Ten Tusscher-Panfilov ionic model. More...

#include <ionic_ttp.h>

Inheritance diagram for TTP:

Classes
class	Parameters
	Model parameters class. More...

Public Member Functions
	TTP ()
	Constructor.

virtual std::unique_ptr< IonicModelParameters >	get_parameters () const override
	Construct an instance of model parameters.

virtual void	read_parameters (const IonicModelParameters &params) override
	Read model parameters from a parameter object.

virtual void	distribute_parameters (const CmMod &cm_mod, const cmType &cm) override
	Distribute model parameters to all parallel processes.

virtual unsigned int	get_calcium_index () const override
	Get the index of Ca_i in the state vector.

Public Member Functions inherited from IonicModel
	IonicModel (const InitialStates &initial_X_, const InitialStates &initial_Xg_, const double Vrest_)
	Constructor.

	IonicModel (const InitialStates &initial_X_, const InitialStates &initial_Xg_, const double Vrest_, const double Vscale_, const double Tscale_, const double Voffset_)
	Constructor with scaling factors.

virtual	~IonicModel ()=default
	Virtual destructor.

void	init (Vector< double > &X, Vector< double > &Xg) const
	Setup model initial conditions.

void	integ (const odeType &ode_solver_params, const int zone_id, const double t, const double dt, const double Istim, const double Ksac, Vector< double > &X, Vector< double > &Xg) const
	Integrate over one time step.

unsigned int	nX () const
	Get the number of state variables.

unsigned int	nG () const
	Get the number of gating variables.

virtual std::vector< std::pair< std::string, int > >	get_output_variables () const
	Get a list of state variables to export to VTU.

std::vector< outputType >	get_registered_outputs () const
	Get output variable information for output registration.

Static Public Attributes
static const std::string	label = "TTP"
	Model label.

static const InitialStates	initial_X
	State variables.

static const InitialStates	initial_Xg
	Gating variables.

static constexpr unsigned int	calcium_index = 3

Protected Member Functions
virtual void	update_g (const unsigned int zone_id, const double dt, const Vector< double > &X, Vector< double > &Xg) const override
	Update gating variables.

virtual Vector< double >	getf (const unsigned int zone_id, const Vector< double > &X, const Vector< double > &Xg, const double I_stim, const double I_sac) const override
	Model right-hand side.

Protected Member Functions inherited from IonicModel
virtual Array< double >	getj (const unsigned int zone_id, const Vector< double > &X, const Vector< double > &Xg, const double Ksac) const
	Model jacobian.

void	integ_fe (const unsigned int zone_id, Vector< double > &X, Vector< double > &Xg, const double Ts, const double Ti, const double Istim, const double Ksac) const
	Integrate the model with the forward Euler method.

void	integ_rk (const unsigned int zone_id, Vector< double > &X, Vector< double > &Xg, const double Ts, const double Ti, const double Istim, const double Ksac) const
	Integrate the model with the fourth-order explicit Runge-Kutta method.

void	integ_cn2 (const unsigned int zone_id, Vector< double > &X, Vector< double > &Xg, const double Ts, const double Ti, const double Istim, const double Ksac, const unsigned int max_iter, const double rtol, const double atol) const
	Integrate the model with the Crank-Nicolson method.

Protected Attributes
Model parameters
double	Rc = 8314.472
	Gas constant [J/mol/K].

double	Tc = 310.0
	Temperature [K].

double	Fc = 96485.3415
	Faraday constant [C/mmol].

double	Cm = 0.185
	Cell capacitance per unit surface area [uF/cm^{2}].

double	sV = 0.2
	Surface to volume ratio [um^{-1}].

double	rho = 162.0
	Cellular resistivity [ \(\Omega\)-cm].

double	V_c = 16.404E-3
	Cytoplasmic volume [um^{3}].

double	V_sr = 1.094E-3
	Sacroplasmic reticulum volume [um^{3}].

double	V_ss = 5.468E-5
	Subspace volume [um^{3}].

