Functions/Subroutines
program	ode_monodomain_2d
	RESOLUTION OF: the monodomain model in cardiac-electrophysiology. More...

subroutine	pde_reaction (a, b, x, t, y, N, Na)

subroutine	massmat (yy, xx)

subroutine	stiffmat (yy, xx)

subroutine	kinv (xx, ierr, bb)

Function/Subroutine Documentation

◆ kinv()

subroutine ode_monodomain_2d::kinv	(	real(rp), dimension(:), intent(inout)	xx,
		logical, intent(out)	ierr,
		real(rp), dimension(:), intent(in)	bb
	)

Definition at line 310 of file ode_monodomain_2d.f90.

◆ massmat()

subroutine ode_monodomain_2d::massmat	(	real(rp), dimension(:), intent(out)	yy,
		real(rp), dimension(:), intent(in)	xx
	)

Definition at line 287 of file ode_monodomain_2d.f90.

◆ ode_monodomain_2d()

program ode_monodomain_2d ( )

RESOLUTION OF: the monodomain model in cardiac-electrophysiology.

This partial differential equation models the spreading of excitation of the transmembrane potential in the cardiac tissue at a macroscopic scale.

It is a parabolic reaction-diffusion equation of the form: for \( x\in \Omega \) and \( t\in '0,T)\)

\( ~~~~~~~~~~~~~~~~\displaystyle{ \frac{{\rm d} Y_i(x,t)}{{\rm d} t } = F_i(Y), \quad \quad i=1\dots N-1,}\)

\( ~~~~~~~~~~~~~~~~\displaystyle{ \frac{\partial V}{\partial t } = \dv( B(x)\nabla V) + I_{\rm ion}(Y) + I_{\rm app}(x,t), \quad {\rm with} \quad V = Y_N. }\),

where \( Y_i(x,t)\in\R\) and \(V(x,t)\in\R\) are scalars unknowns.

Settings:

2D square geometry,
constant anisotropy (horizontal fibres),
Beeler Reuter cellular model (can be switched to TNNP)
smooth stimulation at the origin

Numerical method:

P3 finite elements (can be switched to P1 or P2)
stabilised time stepping method (can be modified):
BDF-SBDF of order 3 for the potential equation
Rush-Larsen of order 3 for the ionic model ODE system

Output: (with the software gmsh)

Potential depolarisation wave spreading
Associated activation times

Charles PIERRE

Definition at line 43 of file ode_monodomain_2d.f90.

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◆ pde_reaction()

subroutine ode_monodomain_2d::pde_reaction	(	real(rp), dimension(na), intent(out)	a,
		real(rp), dimension(n), intent(out)	b,
		real(rp), dimension(3), intent(in)	x,
		real(rp), intent(in)	t,
		real(rp), dimension(n), intent(in)	y,
		integer, intent(in)	N,
		integer, intent(in)	Na
	)

Definition at line 261 of file ode_monodomain_2d.f90.

◆ stiffmat()

subroutine ode_monodomain_2d::stiffmat	(	real(rp), dimension(:), intent(out)	yy,
		real(rp), dimension(:), intent(in)	xx
	)

Definition at line 297 of file ode_monodomain_2d.f90.