where and
are the extracellular potential and transmembrane voltage respectively;
represents
the ionic current variables;
and are conductivity tensors of intracellular
and extracellular spaces respectively;
is the isotropic conductivity of the fluid in which the heart is immersed
(bath and cavities); is the capacitance
per unit area and ß is surface to volume ratio;
and *g* model ionic currents and specify the cell membrane model.
At the tissue-bath interface, continuity of the normal component of the
extracellular current and continuity of are
enforced. The normal component of the intracellular current vanishes at
all tissue boundaries whereas the normal component of the extracellular
current vanishes at the boundaries of the bath.
Numerically, the bidomain equations are decoupled by an operator splitting
approach that leads to a three step scheme involving the solution of a
parabolic PDE, an elliptic PDE and a non-linear system of ODEs at each
time step. In the simplest case both the parabolic PDE and the non-linear
ODE systems are solved via the explicit forward-Euler scheme |