2013, Number 2
Next >>
TIP Rev Esp Cienc Quim Biol 2013; 16 (2)
Modelo de propagación de ondas solitarias en el corazón
Domínguez I, Barrio RA, Varea C, Aragón JL
Language: Spanish
References: 30
Page: 79-92
PDF size: 1046.64 Kb.
ABSTRACT
In cardiac electrical activity, different types of waves meander through the heart. We present a model
of the electrical activity of the heart that proposes that the homogeneous wave fronts propagating
through the heart are in fact solitons. We use a general set of reaction-diffusion equations known as
the Barrio-Varea-Aragón-Maini (BVAM) model
[1] that presents a wealth of non-linear bifurcations, and
we are able to follow the route to chaos, using a mapping of the amplitude equations to the dynamics
of the complex Ginzburg-Landau equation. We study the dynamics of wave fronts numerically in the
BVAM model to describe the mechanisms leading to heart fibrillation and compare the findings with
experimental data.
REFERENCES
Barrio, R.A., Varea, C., Aragón, J.L. & Maini, P.K. A two dimensional numerical study of spatial pattern formation in interactiong turing systems. Bull. Math. Biol. 61, 483 (1999).
Barrio, R.A. Morphogenesis in Introducción a la Física Biológica. Vol. 3. Colín, L.G., Dagdug, L., Picquart, M. & Vázquez, E. (El Colegio Nacional, México, D.F., 2010).
Bub, G., Shrier, A. & Glass, L. Spiral wave generation in heterogeneous excitable media. Phys. Rev. Lett. 85, 058101 (2002).
Barrio, R.A. Aplicaciones del modelo bvam a sistemas complejos. Revista Digital Universitaria, http://www.revista.unam.mx/ vol.11/num6/art55, 11(6) (2010).
Sundnes, J. et al. in Computing the Electrical activity of the Heart, Monographs in Computational Science and Engineering (eds. Bart, T.J. et al.) (Springer, Berlin, 2006).
Garfinkel, A. et al. Quasiperiodicity and chaos in cardiac fibrillation. The Journal of Clinical Investigation 99(2) (1997). Págs. 305-314.
FitzHugh, R.A. Impuses and physiological states in theoretical models of nerve membrane. Biophysical Journal 1, 465 (1961). Págs. 445-466.
Nagumo, J., Arimoto, S. & Yoshizawa, S. An active pulse transmission line simulating nerve axon. Proceedings of the IRE 50(10), 2061–2070 (1962).
Echebarría, B. & Karma, A. Instability and spatiotemporal dynamics of alternants in paced cardiac tissue. Phys. Rev. Lett. 88(20), 208101 (2002).
Hodgkin, A.L. & Huxley, A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500–544 (1952).
Beeler, G.W. & Reuter, H. Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268, 177–210, 1975).
Luo, C.H. & Rudy, Y. A dynamic model of the cardiac action potential. ii. Afterdepolarizations, triggered activity, and potentiation. Circ. Res. 74, 1097–113 (1994).
Rogers, J.M. & McCullock, A.D. A collocation-galerkin fe of cardiac action potential propagation. IEEE Trans. on Biomedical Engineering 41, 743–757 (1994).
Noble, D. A modification of the hodgkin-huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 160, 317–52 (1962).
McAllister, R.E., Noble, D. &Tsien, R.W. Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Physiol. 251, 1–59 (1975).
Luo, C.H. & Rudy, Y. A dynamic model of the cardiac ventricular action potential. i. Simulations of ionic currents and concentration changes. Circ. Res. 74, 1071–96 (1994).
Nygren, A. et al. Mathematical model of an adult human atrial cell: the role of k+ cu- rrents in repolarization. Circ. Res. 82, 63–81 (1998).
Courtemanche, M., Ramírez, R.J. & Nattel, S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol. 275, 301–321 (1998).
Courtemanche, M., Ramírez, R.J. & Nattel, S. Ionic targets for drug therapy and atrial fibrillation-induced electrical remodeling: insights from a mathematical model. Cardiovas. Res. 42, 477–489 (1999).
Turing, A.M. The chemical basis of morphogenesis. Phil.Trans. R. Soc. London B 237(641), 37–72 (1952).
Murray, J.D. Mathematical Biology II: Spatial Models and Biomedical Applications. Vol. 2. Interdisciplinary Applied Mathematics. 3rd ed. (Springer, 2003).
Lepännen, T. Computational Studies of Pattern Formation in Turing Systems. Ph.D. Thesis, Helsinki University of Technology (2004).
Wolley, T.E. et al. Analysis of stationary droplets in a generic turing reaction-diffusion system. Phys. Rev. E. 82, 051929
Varea, C., Barrio, R.A. & Hernández, D. Soliton behaviour in reaction-diffusion model. J. Math. Biol. 54, 797–813 (2007).
Aragón, J.L., Barrio, R.A., Woolley, T.E., Baker, R.E. & Maini, P.K. Non-linear effects on turing patterns: Time oscillations and chaos. Phys. Rev. E., 86, 026201 (2012).
Strogatz, S.H. Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering. Studies in Nonlinearity (Westview Press, Cambridge, MA, 2008).
Newhouse, S., Ruelle, D. & Takens, F. Occurrence of strange axiom a attractors near quasi periodic flows on tm, m ≥ 3. Commun. Math. Phys. 64, 35–40 (1978).
Aragón, J.L., Torres, M., Gil, D., Barrio, R.A. & Maini, P.K. Turing patterns with pentagonal symmetry. Phys. Rev. E. 65, 051913 (2002).
Herlin, A. & Jacquemet, V. Eikonal-base initiation of fribillatory activity in thin walled cardiac propagation models. Chaos 21, 043136 (2011).
Kuramoto, Y. Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, NewYork, 1984).