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An analytical approach of the nonlinear implicit system of partial differential equations on blood flow loop through the arteries in a human body

Author: 
Mohammed Nizam Uddin, A.N.M. Rezaul Karim, and Taslima Akter
Subject Area: 
Physical Sciences and Engineering
Abstract: 

The unsteady flow phenomena dominate the blood stream in arteries. The cardiovascular system in the human body can be defined as an inner loop with a complex liquid flowing in multiple branches. Further, the relationship between viscous and unsteady forces is governed primarily, by the Womersley number, a non-dimensional frequency parameter. By the Finite Element method, the researcher is able to resolve the resultant nonlinear implicit system related to partial differential equation. By generating secondary flow in branches and curves, the normal arterial flow remains laminar. The arteries in the human body remain the living organs, capable of changing and adapt to varying hemodynamic conditions, however, in some particular situations, an abnormal biological response is created by unusual hemodynamic conditions. Due to the skewing of the velocity profile, the creation of pockets, takes place in the cardiovascular system, with which the oscillation of the direction of wall shear stress takes place. These sites remain the core of Atherosclerotic disease and that further, results in stenosis or the narrowing of the artery lumen. Due to stenosis, the human body suffers from turbulence and a reduction of flower due to flow choking and viscous head losses. Further, due to extremely high shear stresses near stenosis throat, the platelets are activated, that, further, leads to thrombosis, that, again, retains the capability of blocking the complete blood flow both to the brain and the heart. For surgical intervention, the detection, as well as quantification of stenosis remains the basis. In future studies, the research related to of arterial blood flow would definitely lead to the accurate hemodynamic flow in any particular patient, the development of the accurate diagnostic tools for quantifying the level of the disease, as well as the design various devices required to mimic as well as alter the flow of the blood. When compared to other research, the field of fluid mechanics offers considerable challenges that involve three-dimensional, pulsatile flows at the edge of turbulence.

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