Vascular Fluid Mechanics, the Arterial Wall, and Atherosclerosis

R. M. Nerem School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405 Fellow ASME.

Atherosclerosis, a disease of large- and medium-size arteries, is the chief cause of death in the United States and in most of the western world. Severe atherosclerosis interferes with blood flow; however, even in the early stages of the disease, i.e. during atherogenesis, there is believed to be an important relationship between the disease processes and the characteristics of the blood flow in the arteries. Atherogenesis involves complex cascades of interactions among many factors. Included in this are fluid mechanical factors which are believed to be a cause of the highly focal nature of the disease. From in vivo studies, there is evidence of hemodynamic influences on the endothelium, on intimal thickening, and on monocyte recruitment. In addition, cell culture studies have demonstrated the important effect of a cell's mechanical environment on structure and function. Most of this evidence is for the endothelial cell, which is believed to be a key mediator of any hemodynamic effect, and it is now well documented that cultured endothelial monolayers, in response to a fluid flow-imposed laminar shear stress, undergo a variety of changes in structure and function. In spite of the progress in recent years, there are many areas in which further work will provide important new information. One of these is in the engineering of the cell culture environment so as to make it more physiologic. Animal studies also are essential in our efforts to understand atherogenesis, and it is clear that we need better information on the pattern of the disease and its temporal development in humans and animal models, as well as the specific underlying biologic events. Complementary to this will be in vitro model studies of arterial fluid mechanics. In addition, one can foresee an increasing role for computer modelling in our efforts to understand the pathophysiology of the atherogenic process. This includes not only computational fluid mechanics, but also modelling the pathobiologic processes taking place within the arterial wall. A key to the atherogenic process may reside in understanding how hemodynamics influences not only intimal smooth muscle cell proliferation, but also the recruitment of the monocyte/macrophage and the formation of foam cells. Finally, it will be necessary to begin to integrate our knowledge of cellular phenomena into a description of the biologic processes within the arterial wall and then to integrate this into a picture of the disease process itself.

Introduction Atherosclerosis, a disease of large- and medium-size arteries, is the chief cause of death in the United States and in most of the western world. Severe atherosclerosis interferes with blood flow; this is particularly important for the heart and brain, with the result being myocardial or cerebral ischemia or even a myocardial infarction or stroke. However, even in the early stages of the disease, there is believed to be an important relationship between the disease processes and the characteristics of the blood flow in the arteries. Atherogenesis, i.e. the initiation of atherosclerosis, starts virtually at birth, and the total disease process is characterized by a time constant on the order of decades. There have been many excellent reviews of what we know about this disease and its evolution, e.g., see references [1-7]. Unfortunately, Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERINO. Manuscript received by the Bioengineering Division December 5, 1991.

although studies have provided us with an assessment of some of the various risk factors which are important, such information simply provides us with correlates of disease occurrence and does not tell us about cause and effect. Thus there are many questions relating to the mechanisms and processes involved which are still unanswered. What we do know is that the disease basically involves complex cascades of interactions among: (i) environmental and genetic factors; (ii) the endogenous cells of the arterial wall, notably endothelial and smooth muscle cells; (iii) formed elements of blood, particularly monocytes and platelets; (iv) plasma proteins, including low density lipoproteins (LDL); and (v) connective tissue elements of the arterial intima. What we also know is that the disease is focal in nature [8, 9], and the results from the PDAY (Pathologic Determinants of Atherosclerosis in Youth) study [10] indicate that the disease pattern is unchanged for subpopulations corresponding to specific risk factors [11]. This suggests that the pattern may be at least in

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part due to hemodynamic-related factors, which by their very nature would have a localizing influence. Thus to the above list we add fluid mechanical factors. These not only are the possible cause of the highly focal nature of the disease [1216], but have led to the concept of geometric risk factors [1719]. The possible role of hemodynamics or fluid mechanics in atherosclerosis has motivated much of the work in cardiovascular mechanics over the past twenty-five years. This brief review will focus on these fluid mechanical factors, i.e. on the influence of hemodynamics, and related factors on the biology of the arterial wall and on the pathobiologic mechanisms involved in the disease process. This will be done by first looking at the arterial wall itself, then at the fluid mechanics of the vascular system, and finally at the endothelium, that cellular monolayer which is the interface between flowing blood and the underlying vessel wall. Although the endothelial cell is only one of the cellular participants in the process of atherosclerotic disease, as the inner lining of the arterial wall it is uniquely positioned to serve as a mediator of hemodynamic or fluid mechanical effects. The Arterial Wall For a large artery, the vessel wall is composed of three distinct layers, an intima, a media, and an adventia. Each of these have their own unique function; however, during the initiation of atherosclerosis, it is the first two that are of most interest, i.e., the intima and the media. Under normal conditions, the intima is composed of little more than the endothelial monolayer and a basement membrane, and the media is composed of vascular smooth muscle cells together with extracellular matrix, primarily collagen and elastin. However, with the onset of the disease process, i.e., during atherogenesis, there are some remarkable changes which take place. These changes initially are focused within the intima and the cellular participants include the vascular endothelial cell, the vascular smooth muscle cell, and the peripheral blood monocyte. Of course, as already noted, the vascular endothelial cell normally resides within intima, and during the early stage of disease the endothelium remains intact. This is not to say that the endothelium is unchanged; on the contrary, this dynamic monolayer in vascular regions with a high predilection for disease exhibits significantly altered properties. Using the pig model, it has been demonstrated that lesion-prone regions, as identified by the incorporation of Evans blue dye, exhibit a thinner endothelial glycocalyx, enhanced permeability and/ or accumulation of albumin, fibrinogen, and LDL, increased monocyte recruitment, and higher endothelial cell turnover rates in comparison to the nonlesion prone, white or unstained regions [20, 21]. It should be noted the blue stained, lesionprone regions were characterized by more polygonally-shaped endothelial cells, while the white regions were populated by highly elongated endothelial cells. This suggests differences in the hemodynamic environment, and as will be discussed later, the difference in biologic function of the endothelium is believed to be due to this differing influence of hemodynamics. A key characteristic of lesion-prone regions is the thickening of the intima which occurs. The degree of intimal thickening has been found to correlate with measures of the hemodynamic environment [13-15, 22], and this thus provides an additional piece of evidence as to the important role of hemodynamics in the disease process. This thickening of the intima is due to the migration and proliferation of vascular smooth muscle cells, emanating from the vessel media [1, 2, 7]. Associated with this is a change in smooth muscle cell phenotype from one contractile in nature to a synthetic type [23], and there is also an alteration in extracellular matrix. Although this intimal thickening is an important part of the atherogenic process, not all thickening of the intima leads to lesion formation [24]. Journal of Biomechanical Engineering

