A Mathematical Model of Pulsatile Blood Flow in Stenotic Vessel Using the Finite Difference Method

Source abstract

Stenosis causes changes in blood flow characteristics that affect velocity distribution, thereby requiring a mathematical model to analyse these changes. This study aims to develop a mathematical model of pulsatile blood flow in a stenosed vessel and to analyse the effects of two degrees of stenosis ( and ) and two Reynolds numbers ( and on the blood flow velocity distribution. The model was developed based on the continuity and Navier–Stokes equations, assuming blood to be a Newtonian fluid. Subsequently, the equations were simplified into a dimensionless form through nondimensionalisation and radial coordinate transformation, and then solved numerically using the Finite Difference method. The simulation results show that increasing the degree of stenosis increases the axial and radial velocities around the stenosis throat, whereas increasing the Reynolds number produces a sharper velocity distribution accompanied by the emergence of local oscillations downstream of the stenotic region. Model validation against the reference shows that the obtained velocity distributions are consistent with previous research, while verification of the flow rate and continuity equation residual demonstrates the numerical consistency of the developed model. Therefore, the developed model is capable of representing the effects of stenosis degree and Reynolds number on the velocity distribution of pulsatile blood flow in a stenosed vessel.