Mathematical Blood Flow Model - Simulations and Data Analysis

Abstract

This paper focuses on developing a mathematical model for the human cardiovascular system, simulating the human femoral artery, and analyzing the simulated data. The model describes the blood as a Newtonian fluid, arteries as tapered elastic pipes, and blood flow as oscillatory. Homotopy Analysis Method (HAM) is used to solve the model equations, and two physical quantities, wall shear stress, and volumetric flow rate are computed. With the help of publicly available data on the human femoral artery for both male and female populations with different ages ranging from 19 years to 60+ and with few other model parameters assigned values based on specific mathematical requirements, we carried out simulations. The data generated is then analyzed using clustering algorithms to discover a natural grouping inherent in the data based on the values of the physical quantities computed in place of age-wise grouping. In each cluster, we used nonlinear regression models to predict the dependent variables.