double	K_o = 5.4
	Extracellular K concentration [mM].

double	Na_o = 140.0
	Extracellular Na concentration [mM].

double	Ca_o = 2.0
	Extracellular Ca concentration [mM].

double	G_Na = 14.838
	Maximal I_Na conductance [nS/pF].

double	G_K1 = 5.405
	Maximal I_K1 conductance [nS/pF].

double	G_to = 0.294
	Maximal I_to conductance [nS/pF].

double	G_Kr = 0.153
	Maximal I_Kr conductance [nS/pF].

double	G_Ks = 0.392
	Maximal I_Ks conductance [nS/pF].

double	p_KNa = 3.E-2
	Relative I_Ks permeability to Na [-].

double	G_CaL = 3.98E-5
	Maximal I_CaL conductance [cm^{3}/uF/ms].

double	K_NaCa = 1000.
	Maximal I_NaCa [pA/pF].

double	gamma = 0.35
	Voltage dependent parameter of I_NaCa [-].

double	K_mCa = 1.38
	Ca_i half-saturation constant for I_NaCa [mM].

double	K_mNai = 87.5
	Na_i half-saturation constant for I_NaCa [mM].

double	K_sat = 0.1
	Saturation factor for I_NaCa [-].

double	alpha = 2.5
	Factor enhancing outward nature of I_NaCa [-].

double	p_NaK = 2.724
	Maximal I_NaK [pA/pF].

double	K_mK = 1.
	K_o half-saturation constant of I_NaK [mM].

double	K_mNa = 40.
	Na_i half-saturation constant of I_NaK [mM].

double	G_pK = 1.46E-2
	Maximal I_pK conductance [nS/pF].

double	G_pCa = 0.1238
	Maximal I_pCa conductance [pA/pF].

double	K_pCa = 5.E-4
	Half-saturation constant of I_pCa [mM].

double	G_bNa = 2.9E-4
	Maximal I_bNa conductance [nS/pF].

double	G_bCa = 5.92E-4
	Maximal I_bCa conductance [nS/pF].

double	Vmax_up = 6.375E-3
	Maximal I_up conductance [mM/ms].

double	K_up = 2.5E-4
	Half-saturation constant of I_up [mM].

double	V_rel = 0.102
	Maximal I_rel conductance [mM/ms].

double	k1p = 0.15
	R to O and RI to I, I_rel transition rate [mM^{-2}/ms].

double	k2p = 4.5E-2
	O to I and R to RI, I_rel transition rate [mM^{-1}/ms].

double	k3 = 6.E-2
	O to R and I to RI, I_rel transition rate [ms^{-1}].

double	k4 = 5.E-3
	I to O and Ri to I, I_rel transition rate [ms^{-1}].

double	EC = 1.5
	Ca_sr half-saturation constant of k_casr [mM].

double	max_sr = 2.5
	Maximum value of k_casr [-].

double	min_sr = 1.
	Minimum value of k_casr [-].

double	V_leak = 3.6E-4
	Maximal I_leak conductance [mM/ms].

double	V_xfer = 3.8E-3
	Maximal I_xfer conductance [mM/ms].

double	Buf_c = 0.2
	Total cytoplasmic buffer concentration [mM].

double	K_bufc = 1.E-3
	Ca_i half-saturation constant for cytplasmic buffer [mM].

double	Buf_sr = 10.
	Total sacroplasmic buffer concentration [mM].

double	K_bufsr = 0.3
	Ca_sr half-saturation constant for subspace buffer [mM].

double	Buf_ss = 0.4
	Total subspace buffer concentration [mM].

double	K_bufss = 2.5E-4
	Ca_ss half-saturation constant for subspace buffer [mM].

Protected Attributes inherited from IonicModel
InitialStates	initial_X
	Initial states.

InitialStates	initial_Xg
	Initial gating variables.

const double	Vrest

const double	Vscale
	Voltage scaling [mV].

const double	Tscale
	Time scaling [ms].

const double	Voffset
	Voltage offset parameter [mV].

