RESPONSE INTERACTION OF ARTERY UNDER MECHANICAL VIBRATION

Abstract

Hypertension or high blood pressure, sometimes called arterial hypertension, is a chronic medical condition in which the blood pressure in the arteries is elevated.  The aim of this work was to analyse mathematically the vibration of the artery and show its relationship to hypertension related cases.  Principles of conservation of mass and momentum inline with Euler-Bernoulis method were used.  By idealising the artery resting on the tissue as an elastic beam that is resting partially on an elastic continuum and simply supported, a boundary value partial differential equation governing the blood- artery- interaction mechanics was formulated. The governing partial differential  equation for the problem was obtained and after linearization was solved using integral methods of Fourier-Laplace Transform.  Simulations for some cases were carried out varying some choice parameters.  Findings show that natural frequency of the artery decreases with increase in the mean arterial pressure (MAP).  It was equally found out that vibration of the artery generally increases with increase in MAP and increase in mode.  It was thus concluded that mechanical vibration of the artery increases with increase in blood pressure, and continuous vibration can lead to fatigue and failure which can cause obstruction in the supply of blood to other parts of the body and may lead to stroke.