Nash-Panfilov active stress model. More...

#include <ActiveStressNashPanfilov.h>

Inheritance diagram for ActiveStressNashPanfilov:

Classes
class	Parameters
	Model parameters class. More...

Public Member Functions
	ActiveStressNashPanfilov ()
	Constructor.

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

Public Member Functions inherited from ActiveStressODE
	ActiveStressODE (const unsigned int n_states, const bool needs_fiber_stretch, const bool needs_fiber_stretch_rate)
	Constructor.

Public Member Functions inherited from ActiveStress
	ActiveStress (const unsigned int n_states_, const bool needs_fiber_stretch, const bool needs_fiber_stretch_rate)
	Constructor.

virtual	~ActiveStress ()=default
	Virtual destructor.

void	read_parameters (const ActiveStressParameters &params)
	Read model parameters from a parameter object.

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

double	get_tension_fibers (const int idx) const
	Get the tension along fibers \(\eta_f \Tact\) at a given point.

double	get_tension_sheets (const int idx) const
	Get the tension along sheets \(\eta_s \Tact\) at a given point.

double	get_tension_sheet_normals (const int idx) const
	Get the tension along sheet normals \(\eta_n \Tact\) at a given point.

virtual void	init (const unsigned int tnNo)
	Initialize the model.

virtual void	advance_time_step (const double t, const double dt, const Vector< double > &calcium, const Vector< double > &fiber_stretch, const Vector< double > &fiber_stretch_rate)
	Advance in time.

bool	needs_fiber_stretch () const
	Whether this model uses the fiber stretch passed to advance_time_step. This flag can be used to determine whether fiber stretch computation can be skipped for efficiency.

bool	needs_fiber_stretch_rate () const
	Whether this model uses the fiber stretch rate passed to advance_time_step. This flag can be used to determine whether fiber stretch rate computation can be skipped for efficiency.

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

Protected Member Functions
virtual void	read_model_specific_parameters (const ActiveStressModelParameters &params) override
	Read model parameters from a parameter object.

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

virtual void	init_local (Vector< double > &state) const override
	Initialize the state vector for a single node.

virtual Vector< double >	getf (const double t, const Vector< double > &state, const double calcium, const double fiber_stretch, const double fiber_stretch_rate) const override
	Compute the rate of change in the state variables.

virtual double	compute_active_tension_local (const Vector< double > &state, const double fiber_stretch) const override
	Compute the active tension for a single node.

Protected Member Functions inherited from ActiveStressODE
virtual void	advance_time_step_local (const double t, const double dt, const double calcium, const double fiber_stretch, const double fiber_stretch_rate, Vector< double > &state) const override
	Advance in time for a single node.

Protected Attributes
Model parameters.
double	epsilon_0

double	epsilon_i

double	xi_T

double	calcium_rest

double	calcium_crit

double	eta_T

Protected Attributes inherited from ActiveStressODE
ODESolver	ode_solver
	ODE solver.

Protected Attributes inherited from ActiveStress
bool	needs_fiber_stretch_
	Backing store for needs_fiber_stretch.

bool	needs_fiber_stretch_rate_
	Backing store for needs_fiber_stretch_rate.

double	time
	Current time. Updated whenever calling advance_time_step.

Array< double >	states
	State variables for the model.

Vector< double >	active_tension
	Active tension at every node.

double	eta_f
	Active tension coefficient along the fiber direction.

double	eta_s
	Active tension coefficient along the sheet direction.

double	eta_n
	Active tension coefficient along the sheet-normal direction.

Additional Inherited Members
Public Types inherited from ActiveStressODE
enum class	ODESolver { ForwardEuler }
	Enumeration of supported ODE solvers. More...

Public Attributes inherited from ActiveStress
const unsigned int	n_states
	Number of state variables for this model.

Detailed Description

Nash-Panfilov active stress model.

This class implements the Nash-Panfilov active stress model [1], with the modifications introduced by Goktepe and Kuhl [2].

The model equations are the following:

\[ \begin{aligned} \dv{\Tact}{t} &= \varepsilon(\calcium)( \eta_\text{T} (\calcium - \calcium_\text{rest}) - \Tact)\;, \\ \varepsilon(\calcium) &= \varepsilon_0 + (\varepsilon_i - \varepsilon_0) \exp(-\exp(-\xi_T (\calcium - \calcium_\text{crit})))\;, \end{aligned} \]

where \(\eta_\text{T}\), \(\calcium_\text{rest}\), \(\calcium_\text{crit}\), \(\varepsilon_0\), \(\varepsilon_i\) and \(\xi_T\) are user-defined model parameters. The function \(\varepsilon(\calcium)\) is a sigmoidal-shaped calcium-dependent time constant (see Figure 3 in [2] for more details).

