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Modeling ventricular excitation: Axial and orthotropic anisotropy effects on wavefronts and potentials. (English) Zbl 1081.92010

Summary: By applying the eikonal approximation to the bidomain model of the cardiac tissue we investigate the influence of the axially isotropic and orthotropic conductivity tensors on the propagation of the excitation wavefronts and on the associated potential distribution and electrograms.

MSC:

92C30 Physiology (general)
78A70 Biological applications of optics and electromagnetic theory
92C35 Physiological flow
65C20 Probabilistic models, generic numerical methods in probability and statistics
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References:

[1] Bellettini, G.; Colli Franzone, P.; Paolini, M., Convergence of front propagation for anisotropic bistable reaction-diffusion equations, Asymp. Anal., 15, 325 (1997) · Zbl 0902.35052
[2] Colli Franzone, P.; Guerri, L.; Tentoni, S., Mathematical modeling of the excitation process in the myocardial tissue: influence of the fiber rotation on the wavefront propagation and the potential field, Math. Biosci., 101, 155 (1990) · Zbl 0723.92007
[3] Colli Franzone, P.; Guerri, L.; Taccardi, B., Spread of excitation in a myocardial volume: simulation studies in a model of anisotropic ventricular muscle, J. Cardiovasc. Electrophysiol., 4, 144 (1993)
[4] Colli Franzone, P.; Guerri, L.; Pennacchio, M.; Taccardi, B., Spread of excitation in 3-D models of the anisotropic cardiac tissue. I: validation of the eikonal approach, Math. Biosci., 113, 145 (1993) · Zbl 0786.92012
[5] Spread of excitation in 3-D models of the anisotropic cardiac tissue. III: effects of ventricular geometry and fiber structure on the potential distribution, Math. Biosci., 151, 51 (1998) · Zbl 0938.92009
[6] Colli Franzone, P.; Pennacchio, M.; Guerri, L., Accurate computation of electrograms in the left ventricular wall, Math. Mod. Meth. Appl. Sci. \(M^3\) AS, 10, 4, 507 (2000) · Zbl 1008.92016
[7] Colli Franzone, P.; Guerri, L.; Pennacchio, M.; Taccardi, B., Anisotropic mechanisms for multiphasic unipolar electrograms. Simulation studies and experimental recordings, Ann. Biomed. Eng., 28, 1 (2000)
[8] Costa, K. D.; May-Newman, K.; Farr, D.; O’Dell, W. G.; McCulloch, A. D.; Omens, J. H., Three-dimensional residual strain in midanterior canine left ventricle, Am. J. Physiol. (Heart Circ. Physiol.), 42, H1968 (1997)
[9] Geselowitz, D. B., On the theory of the electrocardiogram, Proc. IEEE, 77, 857 (1989)
[10] LeGrice, I. J.; Smaill, B. H.; Chai, L. Z.; Edgar, S. G.; Gavin, J. B.; Hunter, P. J., Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog, Am. J. Physiol. 269 (Heart Circ. Physiol.), 38, H571 (1995)
[11] LeGrice, I. J.; Smaill, B. H.; Hunter, P. J., Laminar structure of the heart: a mathematical model, Am. J. Physiol. 272 (Heart Circ. Physiol.), 41, H2466 (1997)
[12] Keener, J. P., An eikonal-curvature equation for the action potential propagation in myocardium, J. Math. Biol., 29, 629 (1991) · Zbl 0744.92015
[13] Henriquez, C. S., Simulating the electrical behavior of cardiac tissue using the bidomain model, Crit. Rev. Biomed. Eng., 21, 1 (1993)
[14] Henriquez, C. S.; Muzikant, A. L.; Smoak, C. K., 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. Electrophysiol., 7, 5, 424 (1996)
[15] Punske, B. B.; Ni, Q.; Lux, R. L.; MacLeod, R. S.; Ershler, P. R.; Dustman, T. J.; Allison, M. J.; Taccardi, B., Spatial methods of epicardial activation time determination in normal hearts, Ann. Biomed. Eng., 31, 1 (2003)
[16] Simms, H. D.; Geselowitz, D. B., Computation of heart surface potentials using the surface source model, J. Cardiovasc. Electrophysiol., 6, 522 (1995)
[17] Streeter, D. D., Gross morphology and fiber geometry of the heart, (Berne, R. M., Handbook of Physiology. Handbook of Physiology, The Heart, Sec. 2: the Cardiovascular System, vol. 1 (1979), Williams and Wilkins: Williams and Wilkins Baltimore, MD), 61, (Chapter 4)
[18] Taccardi, B.; Macchi, E.; Lux, R. L.; Ershler, P. R.; Spaggiari, S.; Baruffi, S.; Vyhmeister, Y., Effect of myocardial fiber direction on epicardial potentials, Circulation, 90, 3076 (1994)
[19] Taccardi, B.; Lux, R. L.; MacLeod, R. S.; Ershler, P. R.; Dustman, T. J.; Scott, M.; Vyhmeister, Y.; Ingebrigtsen, N., Electrocardiographic waveforms and cardiac electric sources, J. Electrocardiol., 29, Suppl., 98 (1994)
[20] Taccardi, B.; Lux, R. L.; Ershler, P. R.; MacLeod, R. S.; Dustman, T. J.; Ingebrigtsen, N., Anatomical architecture and electrical activity of the heart, Acta Cardiol., 52, 2, 91 (1997)
[21] Taccardi, B.; Veronese, S.; Colli Franzone, P.; Guerri, L., Multiple components in the unipolar electrocardiogram: a simulation study in a three-dimensional model of ventricular myocardium, J. Cardiovasc. Electrophysiol., 9, 1062 (1998)
[22] K.A. Tomlinson, Finite elements solution of eikonal equation for excitation wavefront propagation in ventricular myocardium, PhD thesis, University of Auckland, New Zealand, 2000; K.A. Tomlinson, Finite elements solution of eikonal equation for excitation wavefront propagation in ventricular myocardium, PhD thesis, University of Auckland, New Zealand, 2000
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