with distention. Veins are very compliant at low pressures, but become extremely stiff at pressures above 50 mm Hg. At arterial pressures arteries are more compliant than veins. (From [4] with permission of the publisher.)

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thereby restricting their extensibility. Indeed, collagen fibers can be stretched only 2-4%, as contrasted with the 50-70% that elastin can be stretched. When extended, the elastic modulus of collagen is about 1.O x 109 N/M*. Comparing the elastic moduli of collagen and elastin shows that stretched collagen is several hundred to one thousand times as stiff as stretched elastin. These two fibrous proteins are responsible for most of the mechanical behavior of the relaxed vessel wall. When arteries are pressurized and distended circumferentially, the elastic lamellae and some of the collagen fibers in the media are stretched. The collagen fibers in the adventitia are not stretched unless the vessel is overdistended to extreme, nonphysiological levels, such as occurs in an aneurysmal vessel. Thus much of the load on the wall is borne by elastin. Collagen bears much less of the load, and only at large deformations. Estimates of canine arteries show that, at physiological pressures, only about 8% of the collagen in the wall is load bearing in the carotid artery, and 25% of the collagen in the wall is load bearing in the renal, iliac, mesenteric, and coronary arteries [6]. Comparable estimates have not been made for human vessels. The mechanical properties of elastin and collagen determine much of the behavior of both normal and diseased arteries. The abdominal aorta and most systemic conduit arteries are stiffer than intrathoracic ones; the arteries from aged humans are stiffer than those from young ones; the arteries of hypertensive patients are stiffer than those of normotensive individuals. All of these differences correlate with higher collagen-to-elastin ratios in the stiffer vessels. However connective tissue content alone does not completely account for the mechanical characteristics of vessels, suggesting that architectural as well as compositional differences are important determinants of vessel wall behavior. For example, with aging, arteries gradually dilate to large diameters, and also develop thicker walls [7]. The process of dilation stretches and stiffens collagen fibers at progressively lower pressures. This process restricts the intrinsically more extensible elastic fibers. As a result, with age, the arteries of humans exhibit larger diameters and become functionally stiffer at lower pressures, even apart from changes in connective tissue content (Fig. 2). Finally, with age, the elastic fibers become calcified; this further restricts their extensibility.

285

AGE IN YEARS: 75

60 50 40

29

0

50

100

I50

200

PRESSURE mm Hg

Fig. 2. Pressure-diameter curves of thoracic aortas of humans, ages 29 to 85 years old. Reconstructed from Bader [7l.With age, aorta dllates in diameter stiffening elastin and recruiting collagen. This causes increased wall stiffness at progressively lower pressures (broken line). (From Dobrin [4] with permission of the publlsher.)

The arterial wall and hernodynarnics

Blood flow follows the hydraulic equivalent of Ohm’s Law AP Equation 6: F = R where F is flow, AP is the pressure gradient, and R is flow resistance. In a strict sense, blood flow follows the total energy gradient, i.e., the sum consists of both static and kinetic components. However because so little of the energy gradient is kinetic, blood flow may be said to follow the static or mean pressure gradient. This is given by

Equation 7: AP = Pa - Pb where AP is the mean pressure gradient, and Pa and Pb are pressures within the lumen at any points a and b along the length of a vessel, or in fact at any points a and b along the vascular tree. It is important to distinguish the pressure gradient (AP) given by Equation 7 from transmural pressure (PT) given by Equation 1. For example, when a patient with an ischemic lower extremity hangs his limb in a dependent position, gravity increases the pressure in both the arterial and Blood vessel walls also contain glycosaminoglycan venous fluid columns. Although the presence of comground substance. The electrolyte and water retaining petent venous valves may slow the rise of venous presproperties of this material may be of long term impor- sure, the pressure in the arteries and veins ultimately tance, however enzymatic degradation of ground sub- increases equally. As a result, there is no increase in pressure gradient (AP) to facilitate blood flow. Howstance demonstrates that this non-fibrous connective ever, transmural pressure (PT)is increased, depending tissue has little direct effect on wall mechanics. upon the height of the fluid columns and the distensibility of the vessels. Transmural pressure (PT) passively dilates all of the vasculature thereby decreasing

