Dynamical modelling of cardiac electrical activity using bidomain approach: The effects of variation of ionic model parameters

Affiliation(s)

Department of Electrical and Electronics Engineering, Federal University of Agriculture, Abeokuta, Nigeria.

Manchester Institute of Biotechnology, School of Computer Science, The University of Manchester, Manchester, UK.

Department of Electrical and Electronics Engineering, Federal University of Agriculture, Abeokuta, Nigeria.

Manchester Institute of Biotechnology, School of Computer Science, The University of Manchester, Manchester, UK.

ABSTRACT

This work presents the dynamical modelling of cardiac electrical
activity using bidomain approach. It focuses on the effects of variation of the
ionic model parameters on cardiac wave propagation. Cardiac electrical
activity is governed by partial differential equations coupled to a system of
ordinary differential equations. Numerical simulation of these equations is computationally expensive due to their non-linearity and stiffness. Nevertheless, we
adopted the bidomain model due to its ability to reflect the actual cardiac
wave propagation. The derived bidomain equations coupled with FitzHugh-Nagumo’s
ionic equations were time-discretized using explicit forward Euler method and
space-discretized using 2-D network modelling to obtain linearized equations
for transmembrane potential *V _{m}*,
extracellular potential

KEYWORDS

Dynamical Modelling; Cardiac Electrical Activity; Bidomain Model, Ionic Model Parameters; Discretization; Transmembrane Potential

Dynamical Modelling; Cardiac Electrical Activity; Bidomain Model, Ionic Model Parameters; Discretization; Transmembrane Potential

Cite this paper

Ibrahim, A. , Adediji, A. and Olufemi, D. (2013) Dynamical modelling of cardiac electrical activity using bidomain approach: The effects of variation of ionic model parameters.*Journal of Biomedical Science and Engineering*, **6**, 598-608. doi: 10.4236/jbise.2013.66076.

Ibrahim, A. , Adediji, A. and Olufemi, D. (2013) Dynamical modelling of cardiac electrical activity using bidomain approach: The effects of variation of ionic model parameters.

References

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[2] World Health Organization (2010) Global status report on non communicable diseases. http://www.who.int/nmh/publications/ncd_report_full_en.pdf

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[5] Spiteri, R.J. and Dean, R.C. (2008) On the performance of an implicit-explicit Runge-Kutta method in models of cardiac electrical activity. IEEE Transactions on Biomedical Engineering, 55, 1488-1495. doi:10.1109/TBME.2007.914677

[6] Shuaiby, M.S., Mohsen, A.H. and Moumen, E. (2012) Modeling and simulation of the action potential in human cardiac tissue using finite element method. Journal of Communications and Computer Engineering, 2, 21-27.

[7] Alin, A.D., Alexandru, M.M., Mihaela, M. and Corina, M.I. (2011) Numerical simulation in electrocardiography. Revue Roumaine des Sciences Techniques. Série électrotechnique et énergétique, 56, 209-218.

[8] Pormann, J.-B., Henriquez, C.S., Board, J.A., Rose, D.J., Harild, D.M. and Henriquez, A.P. (2000) Computer simulations of cardiac electrophysiology. ACM/IEEE Supercomputing Conference, Duke University, Duke, 4-10 November 2000.

[9] Sundnes, J., Nielsen, B.F., Mardal, K.A., Cai, X., Lines, G.T. and Tveito, A. (2006) On the computational complexity of the bidomain and the monodomain models of electrophysiology. Annals of Biomedical Engineering, 34, 1088-1097. doi:10.1007/s10439-006-9082-z

[10] Mark, P., Bruno, D., Jacques, R., Alain, V. and Ramesh, M.G. (2006) A comparison of monodomain and bidomain reaction-diffusion models of action potential in the human heart. IEEE Transactions on Biomedical Engineering, 53, 2425-2435. doi:10.1109/TBME.2006.880875

[11] Bordas, R., Carpentieri, B., Fotia, G., Maggio, F., Nobes, R., Pitt-Francis, J. and Southern, J. (2009) Simulation of cardiac electrophysiology on next-generation high performance computers. Philosophical Transactions of the Royal Society A, 367, 1951-1969. doi:10.1098/rsta.2008.0298

[12] Linge, S., Southern, J., Hanslien, M., Lines, G.T. and Tveito, A. (2009) Numerical simulation of the bidomain equations. Philosophical Transactions of the Royal Society A, 367, 1931-1950. doi:10.1098/rsta.2008.0306

[13] Belhamadia, Y. (2010) Recent numerical methods in electrocardiology. In: Campolo, D., Ed., New Development in Biomedical Engineering, 151-162. http://www.intechopen.com/book

[14] Henriquez, C.S. (1993) Simulating the electrical behaveiour of cardiac tissue using the bidomain model. Critical Reviews in Biomedical Engineering, 21, 1-77.