Additional Inherited Members
Public Types inherited from IonicModel
using	InitialStates = std::vector< std::pair< std::string, double > >

Detailed Description

Ten Tusscher-Panfilov ionic model.

This class implements the 2006 version of the model, described in the second reference below.

References:

Ten Tusscher, Noble, Noble, Panfilov. A model for human ventricular tissue. American Journal of Physiology - Heart and Circulatory Physiology (2004).
Ten Tusscher, Panfilov. Alternans and spiral breakup in a human ventricular tissue model. American Journal of Physiology - Heart and Circulatory Physiology (2006).

Model parameters are from reference 2 above. Default parameters are for epicardium state (source: https://models.cellml.org/e/80d)

Constructor & Destructor Documentation

◆ TTP()

TTP::TTP ( )

inline

Constructor.

Member Function Documentation

◆ distribute_parameters()

void TTP::distribute_parameters	(	const CmMod &	cm_mod,
		const cmType &	cm
	)

overridevirtual

Distribute model parameters to all parallel processes.

Reimplemented from IonicModel.

◆ get_calcium_index()

virtual unsigned int TTP::get_calcium_index ( ) const

inlineoverridevirtual

Get the index of Ca_i in the state vector.

Implements IonicModel.

◆ get_parameters()

virtual std::unique_ptr< IonicModelParameters > TTP::get_parameters ( ) const

inlineoverridevirtual

Construct an instance of model parameters.

Reimplemented from IonicModel.

◆ getf()

Vector< double > TTP::getf	(	const unsigned int	zone_id,
		const Vector< double > &	X,
		const Vector< double > &	Xg,
		const double	I_stim,
		const double	I_sac
	)		const

overrideprotectedvirtual

Model right-hand side.

Implements IonicModel.

◆ read_parameters()

void TTP::read_parameters ( const IonicModelParameters & params )

overridevirtual

Read model parameters from a parameter object.

Reimplemented from IonicModel.

◆ update_g()

void TTP::update_g	(	const unsigned int	zone_id,
		const double	dt,
		const Vector< double > &	X,
		Vector< double > &	Xg
	)		const

overrideprotectedvirtual

Update gating variables.

The evolution rate of all the gating variables for this model has an expression in the form:

\[ \frac{\text{d}y}{\text{d}t} = \frac{y_\infty(v) - y}{\tau(v)}\;, \]

with \(v\) denotes the transmembrane potential. Assuming \(v\) to be constant over the integration step, the above equation admits the following exact solution:

\[ y^{n+1} = y_\infty(v) - (y_\infty(v) - y^n) e^{-\Delta t / \tau(v)}\;. \]

Accordingly, this function goes through all gating variables, computes the values of \(y_\infty(v)\) and \(\tau(v)\), and updates the gating variables using the above formula.

Parameters

[in]	zone_id	Identifier for the transmural zone (epicardium, endocardium, myocardium).
[in]	dt	Time step.
[in]	X	Vector of state variables.
[out]	Xg	Vector of gating variables.

Implements IonicModel.

Member Data Documentation

◆ alpha

double TTP::alpha = 2.5

protected

Factor enhancing outward nature of I_NaCa [-].

◆ Buf_c

double TTP::Buf_c = 0.2

protected

Total cytoplasmic buffer concentration [mM].

◆ Buf_sr

double TTP::Buf_sr = 10.

protected

Total sacroplasmic buffer concentration [mM].

◆ Buf_ss

double TTP::Buf_ss = 0.4

protected

Total subspace buffer concentration [mM].

◆ Ca_o

double TTP::Ca_o = 2.0

protected

Extracellular Ca concentration [mM].

◆ calcium_index

constexpr unsigned int TTP::calcium_index = 3

staticconstexpr

Index of the intracellular calcium concentration (Ca_i) in the state vector.

◆ Cm

double TTP::Cm = 0.185

protected

Cell capacitance per unit surface area [uF/cm^{2}].