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flow resistance; this leads to an increase in blood flow and some relief of symptoms. There is a physiological price to be paid for this, for the increased transmural pressure (P,) drives fluid across the capillary walls causing tissue edema, ankle swelling, etc. Patients with ischemic limbs also get some relief of symptoms by periodically arising to walk a short distance. Contraction of the leg muscles pumps blood out of the veins, thereby lowering venous pressure. This increases the pressure gradient (AP) from the arteries to the veins, facilitating a modest increase in flow. It is unclear what exercise does to the resistance vessels in the ischemic limb since one might expect these vessels to be maximally dilated, even at rest. The above examples emphasize that P, and A P are not the same, and have quite different physiological effects. Mean arterial pressure falls only a few mm Hg as blood flows from the root of the aorta to the femoral region. This demonstrates that the large conduit arteries offer minimal resistance to mean flow. However the mechanical properties of the conduit arteries do influence some dynamic aspects of hemodynamics. The aorta is cylindrical over short distances, but tapers gradually and becomes progressively stiffer as one progresses from the root of the aorta to the iliac arteries. Because of these geometric and mechanical changes, the pulse pressure tends to increase in amplitude as the pulse travels down the length of the aorta. In addition, pressure waves are reflected from the peripheral vessels, and these add to the pulse arriving from the heart. This addition has a marked effect on pulse pressure, especially increasing systolic pressure. At the same time the dicrotic notch is gradually smoothed as the viscoelastic properties of the arterial tree attenuate high frequency components of the pressure pulse. Because of these changes the pressure wave at the femoral artery is quite different from that at the root of the aorta. This is illustrated in Figure 3. The femoral pressure wave exhibits a steeper rate of rise, a higher systolic pressure, a slightly lower mean pressure, and a more gradual contour than that observed at the root of the aorta. In some cases a new low frequency wave may appear late in diastole. This wave is thought to result from amplification of resonant frequencies by the arterial tree. Mechanical factors that transform the pressure pulse in vivo also can distort the pressure recorded by indwelling arterial catheters in patients. These monitoring systems can damp the pressure pulse. Damping of the pulse is inversely related to the cube of the radius of the indwelling catheter and connecting tubing [11. Therefore overdamping occurs when an artery is cannulated with a small caliber catheter, or when a lining of thrombus develops which narrows the lumen of an adequate size catheter. An overdamped system decreases the systolic pressure and may raise the diastolic pressure slightly. Thus overdamping decreases the

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recorded pulse pressure. It usually does not greatly attenuate mean pressure unless the lumen is severely narrowed. On the other hand, the method by which an indwelling catheter is connected to a remote transducer may cause underdamping of the recorded pulse. Use of a long segment of tubing to connect the indwelling catheter to a transducer permits the momentum of the fluid column oscillating back and forth in the tubing to introduce transient high frequency waves which add to the arterial pressure. This underdamped system increases the recorded systolic pressure, and may lower the recorded diastolic pressure. Thus underdamping tends to increase the recorded pulse pressures. All of these pressure recording problems are obviated by the use of catheter tip manometers, but these are much too costly to be used for routine monitoring of arterial pressure. Because the configuration of the pressure pulse is dependent on the cube of the vessel radius, the form and magnitude of the pressure wave also may be altered as it passes through stenotic areas. Regions of stenosis tend to decrease the pulse pressure and reduce the retrograde components of the flow curve. Pressure and flow velocity profiles also are decreased as blood passes preferentially through small caliber collateral vessels that bridge stenotic areas. However mean pressure usually is only slightly decreased unless the volume of blood delivered through the stenosis and by the small collateral vessels is markedly reduced. The large conduit arteries not only influence the form of the pressure wave, but also offer viscoelastic resistance to the oscillatory components of flow. This resistance to oscillations is termed impedance, and is calculated as the ratio of pulsatile pressure to pulsatile flow. This is computed at each corresponding harmonic frequency and is determined by performing Fourier analyses on both the pressure and flow pulses. Fourier analysis fractionates the complex pressure and flow curves into their constituent sine wave components at each harmonic frequency. Dividing the pressure component by the flow component at each comparable harmonic frequency gives the impedance. Such analysis shows that impedance rises gradually along the aorta with increasing distance from the heart. There also appears to be two discrete pressure reflection sites, one in the brachiocephalic area and another in the region of the iliadfemoral arteries [l]. Although the impedance of the systemic vascular bed is only about 5% of mean systemic resistance, pulmonary impedance may be much greater, and during sympathetic nervous system discharge may be as much as 30% of mean pulmonary resistance. Impedance imposes a dynamic load on the heart, but at present, its significance in causing cardiac pathology is unknown. Human data obtained in the cardiac catheterization laboratory demonstrate that the impedance

