A Novel Poiseuille-Based Mathematical Model for Carotid Artery Blood Flow: Modelling Geometry Interruptions and Vascular Stress during Accidents

Abstract: Carotid artery injuries during accidents are a significant contributor to trauma-related morbidity and mortality, necessitating accurate models for predicting vascular stress and flow disruption. Existing approaches either oversimplify flow and underestimate wall shear stress, neglect trauma-induced geometric interruptions, or require computationally intensive methods unsuitable for emergency use. To address these limitations, this study develops a hybrid Poiseuille–Womersley model that integrates distributed and localized pressure loss terms, a geometric penalty factor for lumen constriction, and pulsatile corrections to capture transient flow dynamics. Analytical derivations supported by simulation reveal that accident-induced reductions in carotid lumen diameter cause disproportionate declines in volumetric flow rate, sharp decreases in wall shear stress, and alterations in velocity fields that cannot be captured by steady-state assumptions. The model thus extends classical hemodynamic formulations to accident scenarios, providing an efficient yet physiologically consistent framework. These results confirm geometry as a primary driver of vascular stress under trauma conditions. The study concludes that lightweight analytical models can complement diagnostic and emergency care tools, offering rapid assessment capability. Policy makers and clinicians are encouraged to incorporate such trauma-informed hemodynamic tools into stroke prevention and emergency response strategies, while future work should focus on clinical validation, patient-specific adaptation, and integration with real-time Doppler imaging. Keywords: Carotid artery, Poiseuille flow, Womersley function, Vascular stress, Geometric interruption, Wall shear stress. Title: A Novel Poiseuille-Based Mathematical Model for Carotid Artery Blood Flow: Modelling Geometry Interruptions and Vascular Stress during Accidents Author: Lucy Jerop Ngetich, Shichikha Maremwa, Kandie Joseph, Momanyi Mogire Krifix International Journal of Recent Research in Mathematics Computer Science and Information Technology ISSN 2350-1022 Vol. 12, Issue 1, April 2025 - September 2025 Page No: 91-103 Paper Publications Website: www.paperpublications.org Published Date: 25-September-2025 DOI: https://doi.org/10.5281/zenodo.17199836 Paper Download Link (Source) https://www.paperpublications.org/upload/book/A%20Novel%20Poiseuille-Based%20Mathematical-25092025-5.pdf