◆ EC

double TTP::EC = 1.5

protected

Ca_sr half-saturation constant of k_casr [mM].

◆ Fc

double TTP::Fc = 96485.3415

protected

Faraday constant [C/mmol].

◆ G_bCa

double TTP::G_bCa = 5.92E-4

protected

Maximal I_bCa conductance [nS/pF].

◆ G_bNa

double TTP::G_bNa = 2.9E-4

protected

Maximal I_bNa conductance [nS/pF].

◆ G_CaL

double TTP::G_CaL = 3.98E-5

protected

Maximal I_CaL conductance [cm^{3}/uF/ms].

◆ G_K1

double TTP::G_K1 = 5.405

protected

Maximal I_K1 conductance [nS/pF].

◆ G_Kr

double TTP::G_Kr = 0.153

protected

Maximal I_Kr conductance [nS/pF].

◆ G_Ks

double TTP::G_Ks = 0.392

protected

Maximal I_Ks conductance [nS/pF].

◆ G_Na

double TTP::G_Na = 14.838

protected

Maximal I_Na conductance [nS/pF].

◆ G_pCa

double TTP::G_pCa = 0.1238

protected

Maximal I_pCa conductance [pA/pF].

◆ G_pK

double TTP::G_pK = 1.46E-2

protected

Maximal I_pK conductance [nS/pF].

◆ G_to

double TTP::G_to = 0.294

protected

Maximal I_to conductance [nS/pF].

◆ gamma

double TTP::gamma = 0.35

protected

Voltage dependent parameter of I_NaCa [-].

◆ initial_X

const InitialStates TTP::initial_X

inlinestatic

Initial value:

= {
      {"V", -85.23}, {"K_i", 136.89}, {"Na_i", 8.6040}, {"Ca_i", 1.26e-4},
      {"Ca_ss", 3.6e-4}, {"Ca_sr", 3.64}, {"R_bar", 0.9073}}

State variables.

◆ initial_Xg

const InitialStates TTP::initial_Xg

inlinestatic

Initial value:

= {
      {"x_r1_rectifier", 6.21e-3}, {"x_r2_rectifier", 0.4712},
      {"x_s_rectifier", 9.5e-3}, {"m_fast_Na", 1.72e-3}, {"h_fast_Na", 0.7444},
      {"j_fast_Na", 0.7045}, {"d_slow_in", 3.373e-5}, {"f_slow_in", 0.7888},
      {"f2_slow_in", 0.9755}, {"fcass_slow_in", 0.9953}, {"s_out", 0.999998},
      {"r_out", 2.42e-8}}

Gating variables.

◆ k1p

double TTP::k1p = 0.15

protected

R to O and RI to I, I_rel transition rate [mM^{-2}/ms].

◆ k2p

double TTP::k2p = 4.5E-2

protected

O to I and R to RI, I_rel transition rate [mM^{-1}/ms].

◆ k3

double TTP::k3 = 6.E-2

protected

O to R and I to RI, I_rel transition rate [ms^{-1}].

◆ k4

double TTP::k4 = 5.E-3

protected

I to O and Ri to I, I_rel transition rate [ms^{-1}].

◆ K_bufc

double TTP::K_bufc = 1.E-3

protected

Ca_i half-saturation constant for cytplasmic buffer [mM].

◆ K_bufsr

double TTP::K_bufsr = 0.3

protected

Ca_sr half-saturation constant for subspace buffer [mM].

◆ K_bufss

double TTP::K_bufss = 2.5E-4

protected

Ca_ss half-saturation constant for subspace buffer [mM].

◆ K_mCa

double TTP::K_mCa = 1.38

protected

Ca_i half-saturation constant for I_NaCa [mM].

◆ K_mK

double TTP::K_mK = 1.

protected

K_o half-saturation constant of I_NaK [mM].

◆ K_mNa

double TTP::K_mNa = 40.

protected

Na_i half-saturation constant of I_NaK [mM].

