1.1.1. cbcbeat.cellmodels package

1.1.1.1. Submodules

1.1.1.2. cbcbeat.cellmodels.beeler_reuter_1977 module

This module contains a Beeler_reuter_1977 cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.beeler_reuter_1977.Beeler_reuter_1977(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.3. cbcbeat.cellmodels.cardiaccellmodel module

This module contains a base class for cardiac cell models.

class cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel(params=None, init_conditions=None)

Base class for cardiac cell models. Specialized cell models should subclass this class.

Essentially, a cell model represents a system of ordinary differential equations. A cell model is here described by two (Python) functions, named F and I. The model describes the behaviour of the transmembrane potential ‘v’ and a number of state variables ‘s’

The function F gives the right-hand side for the evolution of the state variables:

d/dt s = F(v, s)

The function I gives the ionic current. If a single cell is considered, I gives the (negative) right-hand side for the evolution of the transmembrane potential

(*) d/dt v = - I(v, s)

If used in a bidomain setting, the ionic current I enters into the parabolic partial differential equation of the bidomain equations.

If a stimulus is provided via

cell = CardiacCellModel() cell.stimulus = Expression(“I_s(t)”, degree=1)

then I_s is added to the right-hand side of (*), which thus reads

d/dt v = - I(v, s) + I_s

Note that the cardiac cell model stimulus is ignored when the cell model is used a spatially-varying setting (for instance in the bidomain setting). In this case, the user is expected to specify a stimulus for the cardiac model instead.

F(v, s, time=None)

Return right-hand side for state variable evolution.

I(v, s, time=None)

Return the ionic current.

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

initial_conditions()

Return initial conditions for v and s as an Expression.

num_states()

Return number of state variables (in addition to the membrane potential).

parameters()

Return the current parameters.

set_initial_conditions(**init)

Update initial_conditions in model

set_parameters(**params)

Update parameters in model

class cbcbeat.cellmodels.cardiaccellmodel.MultiCellModel(models, keys, markers)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None, index=None)

I(v, s, time=None, index=None)

initial_conditions()

Return initial conditions for v and s as a dolfin.GenericFunction.

keys()

markers()

mesh()

models()

num_models()

num_states()

Return number of state variables (in addition to the membrane potential).

1.1.1.4. cbcbeat.cellmodels.fenton_karma_1998_BR_altered module

This module contains a Fenton_karma_1998_BR_altered cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.fenton_karma_1998_BR_altered.Fenton_karma_1998_BR_altered(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.5. cbcbeat.cellmodels.fenton_karma_1998_MLR1_altered module

This module contains a Fenton_karma_1998_MLR-1_altered cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.fenton_karma_1998_MLR1_altered.Fenton_karma_1998_MLR1_altered(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.6. cbcbeat.cellmodels.fitzhughnagumo module

This module contains a Fitzhughnagumo cardiac cell model

The module was autogenerated from a gotran form file

class cbcbeat.cellmodels.fitzhughnagumo.Fitzhughnagumo(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

NOT_IMPLEMENTED

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.7. cbcbeat.cellmodels.fitzhughnagumo_manual module

This module contains a FitzHugh-Nagumo cardiac cell model

The module was written by hand, in particular it was not autogenerated.

class cbcbeat.cellmodels.fitzhughnagumo_manual.FitzHughNagumoManual(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

A reparametrized FitzHughNagumo model, based on Section 2.4.1 in “Computing the electrical activity in the heart” by Sundnes et al, 2006.

This is a model containing two nonlinear, ODEs for the evolution of the transmembrane potential v and one additional state variable s.

F(v, s, time=None)

Return right-hand side for state variable evolution.

I(v, s, time=None)

Return the ionic current.

static default_initial_conditions()

static default_parameters()

Set-up and return default parameters.

num_states()

Return number of state variables.

1.1.1.8. cbcbeat.cellmodels.grandi_pasqualini_bers_2010 module

This module contains a Grandi_pasqualini_bers_2010 cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.grandi_pasqualini_bers_2010.Grandi_pasqualini_bers_2010(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.9. cbcbeat.cellmodels.nocellmodel module

This module contains a dummy cardiac cell model.

class cbcbeat.cellmodels.nocellmodel.NoCellModel(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

Class representing no cell model (only bidomain equations). It actually just represents a single completely decoupled ODE.

F(v, s, time=None)

I(v, s, time=None)

static default_initial_conditions()

Set-up and return default initial conditions.

num_states()

1.1.1.10. cbcbeat.cellmodels.rogers_mcculloch_manual module

This module contains a Rogers-McCulloch cardiac cell model which is a modified version of the FitzHughNagumo model.

This formulation is based on the description on page 2 of “Optimal control approach ...” by Nagaiah, Kunisch and Plank, 2013, J Math Biol.

The module was written by hand, in particular it was not autogenerated.

class cbcbeat.cellmodels.rogers_mcculloch_manual.RogersMcCulloch(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

The Rogers-McCulloch model is a modified FitzHughNagumo model. This

formulation follows the description on page 2 of “Optimal control approach ...” by Nagaiah, Kunisch and Plank, 2013, J Math Biol with w replaced by s. Note that this model introduces one additional parameter compared to the original 1994 Rogers-McCulloch model.

This is a model containing two nonlinear, ODEs for the evolution of the transmembrane potential v and one additional state variable s:

\[\]

rac{dv}{dt} = - I_{ion}(v, s)

rac{ds}{dt} = F(v, s)

where

\[ \begin{align}\begin{aligned}I_{ion}(v, s) = g v (1 - v/v_th)(1 - v/v_p) + \eta_1 v s\\ F(v, s) = \eta_2 (v/vp - \eta_3 s)\end{aligned}\end{align} \]

F(v, s, time=None)

Return right-hand side for state variable evolution.

I(v, s, time=None)

Return the ionic current.

static default_initial_conditions()

static default_parameters()

Set-up and return default parameters.

num_states()

Return number of state variables.

1.1.1.11. cbcbeat.cellmodels.tentusscher_2004_mcell module

This module contains a Tentusscher_2004_mcell cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.tentusscher_2004_mcell.Tentusscher_2004_mcell(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

NOT_IMPLEMENTED

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.12. cbcbeat.cellmodels.tentusscher_2004_mcell_cont module

This module contains a Tentusscher_2004_mcell_cont cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.tentusscher_2004_mcell_cont.Tentusscher_2004_mcell_cont(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.13. cbcbeat.cellmodels.tentusscher_2004_mcell_disc module

This module contains a Tentusscher_2004_mcell_disc cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.tentusscher_2004_mcell_disc.Tentusscher_2004_mcell_disc(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.14. cbcbeat.cellmodels.tentusscher_panfilov_2006_M_cell module

This module contains a Tentusscher_panfilov_2006_M_cell cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.tentusscher_panfilov_2006_M_cell.Tentusscher_panfilov_2006_M_cell(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.15. cbcbeat.cellmodels.tentusscher_panfilov_2006_epi_cell module

This module contains a Tentusscher_panfilov_2006_epi_cell cardiac cell model

The module was autogenerated from a gotran ode file

class cbcbeat.cellmodels.tentusscher_panfilov_2006_epi_cell.Tentusscher_panfilov_2006_epi_cell(params=None, init_conditions=None)

Bases: cbcbeat.cellmodels.cardiaccellmodel.CardiacCellModel

F(v, s, time=None)

Right hand side for ODE system

I(v, s, time=None)

Transmembrane current

I = -dV/dt

static default_initial_conditions()

Set-up and return default initial conditions.

static default_parameters()

Set-up and return default parameters.

num_states()

1.1.1.16. Module contents