What are the residual stresses doing in our blood vessels?

Abstract

We show that the residual strain and stress in the blood vessels are not zero, and that the zero-stress state of a blood vessel consists of open-sector segments whose opening angles vary along the longitudinal axis of the vessel. When the homeostatic state of the blood vessel is changed, e.g., by a sudden hypertension, the opening angle will change. The time constant of the opening angle change is a few hours (e.g., in the pulmonary artery) or a few days (e.g., in the aorta). From a kinematic point of view, a change of opening angle is a bending of the blood vessel wall, which is caused by a nonuniformly distributed residual strain. From a mechanics point of view, changes of blood pressure and residual strain cause change of stress in the blood vessel wall. Correlating the stress with the change of residual strain yields a fundamental biological law relating the rate of growth or resorption of tissue with the stress in the tissue. Thus, residual stresses are related to the remodeling of the blood vessel wall. Our blood vessel remodels itself when stress changes. The stress-growth law provides a biomechanical foundation for tissue engineering.