MODELLING GEOMETRY INTERRUPTION, VASCULAR STRESS, AND PULSATILITY IN CAROTID ARTERY BLOOD FLOW USING POISEUILLE-BASED EQUATIONS

Abstract

The Poiseuille equations are instrumental in modeling blood flow, particularly within large and medium-sized arteries where laminar flow predominates. Derived under the assumption

of steady, incompressible, Newtonian flow through cylindrical tubes, these equations effec- tively describe vascular dynamics in geometries approximating cylindrical shapes and at low

Reynolds numbers. However, their applicability diminishes in regions characterized by tur- bulence, geometric irregularities, or pulsatile flow, such as those found in the carotid artery.

This study identifies three key research gaps in the application of Poiseuille equations to

carotid artery hemodynamics: (i) the influence of vascular shear stress under turbulent condi- tions, (ii) the deviation introduced by pulsatile flow from the steady-state assumption inherent

in the Poiseuille model, and (iii) the geometric variability of the carotid artery and its under- explored role in altering flow characteristics. To address these gaps, the study introduces a

novel formulation of the Poiseuille equation incorporating geometric drag and pulsatile flow through a Womersley function. Governing equations were formulated based on modified Poiseuille flow and solved numerically using the Finite Volume Method (FVM) implemented

in MATLAB, with custom code developed to simulate time-dependent blood flow. The nu- merical scheme incorporated discretization of the Navier–Stokes equations and was executed

using MATLAB’s built-in solvers and post-processing tools for velocity, pressure, and vascu- lar stress visualization. The simulation results revealed a significant reduction in flow rate and

velocity in regions with geometric interruptions. For example, the peak simulated velocity reduced by approximately 28% in stenosed segments compared to normal arterial sections, demonstrating a nonlinear velocity profile consistent with observed clinical behavior. The simulations further indicated that geometric disturbances, such as stenosis and bifurcations,

resulted in an increase in vascular stress and a pronounced decrease in flow rate (Q), partic- ularly under turbulent conditions. This inverse relationship between vessel radius and flow

dynamics corroborates findings from existing studies on stenotic arteries. Additionally, the analysis demonstrated that as artery radius (r) decreased, vascular stress W(r, t) increased substantially, in line with predictions from Hagen–Poiseuille’s law. Pulsatility during systolic phases further amplified wall shear stress (WSS), thus supporting the third objective of the

study. The findings emphasize the limitations of the classical Poiseuille-based model in tur- bulent and pulsatile regimes and highlight the necessity for more robust modeling approaches

to accurately capture the complex hemodynamics of carotid artery flow under pathological conditions.