**4. Discussion**

The geometric configuration of the aorta undergoes significant changes in various pathological conditions, such as hypertension, atherosclerosis, some infectious diseases, etc. At the same time, it is difficult to determine the stage at which changes in the geometry of the aortic flow channel are still compensatory in nature, and at which they are a manifestation of decompensation. There is no formal approach to the analysis of the geometric configuration of the aorta because the fields of force impact on the aortic wall, both in normal conditions and in the development of pathology, have not been sufficiently studied. The only source of force can be the flow of blood in the lumen of the aorta. However, there is still a discussion

about the structure of this flow. Previously published papers have argued that the swirling flow pattern is of fundamental importance for adequate unseparated blood flow along the aorta. The shape of the lumen (longitudinal-radial size and distribution of elasticity along the aorta) corresponds with high accuracy to the directions of streamlines of the swirling flow described earlier using quasi-stationary equations (2.2). In the present study, an analysis of the spatial geometric configuration of the aorta in normal conditions and in lesions of predominantly proximal or distal sections was carried out. This analysis showed that the factors of the flow structure ( *C*0 and Γ0) and the parameters of approximation of the projection of the aorta on the frontal plane of the human body by a hyperbolic spiral together make it possible to separate these states according to a formal feature.

As a result, new quantitative parameters characterizing the degree of pathological remodeling of the aortic duct and a method for their calculation were proposed. This method is based on a complex analysis of the geometry of the aortic flow channel. This analysis makes it possible to determine the hydrodynamic parameters of the swirling blood flow inside the aortic flow channel, the geometric correspondence of the shape of the flow channel to the direction of the swirling flow streamlines, and to formalize the geometry of the flow channel itself.

The field of shear stresses arising on the channel walls in a swirling flow regime differs significantly from the stresses arising in a fluid flow in laminar or turbulent regimes. Therefore, to analyze the impact of the flow on the walls of blood vessels, it is necessary to consider the twisted structure of the flow and to analyze the shape of the aorta parameters characterizing the degree of this twist— *C*0 and Γ0. The shape of the aorta is also determined by the nature of the swirling blood flow, so the channel geometry was approximated to a hyperbolic spiral. Only in a channel whose shape corresponds to a hyperbolic spiral is it possible to preserve the potentiality of the flow.

In this work, we used the geometric characteristics of the canal associated with the swirling blood flow in the canal lumen ( *C*0 and Γ0), which made it possible to divide the aortas into 2 groups: the first group included normal aortas and aortas with pathology localized in the distal sections, and the second group included aorta with localization of pathology in the proximal sections. The construction of the central line and the approximation of this line to a hyperbolic spiral made it possible to further divide the aorta into 2 groups—the first included normal aorta, the second—aorta with lesions in the proximal and distal sections. At the same time, the error of the results does not exceed the threshold value adopted in experimental medicine (5%). The registered shifts in the values of the given parameters may reflect the type and severity of the pathology and may be considered predictors of critical conditions leading to the formation of aneurysms, dissections, and ruptures of the aortic wall.
