ArticleMathematical biosciences2012
Instabilities of the resting state in a mathematical model of calcium handling in cardiac myocytes.
Article in Mathematical biosciences, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed, 7 citations in OpenAlex.
- Buffering and total calcium levels determine the presence of oscillatory regimes in cardiac cells.PLoS computational biology · 2020Article
- Multiple Dynamical Mechanisms of Phase-2 Early Afterdepolarizations in a Human Ventricular Myocyte Model:Frontiers in physiology · 2019Article
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4 authors at 3 institutions in 2 countries.
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Abstract
We analyze a recently published model of calcium handling in cardiac myocytes in order to find conditions for the presence of instabilities in the resting state of the model. Such instabilities can create calcium waves which in turn may be able to initiate cardiac arrhythmias. The model was developed by Swietach, Spitzer and Vaughan-Jones in order to study the effect, on calcium waves, of varying ryanodine receptor (RyR)-permeability, sarco/endoplasmic reticulum calcium ATPase (SERCA) and calcium diffusion. We study the model using the extracellular calcium concentration c(e) and the maximal velocity of the SERCA-pump v(SERCA) as control parameters. In the (c(e),v(SERCA))-domain we derive an explicit function v∗=v∗(c(e)), and we claim that any resting state based on parameters that lie above the curve (i.e. any pair (c(e),v(SERCA)) such that with v(SERCA) > v∗(c(e))) is unstable in the sense that small perturbations will grow and can eventually turn into a calcium wave. And conversely; any pair (c(e),v(SERCA)) below the curve is stable in the sense that small perturbations to the resting state will decay to rest. This claim is supported by analyzing the stability of the system in terms of computing the eigenmodes of the linearized model. Furthermore, the claim is supported by direct simulations based on the non-linear model. Since the curve separating stable from unstable states is given as an explicit function, we can show how stability depends on other parameters of the model.
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