Abstract
We describe simulations of propagated electrical excitation in threedimensional anisotropic myocardial muscle. According to the bidomain theory, anisotropic electrical conductivities are presented as tensors in the intracellular and interstitial domains (D i and D e, respectively). Under the assumption of equal anisotropy ratio (D i = kD e), subthreshold behaviour of the excitable elements is governed by a parabolic reaction-diffusion equation for the membrane potential, solvable even on a desktop computer. In the case of more general anisotropies (D i ≠ kD e), also the interstitial potential needs to be solved simultaneously from an elliptic partial differential equation, requiring a supercomputer for large arrays of excitable elements. In both cases, the elements obey cellular automata rules in the suprathreshold state.We present preliminary results of the propagated excitation for different anisotropy ratios in a three-dimensional slab geometry.
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References
H.J. Ritsema van Eck, “Digital-computer simulation of cardiac excitation and repolarization in man”. PhD thesis, Dalhousie University, Halifax, Canada, 1972.
L. Tung. A bidomain model for describing ischemic myocardial d-c potentials. PhD thesis, Massachusetts Institute of Technology, 1978.
W.T. Miller III and D.B. Geselowitz. Simulation studies of the electrocardiogram: I. The normal heart. Circ Res, 43: 301–315, 1978.
L.J. Leon and B.M. Horáček. Computer model of excitation and recovery in the anisotropic myocardium. J Electrocardiol, 24: 1–41, 1991.
J. Nenonen, J.A. Edens, L.J. Leon, and B.M. Horáček. Computer model of propagated excitation in the anisotropic human heart: I. Implementation and algorithms. In Computers in Cardiology, pages 545–548, IEEE Computer Society Press, Los Alamitos, CA, 1992.
B.M. Horáček, J. Nenonen, J.A. Edens, and L.J. Leon. Ahybrid computer model of propagated excitation in the anisotropic human ventricular myocardium. In: Biomedical and Life Physics, D.N. Ghista, ed. (Viewer Verlag, Wiesbaden, 1996), pp. 181–190.
D.B. Geselowitz and W.T. Miller III. A bidomain model for anisotropic cardiac muscle. Ann. Biomed. Eng., 11: 191–206, 1983.
P. Colli Franzone, L. Guerri, and S. Tentoni. Mathematical modelling of the excitation process in myocardial tissue: influence of fiber rotation on wavefront propagation and potential field. Math. Biosci., 101: 155–235, 1990.
R. Plonsey. Bioelectric Phenomena. McGraw-Hill, NewYork, 1969.
R. Plonsey and R.C. Barr. Current flow patterns in two-dimensional anisotropic bisyncytia with normal and extreme conductivities. Biophys J, 45: 557–571, 1984.
J.J.B. Jack, D. Noble, and R.W. Tsien. Electric Current Flow in Excitable Cells. Clarendon Press, Oxford, 1975.
R. Hren, J. Nenonen, and B.M. Horacek, “Simulated epicardial potential maps during paced activation reflect myocardial fibrous structure”. Ann Biomed Eng 26: 1022–1035, 1998.
K. Simelius, J. Nenonen, and B.M. Horáček. Bidomain simulations of cardiac activation with large elements. Submitted.
C.H. Luo and Y. Rudy. A dynamic model of the cardiac ventricular action potential I. Simulations of ionic currents and concentration changes. Circ. Res., 74: 1071–1096, 1994.
B. Roth. Action potential propagation in a thick strand of cardiac muscle. Circ. Res., 68: 162–173, 1991.
C.S. Henriquez, A.L. Muzikant, and C.K. Smoak. Anisotropy, fiber curvature, and bath loading effects on activation in thin and thick cardiac tissue preparations: Simulations in a three-dimensional bidomain model. J. Cardiovasc. Electrophys., 7: 424–444, 1996.
B.J. Roth. Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Trans. Biomed. Eng., 44: 326–328, 1997.
R.M. Gulrajani. Models of the electrical activity of the heart and computer simulation of the electrocardiogram. CRC Crit Rev Biomed Eng 16: 1–61, 1988.
A. Muler, and V. Markin. Electrical properties of anisotropic nerve-muscle bisyncytia-III. Steady form of the excitation front. Biofizika 22: 671–675, 1977.
D. Durrer, R.Th. van Dam, G.E. Freud, M.J. Janse, F.J. Mejler, and R.C. Artzbaecher. Total excitation of the isolated human heart. Circulation 41: 899–912, 1970.
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Simelius, K., Nenonen, J., Horáček, B.M. (2001). Simulation of Anisotropic Propagation in the Myocardium with a Hybrid Bidomain Model. In: Katila, T., Nenonen, J., Magnin, I.E., Clarysse, P., Montagnat, J. (eds) Functional Imaging and Modeling of the Heart. FIMH 2001. Lecture Notes in Computer Science, vol 2230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45572-8_20
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DOI: https://doi.org/10.1007/3-540-45572-8_20
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