Novel Mathematical Modelling of Pulsatile Blood Flow in Carotid Arteries via Poiseuille Equation

Abstract

Cardiovascular diseases remain the leading global cause of death, with carotid artery dysfunction contributing significantly to ischemic stroke and long-term disability. The problem addressed in this study is the limited availability of mathematical models that can capture pulsatile blood flow dynamics under accident-induced geometric interruptions, while remaining computationally efficient. To address this gap, the study developed a novel Poiseuille-based framework, incorporating finite volume methods, Gauss–Legendre quadrature, and mesh discretization to model pulsatile flow in the carotid artery. Simulation results demonstrated that flow rate 𝑸 decreases with increasing arterial radius under turbulent conditions, contrary to laminar Poiseuille predictions, due to enhanced vascular stress and backflow. Furthermore, the model confirmed that velocity positively correlates with flow rate, consistent with fluid mechanics principles. These findings emphasize the influence of arterial geometry and turbulence on flow dynamics, aligning with prior studies on stenosis and bifurcations. In conclusion, the research provides a tractable, physiologically relevant model that bridges simplified Poiseuille theory with complex hemodynamic realities. Policy recommendations include supporting the integration of mathematical modeling into stroke risk screening and accident-related diagnostics, while future studies should validate the model with patientspecific imaging and extend it to non-Newtonian blood properties