The Dilemma:

There can be no direct activation or defibrillation with this (homogeneous) model.

Why? Consider the linearized bidomain model:

$${d \over dx}(\sigma_i {d\phi_i \over dx}) - {\chi \over R_m} \phi =0,$$

$${d\over dx}(\sigma_i {d\phi_i\over dx} + \sigma_e {d\phi_e\over dx}) = 0,$$

with

$${d\phi_e\over dx} = -I, \qquad {d\phi_i\over dx} = 0, \qquad{\rm\ at\ } x = 0, L,$$

so that in steady state

$$\phi_s(x) = -I {\sinh({x-{L\over 2}\over \Lambda}) \over \cosh({L\over 2\Lambda})}$$

where $\Lambda^2 = {R_m\over \chi}{\sigma_i\sigma_e\over \sigma_i + \sigma_e}.$