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# 2021, Vol. 6, Issue 4, Part B

##### Mathematical modeling of blood flow

Author(s): Mohd Iqbal Khoja and Bhawna Agrawal

Abstract: The interface between mathematics and biology has initiated and adopted new mathematical areas, where the ideas from mathematics and biology are synergistically applied. In this paper will show mathematical modelling of blood flow with the help of Study of fluid dynamics. Fluid dynamics plays a noteworthy role in fluid flow inside the human body, and modeling of blood flow is an important field in cardiovascular physics. This paper presents a different and simple mathematical model of the blood flow and the blood pressure through Artery. The main fluid component of the cardiovascular system is the blood which flows through the different blood vessels in the body. Though blood is the non-Newtonian fluid, in many cases, it behaves like a Newtonian fluid which is governed by the Navier-Stokes equations. With the assistance of continuity equation and the Navier-Stokes equations, a humble differential equation was derived under some assumption, which is called as the cardiovascular system equation. A procedure of nonlinear partial differential equations for blood flow and the cross-sectional area of the artery was attained. Finite modification method was adopted to explain the equations numerically. The result found is very sensitive to the values of the initial conditions and this supports to clarify the state of hypertension. By applying the reasonable traditions on this Cardiovascular System equation, simple mathematical model of the normal blood flow established. The consequence gained is very sensitive to the values of the initial conditions and this helps to explain the condition of hypertension. Then this model was extended for normal blood pressure using the Poisuelli's equation. At the end of this study, some analysis had been achieved to determine the validity of the proposed model. The analysis displayed that the model can satisfy both the different properties of blood flow and blood pressure.