To study the effects of smooth muscle contraction and relaxation on the strain and stress distribution in the vascular wall, a mathematical model was proposed. The artery was assumed to be a thick-walled orthotropic tube made of nonlinear, incompressible elastic material. Considering that the contraction of smooth muscle generates an active circumferential stress in the wall, a numerical study was performed using data available in the literature. The results obtained showed that smooth muscle contraction affects the residual strains which exist in a ring segment cut out from the artery and exposed to no external load. When the ring specimen is cut radially, it springs open with an opening angle. The predicted monotonic increase of the opening angle with increasing muscular tone was in agreement with recent experimental results reported in the literature. It was shown that basal muscular tone, which exists under physiological conditions, reduces the strain gradient in the arterial wall and yields a near uniform stress distribution. During temporary changes in blood pressure, the increase in muscular tone induced by elevated pressure tends to restore the distribution of circumferential strain in the arterial wall, and to maintain the flow-induced wall shear stress to normal level.

A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load bearing is modulated by the contraction. This novel pseudo-SEF models not only arterial mechanics at maximal VSM contraction but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified with experimentally obtained pressure-radius curves and zero-stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The pressure-radius curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well (r2 > 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone, suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.

Arterial wall stresses are thought to be a major determinant of vascular remodeling both during normal growth and throughout the development of occlusive vascular disease. A completely physiologic mechanical model of the arterial wall should account not only for its residual strains but also for its structural nonhomogeneity. It is known that each layer of the artery wall possesses different mechanical properties, but the distribution of residual strain among the different mechanical components, and thus the true zero stress state, remain unknown. In this study, two different sets of experiments were carried out in order to determine the distribution of residual strains in artery walls, and thus the true zero stress state. In the first, collagen and elastin were selectively eliminated by chemical methods and smooth muscle cells were destroyed by freezing. Dissolving elastin provoked a decrease in the opening angle, while dissolving collagen and destroying smooth muscle cells had no effect. In the second, different wall layers of bovine carotid arteries were removed from the exterior or luminal surfaces by lathing or drilling frozen specimens, and then allowing the frozen material to thaw before measuring residual strain. Lathing material away from the outer surface caused the opening angle of the remaining inner layers to increase. Drilling material from the inside caused the opening angle of the remaining outer layers to decrease. Mechanical nonhomogeneity, including the distribution of residual strains, should thus be considered as an important factor in determining the distribution of stress in the artery wall and the configuration of the true zero stress state.

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