Is axial wall stress compressive in certain arteries?

Abstract

In mathematical-physical models of blood vessels, the "zero-stress state" of the vessel wall is usually defined with reference to the atmospheric pressure (pa approximately 750 mmHg = 100 kPa). Due to this conventional choice, axial and circumferential stresses generated by the (positive) transmural pressure over the radial wall depth can only be positive (in absence of residual stresses) and thus, by definition, only tensile. If the zero-stress state were defined "unconventionally" with reference to vacuum pressure (= 0 mm Hg), the isotropic compressive stress--pa generated by the atmospheric pressure everywhere in the wall would, however, be included in the stress values, and negative (= compressive) stresses would become formally possible. Since materials submitted only to compressions do not need to have the same resistive properties as materials which may also experience tractions, the question whether axial stress (and perhaps also circumferential stress) might be permanently compressive in vessels under physiologic conditions may therefore be important for investigations of the relationship between wall stresses on one side and wall structures, vessel growth, vessel damages, or vessel adaptation processes on the other side. In the present study, radial, circumferential, and axial wall stresses were calculated conventionally and "unconventionally" for three representative "vessel examples." The results clearly suggest that axial wall stress might well be compressive in many vessels. Furthermore, relative differences between conventional and unconventional stress values are quite considerable, and ratios between stresses calculated in the same manner appear to be strongly dependent on the chosen zero-stress state definition.