Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions

Abstract

Remodeling of arterial geometry was studied on the basis of a theoretical model. Sustained hypertension was simulated by a step increase in blood pressure. The artery was considered to be a thick-walled two-layer tube made of nonlinear elastic incompressible material. The basic hypothesis is that the artery remodels its zero-stress configuration in such a way that the strain and stress distributions in the arterial wall under hypertensive conditions are the same as under normotensive conditions. Using this hypothesis, a method for determining the geometrical dimensions of the zero-stress configuration of the hypertensive artery was proposed. To ensure uniqueness of the solution, two side conditions on the remodeling process are imposed: (a) the inner radius of the artery in the unloaded state remains unchanged; and (b) the ratio between the thickness of the inner and outer layer of the hypertensive artery in the zero-stress configuration is known. The model predicts that the arterial wall remodeling causes: (i) an increase of the wall thickness both in the unloaded and physiological states; (ii) an increase of the inner diameter of the hypertensive vessel under high pressure compared to the diameter of the normotensive artery under normal pressure; (iii) the opened-up configuration which arises when the unloaded arterial segment is cut radially still contains residual strains and stresses. These results are consistent with published experimental findings. It is speculated that the origin of residual stresses that exist in the unloaded and opened-up configurations is the stress-modulated growth.