Mathematical Modelling on Functioning of Blood Flow in Arteries and Rheology - Kamboj, Karan; Singh, Vikramjeet; Kumar, Vinod (Communications in Mathematics and Applications, 2025)
Navier-Stokes equations present a comprehensive numerical simulation of arterial flow by integrating fluid dynamics, non-Newtonian blood rheology, and arterial wall mechanics in a coupled framework. Using cylindrical coordinates with axisymmetric assumptions, the flow of blood is presented by the Navier-Stokes equations, while the viscosity and wall dynamics are Carreau-Yasuda non-Newtonian law to reflect the decrease in blood viscosity with increased blood flow. The arterial wall dynamics are represented by a linear elastic model, incorporating radial displacement as a function of internal pressure and wall elasticity. A coupling condition links pressure to wall deformation allowing for accurate simulation of fluid structure interaction. The simulation reveals critical insights into the propagation of pressure and mechanical response of arterial length, the role of shear-dependent viscosity in shaping flow profiles and the transmission and wall compliance effects, validating the physiological relevance of the improved model. The outcomes of this research hold significant potential for applications in cardiovascular diagnostics, treatment strategy, and the design of vascular prosthetics or drug delivery systems.