Thus, it may be a necessary condition, but not a sufficient one. A third cellular participant in the changes within the arterial wall which take place is the peripheral blood monocyte. This formed element of blood is recruited to the arterial wall, and there is evidence suggesting that this recruitment is influenced by hemodynamic environment, with more cells being adherent in Evans blue stained, lesion-prone regions [21]. Once adherent, the monocyte migrates through the endothelium into the intima and becomes an activated macrophage. There are many possible roles for the macrophage within the blood vessel wall [25]. It of course is a part of the immune response system, and it is a phagocytic scavenger. However, it also can secrete mitogens and chemoattractant factors, participate in the generation of reactive oxygen species, and synthesize a number of other biologically active substances. When one adds lipid to this vessel wall "cocktail", e.g., through transport of low density lipoproteins from the blood and across the endothelium, then one has the apparent ingredients which lead to the formation of fatty streaks and lesions. A particular important step is the modification of LDL, e.g., its oxidation, perhaps by the endothelium [3, 5]. In this form it is taken up by the scavenger receptor of the macrophage, resulting in the formation of a foam cell. This in fact may be the normal, phagocytic role of a macrophage; however, it appears that at some point in the process the macrophage/ foam cells become overwhelmed. Perhaps this modified LDL is cytotoxic [26]; whatever the case, there is a breakdown which results in an increasing amount of extracellular lipid and the development of what is known as a fatty streak. This is an early stage in the disease process, but an extremely important one. The additional ingredient of the disease process being focused on here is the hemodynamic environment of the vessel wall. There certainly are few who believe that hemodynamics is directly causative of atherosclerosis, and there is some question as to whether hemodynamics factors even are a necessary part of the "cocktail" mix. What is increasingly accepted is that hemodynamics is a factor which modulates the environment and as such can enhance the predilection for disease in localized regions. Some insight into how this may take place can be gained by recognizing the influence of hemodynamics on the environment in which each of the major cellular participants resides. The endothelial cell, once thought to be a passive, nonthrombogenic barrier, is now recognized as being a dynamic participant [27], capable of being activated and of synthesizing a variety of proteins. At the blood-arterial wall interface, it is acted on directly by the hemodynamic stress imposed by flowing blood. This stress has two components, a normal component, pressure, and a tangential component, shear stress. The pressure is pulsatile, and the endothelial cell both "sees" the pressure directly and "rides" on a basement membrane being cyclically stretched. The endothelial cell also "sees" the wall shear stress associated with the pulsatile flow, and although this stress is order of magnitudes smaller than that due to the pressure, it has received much, some say perhaps even too much, of the attention. As will seen later, endothelial biology has been demonstrated to be influenced by shear stress [28], and we already have noted in vivo investigations which have correlated intimal thickening with a hemodynamic environment characterized by low shear [13-15, 22]. However, whether this is due to low shear stress acting on the endothelial cell, some other feature of a low shear environment, or even setae factor unrelated to shear cannot be said. The vascular smooth muscle cell resides within the vessel wall, normally within the media, but invades the intima as part of the intimal thickening process [1, 2, 7, 24]. Its role in atherogenesis is one involving intimal migration and proliferation [29], and as noted earlier, associated with this may be a phenAUGUST 1992, Vol. 114/275

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otypic change [23, 30]. An alternative explanation is that smooth muscle cell proliferation and arterial remodeling might be the result of a subpopulation of smooth muscle cells with special properties [31]. Smooth muscle cells also synthesize extracellular matrix components [32] and other mediators, e.g., the monocyte-specific chemoattractant, MCP-1 [33]. Since in the early stages of disease the endothelium is intact, then the smooth muscle cell does not see flow directly. Its hemodynamically-induced environment is that due to the cyclic stretching of the arterial wall as the pressure pulses, and in addition there is an indirect hemodynamic effect due to the communication between endothelial and smooth muscle cells [34, 35]. Cell culture studies provide supporting evidence of a cyclic stretch effect on smooth muscle cell function [36-39], and there also is a school of thought which correlates regions of increased predilection for disease with enhanced internal wall stresses [40, 41]. Although this author believes that such stresses must influence smooth muscle cell function and its participation in the disease process, it equally well must be said that the evidence to date is too limited to draw any firm conclusions. The monocyte/macrophage is a major participant in the disease process [25], and it experiences an interesting series of hemodynamic environments. The word "series" is used because in going from a monocyte being carried by flowing blood to a foam cell within the vessel wall, it experiences at least three different types of hemodynamic environments. First, as a blood cell circulating through the vascular system, it sees the same type of hemodynamic or mechanical environment as any other blood cell, e.g., the erythrocyte or the platelet. Of course, we recognize that this environment will be different, depending on whether it is in the center of the blood stream or near the wall, where it may be in the process of adhering. Once adherent to the endothelium, then it resides in a different type of hemodynamic environment, one not unlike that seen by the endothelial cell, and as noted earlier, there is evidence of enhanced adherence of monocytes in Evans blue, lesion-prone regions as compared to white, nonlesion prone regions [21]. Finally, when it invades the intima and becomes a macrophage, it now resides within the vessel wall in an environment like that of the smooth muscle cell, i.e., a cyclic stretch environment. There is another member of the white cell family, which is a cellular participant. This is the T lymphocyte which is part of the body's immune response system and which, in addition to the monocyte/macrophage, has been found in human atherosclerotic lesions [42, 43]. Important in this is the role of cytokines, a group of hormone-like regulatory molecules secreted by T lymphocytes and macrophages, as well as endothelial and smooth muscle cells. Included in the cytokine family are the interleukins, and the function of cytokines ranges from the activation of macrophages to a chemoattractant role, e.g., MCP-1. Cytokines may also govern the interaction of endothelial cells with the coagulation system and thus with platelets [44]. The platelet in fact may have a significant role as a cellular participant. This is particularly true in the later stages where the endothelium is no longer intact; however, in this review the focus will be on atherogenesis, i.e., on the initiation of lesions. Whatever the case, all of these participating cell types reside in a hemodynamically-induced environment. Thus, in the next section we will look at the details of the dynamics of blood flow in the vascular system, i.e., at vascular fluid mechanics. Vascular Fluid Mechanics Studies designed to understand the dynamics of blood flow date back centuries. However, it is only in the last several decades, with the interest in hemodynamics as a localizing factor in atherosclerosis, that attention has been focused on the detailed characteristics of blood flow. During this time of 2 7 6 / V o l . 114, AUGUST 1992