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190F

Fig. 3. Transformation of pressure and flow profiles with increasing distance from the heart. Pressure oscillations increase in amplitude while flow osciiiations decrease in amplitude with transmission. Discussion in text. (From McDonald [l] with permission of the publisher.)

of the systemic circulation is increased in humans with coarctation of the aorta, increasing age, and atherosclerosis. All of these conditions distend and therefore stiffen the walls of the large arteries. Pulmonary vascular impedance also increases with pulmonary hypertension. In experimental animals systemic impedance is increased by feeding them an atherogenic diet. Impedance decreases when the atherogenic diet is withdrawn and the disease regresses. Aneurysms

The development of atherosclerotic plaques causes the lumen of most vessels to narrow. In some cases this may progress to occlusion. Much less frequently vessels dilate and become aneurysmal. The walls of such arteries exhibit thinned, fragmented, overstretched elastic lamellae. Similar histologic changes are observed in arteries treated experimentally with elastase. Vessels so treated dilate markedly, but they do not rupture. By contrast, treatment with collagenase usually causes only slight vessel dilatation (Fig. 4), but predictably causes arterial rupture. Therefore it is evident that elastin provides arteries with their distensibility and plays an important role in maintaining vessels at normal dimensions, whereas that collagen provides arteries with their tensile strength [8]. In humans some arteries are more prone to become aneurysmal than others. For example the internal iliac artery becomes aneurysmal about ten times more frequently than does the adjacent external iliac artery [9].

This is consistent with the observation that enzymatic degradation of the internal iliac causes the vessel to undergo extreme dilatation (Fig. 5 ) and rapid rupture. However to my knowledge, no biochemical or histomechanical data are available to explain the increased susceptibility of the internal iliac artery to become aneurysmal. The pathogenesis of clinical aneurysms is controversial. Aneurysms often are observed to contain atherosclerotic lesions. However atherosclerosis afflicts many patients in the older age group that also develops aneurysms. Therefore it has been suggested that the presence of atherosclerosis may be incidental [lo]. Moreover patients with aneurysmal disease appear to be a distinctly different population than those with atherosclerotic occlusive disease. These two groups develop clinical symptoms of their respective diseases at different ages and they exhibit different long-term clinical courses [lo]. In addition there is a familial tendency to develop aneurysmal disease suggesting the possibility of a genetic mechanism [ll]. In fact, some patients exhibit a generalized arteriomegaly, and are predisposed to develop aneurysms in multiple vessels. Mechanical factors may play a role in the development of aneurysms. In humans the abdominal aorta is the largest systemic artery. It is exposed to the large pulse pressures due to wave transmission and pressure reflection. Because of its large size and the high peak systolic pressure, it is subject to high oscillating distending forces (Equation 2). Therefore it requires considerable wall stress to maintain equilib-

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N=lS N='8

COLLAOENASE 0.8 O . 1

N=rs ELASTASE COLLAQENASE

050

CONTROL

I-Y X w 0 40

PRESSURE rnrn Hg

Fig. 4. Pressure-diameter curves for 56 dog carotid arteries under control conditions and after treatment with elastase or collagenase. Elastase-treated vessels dilated aneurysmally and become stiffer as collagen was recruited. These vessels did not rupture. Collagenase-treatedvessels dilated slightly and ail ruptured. Similar responses were found for human external iliac arteries. (From [8] with permisston of the publisher.)

