Determination of constitutive equations for human arteries from clinical data

Abstract

Stress-strain analyses of vessel walls require appropriate constitutive equations. Determination of constitutive equations is based on experimental data of (i) diameter and length of a vessel segment subject to internal pressure and external axial force, and (ii) the load-free reference geometry. Typical clinical data, however, provide only pressure-diameter relations in the diastolic-systolic pressure range. In order to overcome this problem, an approach is proposed allowing the determination of constitutive equations from clinical data by means of reasonable assumptions regarding in situ configurations and stress states of arterial walls. The approach is based on a two-dimensional Fung-type stored-energy function capturing the characteristic nonlinear and anisotropic responses of arteries. Examples concerning human aortas from a normotensive and a hypertensive subject illustrate the potential of the approach.