25 years or more, much has been learned by fluid mechanicians turning their attention to the vascular system. Still, there is much left for future investigations. What do we know about the pulsatile flow occurring in the large, central arteries in which atherosclerosis develops? To start with we know that the nature of the flow is by and large laminar. For normal arteries, i.e., without any disfigurement due to disease, it is only in the aorta where conditions are such that turbulence could exist, and even there, in an adult, this only occurs at high flow rates, ones associated with exercise. Otherwise, what is observed is turbulent bursts at peak systole, with the energy of the turbulence decaying rapidly during the "backside" of systole as velocities decrease [45]. Once one leaves the aorta and proceeds into the next level of vessel, e.g., the carotids, the coronaries, and the femorals, then the Reynolds number is an order of magnitude less and flow is laminar throughout the entire cycle. Although atherosclerosis is observed in the aorta, it is in these somewhat smaller vessels where the consequences of the disease process are more importantly felt, and here the flow is clearly laminar. The only exception would be the very advanced stages of disease. Now even though the flow is laminar, it still is extremely complex in character [46]. This is demonstrated by the very elegant flow visualization studies of Karino and his co-workers [16, 47]. Not only is the flow pulsatile, but the velocity profiles are asymmetric in shape [48, 49]. This is associated with the complicated geometry of the "plumbing," and the result is that the wall shear stress is not only time varying, but also spatially varying. Examples of this are the aorta [50] and at the bifurcation of the left main coronary artery into the left anterior descending (LAD) and left circumflex (LCFX) coronary arteries where on the flow divider the shear stress will be relatively high, while on the outer lateral wall the shear stress will be low. Furthermore, this picture in the left main coronary bifurcation is compounded by the exact geometry of the bifurcation. For example, the shear stress distribution will depend on the turning angles of the daughter vessels [51]. Thus, depending on whether it is a symmetric bifurcation or one where the LAD is an extension of the left main with the LCFX a side branch, the velocity field and thus the associated wall shear stress can vary considerably [52]. Is this low shear region on the outer, lateral wall of a bifurcation a separated flow region? Although this is certainly a possibility, this is an unanswered question. The only part of the vascular system in which flow separation has been documented to occur is the carotid sinus bulb [53]. In a detailed experimental study of the local velocity field, the wall shear stress was calculated and then correlated with measurements of vessel wall pathology [14]. From this, intimal thickness was found to correlate inversely with low shear, but it equally well correlated with an oscillatory shear index, not surprising since low shear regions also are regions of pronounced oscillations and reversal in shear stress. Unfortunately, from such studies, important as they are, it is impossible to know whether or not it is low shear which is important or some other characteristic of the flow. This could be the oscillatory nature of the shear or something entirely different, e.g., the prolonged particle residence times associated with a separated flow region. Thus, denoting a localized region of the vasculature as low shear is simply a way of naming the region. It does not mean that low shear itself is the "culprit" in the disease process. Another important fluid mechanic phenomena which might be expected to occur in the large, central arteries is that of secondary flows. These are fluid motions which occur in a plane perpendicular to that of the distally directed blood flow and thus are secondary to the primary direction of motion. Such flows, in spite of at least several attempts, have never been measured successfully, although Caro and his co-workers have reported MRI results which show evidence of a secondary flow effect [54]. This is because of the extremely low velocities Transactions of the ASME

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associated with this phenomena, on the order of 1 cm/s. Perktold et al. [55], in a numerical study, calculated the secondary motions in a curved tube with a geometry and flow conditions selected to model the human left main coronary artery. Their results indicate that though the secondary velocities were too low to influence the general shape of the velocity profile, there was an important influence on the wall shear stress. There are at least two other phenomena important to our understanding of vascular fluid mechanics. One of these is the non-Newtonian nature of blood as a fluid. At moderate to high shear rates, blood will act as a Newtonian fluid; however, at low shear rates this will not necessarily be true. The low shear rates required for blood to behave in a non-Newtonian manner are found in large vessels in regions where one has a reversing pulsatile flow and/or flow separation. Ku and Liepsch have shown, using a non-Newtonian, viscoelastic fluid, that the location of separation regions can be dramatically altered as compared to what is observed for a Newtonian fluid [56]. However, the fluid they used was one with long chain polymers which does not completely simulate the rheological behavior of blood. Unfortunately, no one has proposed a fluid model which is better, except for the use of blood itself; and this is an area in which there is more to be done. Finally, the elastic properties of the arterial wall may also influence the detailed characteristics of blood flow. Although the important effect of wall elasticity, even viscoelasticity, on changes in waveform shape as the arterial pulse propagates down the aorta into the lower vascular bed has been demonstrated [57], most in vitro model studies of flow patterns have ignored this effect. This has been based on the assumption that the primary effect of wall properties is on the propagation of the pulse wave and thus on the shape of both the pressure and flow waveforms. If this in fact is true and if waveform shape is correctly simulated, then a rigid model of an arterial segment may be employed, and there are many who in fact feel that effects of wall elasticity on the flow field are small. The exception is low shear regions, although even here, as an example, the effect on the absolute magnitude of the wall shear stress is still small. There are some recent studies, however, which suggest that one must be very careful in the use of the above noted assumption [58-60], and this also is an area deserving of more attention. In concluding this section, it should be emphasized that, although the emphasis here is on hemodynamics and thus on vascular fluid mechanics, this is not in any way meant to minimize the importance of vessel wall mechanics. In fact, there still is much to be learned about the behavior of the arterial wall itself. This includes studies on the influence of structural inhomogeneities on the mechanical properties of blood vessels and on the interaction between microstructural constituents. As part of this and through a combined structural and vascular mechanics model, there will need to be investigations designed to define the microenvironment within the arterial wall, i.e., the stress-strain environment at a cellular level. The vascular smooth muscle cell is a principal participant in the early stages of atherogenesis, and as already noted, there are cell culture studies in which alterations in smooth muscle cell function have been demonstrated under conditions of cyclic stretch. However, it is important for such studies that the microenvironment of a smooth muscle cell residing within the arterial wall be better defined. Information from such investigations then can be integrated into a model which couples the mechanics of the arterial wall with the dynamics of blood flow.