rium (Equation 3), and yet it has fewer elastic lamellae and fewer vasa vasorum per wall thickness than do many other arteries. The role of each of these factors is uncertain. For example, occlusion of the vasa vasorum in the aortic wall of experimental animals produces medial necrosis but does not cause the development of aneurysms. It also has been suggested that endogenous elastases and collagenases may play a role in the development or progression of human aneurysms, and it has been noted that collagenase activity correlates with the size of the aneurysm [12]. Although the activity of these enzymes is increased in the presence of aneurysms, it is unclear whether this enzymatic activity is the cause or the result of dilatation of the aneurysmal vessel. Recently it has been demonstrated that mechanicallyinduced, aneurysm-like poststenotic dilatation also is accompanied by increased collagenase activity [ 131. This suggests that the increased enzymatic activity is the result, and not the cause, of aneurysms. It is evident therefore that the etiology of aneurysms remains unclear. A fascinating problem with respect to the course of aneurysms concerns the fact that they usually enlarge gradually rather than dilate suddenly to rupture. This is difficult to explain for the distending force is Fig. 5. Pressure-diameter curves for human internal iliac arteries. Responses to elastase and collagenase directly related to vessel diameter (Equation 2). Therewere extreme. (From [8] with permission of the pub- fore one must explain how a vessel wall which could lisher.) not generate sufficient retractive force to maintain

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equilibrium at normal dimensions (Equation 3) can provide even more retractive force at larger dimensions where the distending force is much greater. There are both structural and geometric answers to this question. The structural explanation is that dilatation of the arterial wall recruits previously unstretched collagen fibers. As a result, aneurysmally dilated arteries actually are stiffer than normal vessels [8,14]. Of course, new collagen fibers may be laid down in the highly stressed wall as well. The geometric explanation rests on the fact that aneurysms change shape as well as increase in diameter. A normal artery is cylindrical in shape, whereas aneurysms tend to assume a somewhat spherical shape with a neck at each end. Because of the extra curvature in a sphere the wall stress required to maintain equilibrium is reduced. The wall stress for a cylinder is given by Equation 4, while that for a sphere is given by

Equation 8: a,,, = P, x

Cylinder:

u = PT x ri

h

1.

1

2 th

Comparing Equations 4 and 8 shows that the change in shape of an artery to a more spherical configuration reduces the wall stress required to maintain equilibrium by about one half (Fig. 6). However in spite of these structural and geometric advantages, the pathogenic process usually continues, and dilatation of aneurysms progresses with further thinning of the wall. This ultimately leads to rupture. It can be demonstrated arteriographically that the lumen of aneurysms usually is maintained at normal dimensions by a layer of laminated thrombus. However the presence of this material does not mechanically stabilize the wall. First, the thrombus readily transmits the transmural pressure to the wall; therefore it acts as a solidified layer of blood and does not reduce the distending force (Equation 2). At the same time the thrombus is so friable and poorly bonded to the wall that it exerts little if any retractive force (Equation 3). Therefore, although the presence of the thrombus along the margin of the lumen provides a more or less uniform diameter lumen for flow, it contributes little if any mechanical benefit. Another characteristic of aneurysms is their propensity to elongate and become tortuous. The mechanics of aneurysmal tortuosity are discussed in detail below in the section entitled Longitudinal Direction. The critical question regarding aneurysms remains: why do they develop? The data cited above suggest that it is failure of elastin, not collagen, which causes them to form, whereas failure of collagen causes them to rupture. Histologic examination of aneurysms discloses decreased numbers of intact elastic lamellae in the vessel wall, and mechanical analysis suggests that the load in aneurysmal vessels is shifted to collagen (Fig. 4). However, few collagen fibers actually are oriented to bear load. In fact, it has been estimated that only 6.8% of collagen fibers in the normal, intact wall

Sphere:

T x Jr 2h

u = P

Fig. 6. Change in configuration from cylindrical artery to spherical aneurysm reduces wall stress by about one half. (From (81 with permission of the publisher.)

actually are load-bearing [8].It is of interest to note that aneurysms develop in patients that are, on the average, about ten years older than those who develop occlusive disease [lo].All of these observations suggest that failure of reparative processes may cause the formation of aneurysms. Once the load is shifted to collagen, the wall becomes extremely stiff (Fig. 4), depriving the smooth muscle cells of pulsatile motion, a factor known to stimulate the synthesis of elastin and collagen [15].Once these mechanisms have been set in place further degeneration of the wall often appears to be inevitable. Poststenotic dilatation

Aneurysm-like dilatation may occur in vessels just distal to stenoses. This is termed poststenotic dilatation. Radiographic studies show that the length of a dilated poststenotic segment is directly related to the severity of the stenosis. In the past, hemodynamic forces such as jet streams emerging from the lumen of a stenosis were thought to cause poststenotic dilatation. Although such hemodynamic forces may be a factor, mechanical vibrations also have been shown to

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play an important etiologic role [ 171. Animal studies show that poststenotic dilatation develops when an experimental stenosis is tight enough to produce a bruit, but that a stenosis does not develop if a bruit is absent.

