Abstract ODE-based active stress model. More...

#include <ActiveStressODE.h>

Inheritance diagram for ActiveStressODE:

Classes
class	Parameters
	Model parameters class. More...

Public Types
enum class	ODESolver { ForwardEuler }
	Enumeration of supported ODE solvers. More...

Public Member Functions
	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.

virtual std::unique_ptr< ActiveStressModelParameters >	get_parameters () const =0
	Construct an instance of model parameters for this model.

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.

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	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.

virtual Vector< double >	getf (const double t, const Vector< double > &state, const double calcium, const double fiber_stretch, const double fiber_stretch_rate) const =0
	Compute the rate of change in the state variables.

Protected Member Functions inherited from ActiveStress
virtual void	init_local (Vector< double > &state) const =0
	Initialize the state vector for a single node.

virtual double	compute_active_tension_local (const Vector< double > &state, const double fiber_stretch) const =0
	Compute the active tension for a single node.

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

Detailed Description

Abstract ODE-based active stress model.

This class provides an interface for defining active stress models for which the evolution of the state vector \(\astressstate\) is governed by a system of ordinary differential equations (ODEs):

\[ \begin{aligned} \dv{\astressstate}{t} &= \mathbf{F}_\text{AS}(t, \astressstate, \calcium, \fiberstretch, \fiberstretchrate)\;, \\ \Tact &= \Tact(\astressstate, \fiberstretch)\;. \end{aligned} \]

Numerical methods

The ODE system is advanced with one of the methods described in ODESolver. After that, the active tension is computed for every node \(i\) as:

\[ {\Tact}_{i}^{n+1} = \Tact(\astressstate_i^{n+1}, \fiberstretch_i^{n+1})\;. \]

Implementing derived models

To implement a new ODE-based active stress model, the following steps need to be taken:

Create a new class derived from ActiveStressODE.
Override the method init_local (from the base class ActiveStress) to define the initial condition for the state vector at a single node.
Override the method getf to define the right-hand side function \(\mathbf{F}_\text{AS}\) of the ODE system.
Create a new class derived from ActiveStressODE::Parameters to store the parameters specific to the new active stress model.
Override the methods get_parameters, read_parameters and distribute_parameters to manage the parameters of the new active stress model. Both read_parameters and distribute_parameters need to call the corresponding method of ActiveStressODE.
Register the new class into the active stress model factory by using the macro REGISTER_ACTIVE_STRESS_MODEL. The macro should be called in a .cpp file, not in a header file.

Member Enumeration Documentation

◆ ODESolver

enum class ActiveStressODE::ODESolver

strong

Enumeration of supported ODE solvers.

In the documentation of the individual methods below, the subscript \(i\) is used to denote the value of variables at the \(i\)-th node, and the superscript \(n\) is used to denote the time step.

Enumerator

ForwardEuler

Forward Euler.

The state vector is updated as follows:

\[ \astressstate_i^{n+1} = \astressstate_i^n + \Delta t \mathbf{F}_\text{AS}(t^n, \astressstate_i^n, \calcium_i^n, \fiberstretch_i^n, \fiberstretchrate_i^n)\;. \]

Constructor & Destructor Documentation

◆ ActiveStressODE()

ActiveStressODE::ActiveStressODE	(	const unsigned int	n_states,
		const bool	needs_fiber_stretch,
		const bool	needs_fiber_stretch_rate
	)

inline

Constructor.

Parameters

n_states	Number of state variables for this model.
needs_fiber_stretch	See ActiveStress::ActiveStress.
needs_fiber_stretch_rate	See ActiveStress::ActiveStress.

Member Function Documentation

◆ advance_time_step_local()

void ActiveStressODE::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

overrideprotectedvirtual

Advance in time for a single node.

Solves one forward Euler time step for the ODE system.

Parameters

[in]	t	Current time (i.e. the time instant being advanced to).
[in]	dt	Time step size.
[in]	calcium	Calcium concentration at the current node.
[in]	fiber_stretch	Fiber stretch at the current node.
[in]	fiber_stretch_rate	Fiber stretch rate at the current node.
[in,out]	state	State vector for a single node, to be updated by this function.

Todo:: [michelebucelli] It might be necessary or useful to implement other timestepping schemes, e.g. Runge-Kutta. In that case, we might want to expand the interface to support implicit time stepping too, e.g. by adding a method to evaluate the Jacobian matrix of the system, as in IonicModel.

Implements ActiveStress.

◆ distribute_model_specific_parameters()

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

overrideprotectedvirtual

Distribute model parameters to all parallel processes.

Implements ActiveStress.

Reimplemented in ActiveStressNashPanfilov.

◆ getf()

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

protectedpure virtual

Compute the rate of change in the state variables.

Parameters

[in]	t	Current time (i.e. the time instant being advanced to).
[in]	dt	Time step size.
[in]	calcium	Calcium concentration at the current node.
[in]	fiber_stretch	Fiber stretch at the current node.
[in]	fiber_stretch_rate	Fiber stretch rate at the current node.

Returns: A vector containing the rate of change for each state variable.

Implemented in ActiveStressNashPanfilov.

◆ read_model_specific_parameters()

void ActiveStressODE::read_model_specific_parameters ( const ActiveStressModelParameters & params )

overrideprotectedvirtual

Read model parameters from a parameter object.

Implements ActiveStress.

Reimplemented in ActiveStressNashPanfilov.

Member Data Documentation

◆ ode_solver

ODESolver ActiveStressODE::ode_solver

protected

ODE solver.

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

solver/ActiveStressODE.h
solver/ActiveStressODE.cpp

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Numerical methods

Implementing derived models

Member Enumeration Documentation

◆ ODESolver

Constructor & Destructor Documentation

◆ ActiveStressODE()

Member Function Documentation

◆ advance_time_step_local()

◆ distribute_model_specific_parameters()

◆ getf()

◆ read_model_specific_parameters()

Member Data Documentation

◆ ode_solver