endothelium which has received most of the attention of those interested in the role of hemodynamics in atherosclerosis. This, at least in part, is due to its strategic location, positioned between the flowing blood and the underlying vessel wall. As an interface, it might be a mediator of any blood-associated effects on vascular biology, including those due to hemodynamics. There is in fact considerable evidence for this. To start with and as a logical extension of the last section on vascular fluid mechanics, the endothelium serves as a natural aerodynamic 'tufting" of the arterial wall, with the orientation of the endothelial cells reflecting the direction of the flow in the immediate vicinity of the arterial wall [61-63]. Furthermore, if an aortic stenosis is introduced chronically, with a resulting change in the flow pattern, the shape and orientation of endothelial cells in this region have been observed to be altered according to the level of wall shear stress in the new flow environment [64]. Changes in actin microfilament localization [65] are also observed with the introduction of a chronic stenosis; here actin stress fibers are aligned with the direction of flow in high shear regions, while in low shear regions the actin is mostly present in dense peripheral bands. As noted earlier, using the pig model, previous studies have demonstrated that lesion-prone regions, as identified by the incorporation of Evans blue dye, exhibited a thinner glycocalyx, enhanced accumulation of albumin, fibrinogen, and LDL, increased monocyte recruitment, and increased cell turnover rates in comparison to the nonlesion prone, white or unstained regions [20], The lesion prone regions were characterized by polygonally-shaped endothelial cells suggestive of a low shear environment, while the nonlesion prone regions were populated by highly elongated endothelial cells indicative of a high shear environment. Furthermore, the degree of intimal thickening has been correlated with characteristics of the hemodynamic environment, with intimal thickening being greater in low shear regions [13-15, 22]. As important as such in vivo studies have been, they suffer from an inability to define quantitatively the exact features of the hemodynamic environment or of the cellular responses to that environment. This is particularly true of experiments where the biologic end-points represent changes taking place over a period of weeks. Thus, for such experiments one can only note comparative differences between regions qualitatively characterized as high shear and those denoted as low shear. Furthermore, one cannot say whether the effect noted is truly due to wall shear stress, or related to some other feature of the hemodynamic environment as noted previously. For this reason a number of laboratories in the last decade have turned to the use of in vitro cell culture systems to investigate the effect of flow on vascular endothelial biology [66-68]. Cell culture experiments represent a model in which one can study specific mechanisms involved in endothelial biologic responses under well defined flow conditions, ones which in fact more closely model the in vivo environment of endothelial cells. Most of the investigations of flow effects on cultured endothelial cells have focused on the effects of a steady laminar shear stress, and a number of laboratories have contributed to the development of our knowledge in this area. Taken together, these studies show that, for a confluent monolayer of cultured cells, the influence of an elevated shear stress .is to cause a significant alteration in endothelial cell structure and function. Specifically, there results: (i) an elongation in shape and an orientation of the cell's major axis with the direction of flow [66-69]; (ii) a rearrangement of the actin microfilaments into stress fibers aligned with the direction of flow [70-72], accompanied by a concomitant increase in cell stiffness [72]; (iii) an influence on endocytotic processes [7374], including the enhancement of the receptor-mediated bindThe Endothelium ing, internalization, and degradation of LDL [74]; and (iv) the Among the cellular components of the arterial wall, it is the increased expression of PGI2 and tPA [75-77]. In addition, Journal of Biomechanical Engineering

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for subconfluent monolayers, laminar shear stress has been shown to decrease the rate of cell replication [78]; this is in contrast to post-injury monolayer experiments where the influence of shear stress is to increase cell proliferation and migration [79]. Furthermore, there is some evidence that even a confluent monolayer subjected to shear stress will exhibit decreased cell turnover rates [80], and it is clear that this influence of shear stress is on both the intrinsic and extrinsic growth program of the endothelial cell [81, 82]. It should be emphasized that the effect of shear stress on endothelial cell function extends down to the gene expression level [81-84]. An example of this is the shear stress-induced inhibition in the expression of c-myc, a proto-oncogene, in response to the agonist, a-thrombin [82]. Finally, although most studies on the influence of shear stress on cultured vascular endothelial cells have been carried out for steady flow conditions, there are some reports of the use of simple pulsatile flows [73, 75, 78]. More recently Helmlinger et al. [85] have initiated a systematic investigation of pulsatile flows, comparing nonreversing, reversing, and purely oscillatory sinusoidal waveforms. These initial results suggest that there is much still to be learned about the response of vascular endothelial cells to flows which are more physiologically realistic. There are several important, unanswered questions. These include how does an endothelial cell recognize the flow environment in which it resides, and having done so, how does it transduce this signal into the changes in structure and function already noted? There have been a number of studies of the mechanisms involved in this signal recognition and transduction [86-93]. These initially have focused on the latter, i.e., the second messengers associated with the transduction of a flow signal. Such studies indicate that shear does stimulate the phosphoinositide system [86, 87], that there is an elevation in intracellular calcium [88-92], and that there is a translocation of protein kinase C from cytosol to membrane [93]. This all suggests that the second messengers known to be activated by chemical agonists also are stimulated by flow-induced stresses. However, how does an endothelial cell recognize the flow environment in which it resides? There are many possibilities [94]. These include mechanically-activated ion channels [95, 96], the shear rate control of the transport of a small molecule through convection-diffusion coupling [97], an effective "strain gauge" which senses deformation of the cell's cytoskeletal structure, and a "shear" receptor in the cell's membrane, perhaps a G protein [98, 99], but one which is shear sensitive. The issues of signal recognition and transduction are not ones confined to just the influence of shear stress. The endothelial cell, as noted earlier, 'sees' pressure and 'rides' a basement membrane which is being cyclically stretched just as the smooth muscle cell is. Studies on the influence of cyclic stretch indicate important alterations in morphology, cytoskeletal localization, proliferation, and prostacyclin synthesis [100-103]. Finally, other cell types also have been shown to respond to mechanical effects [36-39, 104, 105]. Thus, it appears that mammalian cells of all types respond to mechanical stresses, and the question as to how this recognition occurs is a general one. More than likely, there are multiple pathways which participate in both the recognition and transduction of mechanical signals. Returning to the influence of shear stress on the endothelium, a cartoon in an article written by Libby and Birinyi [106] showed both a "smiling" and a "frowning" endothelial cell. The "frowning" cell is one which is activated, procoagulant, and mitogen producing. The "smiling" one is the normal endothelial cell, nonthrombogenic and anticoagulant. Although perhaps too simplistic, it also may be that the "smiling" endothelial cell is one which resides in a flow environment, thus experiencing the pleasures of fluid dynamics, i.e., of vascular fluid mechanics. 2 7 8 / V o l . 114, AUGUST 1992

