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

Authors: Ketan Naik, P. H. Bhathawala

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.

Keywords: Cardiovascular system, lumped parameter method, mathematical modeling, simulation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129133

References:

[1] K. Hassani, M. Navidbakhsh, M. Abdolrazaghi, Mathematical Modelling and Electrical Analog Equivalent of the Human Cardiovascular System, Cardiovascular Engineering, Springer, pp .45- 51, 2010.
[2] A. Avolio, Multi-branched model of the human arterial system, Medical & Biological engineering & Computing, pp. (1980), pp. 709-718, November 1980.
[3] J. T. Ottesen. M. S. Olufsen, J. K. Larsen, Applied Mathematical Models in Human Physiology, Siam Publication, pp.91-153, 2004.
[4] K. Hassani, M. Navidbakhsh, M. Rostami, Simulation of the cardiovascular system using equivalent electronics system, J biomedical papers of medical faculty of the university Palacky, Olomouc. 150(1):pp. 105-112, May2006.
[5] V C. Rideout, Mathematical and computer modeling of physiological system, New Jersey: Prentice-Hall Inc., pp.27-66,1991
[6] M. S. Olufsen, A.Nadim, On deriving lumped models for blood flow and pressure in the systemic arteries. J Math Biosci Eng.;1(1):61.,2004
[7] A C. Guyton, J E. Hall, Text book of Medical Physiology, Eleventh edition, Elsevier Saunders, pp. 161-214, 2006.
[8] J. Keener, J. Sneyd, Mathematical Physiology, Springer- Verlag, New York.Inc. pp. 434-478, 1998.
[9] L. Formaggia, A. Quarteroni, A. Veneziani , Cardiovascular Mathematics, Modeling and simulation of the circulatory system, Springer- Verlag Italia, Milano 2009.
[10] Agam Kumar Tyagi, Matlab and Simulink for Engineers, Oxford University Press, pp. 111-158, 2012.
[11] Boris JA Kogan, Introduction to computational cardiology, Mathematical Modeling and computer simulation, Springer.
[12] Charles S. Peskin, Numerical Analysis of Blood flow in the Heart, Journal of Computational Physics, 25, 220-252 (1977).
[13] Mohammad Reza Mirzaee, Omid Ghasemalizadeh, and Bahar Firoozabadi Simulating of Human Cardiovascular System and Blood Vessel Obstruction Using Lumped Method World Academy of Science, Engineering and Technology 41 2008, Page(s) No.267-274.
[14] Attinger E. O.; Ann; Ã, A, Simulation of the Cardiovascular System, Annals of the New York Academy of Sciences, 1966, Vol. 128, No. 3, Page(s) 810-829
[15] Beneken J.E.W.; Rideout V.C. The Use of Multiple Models in Cardiovascular System Studies: Transportation and Perturbation Methods,” IEEE Transactions on Biomedical Engineering, October 1968, Vol. BME-15, No. 4, Page(s) 281-289
[16] Rideout V.C.; and Katra J.A. Computer Study of the Pulmonary Circulation, Simulation, May 1969, Vol. 12, No. 5, Page(s) 239-245
[17] Snyder M.F.; Rideout V.C. Computer Simulation Studies of the Venous Circulation, IEEE Transactions on Bio-Medical Engineering, October 1969, Vol.BME-16, No. 4, Page(s) 325-334
[18] Rideout V.C.; Dick D.E. Difference-Differential Equations for Fluid Flow in Distensible Tubes, IEEE Trans Biomed Eng, July 1967, Vol. BME-14, No. 3, Page(s) 171-177
[19] Rideout, V.C, Cardiovascular System Simulation in Biomedical Engineering Education, Biomedical Engineering, IEEE Transactions on, March 1972, Vol. BME-19, No. 2, Page(s) 101-107 73
[20] Snyder M.F.; Rideout V.C.; Hillestad R. J. Computer Modeling of the Human Systemic Arterial Tree, Biomech. (Journal of Biomechanics), 1968 ,Vol. 1, Page(s) 341-353.
[21] John O. Attia, Electronics and Circuit Analysis using Matlab, CRC Press.H. Poor, An Introduction to Signal Detection and Estimation. New York: Springer-Verlag, 1985, ch. 4.
[22] F. Y. Liang, S. Takagi, R. Himeno, and H. Liu. Biomechanical characterization of ventricular-arterial coupling during aging: A multiscale model study. Journal of Biomechanics, 42:692-704, 2009.
[23] Nicolaas Westerhof, Nikos Stergiopulos, Mark I. Noble, Snapshorts of Hemodynamics: An Aid for Clinical Research and Graduate Education. DOI 10.1007/978-1-4419.6363.5_38. @ Springer Science + Business Media. LLC 2010.