[15] Edminister, J.A. (2006) Electromagnetics. 2nd Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi.

[16] Hayt, W.H. and Buck, J.A. (2006) Engineering electromagnetics. 7th Edition, McGraw-Hill Education Private Limited, New Delhi.

[17] Reddy, S.R. (2002) Electromagnetic theory. V. Ramesh Publisher, Chennai.

[18] Matthias, G. (2011) 3D bidomain equation for muscle fibers. M.S. Thesis, Fredrich Alexander Universität Erlangen Nürnberg, Germany.

[19] Vigmond, E.J., dosSantos, R.W., Prassl, A.J., Deo, M. and Plank, G. (2008) Solvers for the cardiac bidomain equations. Progress in Biophysics and Molecular Biology, 96, 3-18. doi:10.1016/j.pbiomolbio.2007.07.012

[20] Boulakia, M., Fernandez, M.A., Gerbeau, J.-F. and Zemzemi, N. (2009) Mathematical modelling of electrocardiograms: A numerical study. Annals of Biomedical Engineering, 38, 1071-1097. doi:10.1007/s10439-009-9873-0

[21] Boulakia, M., Fernandez, M.A., Gerbeau, J.-F. and Zemzemi, N. (2007) Towards the numerical simulation of electrocardiograms. In: Sachse, F.B. and Seemann, G., Eds., Functional Imaging and Modeling of the Heart, Springer-Verlag, Berlin, 240-249.

[22] Niels, O.F. (2003) Bidomain model of cardiac excitation. http://pages.physics.cornell.edu

[23] Quarteroni, A., Sacco, R. and Saleri, F. (2007) Numerical mathematics. Text in Applied Mathematics, Vol. 37, Springer-Verlag, Berlin.

[24] Nigel, F.H. (1992) Efficient simulation of action potential propagation in a bidomain. Ph.D. Thesis, Duke University, Durhan.

[25] Rocha, B.M., Campros, F.O., Planck, G., dos-Santos, R.W., Liebmann, M. and Haase, G.C. (2009) Simulation of electrical activity in the heart with graphical processing units. Austria SFB Report No. 2009-016.

[26] Dada, J.O. and Mendes, P. (2011) Multiscale modelling and simulation in systems biology. Integrative Biology, 3, 86-96. doi:10.1039/c0ib00075b

[27] Dada, J.O. and Mendes, P. (2012) Many Cell: A multiscale simulator for cellular systems. In: Gilbert, D. and Heiner, M., Eds., LNCS, Springer, Heidelberg, 7605, 366369.

[1] Ekwunife, O.I. and Aguwa, C.N. (2011) A meta-analysis of prevalence rate of hypertension in Nigeria populations. Journal of Public Health and Epidemiology, 3, 604-607.

[2] World Health Organization (2010) Global status report on non communicable diseases. http://www.who.int/nmh/publications/ncd_report_full_en.pdf

[3] Wiki (2011) Electrophysiology. http://en.wikipedia.org/wiki/electrophysiology

[4] DiMasi, J.A., Hansen, R.W. and Grabowski, H.G. (2003) The price of innovation: New estimates of drug development costs. Journal of Health Economics, 22, 151-185. doi:10.1016/S01676296(02)00126-1

[5] Spiteri, R.J. and Dean, R.C. (2008) On the performance of an implicit-explicit Runge-Kutta method in models of cardiac electrical activity. IEEE Transactions on Biomedical Engineering, 55, 1488-1495. doi:10.1109/TBME.2007.914677

[6] Shuaiby, M.S., Mohsen, A.H. and Moumen, E. (2012) Modeling and simulation of the action potential in human cardiac tissue using finite element method. Journal of Communications and Computer Engineering, 2, 21-27.

[7] Alin, A.D., Alexandru, M.M., Mihaela, M. and Corina, M.I. (2011) Numerical simulation in electrocardiography. Revue Roumaine des Sciences Techniques. Série électrotechnique et énergétique, 56, 209-218.

