Beeler Reuter ionic model More...

Functions/Subroutines
subroutine, public	br_y0 (Y)
	re-computed rest state (solving F(Y0)=0) More...

subroutine	br_gating_variables (a, b, V)
	Model IONIC_BR: Gating variables \( w = (w_1, \dots, w_{\rm NW}) \) dw_i/dt = (w_i-w_{i,~})/{i} \( <b>OUTPUT:</b> for \)=1,,{ NW} \( - a(i) = \) 1/ \( - b(i) = \) -w_{i,~})/ More...

subroutine, public	br_ab_0 (a, b, I, Y, N, Na)
	Model IONIC_BR: reaction term More...

subroutine, public	br_ab_w (a, b, I, Y, N, Na)
	Model IONIC_BR: reaction term More...

subroutine, public	br_ab_wv (a, b, I, Y, N, Na)
	Model IONIC_BR: reaction term More...

subroutine, public	br_ilist (IList, Y)

subroutine	itot_dv (a, b, Y)

real(rp) function	i_k1 (Y)

real(rp) function	i_s (Y)

real(rp) function	i_x1 (Y)

real(rp) function	i_na (Y)

subroutine	i_na_dv (a, b, Y)

real(rp) function	ff (x, a, b)

real(rp) function	i_s_sp (Y)

subroutine, public	br_sp_ilist (IList, Y)
	Model IONIC_BR_SP: ionic current list More...

subroutine, public	br_sp_y0 (Y)
	Model IONIC_BR_SP: rest state More...

subroutine, public	br_sp_ab_w (a, b, I, Y, N, Na)
	Model IONIC_BR_SP: reaction term More...

Variables
integer, parameter, public	br_ny = 8

integer, parameter, public	br_nw = 6

integer, parameter, public	br_ni = 4

integer, parameter	jna = 1

integer, parameter	js = 2

integer, parameter	jx1 = 3

integer, parameter	jk1 = 4

integer, parameter	ym = 1

integer, parameter	yh = 2

integer, parameter	yj = 3

integer, parameter	yd = 4

integer, parameter	yf = 5

integer, parameter	yx1 = 6

integer, parameter	ycai = 7

integer, parameter	yv = 8

real(rp), parameter	rtsf = 26.713760659695648_RP

real(rp), parameter	fsrt = 1._RP/(RTsF)

real(rp), parameter	cm = 1.0_RP

real(rp), parameter	g_na = 4.0_RP

real(rp), parameter	g_nac = 0.003_RP

real(rp), parameter	g_s = 0.09_RP

real(rp), parameter	ena = 50.0_RP

real(rp), parameter	c_ix1 = exp(0.04_RP*(77._RP-35._RP))

Detailed Description

Beeler Reuter ionic model

State variable \( Y = ^T[w,c,v]\in\R^N\), \( N = 8\)

\( w\in \R^{N_w}\) gating variables, \( N_w = 6\)
\( c \in \R^1\) concentrations
\( V\in\R \) membrane potential

Membrane ionic currents \( I = (I_1,\dots,I_{N_I})\), \(N_I=4\).

The Beeler Reuter model is available with the formulations (see ionicModel_mod detailed description):

IONIC_BR with \( N_a = N_w\)
IONIC_BR_0 with \( N_a = 0\)
IONIC_BR_WV with \( N_a = N\)

A modified version of the Beeler Reuter model to simulate spiral waves is proposed

IONIC_BR_SP with \( N_a = N_w\)

Author: Charles Pierre.

Function/Subroutine Documentation

◆ br_ab_0()

subroutine, public br_mod::br_ab_0	(	real(rp), dimension(na), intent(out)	a,
		real(rp), dimension(n), intent(out)	b,
		real(rp), intent(in)	I,
		real(rp), dimension(n), intent(in)	Y,
		integer, intent(in)	N,
		integer, intent(in)	Na
	)

Model IONIC_BR: reaction term

The linear part 'a' has size 0

The linear part 'a' is void !

Definition at line 159 of file br_mod.f90.

