Bending of Blood Vessel Wall: Stress-Strain Laws of the Intima-Media and Adventitial Layers

In order to determine the stress-strain relationship of the inner (intima and media) and outer (adventitia) layers of blood vessels in the neighborhood of the zero-stress state, bending experiments were performed on aortic strips of rats. In the experiments, one end of a strip was clamped, and a force was applied on the other end. The deflection curves of the strips were measured. By regarding the aortic strip as a curved beam, the classical beam theory was employed to analyze the strain distribution from the experimental data. A computer program dealing with nonlinear equations and nonlinear least squares optimization was developed. Strains were referred to the zero-stress state. The load-deflection relationship was then used to determine the stress-strain relationship. Certain forms of the stress-strain laws were assumed. The linear laws fit the experimental data accurately, probably because the strains during bending are quite small, although the rotations are large. The Young's modulus of the inner layer, which consists of endothelial and smooth muscle cells and elastic lamina, was found to be three to four times larger than that of the outer layer which consists of collagen with a small amount of fibroblasts and elastin. The residual stresses and strains at the no-load state were calculated from the deduced stress-strain relationship. It is shown that large errors (up to 50 percent) in the values of the residual strains will occur if the wall material was treated as homogeneous, i.e., if the layered constitution was ignored.