Abstract
This article presents a detailed analytical evaluation and comprehensive description of a mathematical model designed to simulate blood flow within the human cardiovascular system. The primary objective of this research is to develop a computational model capable of accurately simulating blood flow dynamics and to assess the variations in results using different numerical methods for solving the Navier-Stokes equations, which govern fluid motion. To achieve this, the study begins with an in-depth examination of the anatomy of the cardiovascular system, including various cardiovascular diseases such as stenosis and atherosclerosis, which significantly affect blood flow. The model incorporates important characteristics of blood, treating it as a viscous fluid under laminar flow conditions. Using the Navier-Stokes equations, it was developed a Python-based model to simulate these flow conditions and solve for different flow variables, such as velocity and pressure fields, under both normal and pathological conditions. The computational model was developed using two numerical methods: the Euler method and the Alternating Direction Implicit (ADI) method, which were compared in terms of their computational efficiency and accuracy. The simulations generated insights into how plaque buildup (stenosis) affects blood flow by altering wall shear stress and velocity profiles. This model, while built on foundational fluid dynamics principles, serves as an essential step towards creating a virtual reality (VR) surgical simulator for cardiovascular procedures. This simulator aims to assist surgeons in visualizing and planning surgical interventions by providing an interactive and realistic environment for studying blood flow and related complications.