Mathematical Modeling of Human Cardiovascular System: A Lumped Parameter Approach and Simulation

Abstract—The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.

[1]  V C Rideout,et al.  The use of multiple models in cardiovascular system studies: transport and perturbation methods. , 1968, IEEE transactions on bio-medical engineering.

[2]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[3]  V C Rideout,et al.  Cardiovascular system simulation in biomedical engineering education. , 1972, IEEE transactions on bio-medical engineering.

[4]  M. Olufsen,et al.  On deriving lumped models for blood flow and pressure in the systemic arteries. , 2004, Mathematical biosciences and engineering : MBE.

[5]  A. Guyton,et al.  Text book of medical physiology , 2013 .

[6]  B. Westerhof,et al.  Snapshots of Hemodynamics: An Aid for Clinical Research and Graduate Education , 2018 .

[7]  E. Attinger,et al.  SIMULATION OF THE CARDIOVASCULAR SYSTEM * , 1966 .

[8]  Mostafa Rostami,et al.  Simulation of the cardiovascular system using equivalent electronic system. , 2006, Biomedical papers of the Medical Faculty of the University Palacky, Olomouc, Czechoslovakia.

[9]  Boris Kogan.  Introduction to Computational Cardiology: Mathematical Modeling and Computer Simulation , 2009 .

[10]  V. Rideout,et al.  Difference-differential equations for fluid flow in distensible tubes. , 1967, IEEE transactions on bio-medical engineering.

[11]  James P. Keener,et al.  Mathematical physiology , 1998 .

[12]  M. F. Snyder,et al.  Computer simulation studies of the venous circulation. , 1969, IEEE transactions on bio-medical engineering.

[13]  A. P. Avó.  Multi-branched model of the human arterial system , 2006 .

[14]  Vincent C. Rideout,et al.  Mathematical and Computer Modeling of Physiological Systems , 1991 .

[15]  R. Himeno,et al.  Biomechanical characterization of ventricular-arterial coupling during aging: a multi-scale model study. , 2009, Journal of biomechanics.

[16]  Agam Kumar Tyagi,et al.  MATLAB and SIMULINK for Engineers , 2012 .

[17]  John O. Attia.  Electronics and Circuit Analysis Using MATLAB , 1999 .

[18]  R J Hillestad,et al.  Computer modeling of the human systemic arterial tree. , 1968, Journal of biomechanics.

[19]  Kamran Hassani,et al.  Mathematical Modelling and Electrical Analog Equivalent of the Human Cardiovascular System , 2010, Cardiovascular engineering.

[20]  V. Rideout,et al.  Computer simulation study of the pulmonary circulation , 1969 .