The Lamé Problem Applied to a Blood Vessel with an Active Wall

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Abstract—In this paper we consider a two-dimensional problem of the stress distribution in the wall of a blood vessel with a lumen size that may vary depending on activation of smooth-muscle cells. Based on experimental data, the dependence of the circumferential stress on the parameter of smooth-muscle activation was obtained and the dependence of the latter on the cell membrane potential was described. It has been shown that contractile activity in smooth muscles (myogenic reaction) produces a significant decrease in the stresses. The maximum value of circumferential stress is achieved at the outer vessel wall, whereas the maximum value of the radial stress is reached at the inner wall. The contractions of the smooth-muscle cells reduce the circumferential stretch and smooth out the heterogeneity of its distribution in the vessel wall.