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It is now an established fact that blood flow in the heart and the major vessels has normally a helical pattern. The structure of this flow is described by the exact solution of the nonstationary hydrodynamics equations for a class of self-organized tornado-like jets of viscous fluids. Our previous studies have shown that the geometry of the aortic channel corresponds to streamlines of this class throughout the cardiac cycle, which is supported by a special distribution of viscoelastic properties of the flow channel wall along the aorta. As a result of age-related pathological processes and/or their surgical correction, normal viscoelastic characteristics of vessel walls inevitably become impaired. A diversity of impairments in the structure of the cardiovascular system causes negative alterations in the normal geometrical configuration of biological flow channels. Thus, any pathological alterations in vessel channels are accompanied by deteriorations in the structural parameters of blood flow. However, a direct experimental study of all the diversity of vessel lesions is associated with considerable complications. Thus, no studies have been conducted so far to identify the regularities of alterations in the structural parameters of a swirling blood flow in different pathological conditions of the vessel channel. In this study, we have created a physical model of the flow channel of the aorta, which was based on the nonlinear distribution of transverse elasticity in the walls of the aorta along its length. Further, we created a computer simulation of the constructed model flow channel dynamics throughout the cardiac cycle in correspondence with the standard curve for blood pressure changes. The simulation results were interpreted within the semi-empirical theory of self-organized tornado-like jets of viscous fluids. This interpretation allowed us to formulate the time-dependent quantitative characteristics establishing functional relations between the structure of blood flow and the geometry of the flow channel of the aorta throughout the cardiac cycle.