◆ K_mNai

double TTP::K_mNai = 87.5

protected

Na_i half-saturation constant for I_NaCa [mM].

◆ K_NaCa

double TTP::K_NaCa = 1000.

protected

Maximal I_NaCa [pA/pF].

◆ K_o

double TTP::K_o = 5.4

protected

Extracellular K concentration [mM].

◆ K_pCa

double TTP::K_pCa = 5.E-4

protected

Half-saturation constant of I_pCa [mM].

◆ K_sat

double TTP::K_sat = 0.1

protected

Saturation factor for I_NaCa [-].

◆ K_up

double TTP::K_up = 2.5E-4

protected

Half-saturation constant of I_up [mM].

◆ label

const std::string TTP::label = "TTP"

inlinestatic

Model label.

◆ max_sr

double TTP::max_sr = 2.5

protected

Maximum value of k_casr [-].

◆ min_sr

double TTP::min_sr = 1.

protected

Minimum value of k_casr [-].

◆ Na_o

double TTP::Na_o = 140.0

protected

Extracellular Na concentration [mM].

◆ p_KNa

double TTP::p_KNa = 3.E-2

protected

Relative I_Ks permeability to Na [-].

◆ p_NaK

double TTP::p_NaK = 2.724

protected

Maximal I_NaK [pA/pF].

◆ Rc

double TTP::Rc = 8314.472

protected

Gas constant [J/mol/K].

◆ rho

double TTP::rho = 162.0

protected

Cellular resistivity [ \(\Omega\)-cm].

◆ sV

double TTP::sV = 0.2

protected

Surface to volume ratio [um^{-1}].

◆ Tc

double TTP::Tc = 310.0

protected

Temperature [K].

◆ V_c

double TTP::V_c = 16.404E-3

protected

Cytoplasmic volume [um^{3}].

◆ V_leak

double TTP::V_leak = 3.6E-4

protected

Maximal I_leak conductance [mM/ms].

◆ V_rel

double TTP::V_rel = 0.102

protected

Maximal I_rel conductance [mM/ms].

◆ V_sr

double TTP::V_sr = 1.094E-3

protected

Sacroplasmic reticulum volume [um^{3}].

◆ V_ss

double TTP::V_ss = 5.468E-5

protected

Subspace volume [um^{3}].

◆ V_xfer

double TTP::V_xfer = 3.8E-3

protected

Maximal I_xfer conductance [mM/ms].

◆ Vmax_up

double TTP::Vmax_up = 6.375E-3

protected

Maximal I_up conductance [mM/ms].

The documentation for this class was generated from the following files:

solver/ionic_ttp.h
solver/ionic_ttp.cpp

Classes

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TTP()

Member Function Documentation

◆ distribute_parameters()

◆ get_calcium_index()

◆ get_parameters()

◆ getf()

◆ read_parameters()

◆ update_g()

Member Data Documentation

◆ alpha

◆ Buf_c

◆ Buf_sr

◆ Buf_ss

◆ Ca_o

◆ calcium_index

◆ Cm

◆ EC

◆ Fc

◆ G_bCa

◆ G_bNa

◆ G_CaL

◆ G_K1

◆ G_Kr

◆ G_Ks

◆ G_Na

◆ G_pCa

◆ G_pK

◆ G_to

◆ gamma

◆ initial_X

◆ initial_Xg

◆ k1p

◆ k2p

◆ k3

◆ k4

◆ K_bufc

◆ K_bufsr

◆ K_bufss

◆ K_mCa

◆ K_mK

◆ K_mNa

◆ K_mNai

◆ K_NaCa

◆ K_o

◆ K_pCa

◆ K_sat

◆ K_up

◆ label

◆ max_sr

◆ min_sr

◆ Na_o

◆ p_KNa

◆ p_NaK

◆ Rc

◆ rho

◆ sV

◆ Tc

◆ V_c

◆ V_leak

◆ V_rel

◆ V_sr

◆ V_ss

◆ V_xfer

◆ Vmax_up