Formulation
Being the domain boundary of the model, the monodomain model can be formulated as follows where is the intracellular conductivity tensor, is the transmembrane potential, is the transmembrane ionic current per unit area, is the membrane capacitance per unit area, is the intra- to extracellular conductivity ratio, and is the membrane surface area per unit volume (of tissue).Derivation
The monodomain model can be easily derived from the bidomain model. This last one can be written as Assuming equal anisotropy ratios, i.e. , the second equation can be written as Then, inserting this into the first bidomain equation gives the unique equation of the monodomain modelBoundary conditions
Differently from the bidomain model, usually the monodomain model is equipped with an isoltad boundary condition, which means that it is assumed that there is not current that can flow from or to the domain (usually the heart). Mathematically, this is done imposing a zero transmembrane potential flux, ''i.e.'': : where is the unit outward normal of the domain and is the domain boundary.See also
* Bidomain model * Forward problem of electrocardiologyReferences
Cardiac electrophysiology Differential equations Electrophysiology Partial differential equations Biological theorems {{Applied-math-stub