Membrane models

Electrophysiological membrane models for use in cardiac simulations. More...

Classes
struct	Kaskade::MembraneModelBase< Derived, n >
	Convenience base class for membrane models providing numerical differentiation. More...
struct	Kaskade::AlievPanfilov
	Phenomenological model by Aliev and Panfilov. More...
struct	Kaskade::PhysiologicalAlievPanfilov
	Phenomenological model based on Aliev and Panfilov, scaled to physiological values. More...
class	Kaskade::FentonKarma
	The 3-variable Fenton-Karma membrane model. More...
struct	Kaskade::TenTusscher16
	Physiologcial model by tenTusscher et al. More...
struct	Kaskade::TenTusscher18
	Physiologcial model by tenTusscher et al. (2006) More...
struct	Kaskade::ActiveStressModelBase< Derived, n, m >
	Convenience base class for active stress generation models providing numerical differentiation. More...

Detailed Description

Electrophysiological membrane models for use in cardiac simulations.

This module contains electrophysiological cell membrane models defining the transmembrane ionic current depending on the transmembrane voltage and so-called gating variables, which define the internal state of ion channels in the membrane or ion concentrations inside certain cell compartments. These states and concentrations evolve themselves, again depending on transmembrane voltage and gating variables. This evolution is defined by a membrane model as well.

Additionally, models for active tensile stress generation in muscle cells are defined here.

A lot of membrane models are available at the CellML site (http://www.cellml.org/).

Membrane models describe ODEs for the transmembrane voltage \( u \) and gating variables \( v \):

\[ \begin{aligned} \dot u &= I(u,v) \\ \dot v &= f(u,v) \end{aligned} \]

Here, \( I \) is the transmembrane current and \( f \) the gating dynamic. These two functions and their deriviatives are defined by membrane models.

Active stress generation models define ann ODE for the tensile stress generated in muscle cells.

\[ \begin{aligned} \dot s &= f(s,t) \\ a &= g(s) \end{aligned} \]

Here, \( s \) is the internal state of the stress generation system, \( t \) are trigger variables, e.g., calcium ion concentration, and \( a \) is the active stress. The functions \( f \) and \( g \) and their derivatives are defined by active stress models.