Mathematical modeling of the heart

Muhammad Shoaib, M. A. Haque, M. Asaduzzaman
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引用次数: 11

Abstract

This paper presents a new mathematical model of the human heart. Heart is the mother component of the cardiovascular system that consists of four chambers and it is responsible for collecting blood from different parts of the body and pumping the required blood throughout the body. Although 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 help of continuity equation and the Navier-Stokes equations, a simple differential equation was derived under some assumption which is called as the master equation. Then by applying the logical assumption on this master equation, the general mathematical model of the normal heart was developed. From the graphical analysis, the heart rate at the normal condition was estimated. At the end of this study, some analysis had been performed whether the proposed model can represents the different heart abnormalities like heart blockage, leakage etc. The analysis showed that the model can satisfy both the normal and abnormal condition of the heart.
心脏的数学建模
本文提出了一种新的人体心脏数学模型。心脏是由四个腔室组成的心血管系统的主要组成部分,它负责从身体的不同部位收集血液,并将所需的血液输送到全身。虽然血液是非牛顿流体,但在许多情况下,它的行为就像牛顿流体一样,受纳维-斯托克斯方程的支配。利用连续性方程和Navier-Stokes方程,在一定的假设条件下导出了一个简单的微分方程,称为主方程。然后应用该主方程的逻辑假设,建立了正常心脏的一般数学模型。通过图形分析,估计正常情况下的心率。在本研究的最后,我们对所提出的模型是否能够代表心脏阻塞、心脏渗漏等不同的心脏异常进行了分析。分析表明,该模型既能满足正常状态,又能满足异常状态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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