Wave-propagation dynamics in an anisotropic excitable medium

Bidomain models for simulating the propagation of electrical activation in the heart treat the myocardium as an anisotropic excitable medium with conductivity coefficients σ_l,t^i,e, where i and e refer to intracellular and extracellular space, and l and t indicate whether conductivity is along (l) or transverse (t) to the local fibre direction. These models are made computationally tractable by the equal anisotropy ratio assumption, which states that σ_l^e/σ _lⁱ= σ_t^e/σ _tⁱ = k, for some scalar constant k. Although it is doubtful that this assumption is valid, it has been the only means of reducing the complex coupled systems of nonlinear partial differential equations to a single reaction-diffusion problem. By introducing a simple perturbation argument, we achieved an equivalent reduction-with a de-coupling tensor expressed in terms of the harmonic means σ_l,t^i,e σ_l,t^i,e/(σ_l,t^i,e + σ_l,t^i,e) of the conductivity parameters-thus preserving the critical information conveyed by conductivity parameters without resorting to the assumption regarding their ratios. Numerical simulations in a realistic tissue volume were performed to assess the consequences of this alternate formulation.