Here is the call graph for this function:

◆ br_ab_w()

subroutine, public br_mod::br_ab_w	(	real(rp), dimension(na), intent(out)	a,
		real(rp), dimension(n), intent(out)	b,
		real(rp), intent(in)	I,
		real(rp), dimension(n), intent(in)	Y,
		integer, intent(in)	N,
		integer, intent(in)	Na
	)

Model IONIC_BR: reaction term

The linear part 'a' has size Na = NW and is equal to \( 1/\tau_i \) for the gating variables

Definition at line 189 of file br_mod.f90.

Here is the call graph for this function:

◆ br_ab_wv()

subroutine, public br_mod::br_ab_wv	(	real(rp), dimension(na), intent(out)	a,
		real(rp), dimension(n), intent(out)	b,
		real(rp), intent(in)	I,
		real(rp), dimension(n), intent(in)	Y,
		integer, intent(in)	N,
		integer, intent(in)	Na
	)

Model IONIC_BR: reaction term

The linear part 'a' has size Na = NY

Stabilisation on the gating variables + potential

Definition at line 217 of file br_mod.f90.

Here is the call graph for this function:

◆ br_gating_variables()

subroutine br_mod::br_gating_variables	(	real(rp), dimension(br_nw), intent(out)	a,
		real(rp), dimension(br_nw), intent(out)	b,
		real(rp), intent(in)	V
	)

private

Model IONIC_BR: Gating variables \( w = (w_1, \dots, w_{\rm NW}) \) dw_i/dt = (w_i-w_{i,~})/{i} \( <b>OUTPUT:</b> for \)=1,,{ NW} \( - a(i) = \) 1/ \( - b(i) = \) -w_{i,~})/

Definition at line 119 of file br_mod.f90.

◆ br_ilist()

subroutine, public br_mod::br_ilist	(	real(rp), dimension(br_ni), intent(out)	IList,
		real(rp), dimension(br_ny), intent(in)	Y
	)

Definition at line 247 of file br_mod.f90.

Here is the call graph for this function:

◆ br_sp_ab_w()

subroutine, public br_mod::br_sp_ab_w	(	real(rp), dimension(na), intent(out)	a,
		real(rp), dimension(n), intent(out)	b,
		real(rp), intent(in)	I,
		real(rp), dimension(n), intent(in)	Y,
		integer, intent(in)	N,
		integer, intent(in)	Na
	)

Model IONIC_BR_SP: reaction term

The linear part 'a' has size Na = NW and is equal to \( 1/\tau_i \) for the gating variables

Definition at line 408 of file br_mod.f90.

Here is the call graph for this function:

◆ br_sp_ilist()

subroutine, public br_mod::br_sp_ilist	(	real(rp), dimension(br_ni), intent(out)	IList,
		real(rp), dimension(br_ny), intent(in)	Y
	)

Model IONIC_BR_SP: ionic current list

Definition at line 375 of file br_mod.f90.

Here is the call graph for this function:

◆ br_sp_y0()

subroutine, public br_mod::br_sp_y0 ( real(rp), dimension(br_ny) Y )

Model IONIC_BR_SP: rest state

Definition at line 389 of file br_mod.f90.

Here is the call graph for this function:

◆ br_y0()

subroutine, public br_mod::br_y0 ( real(rp), dimension(br_ny), intent(out) Y )

re-computed rest state (solving F(Y0)=0)

Definition at line 89 of file br_mod.f90.

Here is the call graph for this function:

◆ ff()

real(rp) function br_mod::ff	(	real(rp), intent(in)	x,
		real(rp), intent(in)	a,
		real(rp), intent(in)	b
	)

private

Definition at line 345 of file br_mod.f90.

◆ i_k1()

real(rp) function br_mod::i_k1 ( real(rp), dimension(br_ny), intent(in) Y )

private

Definition at line 273 of file br_mod.f90.

◆ i_na()

real(rp) function br_mod::i_na ( real(rp), dimension(br_ny), intent(in) Y )

private

Definition at line 324 of file br_mod.f90.

◆ i_na_dv()

subroutine br_mod::i_na_dv	(	real(rp)	a,
		real(rp)	b,
		real(rp), dimension(br_ny), intent(in)	Y
	)

private

Definition at line 336 of file br_mod.f90.

◆ i_s()

real(rp) function br_mod::i_s ( real(rp), dimension(br_ny), intent(in) Y )

private

Definition at line 298 of file br_mod.f90.

