Bidomain equations for the heart
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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