Generalized Geometric Analysis of Blood Vessel Subdivisions and Fluid Mechanics (Contemporary Mathematics, 2025)
This study proposes simplified geometric analyses of the subdivisions of blood vessels and extends the fluid-mechanical analysis to derive generalized equilibrium solutions. Departing from the traditional emphasis on symmetrical subdivisions in which one vessel splits into two, we delve into a broader scenario in which a single vessel divides into multiple branches. This exploration advances our understanding of blood vessel fluid mechanics and extends its application to biomechanical contexts. Methodologically, we integrate principles from physics, physiology, geometry, and optimality analysis. The results reveal generalized optimal solutions for the original radius of the vessel compared to bifurcated radii and optimal solutions for bifurcated angles. These findings play a significant and pivotal role in evolution, improving our comprehension of vascular mechanics and paving the way for further applications in understanding hemodynamics and the evolutionary processes of vascular systems in various animals.
Keywords: evolution of blood vessels; blood vessel subdivisions; fluid mechanics; biomechanics; generalized equilibrium solutions; optimal solutions