◆ i_s_sp()

real(rp) function br_mod::i_s_sp ( real(rp), dimension(br_ny), intent(in) Y )

private

Definition at line 362 of file br_mod.f90.

◆ i_x1()

real(rp) function br_mod::i_x1 ( real(rp), dimension(br_ny), intent(in) Y )

private

Definition at line 310 of file br_mod.f90.

◆ itot_dv()

subroutine br_mod::itot_dv	(	real(rp)	a,
		real(rp)	b,
		real(rp), dimension(br_ny), intent(in)	Y
	)

private

Definition at line 261 of file br_mod.f90.

Here is the call graph for this function:

Variable Documentation

◆ br_ni

integer, parameter, public br_mod::br_ni = 4

Definition at line 52 of file br_mod.f90.

◆ br_nw

integer, parameter, public br_mod::br_nw = 6

Definition at line 51 of file br_mod.f90.

◆ br_ny

integer, parameter, public br_mod::br_ny = 8

Definition at line 50 of file br_mod.f90.

◆ c_ix1

real(rp), parameter br_mod::c_ix1 = exp(0.04_RP*(77._RP-35._RP))

private

Definition at line 82 of file br_mod.f90.

◆ cm

real(rp), parameter br_mod::cm = 1.0_RP

private

Definition at line 77 of file br_mod.f90.

◆ ena

real(rp), parameter br_mod::ena = 50.0_RP

private

Definition at line 81 of file br_mod.f90.

◆ fsrt

real(rp), parameter br_mod::fsrt = 1._RP/(RTsF)

private

Definition at line 76 of file br_mod.f90.

◆ g_na

real(rp), parameter br_mod::g_na = 4.0_RP

private

Definition at line 78 of file br_mod.f90.

◆ g_nac

real(rp), parameter br_mod::g_nac = 0.003_RP

private

Definition at line 79 of file br_mod.f90.

◆ g_s

real(rp), parameter br_mod::g_s = 0.09_RP

private

Definition at line 80 of file br_mod.f90.

◆ jk1

integer, parameter br_mod::jk1 = 4

private

Definition at line 58 of file br_mod.f90.

◆ jna

integer, parameter br_mod::jna = 1

private

Definition at line 55 of file br_mod.f90.

◆ js

integer, parameter br_mod::js = 2

private

Definition at line 56 of file br_mod.f90.

◆ jx1

integer, parameter br_mod::jx1 = 3

private

Definition at line 57 of file br_mod.f90.

◆ rtsf

real(rp), parameter br_mod::rtsf = 26.713760659695648_RP

private

Definition at line 75 of file br_mod.f90.

◆ ycai

integer, parameter br_mod::ycai = 7

private

Definition at line 67 of file br_mod.f90.

◆ yd

integer, parameter br_mod::yd = 4

private

Definition at line 64 of file br_mod.f90.

◆ yf

integer, parameter br_mod::yf = 5

private

Definition at line 65 of file br_mod.f90.

◆ yh

integer, parameter br_mod::yh = 2

private

Definition at line 62 of file br_mod.f90.

◆ yj

integer, parameter br_mod::yj = 3

private

Definition at line 63 of file br_mod.f90.

◆ ym

integer, parameter br_mod::ym = 1

private

Definition at line 61 of file br_mod.f90.

◆ yv

integer, parameter br_mod::yv = 8

private

Definition at line 68 of file br_mod.f90.

◆ yx1

integer, parameter br_mod::yx1 = 6

private

Definition at line 66 of file br_mod.f90.

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ br_ab_0()

◆ br_ab_w()

◆ br_ab_wv()

◆ br_gating_variables()

◆ br_ilist()

◆ br_sp_ab_w()

◆ br_sp_ilist()

◆ br_sp_y0()

◆ br_y0()

◆ ff()

◆ i_k1()

◆ i_na()

◆ i_na_dv()

◆ i_s()

◆ i_s_sp()

◆ i_x1()

◆ itot_dv()

Variable Documentation

◆ br_ni

◆ br_nw

◆ br_ny

◆ c_ix1

◆ cm

◆ ena

◆ fsrt

◆ g_na

◆ g_nac

◆ g_s

◆ jk1

◆ jna

◆ js

◆ jx1

◆ rtsf

◆ ycai

◆ yd

◆ yf

◆ yh

◆ yj

◆ ym

◆ yv

◆ yx1