## 4 Discussion  
The twisted structure of the blood flow can only be formed in a flow channel with a certain geometrical configuration. This configuration is determined by the direction of the flow lines, whose three-dimensional velocity field is described by the Kiknadze-Krasnov equations [3]:  
\[\left\{ \begin{array}{c}u_{z}=2C_{0}(t)z\\ u_{r}=-C_{0}(t)r\\ u_{\varphi}=\frac{\Gamma_{0}(t)}{2\pi r}*\left(1-e^{-\frac{C_{0}(t)^{2}}{2 \varphi}}\right)\end{array} \right.\]  
where \(u_{z}\), \(u_{r}\), and \(u_{\varphi}\) are velocity components, \(\
u\) is kinematic viscosity, and the unsteadiness and evolution of the flow are determined by the behavior of the time-dependent functions  
Figure 6: Joint images, from two angles, of 3D models: triangulation model of the left heart and aorta (gray); analytical model approximating the shape of the atrium (purple); analytical surface approximating the left ventricle-aorta system (red); torus approximating the concave streamlined surface at the site of ventricular jet initiation (blue). \(C_{0}(t)\) and \(\Gamma_{0}(t)\). \(C_{0}(t)\) is an arbitrary function of time representing, in a physical sense, the gradient of the longitudinal component of velocity (s\({}^{-1}\)), \(\Gamma_{0}(t)\) is an arbitrary function of time corresponding in the physical sense to the circulation of the medium (m\({}^{2}\)/s). To ensure potential flow, the curvature of the streamlined surfaces of the flow channel must satisfy these conditions. As previously published, there are several mechanisms that serve to generate such flow. These mechanisms act at all stages of the development of a swirling jet and include the twisting action of the atrial contraction and the convergence of the left atrial channel, the action of the trabecular apparatus and the rotational motion of the left ventricle, the specific elasticity distribution and the convergence of the aortic flow channel, and the geometry of the branching of the main branches of the aorta [5]. However, a coherent formal description of the geometric configuration of the flow channel in the section from the left atrium to the end of the aorta is still lacking. This is due to the fact that such a description has not been based on a coherent concept justifying the principles of self-organization of flow and flow channels. The possibility of developing such a concept arose with the appearance of accurate Kiknadze-Krasnov solutions and hydrodynamic studies of centripetal swirling flows of viscous fluids [13]. It turned out that both the hydrodynamic structure of the blood flow and the streamlined boundaries of the channel in the central circulatory regions contain many features by which we can judge the applicability of these solutions. The proposed approach allows us to study not only static states of the channel, but also dynamic changes in its configuration according to pulsation oscillations. It has also become possible to describe the general geometric configuration of the heart and aorta in terms of geometric constructions. A similar problem was solved in [18], but in that work there was no concept according to which the approximation was carried out and there was no reference to the hydrodynamic characteristics of the flow. Within the framework of this study, there are still some unresolved issues, particularly the stage of describing the separate parts of the left atrium and the left ventricular apex. In addition, the description of the geometrical regularities of the main branches of the aorta using the same approach has not been completed. The right side of the heart has not been studied at all. This will be the subject of our further studies. The results of this study allow us to take a new look at the processes of vasculature formation in phylo- and ontogenesis, the influence of vascular channel degradation on aging processes, and the pathogenesis of a number of circulatory diseases.