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data to actually support most of these presumed benefits. In the case of biodegradable grafts, compliant materials have been shown to stimulate the regeneration of elastic lamellae [19]. Of all graft materials examined, autogenous veins are among the most compliant, but this is true only at pressures between 0 and 50 mm Hg [20]. At arterial pressures veins and vein grafts are extremely stiff and, in fact, are much stiffer than normal arteries (See Fig. 1).

When a bruit is present, poststenotic dilatation usually may appear as early as 24 hours, enlarges, and may achieve stable dimensions in as few as ten days. If the stenosis is surgically corrected and the bruit is removed, then the dilated poststenotic segment usually Veins used as bypass grafts develop intimal hyperregresses quite rapidly, in some cases in as little as ten plasia and medial thickening. In some cases intimal days. However the most persuasive evidence that hyperplasia can proceed to the point where it leads to mechanical vibrations cause poststenotic dilatation graft thrombosis. Experimental studies have demoncomes from in vitro studies. Vibration of isolated strated that mechanical injury induced during harvest, human arteries mounted in a chamber produces distention, and preparation of the vein plays an poststenotic-like dilatation, even if there is no blood important role in causing intimal hyperplasia [211. flowing through the lumen of the vessel [17]. This However, even if the vein is meticulously prepared, indicates that vibrating motion itself has a direct effect intimal hyperplasia still develops to some extent. In on the structural elements in the wall. The frequencies this case intimal hyperplasia in vein grafts correlates of vibration which produce dilatation increase with with low flow velocity and low shear stress at the patient age; this correlates with the increasing collagen blood-intima interface [22,23]. content and rising stiffness of the wall that occurs with This correlation of flow characteristics with histoaging. Mechanical analysis of vessels that have underlogic changes correlates with several experimental and gone poststenotic dilatation points to alterations in the clinical observations. Intimal hyperplasia occurs more properties of elastin [16]. However, the rapidity with exuberantly in end-to-side grafts than in end-to-end which dilatation appears and regresses suggests that grafts [23]; this may result from the fact that the crossalterations in smooth muscle tone also may be imporsectional area of the lumen is greater in an end-to-side tant. Because of the demonstrated role of arterial anastomosis than in an end-to-end anastomosis. vibrations in producing arterial dilatation, it may be Because of this, the flow velocity is lower through endsuggested that vibrations also may contribute to the to-side anastomoses and is inversely related to square formation of aneurysms. of the effective radius. For another example, when used for coronary artery bypass, saphenous vein grafts have a lower 10-year patency rate than do internal Vascular grafts mammary artery grafts. The saphenous veins are In the past few years a great deal of attention has larger and may be expected to have about one third the been directed to the chemical and mechanical proper- flow velocity of the mammary artery grafts [20]. ties of conduits used for bypass grafts. One clinical Although other factors also may be important in the study showed a linear correlation between mechanical preceding examples, it is apparent that flow velocity compliance and the two year patency rate of grafts and shear stress may play important roles in the devel[18]. The relative compliance of the grafts was: host opment and distribution of intimal hyperplasia. artery > saphenous vein > umbilical vein > bovine On the other hand, thickening of the media correheterograft > Dacron > PTFE (Gore-Tex). However lates with circumferential deformation; it is not related the grafts examined differ in many ways other than to flow, shear stress, or deformations in other direcjust compliance characteristics. They differ with tions [24]. Moreover, medial thickening is independent respect to the anatomic location placed, diameter, of intimal hyperplasia [23]. This agrees with experiflow rate, porosity, thrombogenicity of their intimal mental studies which have shown that oscillating surfaces, and the extent to which the grafts are incordeformation of vascular muscle cells in vitro stimuporated into the surrounding connective tissues. Each lates them to synthesize elastin and collagen [15], and of these properties is known to influence patency the fact that smooth muscle cells in intact vessels are rates. Graft compliance also may be important at oriented predominantly in the circumferential direcanastomoses. Inequality of vessel motion resulting tion. This explanation is consistent with the thickening from unequal compliance of the graft, and the native of the media observed in veins dilated by arterial presartery can cause extreme stress concentrations at the sures, and the thickening of the media observed in suture line. This may cause the suture to shear gradu- arteries exposed to hypertensive arterial pressures. ally through the vessel wall. Other presumed benefits An unresolved issue regarding grafts concerns that of compliant grafts is that they maintain a normal pulse configuration, provide greater blood flow, and of ideal graft compliance. Possibilities include: 1) high cause decreased platelet injury. However there is little compliance, 2) normal vein compliance, 3) compliance

