Activation dynamics in anisotropic cardiac tissue via decoupling

Bidomain theory for cardiac tissue assumes two interpenetrating anisotropic media - intracellular (i) and extracellular (e) - connected everywhere via a cell membrane; four local parameters σ_l,t^i,e specify conductivities in the longitudinal (l) and transverse (t) directions with respect to cardiac muscle fibers. The full bidomain model for the propagation of electrical activation consists of coupled elliptic-parabolic partial differential equations for the transmembrane potential v_m and extracellular potential ø_e, together with quasistatic equations for the flow of current in the extracardiac regions. In this work we develop a preliminary assessment of the consequences of neglecting the effect of the passive extracardiac tissue and intracardiac blood masses on wave propagation in isolated whole heart models and describe a decoupling procedure, which requires no assumptions on the anisotropic conductivities and which yields a single reaction-diffusion equation for simulating the propagation of activation. This reduction to a decoupled model is justified in terms of the dimensionless parameter ε = (σ_l ⁱσ_t^e - σ_t ⁱσ_l^e)/(σ_lⁱ+ σ_l^e)(σ_tⁱ+ σ_t^e). Numerical simulations are generated which compare propagation in a sheet H of cardiac tissue using the full bidomain model, an isolated bidomain model, and the decoupled model. Preliminary results suggest that the decoupled model may be adequate for studying general properties of cardiac dynamics in isolated whole heart models.