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Bidomain equations for the heart

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Old   August 23, 2010, 05:39
Default Bidomain equations for the heart
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Has anyone attempted to implement the bidomain equations (*) for the heart in OpenFOAM?

These equations model the flow of current of a heart inside a conductive medium, making it an inner domain problem where the flow among the domains is determined by set of ODE's.

Is there any related flow problem where boundary conditions determined by ODE's are simultaneously solved?

*Here is a more extensive description of the model

The bidomain equations model the electrical activity of the heart inside a conductive medium. Each of two domains (conductive medium, heart) is basically a Laplace domain (div(s*grad(Phi)) = 0) where Phi is the potential, s the conductivity. The most interesting part is however the interface of the two (a membrane) where the flow (current) is:
a. Conserved: the flow leaving one domain is identical to the one entering the other

div(s*grad(Phi_e)) = -div(s*grad(Phi_i))


b. Dependent on the potential difference: the potential difference at any point in the membrane (difference of the potential at the same point inside and outside V=Phi_i - Phi_e) determines the flow from one domain to the other.

Item b. can be considered a "dynamic" boundary condition, which is a system of ODEs of the form:

div(s*grad(Phi_e)) = f(dV/dt, V, u)
du/dt = g(u)

u a vector of states of the membrane.
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Old   June 27, 2023, 10:12
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This is an old thread, but in case others are interested, I have implemented a basic mono-domain model in OpenFOAM using the available ODE solver class. You can find the code at where the method is (will be) described at the 18th OpenFOAM Workshop (

Maybe others have created similar implementations; in that case, I am also interested to see them.
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bidomain, biomedical, electric field, interface, potential

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