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which matches as closely as possible that of the native arteries, 4) low compliance, i.e., stiff grafts. One popular concept is that of “matched compliance”, ie., equivalence of compliance of graft and native arteries. This problem is made complex by the fact that veins are extremely stiff when distended by arterial pressures, and that the arteries to which veins are anastomosed may be compliant if they are normal, or may be quite stiff if they are diseased. This important question of ideal graft compliance remains to be answered.

29 1

Vascular muscle also may be stimulated to contract in response to extension (myogenic contraction) or in response to mechanical vibrations, and there is evidence that vibrations 50 Hz in frequency and 500 pm in amplitude temporarily elicit increased pharmacologic sensitivity to vasoactive agents [26]. Such increased sensitivity may be the mechanism of digital vasoconstriction seen in patients who operate pneumatic hammers and chain saws.

Contracted arteries

Smooth muscle cells represent the majority of living cells in blood vessel walls. These cells are oriented circumferentially in most vessels. When excited they develop active contractile stress slowly, but once contracted, are as strong as skeletal muscle [3]. It is worthwhile to consider the consequences of active muscle contraction. According to Poiseuille’s Law, resistance to flow is inversely related to the fourth power of the vessel radius. Because of the large diameter of the relaxed conduit arteries, these vessels offer little resistance to flow. Indeed, it is well recognized clinically that even 50% narrowing of a conduit vessel usually has negligible effect on resistance. Because of the relatively few muscle cells in their walls, active contraction of the conduit arteries produces little decrease in diameter and has a negligible effect on blood flow. On the other hand, the arterioles are very small and, even when relaxed, are the site of most flow resistance. There are many smooth muscle cells in their walls, and active constriction of arterioles can have a significant effect on resistance. For example, active contraction of an arteriole to 1/3 of its original diameter increases flow resistance 81 fold. It is evident therefore that active muscular contraction of the small resistance vessels, but not the conduit arteries, can have a significant effect on the redistribution of blood flow. Vascular smooth muscle usually contracts under sympathetic nervous system control, but it can also undergo intense focal contraction or “spasm”. Although uncommon, spasm is of great clinical significance when it occurs in small distributing vessels. When spasm occurs in the cerebral circulation it can have profound, life-threatening neurologic consequences. When spasm occurs in the coronary arteries it may cause “Prinzmetal‘s angina”. This usually occurs adjacent to an atherosclerotic plaque and may result from 1) an abnormality or injury to the intima with the loss of the endogenous vasodilators normally released by the endothelial cells, 2) increased local concentrations of vasoactive agents due to proliferation of the vasa vasorum in the vessel wall near atherosclerotic plaques [25], or 3) increased sensitivity of smooth muscle cells.