Note: The published formulations [1,2] are driven by transmembrane potential. This implementation substitutes intracellular calcium, with \(\eta_T\), \(\calcium_\text{rest}\), \(\xi_T\), and \(\calcium_\text{crit}\) corresponding to \(k_\sigma\), \(\Phi_r\), \(\xi\), and \(\bar{\Phi}\) in [2], respectively.; The sensitivity of the model to calcium is controlled by the paramter \(\eta_\text{T}\), which has the same units of active tension over calcium. Therefore, if the ionic model providing the calcium is phenomenological (see IonicModel) and calcium is non-dimensional, this parameter may need to be rescaled as well. Similar considerations apply to \(\xi_T\).

References:

Constructor & Destructor Documentation

◆ ActiveStressNashPanfilov()

ActiveStressNashPanfilov::ActiveStressNashPanfilov ( )

inline

Constructor.

Member Function Documentation

◆ compute_active_tension_local()

double ActiveStressNashPanfilov::compute_active_tension_local	(	const Vector< double > &	state,
		const double	fiber_stretch
	)		const

overrideprotectedvirtual

Compute the active tension for a single node.

Implements ActiveStress.

◆ distribute_model_specific_parameters()

void ActiveStressNashPanfilov::distribute_model_specific_parameters	(	const CmMod &	cm_mod,
		const cmType &	cm
	)

overrideprotectedvirtual

Distribute model parameters to all parallel processes.

Reimplemented from ActiveStressODE.

◆ get_parameters()

virtual std::unique_ptr< ActiveStressModelParameters > ActiveStressNashPanfilov::get_parameters ( ) const

inlineoverridevirtual

Construct an instance of model parameters.

Implements ActiveStress.

◆ getf()

Vector< double > ActiveStressNashPanfilov::getf	(	const double	t,
		const Vector< double > &	state,
		const double	calcium,
		const double	fiber_stretch,
		const double	fiber_stretch_rate
	)		const

overrideprotectedvirtual

Compute the rate of change in the state variables.

Implements ActiveStressODE.

◆ init_local()

void ActiveStressNashPanfilov::init_local ( Vector< double > & state ) const

overrideprotectedvirtual

Initialize the state vector for a single node.

Parameters

[out] state State vector for a single node, to be initialized by this function.

Implements ActiveStress.

◆ read_model_specific_parameters()

void ActiveStressNashPanfilov::read_model_specific_parameters ( const ActiveStressModelParameters & params )

overrideprotectedvirtual

Read model parameters from a parameter object.

Reimplemented from ActiveStressODE.

Member Data Documentation

◆ calcium_crit

double ActiveStressNashPanfilov::calcium_crit

protected

Critical calcium value, i.e. the threshold value for switching between minimum and maximum time constant.

◆ calcium_rest

double ActiveStressNashPanfilov::calcium_rest

protected

Resting calcium value. Active tension will increase if calcium is above this value.

◆ epsilon_0

double ActiveStressNashPanfilov::epsilon_0

protected

Minimum time constant \(\varepsilon_0\). The unit of measure for this parameter must be the inverse of the unit of measure for time.

◆ epsilon_i

double ActiveStressNashPanfilov::epsilon_i

protected

Maximum time constant \(\varepsilon_i\). The unit of measure for this parameter must be the inverse of the unit of measure for time.

◆ eta_T

double ActiveStressNashPanfilov::eta_T

protected

\(\eta_T\). The unit of measure for this parameter must be the ratio of the unit for tension and the unit for calcium concentration.

◆ label

const std::string ActiveStressNashPanfilov::label = "NashPanfilov"

inlinestatic

Model label.

◆ xi_T

double ActiveStressNashPanfilov::xi_T

protected

Sigmoidal function steepness \(\xi_T\). The unit of measure for this parameter must be the inverse of the unit of measure for calcium concentration.

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

solver/ActiveStressNashPanfilov.h
solver/ActiveStressNashPanfilov.cpp

Classes

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ActiveStressNashPanfilov()

Member Function Documentation

◆ compute_active_tension_local()

◆ distribute_model_specific_parameters()

◆ get_parameters()

◆ getf()

◆ init_local()

◆ read_model_specific_parameters()

Member Data Documentation

◆ calcium_crit

◆ calcium_rest

◆ epsilon_0

◆ epsilon_i

◆ eta_T

◆ label

◆ xi_T