Possible Resolution: Resistive inhomogeneities via gap junctions, fiber geometry and rotation, etc.

Suppose that $\sigma_i = \sigma_i(x)$, $\sigma_e = \sigma_e(x)$. Then the bidomain model (in 1D) reduces to

$$\chi (C_m{\partial\phi \over \partial \tau} + I_m ) = {\part... ...\over\partial x}\left({\sigma_i\over \sigma_e+\sigma_i}\right)$$

and in steady state: