Phenomenological model by Aliev and Panfilov. More...
#include <membraneModels.hh>
Detailed Description
Phenomenological model by Aliev and Panfilov.
A phenomenological model with just one gating variables. This is supposed to be used in the monodomain-like system
\[ \begin{aligned} \dot u &= \mathrm{div}(\sigma\nabla u) - k u(u-a)(u-1) - uv \\ \dot v &= \epsilon(u,v)(-v - ku(u-1-a)) \end{aligned} \]
with \( \epsilon(u,v) = \epsilon_0 + \mu_1 v / (u+\mu_2) \).
The (dimensionless) transmembrane voltage \( u \) covers a range [0,1], and can be translated back to physiological values \( U \) by \( U = u/10 - 0.08 \) [V]. Similarly, the time \( t \) in the model is dimensionless, and can be translated back to real time \( T \) by \( T = 0.0129 t \) [s].
- See also
- PhysiologicalAlievPanfilov
References
[1] Aliev, Panfilov. Chaos, Solitions, and Fractals 7(3):293-301, 1996.
Definition at line 280 of file membraneModels.hh.
Public Types | |
| typedef Dune::FieldVector< double, nGating > | Gating |
| typedef Dune::FieldMatrix< double, nGating, nGating > | GatingJacobian |
Public Member Functions | |
| AlievPanfilov () | |
| Default constructor. More... | |
| double | current (double u, Gating const &v) const |
| The transmembrane ion current. More... | |
| double | current_du (double u, Gating const &v) const |
| The transmembrane ion current derivative w.r.t. the transmembrane voltage. More... | |
| Gating | current_dv (double u, Gating const &v) const |
| The transmembrane ion current derivative w.r.t. the gating variables. More... | |
| Gating | gatingRhs (double u, Gating const &v, double Istim=0) const |
| The right hand side for the evolution of gating variables. More... | |
| Gating | gatingRhs_du (double u, Gating const &v) const |
| The derivative of the right hand side for the evolution of gating variables w.r.t. the transmembrane voltage. More... | |
| GatingJacobian | gatingRhs_dv (double u, Gating const &v) const |
| The derivative of the right hand side for the evolution of gating variables w.r.t. the gating variables. More... | |
| std::string const & | name () const |
| Human-readable name of the membrane model. More... | |
| std::pair< double, Gating > const & | restState () const |
| Value of the resting state fixed point. More... | |
| double | current_du (double u, Gating const &v, double h=1e-5) const |
| The transmembrane ion current derivative w.r.t. the transmembrane voltage. More... | |
Static Public Attributes | |
| static int const | nGating = 1 |
| number of gating variables More... | |
Protected Member Functions | |
| void | setRestState (double uFix, Gating const &vFix) |
| Accepts an (approximate) resting state. More... | |
Member Typedef Documentation
◆ Gating
| typedef Dune::FieldVector<double,nGating> Kaskade::AlievPanfilov::Gating |
Definition at line 287 of file membraneModels.hh.
◆ GatingJacobian
| typedef Dune::FieldMatrix<double,nGating,nGating> Kaskade::AlievPanfilov::GatingJacobian |
Definition at line 288 of file membraneModels.hh.
Constructor & Destructor Documentation
◆ AlievPanfilov()
| Kaskade::AlievPanfilov::AlievPanfilov | ( | ) |
Default constructor.
Member Function Documentation
◆ current()
| double Kaskade::AlievPanfilov::current | ( | double | u, |
| Gating const & | v | ||
| ) | const |
The transmembrane ion current.
- Parameters
-
u transmembrane voltage v gating variables
◆ current_du() [1/2]
| double Kaskade::AlievPanfilov::current_du | ( | double | u, |
| Gating const & | v | ||
| ) | const |
The transmembrane ion current derivative w.r.t. the transmembrane voltage.
- Parameters
-
u transmembrane voltage v gating variables
◆ current_du() [2/2]
|
inlineinherited |
The transmembrane ion current derivative w.r.t. the transmembrane voltage.
This is a default implementation based on numerical differentiation. Overload this if a better implementation is available.
- Parameters
-
u transmembrane voltage [V] v gating variables
h step size for numerical differentiation
Definition at line 109 of file membraneModels.hh.
◆ current_dv()
The transmembrane ion current derivative w.r.t. the gating variables.
- Parameters
-
u transmembrane voltage v gating variables
◆ gatingRhs()
The right hand side for the evolution of gating variables.
- Parameters
-
u transmembrane voltage v gating variables
◆ gatingRhs_du()
The derivative of the right hand side for the evolution of gating variables w.r.t. the transmembrane voltage.
- Parameters
-
u transmembrane voltage v gating variables
◆ gatingRhs_dv()
| GatingJacobian Kaskade::AlievPanfilov::gatingRhs_dv | ( | double | u, |
| Gating const & | v | ||
| ) | const |
The derivative of the right hand side for the evolution of gating variables w.r.t. the gating variables.
- Parameters
-
u transmembrane voltage v gating variables
◆ name()
|
inlineinherited |
Human-readable name of the membrane model.
Definition at line 93 of file membraneModels.hh.
◆ restState()
|
inlineinherited |
Value of the resting state fixed point.
Definition at line 98 of file membraneModels.hh.
◆ setRestState()
|
inlineprotectedinherited |
Accepts an (approximate) resting state.
- Parameters
-
uFix approximate resting state of the transmembrane voltage vFix approximate resting state of the gating variables
The method shall be used by derived classes to provide an approximate value of the resting state (which needs to be a stable fixed point). A few iterations of Newton's method are performed in order to obtain an accurate value.
Definition at line 181 of file membraneModels.hh.
Member Data Documentation
◆ nGating
|
static |
number of gating variables
Definition at line 285 of file membraneModels.hh.
The documentation for this struct was generated from the following file:
