A Simplified Ventricular Myocyte Model
Penny
Noble
Oxford University
Model Status
This CellML model runs in OpenCell and COR to reproduce the published results. This particular version of the CellML model has had a stimulus protocol added to allow it to simulate trains of action potentials. 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
ABSTRACT: Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized.
The 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. PubMed ID: 12779708
cell diagram
A schematic diagram of the three ionic currents described by the Fenton-Karma model of a ventricular myocyte.
$\frac{d u}{d \mathrm{time}}=-(\mathrm{J\_fi}+\mathrm{J\_so}+\mathrm{J\_si}+\mathrm{J\_stim})\mathrm{Vm}=\mathrm{V\_0}+u(\mathrm{V\_fi}-\mathrm{V\_0})$
$p=\begin{cases}0 & \text{if $u< \mathrm{u\_c}$}\\ 1 & \text{otherwise}\end{cases}$
$q=\begin{cases}0 & \text{if $u< \mathrm{u\_v}$}\\ 1 & \text{otherwise}\end{cases}$
$\mathrm{tau\_d}=\frac{\mathrm{Cm}}{\mathrm{g\_fi\_max}}\mathrm{J\_fi}=\frac{-vp(1-u)(u-\mathrm{u\_c})}{\mathrm{tau\_d}}$
$\mathrm{tau\_v\_minus}=q\mathrm{tau\_v1\_minus}-1\mathrm{tau\_v2\_minus}\frac{d v}{d \mathrm{time}}=\frac{(1-p)(1-v)}{\mathrm{tau\_v\_minus}}-\frac{pv}{\mathrm{tau\_v\_plus}}$
$\mathrm{J\_so}=\frac{u(1-p)}{\mathrm{tau\_0}}+\frac{p}{\mathrm{tau\_r}}$
$\mathrm{J\_si}=\frac{-w(1+\tanh (k(u-\mathrm{u\_csi})))}{2\mathrm{tau\_si}}$
$\frac{d w}{d \mathrm{time}}=\frac{(1-p)(1-w)}{\mathrm{tau\_w\_minus}}-\frac{pw}{\mathrm{tau\_w\_plus}}$
$\mathrm{Istim}=\begin{cases}\mathrm{IstimAmplitude} & \text{if $(\mathrm{time}\ge \mathrm{IstimStart})\land (\mathrm{time}\le \mathrm{IstimEnd})\land (\mathrm{time}-\mathrm{IstimStart}-\lfloor \frac{\mathrm{time}-\mathrm{IstimStart}}{\mathrm{IstimPeriod}}\rfloor \mathrm{IstimPeriod}\le \mathrm{IstimPulseDuration})$}\\ 0 & \text{otherwise}\end{cases}$
F
Fenton
Chaos
2007-11-29T10:20:43+13:00
A stimulus protocol was added to this model to allow simulation of a train of action potentials. The amplitude (-0.2 per second) and duration (1ms) of the stimulus was taken from the single stimulus in Penny's file.
A
Karma
2006-01-01
unknown
keyword
Ventricular Myocyte
myocardium
electrophysiology
vortex dynamics
cardiac
3d
2007-06-15T11:59:02+12:00
This version & variant was created by Penny Noble of Oxford University and uses the parameters of the modified Luo-Rudy 1994 model.
Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
8 1
20
47
James Lawson
unknown
unknown
unknown
Penny
Noble
J
Units checked, curated.
Penny
Noble
J
2006-05-10T00:00:00+00:00
12779708
10000
Oxford University
Department of Physiology, Anatomy & Genetics
Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation (BR Model)
Department of Physiology, Anatomy & Genetics, University of Oxford
unknown
unknown
1998-03-01
James Lawson
unknown
James
Lawson
Richard
This version has been modified from version 03 to add a stimulus protocol to allow simulation of trains of action potentials. Version 03 was created and curated by Penny Noble of Oxford University.
penny.noble@dpag.ox.ac.uk