Computational modeling of squeezed blood flow in deformable veins: Application to calf muscle pump during walking

This study introduces a three-dimensional mathematical model to simulate blood flow in the calf muscle, conceptualized as a non-Newtonian fluid within a vertical conduit experiencing a squeezing motion. The model includes hybrid nanoparticles (Ag-Fe3O4) and takes into account the effects of an external magnetic field, such as the Hall current effect, and an external heating source. The governing system, based on the basic laws of conservation of mass, momentum, energy, and nanoparticle concentration, is made up of a group of partial differential equations that are linked together. A similarity transformation technique turns these equations into a system of nonlinear ordinary differential equations. The Optimal Homotopy Asymptotic Method (OHAM) is used to analytically solve the resulting system. The analysis examines essential physiological parameters such as pressure, velocity components, temperature, and nanoparticle concentration to clarify their behavior under the influence of combined physical effects. The graphical and tabular results show that the hybrid nanoparticle case has the highest pressure profiles. This suggests that there is a synergistic effect that makes flow resistance stronger. This suggests a possible trade-off in nanoparticle-enhanced therapies; although advantageous for targeted drug delivery or diagnostic imaging, elevated concentrations may disrupt normal hemodynamics by increasing metabolic strain or compromising oxygen delivery.