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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
object
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 behavior 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.
- class cbcbeat.cellmodels.cardiaccellmodel.MultiCellModel(models, keys, markers)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
NOT_IMPLEMENTED
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)[source]#
Bases:
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.
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
Class representing no cell model (only bidomain equations). It actually just represents a single completely decoupled ODE.
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)[source]#
Bases:
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
\[ \begin{align}\begin{aligned}I_{ion}(v, s) = g v (1 - v/v_th)(1 - v/v_p) + \eta_1 v s\\ F(v, s) = \eta_2 (v/vp - \eta_3 s)\end{aligned}\end{align} \]
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)[source]#
Bases:
CardiacCellModel
NOT_IMPLEMENTED
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
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)[source]#
Bases:
CardiacCellModel
1.1.1.16. Module contents#
- class cbcbeat.cellmodels.Beeler_reuter_1977(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
- class cbcbeat.cellmodels.CardiacCellModel(params=None, init_conditions=None)[source]#
Bases:
object
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 behavior 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.
- class cbcbeat.cellmodels.Fenton_karma_1998_BR_altered(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
- class cbcbeat.cellmodels.Fenton_karma_1998_MLR1_altered(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
- class cbcbeat.cellmodels.FitzHughNagumoManual(params=None, init_conditions=None)[source]#
Bases:
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.
- class cbcbeat.cellmodels.MultiCellModel(models, keys, markers)[source]#
Bases:
CardiacCellModel
- class cbcbeat.cellmodels.NoCellModel(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
Class representing no cell model (only bidomain equations). It actually just represents a single completely decoupled ODE.
- class cbcbeat.cellmodels.RogersMcCulloch(params=None, init_conditions=None)[source]#
Bases:
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
\[ \begin{align}\begin{aligned}I_{ion}(v, s) = g v (1 - v/v_th)(1 - v/v_p) + \eta_1 v s\\ F(v, s) = \eta_2 (v/vp - \eta_3 s)\end{aligned}\end{align} \]
- class cbcbeat.cellmodels.Tentusscher_2004_mcell(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
NOT_IMPLEMENTED
- class cbcbeat.cellmodels.Tentusscher_panfilov_2006_M_cell(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel
- class cbcbeat.cellmodels.Tentusscher_panfilov_2006_epi_cell(params=None, init_conditions=None)[source]#
Bases:
CardiacCellModel