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.
 K. Hassani, M. Navidbakhsh, M. Abdolrazaghi, Mathematical
Modelling and Electrical Analog Equivalent of the Human
Cardiovascular System, Cardiovascular Engineering, Springer, pp .45-
 A. Avolio, Multi-branched model of the human arterial system, Medical
& Biological engineering & Computing, pp. (1980), pp. 709-718,
 J. T. Ottesen. M. S. Olufsen, J. K. Larsen, Applied Mathematical Models
in Human Physiology, Siam Publication, pp.91-153, 2004.
 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.
 V C. Rideout, Mathematical and computer modeling of physiological
system, New Jersey: Prentice-Hall Inc., pp.27-66,1991
 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
 A C. Guyton, J E. Hall, Text book of Medical Physiology, Eleventh
edition, Elsevier Saunders, pp. 161-214, 2006.
 J. Keener, J. Sneyd, Mathematical Physiology, Springer- Verlag, New
York.Inc. pp. 434-478, 1998.
 L. Formaggia, A. Quarteroni, A. Veneziani , Cardiovascular
Mathematics, Modeling and simulation of the circulatory system,
Springer- Verlag Italia, Milano 2009.
 Agam Kumar Tyagi, Matlab and Simulink for Engineers, Oxford
University Press, pp. 111-158, 2012.
 Boris JA Kogan, Introduction to computational cardiology,
Mathematical Modeling and computer simulation, Springer.
 Charles S. Peskin, Numerical Analysis of Blood flow in the Heart,
Journal of Computational Physics, 25, 220-252 (1977).
 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.
 Attinger E. O.; Ann; Ã, A, Simulation of the Cardiovascular System,
Annals of the New York Academy of Sciences, 1966, Vol. 128, No. 3,
 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
 Rideout V.C.; and Katra J.A. Computer Study of the Pulmonary
Circulation, Simulation, May 1969, Vol. 12, No. 5, Page(s) 239-245
 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
 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
 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
 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.
 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.
 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.
 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.