A Novel Poiseuille Equation Framework for Pulsatile Flow Dynamics in Accident-Induced Carotid Artery Constrictions

Abstract

Stroke and carotid artery injury remain significant contributors to global morbidity, with accident-induced disruptions in blood flow presenting acute clinical risks. Existing modelling approaches are either overly simplistic, relying on steady Poiseuille theory, or computationally demanding, as in fluid–structure interaction simulations, which limits their use in real-time diagnostic settings. This paper proposes a novel Poiseuille-based mathematical model that incorporates accident-like geometry interruptions and pulsatility via a nine-point stencil, a geometrypenalty factor, and a Womersley-inspired correction term. Using physiologically validated parameters for viscosity, density, and pressure gradients, the model reproduces key hemodynamic markers including volumetric flow, velocity fields, and wall shear stress under both normal and obstructed conditions. The findings show that even modest reductions in lumen radius lead to sharp declines in flow and shear, while pulsatility modifies waveform oscillations without altering the magnitude of disruption. The study concludes that geometry remains the primary driver of hemodynamic collapse, while pulsatility governs temporal detail. By providing a computationally efficient and clinically interpretable surrogate, the model bridges the gap between oversimplified analytical solutions and resource-intensive CFD. It is recommended that such reduced-order frameworks be integrated into clinical risk screening and trauma diagnostics, with future work directed toward validation against patient-specific data and incorporation of non-Newtonian blood properties.