Numerical Simulation of Flow in an Artery using One-dimensional System of Hyperbolic Quasilinear PDEs

Abstract

The incidence of arterial diseases has led to a rise in the use of mathematical and numerical tools to understand arterial hemodynamics. Many studies have used three- dimensional models to mimic blood flow in arteries. However, this has a significant computational cost and power. To answer the growing demand for a computationally cheap numerical model, this work established a mathematical model for simulating and forecasting blood flow dynamics in an arterial channel. The time- dependent one-dimensional hyperbolic system of quasilinear partial differential equations was developed by taking physical momentum and mass conservation principles into consideration. This fluid-structure interaction model includes an elastic mural model for the compliant artery wall material. The combined arterial flow model was solved to mimic flow in the iliac artery using the method of lines. The findings showed that the suggested one-dimensional model can properly describe artery hemodynamics. Furthermore, the simulations created for idealized healthy states might serve as a foundation for numerical simulations of pathological states in the artery.