Key result
Exact hydrodynamic equations for centripetal swirling flows accurately approximate left heart and aortic streamlined surfaces.
The study provides a mathematical parameterization of the left heart and aorta flow channels based on the hydrodynamics of swirling viscous fluid flows.
Using the normal dynamic anatomy of the left heart and aorta as an example, it has been shown that the streamlined surfaces of the flow channels in this segment of the circulation can be approximated with sufficient accuracy by the dependences for the streamlines obtained from the exact solution of the basic equations of hydrodynamics for the class of centripetal swirling viscous fluid flows. It has been shown that, in three consecutive segments of the blood channel, from the left atrium to the end of the aorta, at the moment of maximum flow velocity, the geometrical configuration of the channel satisfies the condition of constancy of the product of the longitudinal and the square of the radial coordinate, and the zone of jet initiation is limited by a concave streamlined surface. The curvature of the flow channel axis has no effect on the hydrodynamic structure of the flow, since it is coherent with the directions of the streamlines.
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Beglov et al. (2025) studied Normal dynamic anatomy of the left heart and aorta. Parameterization of streamlined surfaces using hydrodynamics equations was evaluated on Geometrical configuration of the channel and hydrodynamic structure of the flow. The streamlined surfaces of the left heart and aorta flow channels can be accurately approximated using exact solutions of hydrodynamics equations for centripetal swirling viscous fluid flows.
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