Discussion The initiation of atherosclerosis has been viewed by many as a response to injury, as perhaps wound healing gone wrong. Although as initially put forward the response was believed to be due to traumatic injury [1], either chemical or mechanical, it is now believed that any injury is of a much more subtle form. This is because of the fact that the endothelium remains intact during the early disease stages. This does not mean that the endothelial cell is functioning normally; its function may be abnormal. Of course it may be that the vascular endothelial cell is functioning within normal, physiologic limits, and that the abnormality is not the endothelial cell, but rather the environment in which it finds itself, one with which it cannot cope. This environment may include high plasma lipid levels; but it also includes a hemodynamic component, and it may well be, in fact it should be expected, that an endothelial cell in a low shear region, being different from an endothelial cell in a high shear region, handles whatever abnormalities it is presented differently from its high shear "cousin." Although this is perhaps speculative, what we do know is that the vascular endothelium is influenced by its hemodynamic environment and that, as stated before, it remains intact during the early stages in the development of lesions. What follows includes smooth muscle cell migration and proliferation leading to intimal thickening; as part of this alterations in extracellular matrix; the recruitment of monocytes, which then become activated macrophages; these then take up lipid, e.g., some modified, perhaps oxidized form of LDL, and this leads to the formation of foam cells; and these in turn become overwhelmed by this lipid, resulting in the presence of significant amounts of extracellular lipid [7]. Smooth muscle cell proliferation is a key event in the development of lesions, and a number of investigators have attempted to study this experimentally. One model has involved the use of a balloon catheter to produce total endothelial denudation; however, as Reidy and Jackson [107] have discussed, such traumatic damage to the arterial wall, in which the media also is injured, does not simulate the intimal thickening associated with atherosclerosis. Their studies in fact suggest that smooth muscle proliferation can be induced by factors present in the arterial wall and does not require exogenous factors. In recent years there has been a considerable focus on the oxidative modification of LDL and the resulting implications for atherogenesis [3, 5]. LDL as it normally circulates may be relatively benign. Only when it has undergone modification, either oxidatively [108] or by some other mechanism, does it acquire the ability to induce injury to the arterial wall. Not only does it become cytotoxic as noted earlier, but oxidized LDL, as compared to native LDL, is recognized by the scavenger receptor and thus taken up much more rapidly [109], The result of this is the formation of foam cells, a key feature of early lesions. Endothelial cells and smooth muscle cells [110], as well as monocytes and macrophages [26], have been reported to oxidatively modify LDL, which in turn may modify endothelial function, even producing dysfunction [111]. For the endothelial cell and the smooth muscle cell, we have already discussed the influence of mechanical environment, and there is every reason to believe that there are similar effects on the moncyte/ macrophage. However, to date there have been no studies designed to investigate hemodynamic effects on the oxidative environment of the arterial wall and more specifically on any hemodynamic modulation of cell-induced LDL oxidation. What we do know is that shear stress does alter NO release [112] and that NO in turn influences leukocyte adhesion [113]. It also has been suggested that NO produced by endothelial cells may scavenge oxygen free radicals, in doing so providing protection to the vessel wall [114]. Taken together with the above noted demonstrated influence of shear stress on NO Transactions of the ASME

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release by endothelial cells, this is strongly suggestive of a link between hemodynamics and the oxidative environment of the vessel wall which is known to be important to mechanisms involved in the disease process [5, 7]. Another important process in this is that involving the transport of LDL from blood, across the endothelium, and into the intima. What controls endothelial permeability? Recent results suggest that there is an influence of mitosis on this, with regions of higher cell turnover rate being leakier as proposed by Weinbaum and his co-workers [115-117]. There also is enhanced permeability associated with cells in the process of dying or sloughing off [118]. Is intimal LDL accumulation simply the result of an influx due to some regions having higher permeability? In fact, the results reported by Schwenke and Carew [119] suggest that there is some type of selective retention. In this the role of the internal elastic lamina as a barrier to transport may be important. It should be noted that one dilemma in our understanding seems recently to have been resolved. In the human and in most animals, flow dividers at arterial bifurcations in general were spared, i.e., there were no fatty streaks induced in these regions in short term, high cholesterol diet experiments. The one exception was the intercostal branches of the rabbit [120], However, Yoshida and his co-workers have conducted a series of experiments in which they examined in the rabbit both the characteristics of the arterial wall and the detailed flow pattern [121], the latter done using the technique of Karino [47]. Yoshida has concluded that, due to the unique geometry of the rabbit's intercostal branch, the fatty streak region on the flow divider in fact is a relatively low shear region and not a high shear one as previously thought. This of course suggests that one must be extremely cautious in characterizing a region as low shear or high shear and that this can only be done if one has conducted the necessary detailed fluid mechanic studies. Although much of the emphasis in this review has been on the influence of hemodynamics on the vascular endothelial cell, this simply has been because it is this cell about which we know the most. The endothelial cell is the interface between flowing blood and the underlying wall, and thus logically is a mediator of a hemodynamic influence. The focus perhaps also has been on the endothelial cell because it has readily lent itself to cell culture studies where the experimental apparatus employed could be engineered to include flow. However, understanding why there has been a focus on the endothelial cell in terms of a role of hemodynamics in atherosclerosis is not meant to in any way preclude the importance of hemodynamic or mechanical effects on other cellular participants. In fact, there is a great need for studies designed to investigate such effects on the function of the vascular smooth muscle cell, for which there have been some studies [36-39]; the monocyte-macrophage, for which there have been basically no investigations; and other, equally unstudied cell types, e.g., the T-lymphocyte. Some of this needed research, including further studies focused on the vascular endothelial cell, will take place through the use of cell culture. As part of this, the cell culture environment will need to be better engineered so as to make it more physiologic. This should include a more suitable representation of the mechanical nature of the in vivo environment; however, in this attention should also be given to the media and the extracellular matrix employed, and the influence of neighboring cells. In regard to the latter, for the endothelial cell this means studying the influence of flow on endothelial cells co-cultured with smooth muscle cells. Also, cell culture studies must move beyond simply adding to a list of properties altered by flow or cyclic stretch. Such studies should focus on mechanisms of signal recognition and transduction, on how mechanical factors regulate gene expression, and on the specific processes believed to be important to the development of the disease itself. Mathematical modeling approaches also should prove to be Journal of Biomechanical Engineering

