  Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo
transport subject to current noise, i.e., subject to stochastic forcing modeled
by a cylindrical Wiener process. It is shown that this set of equations admits
a unique global, strong pathwise solution within the setting of critical
spaces. The proof is based on combining methods from stochastic and
deterministic maximal regularity. In addition, the method of extrapolation
spaces from deterministic evolution equations is transferred to the stochastic
setting.
