AbstractBackwardEulerCardiacCell< SIZE > Class Template Reference

#include <AbstractBackwardEulerCardiacCell.hpp>

Collaboration diagram for AbstractBackwardEulerCardiacCell< SIZE >:

Public Member Functions
	AbstractBackwardEulerCardiacCell (unsigned numberOfStateVariables, unsigned voltageIndex, boost::shared_ptr< AbstractStimulusFunction > pIntracellularStimulus)
virtual	~AbstractBackwardEulerCardiacCell ()
virtual void	ComputeResidual (double time, const double rCurrentGuess[SIZE], double rResidual[SIZE])=0
virtual void	ComputeJacobian (double time, const double rCurrentGuess[SIZE], double rJacobian[SIZE][SIZE])=0
virtual OdeSolution	Compute (double tStart, double tEnd)
virtual void	ComputeExceptVoltage (double tStart, double tEnd)
Protected Member Functions
virtual void	ComputeOneStepExceptVoltage (double tStart)=0
virtual void	UpdateTransmembranePotential (double time)=0
Private Member Functions
template<class Archive >
void	serialize (Archive &archive, const unsigned int version)
void	EvaluateYDerivatives (double time, const std::vector< double > &rY, std::vector< double > &rDY)
Friends
class	boost::serialization::access

Detailed Description

template<unsigned SIZE>
class AbstractBackwardEulerCardiacCell< SIZE >

This is the base class for cardiac cells solved using a (decoupled) backward Euler approach.

The basic approach to solving such models is:

Update the transmembrane potential, either from solving an external PDE, or using a forward Euler step.
Update any gating variables (or similar) using a backward euler step. Suitable ODEs can be written in the form . The update expression is then $u_n = ( u_{n-1} + g(V_n)*dt ) / ( 1 - h(V_n)*dt )$ .
Update the remaining state variables using Newton's method to solve the nonlinear system $U_n - U_{n-1} = dt*F(U_n, V_n)$ . The template parameter to the class specifies the size of this nonlinear system.

Definition at line 57 of file AbstractBackwardEulerCardiacCell.hpp.

Constructor & Destructor Documentation

template<unsigned SIZE>

AbstractBackwardEulerCardiacCell< SIZE >::AbstractBackwardEulerCardiacCell	(	unsigned	numberOfStateVariables,
		unsigned	voltageIndex,
		boost::shared_ptr< AbstractStimulusFunction >	pIntracellularStimulus
	)			`[inline]`

Standard constructor for a cell.

Parameters:

	numberOfStateVariables	the size of the ODE system
	voltageIndex	the index of the variable representing the transmembrane potential within the state variable vector
	pIntracellularStimulus	the intracellular stimulus function

Some notes for future reference:

We may want to remove the timestep from this class, and instead pass it to the Compute* methods, especially if variable timestepping is to be used.
It's a pity that inheriting from AbstractCardiacCell forces us to store a null pointer (for the unused ODE solver) in every instance. We may want to revisit this design decision at a later date.

Definition at line 185 of file AbstractBackwardEulerCardiacCell.hpp.

template<unsigned SIZE>

AbstractBackwardEulerCardiacCell< SIZE >::~AbstractBackwardEulerCardiacCell ( ) [inline, virtual]

Virtual destructor

Definition at line 196 of file AbstractBackwardEulerCardiacCell.hpp.

Member Function Documentation

template<unsigned SIZE>

OdeSolution AbstractBackwardEulerCardiacCell< SIZE >::Compute	(	double	tStart,
		double	tEnd
	)			`[inline, virtual]`

Simulates this cell's behaviour between the time interval [tStart, tEnd], with timestep mDt. Uses a forward Euler step to update the transmembrane potential at each timestep.

The length of the time interval must be a multiple of the timestep.

Parameters:

	tStart	beginning of the time interval to simulate
	tEnd	end of the time interval to simulate

Returns:: the values of each state variable, at mDt intervals.

Reimplemented from AbstractCardiacCell.

Definition at line 200 of file AbstractBackwardEulerCardiacCell.hpp.

References AbstractBackwardEulerCardiacCell< SIZE >::ComputeOneStepExceptVoltage(), AbstractCardiacCell::mDt, AbstractOdeSystem::mpSystemInfo, OdeSolution::rGetSolutions(), AbstractOdeSystem::rGetStateVariables(), OdeSolution::rGetTimes(), OdeSolution::SetNumberOfTimeSteps(), OdeSolution::SetOdeSystemInformation(), AbstractBackwardEulerCardiacCell< SIZE >::UpdateTransmembranePotential(), and AbstractCardiacCell::VerifyStateVariables().

template<unsigned SIZE>

void AbstractBackwardEulerCardiacCell< SIZE >::ComputeExceptVoltage	(	double	tStart,
		double	tEnd
	)			`[inline, virtual]`

Simulates this cell's behaviour between the time interval [tStart, tEnd], with timestep mDt. The transmembrane potential is kept fixed throughout.

The length of the time interval must be a multiple of the timestep.

Parameters:

	tStart	beginning of the time interval to simulate
	tEnd	end of the time interval to simulate

Reimplemented from AbstractCardiacCell.

Definition at line 242 of file AbstractBackwardEulerCardiacCell.hpp.

References AbstractBackwardEulerCardiacCell< SIZE >::ComputeOneStepExceptVoltage(), AbstractCardiacCell::mDt, and AbstractCardiacCell::VerifyStateVariables().

template<unsigned SIZE>

virtual void AbstractBackwardEulerCardiacCell< SIZE >::ComputeJacobian	(	double	time,
		const double	rCurrentGuess[SIZE],
		double	rJacobian[SIZE][SIZE]
	)			`[pure virtual]`

Compute the Jacobian matrix for the nonlinear system portion of the cell model.

Parameters:

	time	the current time
	rCurrentGuess	the current guess for
	rJacobian	to be filled in with the Jacobian matrix

template<unsigned SIZE>

virtual void AbstractBackwardEulerCardiacCell< SIZE >::ComputeOneStepExceptVoltage ( double tStart ) [protected, pure virtual]

Compute the values of all state variables, except the voltage, using backward Euler, for one timestep from tStart.

Note:: This method must be provided by subclasses.

Parameters:

tStart

start of this timestep

Implemented in CML_luo_rudy_1991_pe_lut_be, BackwardEulerFoxModel2002Modified, BackwardEulerLuoRudyIModel1991, BackwardEulerMahajanModel2008, BackwardEulerNobleVargheseKohlNoble1998, and BackwardEulerTenTusscher2006.

Referenced by AbstractBackwardEulerCardiacCell< SIZE >::Compute(), and AbstractBackwardEulerCardiacCell< SIZE >::ComputeExceptVoltage().

template<unsigned SIZE>

virtual void AbstractBackwardEulerCardiacCell< SIZE >::ComputeResidual	(	double	time,
		const double	rCurrentGuess[SIZE],
		double	rResidual[SIZE]
	)			`[pure virtual]`

Compute the residual of the nonlinear system portion of the cell model.

Parameters:

	time	the current time
	rCurrentGuess	the current guess for
	rResidual	to be filled in with the residual vector

template<unsigned SIZE>

void AbstractBackwardEulerCardiacCell< SIZE >::EvaluateYDerivatives	(	double	time,
		const std::vector< double > &	rY,
		std::vector< double > &	rDY
	)			`[inline, private, virtual]`