The monodomain model is a reduction of the bidomain model of the electrical propagation in myocardial tissue.
The reduction comes from assuming that the intra- and extracellular domains have equal anisotropy ratios.
Although not as physiologically accurate as the bidomain model, it is still adequate in some cases, and has reduced complexity.
the spatial domain, and
the final time, the monodomain model can be formulated as follows[2]
λ
1 + λ
= χ
ion
is the intracellular conductivity tensor,
is the transmembrane potential,
is the transmembrane ionic current per unit area,
is the membrane capacitance per unit area,
λ
is the intra- to extracellular conductivity ratio, and
is the membrane surface area per unit volume (of tissue).
[1] The monodomain model can be easily derived from the bidomain model.
{\displaystyle {\begin{aligned}\nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v\right)+\nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v_{e}\right)&=\chi \left(C_{m}{\frac {\partial v}{\partial t}}+I_{\text{ion}}\right)\\\nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v\right)+\nabla \cdot \left(\left(\mathbf {\Sigma } _{i}+\mathbf {\Sigma } _{e}\right)\nabla v_{e}\right)&=0\end{aligned}}}
Assuming equal anisotropy ratios, i.e.
, the second equation can be written as[1]
Then, inserting this into the first bidomain equation gives the unique equation of the monodomain model[1]
Differently from the bidomain model, the monodomain model is usually equipped with an isolated boundary condition, which means that it is assumed that there is not current that can flow from or to the domain (usually the heart).
[3][4] Mathematically, this is done imposing a zero transmembrane potential flux (homogeneous Neumann boundary condition), i.e.:[4] where
is the unit outward normal of the domain and
is the domain boundary.
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