important. This will certainly be true in the area of arterial fluid mechanics where the ability to calculate unsteady, threedimensional flows in complex, elastic geometries is now here. The use of computational mechanics in addition will add to our understanding of tissue mechanics and to the problems described in an earlier section. However, the use of mathematical models and computational techniques needs to be extended to include the calculation of the time course of biological changes within the arterial wall and even to cellular and subcellular levels. In regard to the former, there has only been one report, in this case focusing on the process of intimal thickening [122], and the only published investigations of intracellular phenomena have been limited to specific sub-cellular processes, with not one modeling the entire cellular response. In addition, of course, there is a continuing need for in vivo investigations. These should include quantitative studies of both the spatial and temporal nature of events, not only the disease pattern, but also specific markers of biologic and pathobiologic processes using molecular biology probes. Complementary to these will be model studies, designed either to investigate the fluid mechanics or the arterial wall mechanics intrinsic to the pulsatile flow of blood through a vessel. Such studies should include the investigation of geometric and structural effects so as to provide further insight in the possible role of geometry as a risk factor. Although speculative in that it has never been demonstrated, vascular geometry as a risk factor might be part of an individual's family history. Its important could arise from the influence of vascular geometry on local hemodynamic details, which in turn modifies the pathobiologic mechanisms involved in the disease process. In essence, geometry has important effects on the fluid mechanics within the vascular system, and the resulting local hemodynamic factors provide for the mechanical environment of the cellular participants. This then influences such basic atherogenic mechanisms as smooth muscle cell migration into the intima and proliferation, connective tissue synthesis, and monocyte/macrophage recruitment and the formation of foam cells. In concluding this review, it again should be emphasized that the focus has been on atherogenesis, i.e., on the initiation of the disease. However, hemodynamics does not just play a role in these early, initiating events; it presumably is a factor in the more advanced stages of disease. In these later stages the role of hemodynamics may be considerably different. Due to the disfigurement of the vessel, there will be an alteration in hemodynamics, including the detailed characteristics of the flow. As a result, disturbances or even turbulence may be present in the flow, and as has been demonstrated by Davies et al. [123] in cell culture studies, the influence of a turbulent flow on an endothelial monolayer may be far different than that of a laminar flow. In these more advanced stages, the endothelium may be disrupted, and then platelet adherence/ aggregation will be important. Furthermore, in the very advanced disease stages, plaque rupture becomes an issue [124], and the hemodynamic environment may be a contributing factor. Finally, from a historical perspective the study of the role of hemodynamics in atherosclerosis has moved forward in a series of 'chapters.' From this viewpoint, the 1960's could be called the 'high shear/low shear' years [12, 125]. Although seemingly pitting these two conflicting effects against one another, for those involved this was never meant to be the case. Out of this came the 1970's, what I call the 'pattern' years. This was a period of time when there was considerable emphasis on experimentally measuring both the pattern of disease and the pattern of the velocity field, i.e., velocity profile information, and then attempting to correlate these. As useful as this was, it only provided implicit evidence, i.e., guilt by association. It 'begged' the question as to whether or not there was an influence of hemodynamics on vascular biology. Thus, AUGUST 1992, Vol. 114/279

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with the development of cell culture, a number of laboratories moved in the 1980's into this area in order to study the influence of flow, with as noted earlier the particular focus being on the vascular endothelial cell. This decade of the 80's I have termed 'flow: at the heart of cell biology,' taking advantage of an advertisement a few years ago by the St. Louis-based company, Invitron. What about the 1990's? I do not presume to have prognostic powers; however, as a postscript, in the closing discussion of the Symposium on Hemodynamics and the Arterial Wall held at the 1990 World Congress on Biomechanics, it was suggested by E. A. Sprague (San Antonio, TX) that the decade currently taking place will represent the 'integration' years. This will be because of the need to begin to integrate our knowledge of sub-cellular phenomena taking place in response to hemodynamic events into an integrated picture of alterations in cell structure and function. We also need to integrate our knowledge of cell biology into a description of the biologic processes of the arterial wall which are exhibited in response to hemodynamics. Finally, we need to integrate this into a picture of the disease process itself and how hemodynamic factors exert themselves. Acknowledgment This manuscript is based on a presentation made as the opening plenary lecture at the World Congress on Biomechanics held at the University of California, San Diego in La Jolla, California, Aug. 31-Sept. 4, 1990. The research in the author's own laboratory, which provided a foundation for this review, was supported by National Institutes of Health grants HL-26890 and HL-41175 and National Science Foundation grant ECS-8815656. The author thanks R. W. Alexander, B. C. Berk, P. R. Girard, D. N. Ku, C. J. Schwartz, E. A. Sprague, R. P. Vito, and his graduate students, past and present, for their contributions to the work and ideas reflected in this review. References 1 Ross, R., and Glomset, J., "The Pathogenesis of Atherosclerosis," New England J. Med., Vol. 295, 1976, pp. 369-377, 420-425. 2 Ross, R., "Atherosclerosis: A Problem of Biology of Arterial Wall Cells and Their Interaction with Blood Components," Atherosclerosis, Vol. I, 1981, pp. 293-311. 3 Steinberg, D., "Lipoproteins and Atherosclerosis: A Look Back and a Look Ahead," Arteriosclerosis, Vol. 3, 1983, pp. 283-301. 4 Glagov, S., Zarins, C. K., Giddens, D. P., and Davis, H. R., Jr., "Atherosclerosis: What is the Nature of the Plaque?" Vascular Diseases: current research and clinical applications. DE Strandness, Jr., P. Didishein, A. W. Glowes, J. T. Watson (eds). Grune and Stratton, Orlando, pp. 15-33, 1987. 5 Steinberg, D., Pathasarathy, S., Carew, T. E., Khoo, J. C , and Witzum, J. L., "Beyond Cholesterol: Modifications of Low-Density Lipoprotein that Increase its Atherogenicity," New England J. Med., Vol. 320, 1989, pp. 915924. 6 Ross, R., "Mechanicsms of Atherosclerosis—A Review," Adv. Nephrol., Vol. 19, 1990, p. 79. 7 Schwartz, C. J., Valente, A. J., Sprague, E. A.,Kelley, J. L., andNerem, R. M., "The Pathogenesis of Atherosclerosis: An Overview," Clinical Cardiology, Vol. 14, 1991, No. 1, pp. 1-16. 8 Montenegro, M. R., and Eggen, D. A., "Topography of Atherosclerosis in the Coronary Arteries," Lab. Invest., Vol. 18, 1968, pp. 586-593. 9 Schwartz, C. J., and Mitchell, J. R. A., "Observations on Localizations of Arterial Plaques," Circ. Res., Vol. 11, 1972, pp. 63-73. 10 Wissler, R. W., et al., "Relationship of Atherosclerosis in Young Men to Serum Lipoprotein Cholesterol Concentrations and Smoking," J. Amer. Med. Assoc, Vol. 264, 1990, pp. 3018-3024. 11 Cornhill, J. F. (private communication). 12 Caro, C. G., Fitz-Gerald, J. M., and Schroter, R. C , "Atheroma and Arterial Wall Shear. Observation, Correlation and Proposal of a Shear-Dependent Mass Transfer Mechanism for Atherogenesis," Proc. Roy. Soc., London, Series B, Vol. 177, 1971, pp. 109-159. 13 Grottum, P., Svindland, A., and Walloe, L., "Localization of Atherosclerotic Lesions in the Bifurcation of the Left Main Coronary Artery," Atherosclerosis, Vol. 47, 1983, pp. 55-62. 14 Ku, D. N., Giddens, D. P., Zarins, C. K., and Glagov, S., "Pulsatile Flow and Atherosclerosis in the Human Carotid Bifurcation," Artheriosclerosis, Vol. 5, 1985, pp. 293-302. 15 Friedman, M. H., Peters, O. J., Bargeron, C. B., Hutchins, G. M., and

