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Modeling heat transfer in cardiac tissue

Rotating spiral waves of electrical activity, experimentally observed in excitable biological tissues, play a central role in heart dynamics in reason of their connection with arrhythmias and fibrillation. Many mathematical models fine tuned on experiments have been developed in order to quantitatively understand and control these life threatening events. Usually these models neglected the role of heat transfer and temperature changes, which are relevant to the cardiac electrical system [1,2]. In particular experiments were devoted also to understand the cardiac heat production possibly associated with its mechanical work [3]. Moreover, during heart surgery, thermal cooling can influence cardiac activity in a marked way: notably arrhythmias and fibrillations can occur during the re-thermalization from hypothermia although the use of a controlled hypothermic protocols for the right atrium have been recently shown to reduce postoperative atrial fibrillation [4]. It appears mandatory then to include thermal effects in existing mathematical models. In this paper, adopting a scheme already presented in recent publications on neural and intestinal excitable tissues [5,6,7], we present a thermo-electric ionic model of miocardial tissue accounting for heat transfer effects. More in detail we analyze the problem using Fenton-Karma electrophysiological cardiac model with temperature dependent gradients and coupled with Pennes' bio-heat equation stressing the role of thermal inhomogeneities in promoting arrhythmogenic events. 
 
References 
[1] E. S. D. Brown, “Temperature and the Responsive Mechanism of Cardiac Muscle: I. Temperature and the Duration of Contraction”, J. Exp. Biol. vol.7: 373-384 (1930). 
[2] E. S. D. Brown, “Temperature and the Responsive Mechanism of Cardiac Muscle: II. Temperature and The Rate of the Rhythm of the Isolated Sinus”, J. Exp. Biol. vol.7:385-389 (1930). 
[3] C. L. Gibbs, J B Chapman, “Cardiac Heat Production”, Annual Review of Physiology, October, Vol. 41: 507-519 (1979). 
[4] M. A. J. M. Huybregts R. de Vroege and W. van Oeveren, A New System for Right Atrial Cooling, Ann Thorac Surg ;vol. 85:1421-1424 (2008). 
[5] D. Bini, C. Cherubini and S. Filippi, “Heat Transfer in FitzHugh-Nagumo model”, Phys Rev.E vol.74: 041905 (2006). 
[6] D. Bini, C. Cherubini and S. Filippi, “On vortices heating biological excitable media ”, Chaos, Solitons & Fractals, ,vol.42: 2057-2066 (2009). 
[7] A. Gizzi, C. Cherubini, S. Migliori, R. Alloni, R. Portuesi and S. Filippi, “On the electrical intestine turbulence induced by temperature changes”, Physical Biology , in press (2010).