Stress gradients in the walls of large arteries

Elastic behavior of vascular wall, assuming the vessels to be ‘thick-walled’ and utilizing finite deformation theory, was investigated. It was found that canine carotid arterial wall is neither isotropic nor transversely isotropic. Previously, stress-strain relations were obtained for carotid arteries on the basis of membrane theory (Doyle and Dobrin, 1971). Since strain gradients across the wall are fairly steep, the applicability of such expressions, for pointwise evaluation of stress, required examination. The study indicated that these relationships between mean circumferential stress and mean extension ratio in the circumferential direction could be used to relate the specific circumferential stress value to the specific extension ratio at any designated point within the wall. From this analysis it was possible to evaluate circumferential and radial wall stresses. Both of these stresses are maximal at the inner surface of the intima. At this point the radial stress is equal to the transmural pressure and is compressive, while the circumferential stress is tensile and is 1·5 to 2 times the value of the mean stress, i.e. the product of transmural pressure and the ratio of internal radius-to-wall thickness. Both stresses are lowest at the outer edge of the adventitia. These stress distributions were considered with respect to the spacing of the elastic lamellae and the absence of discernible vasa vasora in the inner third of the wall.