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86 Nollert.M. U., Eskin, S.G., and Mclntire, L. V., "Shear Stress Increases Inositol Trishosphate Levels in Human Endothelial Cells," Biochem. Biophys. Res. Commun., Vol. 170, 1990, pp. 281-287. 87 Prasad, A. R. S., Nerem, R. M., Schwartz, C. J., and Sprague, E. A., "Stimulation of Phosphoinositide Hydrolysis in Bovine Aortic Endothelial Cells Exposed to Elevated Shear Stress," J. Cell. Biol., Vol. 109, (abstract), 1989, pp. 331a. 88 Ando, J., Komatsuda, T., and Kamiya, A., "Cytoplasmic Calcium Responses to Fluid Shear Stress in Cultured Vascular Endothelial Cells," In Vitro CellDev. Biol., Vol. 24, 1988, pp. 871-877. 89 Mo, M., Eskin, S. G., and Schilling, W. P . , "Flow-Induced Changes in Ca 2+ Signaling of Vascular Endothelial Cells: Effect of Shear Stress and A T P , " Am. J. Physiol., Vol. 260, 1991, pp. H1698-H1707. 90 Dull, R. O., and Davies, P . F., "Flow Modulation of Agonist (ATP)Response (Ca + + ) Coupling in Vascular Endothelial Cells," Am. J. Physiol, Vol. 261, 1991, pp. H149-154. 91 Shen, J., and Dewey, C. F., Jr., "Fluid Shear Stress Modulates Cytosolic Free Calcium in Vascular Endothelial Cells," Am. J. Physiol., Vol. 262 (Cell Physiol, Vol. 31), 1992, pp. C384-390. 92 Geiger, R. V., Berk, B. C , Alexander, R. W., and Nerem, R. M., "FlowInduced Calcium Transients on Single Endothelial Cells: Spatial and Temporal Analysis," Am. J. Physiol.: (CellPhysiol262, Vol. 31), 1992, pp. C1411-1417. 93 Girard, P. R., and Nerem, R. M., "Role of Protein Kinase C in the Transduction of Shear Stress to Alterations in Endothelial Cell Morphology," J. Cell Biochem., Vol. 14E, (abstract), 1990, p. 210. 94 Watson, P. A., "Function Follows Form: Generation of Intracellular Signals by Cell Deformation," FASEB J., Vol. 5, 1991, pp. 2013-2019. 95 Olesen, S. P., Clapham, D. E., and Davies, P. F., "Hemodynamic Shear Stress Activates a K + Current in Vascular Endothelial Cells," Nature, Vol. 331, 1987, pp. 168-170. 96 Lansman, J. B., Hallam, T. J., and Rink, T. J., "Single Stretch-Activated Ion Channels in Vascular Endothelial Cells as Mechanotransducers?" Nature, Vol. 325, 1987, pp. 811-813.

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97 Nollert, M. V., and Mclntire, L. V., "Convective Mass Transfer Effects on the Intracellular Calcium Response of Endothelial Cells," ASME JOURNAL OF BlOMECHANICAL ENGINEERING, p p . 3 3 2 - 3 3 7 . .

112 Taylor, W. R., Harrison, D. G., Nerem, R. M., Peterson, T. E., and Alexander, R. W., "Characterization of the Release of Endothelium-Derived Nitrogen Oxides by Shear Stress," FASEB J., Vol. 56, No. 6, (abstract), 1991, p. A1727. 113 Kubes, P., Suzuki, M., and Granger, D. N., "Nitric Oxide: An Endogenous Modulator of Leukocyte Adhesion," Proc. Natl. Acad. Sci. USA, Vol. 88, 1991, pp. 4651-4655. 114 Feigl, E. O., "EDRF—A Protective Factor?" Nature, Vol. 331, 1988, pp. 490-491. 115 Chien, S., Lin, S.-J., Weinbaum, S., Lee, M. M. L., and Jan, K.-M., "The Role of Arterial Endothelial Cell Mitosis in Macromolecular Permeability," Adv. Expert. Med., Biol., Vol. 242, 1988, pp. 59-73.