Hypertension

Chronic high blood pressure is one of the more common afflictions in modern society. Both experimental data and clinical observations demonstrate that hypertension is associated with increased peripheral flow resistance suggesting that systemic hypertension is largely a disease of the small resistance vessels. Both the total number of muscle cells present in the media, as well as the cross-sectional area occupied by the media in the resistance vessels are increased. This results in increased contractile force by the vessel wall. Indeed, experimental studies show that constriction of the resistance vessels can elevate arterial pressure 34 mm Hg more in hypertensive animals than in normotensive animals [27]. With hypertension the vascular muscle also exhibits altered pharmacologic sensitivity to vasoactive agents. The muscle in these vessels exhibits incomplete relaxation and spontaneous contractions, two characteristics rarely seen in the arteries of normotensive animals. Incomplete relaxation and spontaneous contractions both can cause increased flow resistance. These abnormal contractile characteristics result from decreased binding of calcium by the muscle cell plasma membrane, an observation that provides a rationale for the clinical use of calcium channel blocking agents to treat hypertension and control vascular spasm. Changes occur in the conduit arteries of hypertensive subjects as well as in the resistance vessels. The large arteries exhibit thickening of the media, increased connective tissue content, and increased resistance to distention. This increased wall stiffness also tends to raise arterial pressure. The histological and mechanical changes seen in the conduit arteries are not observed in vessels protected from elevated arterial pressure in hypertensive animals. This suggests that they occur as a result of exposure to the elevated pressures. With pharmacological lowering of arterial pressure in female subjects, the increased connective tissue content of the vessel wall observed with hypertension largely reverts to normal. In males reversal is incomplete [28].

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292

LONGITUDINAL DIRECTION Normal arteries

During each cardiac cycle the descending thoracic aorta lengthens about one percent; at the same time the abdominal aorta shortens by an equivalent amount [2]. In contrast to these small values, during each cardiac cycle, the ascending thoracic aorta and pulmonary arteries extend 5-10070 [2]. However these large values do not result from the oscillating pressure; instead they are caused by overall movement of the heart. Most conduit arteries are like the abdominal aorta, ie., they exhibit negligible changes in length during each pressure cycle. In spite.of the fact that conduit arteries exhibit negligible changes in length in response to alterations in pressure, they do change length with alterations in body position. This is seen with hyperextension of the cervical spine or extension of the knee joint. This demonstrates that the conduit arteries are stretched by traction, and is evidenced by the fact that vessels retract when they are transsected. Traction results from the pull exerted by branch vessels and perivascular connective tissues. These elements not only hold vessels, but also stretch them. Traction is low in the newborn, increases during the neonatal period as the body grows more rapidly than the vessels [29], reaches a maximum in the adult, then decreases with age [3]. Tortuosity

When arteries are forced to lengthen excessively they may buckle between constraining branches and become tortuous. One may ask then what causes a vessel to lengthen excessively. In order to understand this it is necessary to consider the forces acting on a vessel in the longitudinal direction. There are two forces that cause a vessel to lengthen, and one retractive force which opposes lengthening. These forces are depicted in Figure 7. The first lengthening force is that due to traction (FT).This is exerted by side branches and perivascular connective tissues, and keeps vessels stretched. The traction force cannot be computed analytically, but must be determined by experiment. The second lengthening force is due to pressure pushing the vessel to greater lengths from within (F,). As shown by the top diagram of Figure 7, the force due to pressure (Fp) is given by the product of pressure, pi, and radius squared. The middle diagram of Figure 7 shows that the forces due to traction (F,) and pressure (F,) add to give the net force lengthening the vessel (F,). Figure 8 shows in detail the addition of pressure and traction forces in an artery that is pressurized while held by traction at in situ length. In the unpressurized artery, all the longitudinal force is due to traction. As

a

Fig. 7. Lon ltudlnal forces actln on an artery In vivo (From [a01 b l t h permission of t e publisher.). Top: Forces due to traction (F,) and pressure (Fp) tend to elongate vessel. M/dd/e: Forces due to traction (FT) and pressure (Fp) add to give net longltudlnal force extending the vessel (Fd. Bottom: Net force (FJ Is opposed by retractive force (FR) exerted by the stretched wall. At equlllbrlum F, = FR, and the vessel exhibits a stable length.

the pressure is increased the force due to pressure (Fp) rises and the vessel extends very slightly; this causes the traction force to fall. As a result, the algebraic sum of F T and F,, the net longitudinal force (F,), remains nearly constant until very high pressures are encountered. Therefore the vessel is subject to almost constant longitudinal force over a wide range of physiological pressures. This explains why vessels exhibit nearly constant length in vivo even when exposed to a wide range of pressures. The extended vessel generates a retractive force (F,), just as a stretched spring tends to snap back with a retractive force. As shown in the bottom diagram of Figure 7, this retractive force (FR) opposes the net force lengthening the vessel (F,). As long as these forces, F, and F,, are in equilibrium, the vessel will remain at an extended, but virtually constant length. What then causes a non-equilibrium condition to

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rysms become tortuous because of both increased force due to pressure (IF,) and decreased retractive force that accompanies failure of elastin (IFR).

