Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure

Abstract

Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

“…C(s) is the net ratio of constrictors to dilators and k mðactÞ h ðsÞ evolves via a first order equation [15,19]. Similar to the earlier work on arterial adaptations [15,19], C(s) ¼ C B À C s Ds w , where C B is the basal constrictor to dilator ratio and C s is a scaling factor for shear stress induced changes in constrictor concentration. The active behavior is taken with respect to individual unloaded configurations for smooth muscle, not the entire mixture.…”

“…A point-to-point comparison [22] between 2D and 3D models showed that the 2D models accurately predict adaptive changes in geometry and stiffness and thereby capture salient aspects of G&R sufficient for clinical and fluid-structure interaction studies [19,23]. Hence, here, we briefly describe pertinent aspects for a thin-walled cylindrical tube.…”

“…The G&R formulation is based on a constrained mixture theory developed for arteries, details of which can be found in prior work [12,14,[19][20][21]. A point-to-point comparison [22] between 2D and 3D models showed that the 2D models accurately predict adaptive changes in geometry and stiffness and thereby capture salient aspects of G&R sufficient for clinical and fluid-structure interaction studies [19,23].…”

“…where P is the transmural pressure, a is the luminal radius, h is the deformed wall thickness, f is the axial force, and Ca þþ denotes intracellular calcium [19]. The superscripts "pas" and "act" indicate passive and active, respectively.…”

“…Note that the stored elastic energy for a constituent k depends on the right Cauchy-Green tensor (C k nðsÞ ) for that constituent defined with respect to its individual natural configuration n(s) [19]. Equations (5) and (6) …”