Fenton, Karma, 1998

Model Status

This version of this model has had a stimulus protocol added (James Lawson, 15/06/07) to allow it to simulate trains of action potentials. The previous version was created by Penny Noble of Oxford University, and is known to read in COR and PCEnv. The parameter values used in this variant (BR) of the Fenton-Karma model are consistent with the original Beeler-Reuter model (see Table 1 of the 1998 model errata). Simulations of this CellML model can be run using CMISS.

Model Structure

Ventricular fibrillation (VF) is a disorganised electrical wave activity that disrupts the regular and synchronised contraction of the ventricular muscle and consequently destroys the main pumping function of the heart. Research to date has suggested that electrical vortices are the mechanism underlying VF. These are manisfested in the 2D heart as spiral waves, and in the 3D heart as scroll waves of action potential. Compared with the extensive knowledge available on vortex filament behaviour in an isotropic medium, relatively little is known about how the vortices behave in the anisotropic ventricular muscle. This 1998 publication by Fenton and Karma (fully referenced below) explores the dynamics of the vortex filament in continuous myocardium via numerical simulation.

Over the past 25 to 30 years, mathematical models that describe ventricular action potential have become increasingly complex as new experimental data has become available and has been incorporated into the mathematical equations. Although these complex models are more realistic, they are also computationally expensive to run, and isolating subsets of essential parameters from the model is difficult. One traditional method for avoiding this complexity is to use simplified models such as the FitzHugh-Nagumo model, 1961. However, these simplified models have been criticised as being too simple and as not having the capacity to fully capture certain important features of the ventricular action potential.

The modelling approach that Fenton and Karma take is to use a simplified ionic model of ventricular action potential with three membrane currents. This model retains enough detail to quantitatively reproduce the behaviour of the ventricular action potential captured by the more complex ionic models of cardiac action potential (such as the Beeler-Reuter 1977 model, and the original Luo-Rudy 1991 model), but it is less computationally expensive than these other models.

The three currents in the Fenton-Karma model are:

  • Ifi , a fast inward current which corresponds to the INa current

    • ;

  • Iso , a slow outward current which corresponds to the IK current

    • ; and

  • Isi , a slow inward current which corresponds to the ICa current

    • .

(see the figure below). The authors choose to use these labels as opposed to Na, K and Ca, as a reminder that Ifi , Iso , and Isi do not actually represent measured currents, but only their activation, inactivation and reactivation dynamics which are needed to quantitatively reproduce restitution properties.

Model validation indicates that this simplified model is able to faithfully reproduce the 2D patterns of reentry of the more complex models.

The complete original paper reference is cited below:

Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation, Flavio Fenton and Alain Karma, 1998, Chaos , 8, 20-47. (Full text (HTML) and PDF versions of the article are available to subscribers on the Chaos website.) PubMed ID: 12779708

A schematic diagram of the three ionic currents described by the Fenton-Karma model of a ventricular myocyte.

The Fenton-Karma model has been described here in CellML (the raw CellML description of the Fenton-Karma model can be downloaded in various formats as described in ).