[8] Pormann, J.-B., Henriquez, C.S., Board, J.A., Rose, D.J., Harild, D.M. and Henriquez, A.P. (2000) Computer simulations of cardiac electrophysiology. ACM/IEEE Supercomputing Conference, Duke University, Duke, 4-10 November 2000.

[9] Sundnes, J., Nielsen, B.F., Mardal, K.A., Cai, X., Lines, G.T. and Tveito, A. (2006) On the computational complexity of the bidomain and the monodomain models of electrophysiology. Annals of Biomedical Engineering, 34, 1088-1097. doi:10.1007/s10439-006-9082-z

[10] Mark, P., Bruno, D., Jacques, R., Alain, V. and Ramesh, M.G. (2006) A comparison of monodomain and bidomain reaction-diffusion models of action potential in the human heart. IEEE Transactions on Biomedical Engineering, 53, 2425-2435. doi:10.1109/TBME.2006.880875

[11] Bordas, R., Carpentieri, B., Fotia, G., Maggio, F., Nobes, R., Pitt-Francis, J. and Southern, J. (2009) Simulation of cardiac electrophysiology on next-generation high performance computers. Philosophical Transactions of the Royal Society A, 367, 1951-1969. doi:10.1098/rsta.2008.0298

[12] Linge, S., Southern, J., Hanslien, M., Lines, G.T. and Tveito, A. (2009) Numerical simulation of the bidomain equations. Philosophical Transactions of the Royal Society A, 367, 1931-1950. doi:10.1098/rsta.2008.0306

[13] Belhamadia, Y. (2010) Recent numerical methods in electrocardiology. In: Campolo, D., Ed., New Development in Biomedical Engineering, 151-162. http://www.intechopen.com/book

[14] Henriquez, C.S. (1993) Simulating the electrical behaveiour of cardiac tissue using the bidomain model. Critical Reviews in Biomedical Engineering, 21, 1-77.

[15] Edminister, J.A. (2006) Electromagnetics. 2nd Edition, Tata McGraw-Hill Publishing Company Limited, New Delhi.

[16] Hayt, W.H. and Buck, J.A. (2006) Engineering electromagnetics. 7th Edition, McGraw-Hill Education Private Limited, New Delhi.

[17] Reddy, S.R. (2002) Electromagnetic theory. V. Ramesh Publisher, Chennai.

[18] Matthias, G. (2011) 3D bidomain equation for muscle fibers. M.S. Thesis, Fredrich Alexander Universität Erlangen Nürnberg, Germany.

[19] Vigmond, E.J., dosSantos, R.W., Prassl, A.J., Deo, M. and Plank, G. (2008) Solvers for the cardiac bidomain equations. Progress in Biophysics and Molecular Biology, 96, 3-18. doi:10.1016/j.pbiomolbio.2007.07.012

[20] Boulakia, M., Fernandez, M.A., Gerbeau, J.-F. and Zemzemi, N. (2009) Mathematical modelling of electrocardiograms: A numerical study. Annals of Biomedical Engineering, 38, 1071-1097. doi:10.1007/s10439-009-9873-0

[21] Boulakia, M., Fernandez, M.A., Gerbeau, J.-F. and Zemzemi, N. (2007) Towards the numerical simulation of electrocardiograms. In: Sachse, F.B. and Seemann, G., Eds., Functional Imaging and Modeling of the Heart, Springer-Verlag, Berlin, 240-249.

[22] Niels, O.F. (2003) Bidomain model of cardiac excitation. http://pages.physics.cornell.edu

[23] Quarteroni, A., Sacco, R. and Saleri, F. (2007) Numerical mathematics. Text in Applied Mathematics, Vol. 37, Springer-Verlag, Berlin.

[24] Nigel, F.H. (1992) Efficient simulation of action potential propagation in a bidomain. Ph.D. Thesis, Duke University, Durhan.

[25] Rocha, B.M., Campros, F.O., Planck, G., dos-Santos, R.W., Liebmann, M. and Haase, G.C. (2009) Simulation of electrical activity in the heart with graphical processing units. Austria SFB Report No. 2009-016.

[26] Dada, J.O. and Mendes, P. (2011) Multiscale modelling and simulation in systems biology. Integrative Biology, 3, 86-96. doi:10.1039/c0ib00075b

[27] Dada, J.O. and Mendes, P. (2012) Many Cell: A multiscale simulator for cellular systems. In: Gilbert, D. and Heiner, M., Eds., LNCS, Springer, Heidelberg, 7605, 366369.