Monodomain model - Alchetron, The Free Social Encyclopedia

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.

Formulation

The monodomain model can be formulated as follows

λ 1 + λ ∇ ⋅ ( Σ i ∇ v ) = χ ( C m ∂ v ∂ t + I ion ) ,

where Σ i is the intracellular conductivity tensor, v is the transmembrane potential, I ion is the transmembrane ionic current per unit area, C m is the membrane conductivity per unit area, λ is the intra- to extracellular conductivity ratio, and χ is the membrane surface area per unit volume (of tissue).

Derivation

The bidomain model can be written as

∇ ⋅ ( Σ i ∇ v ) + ∇ ⋅ ( Σ i ∇ v e ) = χ ( C m ∂ v ∂ t + I ion ) ∇ ⋅ ( Σ i ∇ v ) + ∇ ⋅ ( ( Σ i + Σ e ) ∇ v e ) = 0

Assuming equal anisotropy ratios, i.e. Σ e = λ Σ i , the second equation can be written

∇ ⋅ ( Σ i ∇ v e ) = − 1 1 + λ ∇ ⋅ ( Σ i ∇ v ) .

Inserting this into the first bidomain equation gives

λ 1 + λ ∇ ⋅ ( Σ i ∇ v ) = χ ( C m ∂ v ∂ t + I ion ) .

References

Monodomain model Wikipedia

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Contents

Formulation

Derivation

References