# Mathematical Modelling and Simulation of Blood Flow in the Human Ascending Aorta: An Analytical Approach

### Abstract

The pulsatile behaviour of blood flow through a healthy aorta was modelled using Navier-Stokes and continuity

equations, while the nature of the aorta wall was accounted for by Hooke’s law. The resulting balance equations

were transformed by using Reynolds transport theorem, and the variables expressed in Fourier modes. Substitution resulted in just one equation expressed in terms of Bessel functions, and which required one characteristic independent variable, k, to be determined. This was obtained by using Wolfram Mathematica to solve the equation along with aorta wall and blood properties (obtained from literature). The characteristic k value used for the prediction of the pulsatile nature of the flow was obtained as 0.139983 + 0.0590188i. Simulated results with

this k value showed variation in blood pressure, aorta expansion and elongation, for a healthy heart to be within typical ranges of 80 – 120 mmHg, and 0 – 4mm respectively. The wavelength and wave speed generated by the blood flow was determined as 14.0848m and 53.8626m/s respectively.

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