0 3.0X

Longltudlnal shear stress

W'

Y

a 0'c' % J

Another source of longitudinal force is that which results from the flow of blood over the endothelial surface, i.e., blood-intima shear stress. Although this is negligible in magnitude compared with the forces due to traction and pressure, shear stress is important for maintaining normal endothelial morphology.

l.51.00.5-

o 60

120

180

240

2

300

PRESSURE m m Hg

Fig. 8. Lon ltudlnal forces for an artery that Is pressurized whfe held at In situ length. As pressure Is Increased force due to pressure (F ) Increases and force due to traction (FT) declines. The sum of Fp and FT give net longltudlnal force (FJ. Data show F, remains nearly constant until high pressures are encountered. Therefore vessel Is subjected to nearly constant longitudlnal force leading to relatively unchanging length. (Reconstructed from data of Dobrln and Doyle [32].Wlth permlsslon of the Amerlcan Heart Assoclatlon.)

develop wherein excessive vessel lengthening occurs? This develops when the balance of forces described above is disturbed. It occurs with several common clinical conditions. It is seen in aged, hypertensive patients, and often is evident in the superficial temporal artery. Hypertension is associated with increased force due to pressure (IF,), while age is associated with decreased retractive force (1FR) as the aging vessel loses its elasticity. As a result the normal equilibrium between F, and F R is disturbed. It is for this reason that tortuosity is so often seen in aged, hypertensive patients. Longitudinal retractive force (FR) is provided almost entirely by the wall elastin [30]. Therefore disruption of the elastic lamellae may be expected to result in the development of vessel lengthening. This is precisely the defect found in the vessel walls of patients with congenital kinking of arteries. Excessive lengthening also is seen with aneurysms and ectatic arteries. These vessels dilate chiefly because of disrupted elastic lamellae. As noted above [30], elastin also is the chief source of the longitudinal retractive force (FR) exerted by the wall. Therefore the aneurysmal vessel offers decreased retractive force (IFR). Because the force due to pressure (F,) varies with the square of the vessel radius, this force is greatly increased in aneurysms and ectatic vessels. For example, F, is increased 16-fold in an 8 cm aneurysm as compared with a normal 2 cm aorta. Thus aneu-

Endothelial cells exposed to usual shear stresses exhibit a mildly elongated configuration. However where flow is turbulent and shear stress is disturbed, the cells exhibit a more cuboidal shape. Although extremely high shear stresses can injure the endothelium, a moderate level of steady shear seems necessary for a normal single layer endothelium. Low shear rates are associated with the development of intimal hyperplasia in vein grafts [24], and the acceleration of atherosclerosis [31]. Both observations suggest that moderate flow velocity with its accompanying shear stress prevents the adherence of platelets, leukocytes. and atherogenic material. Platelets and leukocytes are known to release growth factors which facilitate the proliferation of endothelial cells.

RADIAL DIRECTION Pressure in the artery lumen exerts a stress directed radially outward against the intima and across the vessel wall. This stress is greatest at the intima where it is equivalent to blood pressure; it declines in a curvilinear fashion to vanish at the outer margin of the vessel. Although radial stress is only 5-10% of the tensile stresses in the circumferential and longitudinal directions, radial stress is compressive. Therefore it squeezes intramural structures, especially those in the inner third or inner half of the wall. It is of interest that, in thick-walled arteries, vasa vasorum are found in the outer regions of the wall, but are not normally found in the inner third or inner half of the wall. From a mechanical perspective it is likely that any vasa located in the inner regions would be occluded by the surrounding compressive forces. However vasa vasorum are found in the inner regions when there is a subendothelial atherosclerotic plaque. This suggests that the plaque may act as a stressbearing member, protecting the vasa vasorum from excessive compression. This is comparable to the role of steel rods embedded in concrete in the construction of highway roadbeds. In any case the proliferation of vasa vasorum surrounding an atherosclerotic plaque may increase the quantity of vasoconstrictor agents delivered to the vascular muscle. It has been suggested

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that this may be a mechanism of Prinzmetal's angina

PI.

17. 18.

REFERENCES

19.

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