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A. E. Medvedev, V. I. Samsonov, and V. M. FominThe issue of the optimal (from the viewpoint of strength) structure of blood vessels of a living organism is considered. It is shown that the angle of packing of muscular fibers in vessels is optimal in terms of strength of arteries.Based on extensive clinical research [1], blood vessels (arteries and arterioles) can be presented as a multilayer shell. Smooth muscles in large blood vessels are known to be aligned at an angle ϕ = 30-50 • to the vessel centerline. The angle ϕ increases with decreasing blood-vessel diameter ( Fig. 1), i.e., in moving downward in the circulatory system from arteries to arterioles and further to capillaries. The angle of inclination of smooth muscles in small blood vessels approaches 90 • . Figure 2 shows the general structure of arteries and arterioles. They consist of an inner layer (tunica interna), medium layer (tunica media), and outer layer (tunica externa). The inner layer consists of endotherlium and an internal elastic membrane. The medium layer consists of smooth-muscle cells and a certain amount of fibroplastic elements and collagen fibers. The number of fibroplastic elements and collagen fibers varies in different arteries (elastic, muscular-elastic, and muscular types). There are few elastic fibers in arterioles, but precapillary sphincters are present. The density of muscle cells in the arteriole walls depends on the distance between the arteriole and the parent small artery. The outer layer consists of an external elastic membrane and a loose fibrous connective tissue.Let us consider the medium layer of the blood vessel in more detail. The smooth-muscle cells and fibers form an elastomotor helix (see [2]) inclined to the vessel centerline. The angle between the elastomotor helix winding and the longitudinal axis of the vessel is 30-50 • in large arteries, gradually increasing as the vessel diameter decreases. In small arterioles, the winding direction is closer to circular [1][2][3][4][5]. With an increase in years, the number of layers of the helical winding of muscular fibers increases from three layers (at the age of 12) to six layers (at the age of 20) [2].Elastic properties of vascular walls play a significant role in oscillatory motion of blood. The elastic state of artery walls is not stable. It changes reflexively due to activity of muscular elements, which are nonuniformly distributed in various parts of the arterial network. Depending on organism demands (level of blood circulation), the elastic properties of vascular walls can vary. Therefore, the modulus of elasticity of vascular walls depends on the functional state of muscular elements and on the degree of passive stress of the connective tissue of the vessel.Let us consider the blood-vessel wall (Fig. 3) as a binder with embedded muscular elements (reinforcing fibers).Let the volume fraction of fibers be ω s . The family of reinforcing fibers is aligned at an angle ϕ to the vessel centerline (dashed straight line in Fig. 3). The volume fraction of the binder ...

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