CellML 1.0 version of the model which stabilises at 1Hz

Model Status

This CellML model is known to run in both COR and PCEnv to recreate the published results. The units have been checked and they are consistent. This particular version of the CellML model was translated from the author's original Matlab code and it stabilises at 1Hz.

Please note that this model is relatively stiff. If you run the model using the default COR settings, you will get a message that reads: "Problem with the CVODE integrator: at t=0.00170178, mxstep steps taken before reaching tout." This basically means that you have to increase the maximum number of steps which is, by default, set to 500. Such a value is sufficient for most ODE problems, but not for ODE problems that have very stiff ODEs, such as the current model. Anyway, you will see that the model runs fine if you increase the value to something like 5000. Note that you also need to set the maximum time step to a sensible value, i.e. the duration of the stimulus which is here 1 ms.

Regarding PCEnv, it uses a higher value than COR for the maximum number of steps, which is why the model will run in PCEnv without having to change this particular setting. Otherwise, like in COR there is a need to set the maximum time step to a sensible value. PCEnv uses a default value of 1 s for the Pasek model, which is clearly not small enough as can be seen when running the model for 10 s. If one uses 0.001 s, then everything is fine.

Model Structure

ABSTRACT: The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.

The original paper reference is cited below:

The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes, Michal Pasek, Jiri Simurda, and Georges Christe, 2006, Philosophical Transactions of The Royal Society A, 81, 3029-3051. PubMed ID: 16608703

Note that this model is based on a quantitative description of electrical activity of the rat ventricular myocyte proposed by Pandit et al. (2001), which has also been described in CellML and can be found in the CellML Model Respository.