98 Simon, M. I., Strathmann, M. P., and Gautam, N., "Diversity of G Proteins in Signal Transduction," Science, Vol. 252, 1991, pp. 802-808. 99 Brown, A. M., " A Cellular Logic for G Protein Coupled Ion Channel Pathways," FASEB J., Vol. 5, 1991, pp. 2175-2179. 100 Sumpio, B. E., Banes, A. J., Levin, L. G., and Johnson, G., Jr., "Mechanical Stress Stimulates Aortic Endothelial Cells to Proliferate," J. Vase. Surg., Vol. 6, 1987, pp. 252-256. 101 Sumpio, B. E., and Banes, A. J., "Prostacyclin Synthetic Activity in Cultured Aortic Endothelial Cells Undergoing Cyclic Stretch," Surgery, Vol. 104, 1988, pp. 383-389. 116 Lin, S.-J., Jan, K.-M., Weinbaum, S., and Chien, S., "Transendothelial 102 Shirinsky, V. P., Antonov, A. S., Birukov, K. G., Sobolevsky, A. V., Transport of Low Density Lipoprotein in Association with Cell Mitosis in Rat Romanov, Y. A., Kabaeva, N. V., Anonova, G. N., and Smirnov, V. N., Aorta," Arteriosclerosis, Vol. 9, 1989, pp. 230-236. "Mechano-Chemical Control of Human Endothelium Orientation and Size," 117 Yuan, F., Chien, S., and Weinbaum, S., " A New View of Convective/. Cell Biol., Vol. 109, 1989, pp. 331-339. Diffusive Transport Processes in the Arterial Intima," ASME JOURNAL OF BIO103 Dartsch, P. C , and Betz, E., "Response of Cultured Endothelial Cells MECHANICAL ENGINEERING, Vol. 113, 1991, pp. 314-329. to Mechanical Stimulation," Basic Res. Cardiol., Vol. 84, 1989, pp. 268-281. 118 Chuang, P., Cheng, H., Lin, S., Jan, K., and Chien, S., "Macromo104 Stathopopoulos, N. A., and Heliums, J. D., "Shear Stress Effects on lecular Transport Across Arterial and Venous Endothelium in Rats: Studies with Human Embryonic Kidney Cells In Vitro," Bioengr. Biotech., Vol. 27, 1985, Evans Blue-Albumin and Horseradish Peroxidase," Arteriosclerosis, Vol. 10, pp. 1021-1026. 1990, pp. 188-197. 105 Vanhee, C , Nerem, R. M., and Girard, P. R., "Influence of Fluid119 Schwenke, D. C , and Carew, T. E., "Initiation of Atherosclerotic LeInduced Shear Stress on Cell Proliferation in NIH 3T3 Fibroblasts," Bioprocess Engineering Symposium, ASME Winter Annual Meeting, Atlanta, GA, Dec. sions in Cholesterol-Fed Rabbits: II. Selective Retention of LDL vs. Selective Increases in LDL Permeability in Susceptible Sites of Arteries, "Arteriosclerosis, 1-6, 1991, BED-Vol. 21: 27-28, 1991. Vol. 9, 1989, pp. 908-918. 106 Libby, P., and Birinyi, L. K., "The Dynamic Nature of Vascular En120 Cornhill, J. F., and Roach, M. R., " A Quantitative Study of the Lodothelial Functions," Endothelialization of Vascular Grafts, P. P. Zilla, R. D. calization of Atherosclerotic Lesions in the Rabbit Aorta," Atherosclerosis, Fasol, and M. Dentsch, eds., Karger, Basel, Switzerland, 1987, pp. 80-89. Vol. 23, 1976, pp. 489-501. 107 Reidy, M. A., and Jackson, C. L., "Factors Controlling Growth of Arterial Cells Following Injury," Toxic. Pathol., Vol. 18, No. 4, 1990, pp. 547121 Yoshida, Y., Okano, M., Wang, S., Kobayashi, M., and Shimisu, M., 553. "Endothelial Functions Modulated by Hemorheological Forces," Proceedings 108 Palinski, W., Rosenfeld, M. E., Yla-Herttuala, S., Gunner, G. C , Socher, of the 9th International Symposium on Atherosclerosis (in press). S. S., Butler, S. W., Parthasarathy, S., Carew, T. E., Steinberg, D., and Witzum, 122 Friedman, M. H., " A Biologically Plausible Model of Thickening of J. L., "LDL Undergoes Oxidative Modification In Vivo," Proc. Natl. Acad. Arterial Intima Under Shear," Arteriosclerosis, Vol. 9, 1989, pp. 511-522. Sci., USA, Vol. 86, 1989, pp. 1372-1380. 123 Davies, P . F., Remuzzi, A., Gordon, E. J., Dewey, C. F., Jr., and 109 Khoo, J. C. Miller, E., McLoughlin, P., and Steinberg, D., "Enhanced Gimbrone, M. A., Jr., "Turbulent Shear Stress Induces Vascular Endothelial Macrophage Uptake of Low Density Lipoprotein After Self-Aggregation," ArCell Turnover In Vitro," Proc. Natl. Acad. Sci., USA, Vol. 1986, pp. 2114teriosclerosis, Vol. 8, 1988, pp. 348-356. 2117. 110 Morel, D. W., DiCorleto, P. E., and Chisholm, G. M., "Endothelial 124 Born, G. V. R., and Richardson, P., "Mechanical Properties of Human and Smooth Muscle Cells Alter Low Density Lipoprotein In Vitro by Free Radical Atherosclerotic Lesions," Pathobiology of the Human Atherosclerotic Plaque, Oxidation," Arteriosclerosis, Vol. 4, 1984, pp. 357-364. S. Glagov, W. P. Newman, III, and S. A. Schaffer, eds., Springer-Verlag, New 111 Shatos, M. A., Doherty, J. M., andHoak, J. C , "Alterations in Human York, 1990, pp. 413-423. Vascular Endothelial Cell Function by Oxygen Free Radicals: Platelet Adherence 125 Fry, D. L., "Acute Vascular Endothelial Changes Associated with Inand Prostacyclin Release," Arteriosclerosis and Thrombosis, Vol. 11, 1991, pp. creased Blood Velocity Gradients," Circ. Res., Vol. 22, 1968, pp. 165-182. 594-601.

Contents (continued) 398

A Numerical Study of the Shape of the Surface Separating Flow Into Branches in Microvascular Bifurcations G. Enden and A. S. Popel

406

Insights From In-Vitro Flow Visualization Into the Mechanisms of Systolic Anterior Motion of the Mitral Valve in Hypertrophic Cardiomyopathy Under Steady Flow Conditions X. P. Lefebvre, A. P. Yoganathan, and R. A. Levine

Technical Briefs 414

Shear Stability of an Elastomeric Disk Spacer Within an Intervertebral Joint: A Parametric Study M. V. Hawkins, M. C. Zimmerman, J. R. Parsons, F. M. Carter, N. A. Langrana, and C. K. Lee

416

Pressure Drops Through Arterial Stenosis Models in Steady Flow Condition S. Cavalcanti, P. Bolelli, and E. Belardinelli

418

Pretension Critically Affects the Incremental Strain Field on Pressure-Loaded Cell Substrate Membranes G. W. Broadland, A. T. Dolovich, and J. E. Davies

421

Adaptive Control of Above Knee Electro-Hydraulic Prosthesis T. K. Wang, M. S. Ju, and Y. G. Tsuei

Announcements and Special Notices 300

Transactions Change of Address Form

425

Calendar of Events

2 8 2 / V o l . 114, A U G U S T 1992

T r a n s a c t i o n s of t h e A S M E

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