Complementary roles of theoretical modeling and computer-controlled experimentation in vascular growth and remodeling
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It is well known that many tissues grow and remodel in response to an altered mechanical environment. In the vasculature, for example, arteries exposed to increased blood pressure tend to thicken, those exposed to increased flow tend to dilate, and those exposed to increased axial extension tend to lengthen. These adaptations correlate well with the stresses in the tissue. Kamiya and Togawa (1980) suggested that mean 'wall shear stress was the predominant factor in initiating and controlling the adaptive response [enlargement of the lumen]' in cases of sustained increases in flow. Clark and Glagov (1985) found that the mean circumferential stress correlates well with aortic thickening during normal development whereas Jackson et al. (2002) suggest that the axial stress may also be regulated via G&R mechanisms. Recall, therefore, that equations for the mean wall shear stress (w), mean circumferential stress () and mean axial stress (z), and typical homeostatic values, are w = 4Q/pa3 1.5Pa, = Pa/h 150 kPa, z = f/h(2a + h) 125 kPa, (1) respectively, where Q is the luminal flow, P is the transmural pressure, f is the axial force, a is the luminal radius, h is the thickness of the vessel wall, and is the viscosity of blood. In addition, it appears that not only do the mean stresses correlate well with vascular growth and remodeling (G&R), so too do the local stresses. Stress analyses performed based on mechanical data from healthy arteries suggest that, when one includes material non-linearities, anisotropy, finite deformations, residual stress, and a basal smooth muscle contribution, the distribution of stress across the arterial wall under physiological loading is nearly uniform. Non-physiologic loading, however, often results in non-uniform stress distributions across the wall; for example, supraphysiologic pressures may produce a greater increase in stress at locations near the inner versus the outer wall. Matsumoto and Hayashi (1996) illustrated well that not only do blood vessels thicken in response to sustained increases in pressure, but also different layers thicken to different degrees, with the innermost layers thickening more early on than outer layers. These results, and many others, suggest that the vascular endothelial, smooth muscle, and fibroblast cells sense and adapt their local mechanical environment so as to achieve a preferred homeostatic state. In this paper, we describe the parallel and complementary approaches of developing a theoretical framework capable of testing competing hypotheses regarding the underlying mechanisms of G&R and devising an experimental approach to test theoretical predictions that support or oppose underlying hypotheses. In particular, we outline our approach toward developing a fundamentally new mathematical framework for vascular G&R and describe a novel experimental system for subjecting isolated (~500 m diameter) arteries to well controlled loads for multiple days. 2006 Springer-Verlag Berlin Heidelberg.
