Mathematical Methods for Fluid Flow in Bioengineering Systems

Abstract

Fluid flow plays a crucial role in numerous bioengineering applications including cardiovascular dynamics, respiratory mechanics, and drug delivery systems. Mathematical modeling of fluid flow within biological systems enables the prediction, simulation, and optimization of these processes to improve diagnostic and therapeutic techniques. This article reviews fundamental mathematical methods employed for modeling fluid flow in bioengineering systems, focusing on the governing equations, computational approaches, and relevant boundary conditions. Emphasis is placed on both Newtonian and non-Newtonian fluid behavior, coupled fluid-structure interactions, and numerical techniques such as finite element and finite volume methods. The paper also highlights recent advances and challenges in simulating complex biological flows, supported by a sample computational graph demonstrating velocity profiles in a blood vessel.