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775:{\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}}}
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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). Mathematically, this is done imposing a zero transmembrane potential
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335:{\displaystyle {\frac {\lambda }{1+\lambda }}\nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v\right)=\chi \left(C_{m}{\frac {\partial v}{\partial t}}+I_{\text{ion}}\right)\quad \quad {\text{in }}\mathbb {T} \times (0,T),}
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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
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943:{\displaystyle \nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v_{e}\right)=-{\frac {1}{1+\lambda }}\nabla \cdot \left(\mathbf {\Sigma } _{i}\nabla v\right).}
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Boulakia, Muriel; Cazeau, Serge; Fernández, Miguel A.; Gerbeau, Jean-Frédéric; Zemzemi, Nejib (24 December 2009).
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Mathematically modelling the electrical activity of the heart : from cell to body surface and back again
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Then, inserting this into the first bidomain equation gives the unique equation of the monodomain model
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the final time, the monodomain model can be formulated as follows
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1395:"Mathematical Modeling of Electrocardiograms: A Numerical Study"
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Pullan, Andrew J.; Buist, Martin L.; Cheng, Leo K. (2005).
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is the membrane surface area per unit volume (of tissue).
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is the intra- to extracellular conductivity ratio, and
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Rossi, Simone; Griffith, Boyce E. (1 September 2017).
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The monodomain model can be easily derived from the
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1312:(2nd ed.). Springer.
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38:Please help
33:verification
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135:Formulation
1501:Categories
1261:References
491:Derivation
96:April 2014
66:newspapers
1359:1054-1500
1223:∂
1163:×
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