### 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 [1] 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 vSERCA as control parameters. In the (ce,vSERCA)-domain we derive an explicit function v*=v*(ce), and we claim that any resting state based on parameters that lie above the curve (i.e. any pair (ce,vSERCA) such that with vSERCA>v*(ce)) is unstable in the sense that small perturbations will grow and can eventually turn into a calcium wave. And conversely; any pair (ce,vSERCA) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 97-107 |

Number of pages | 11 |

Journal | Mathematical Biosciences |

Volume | 236 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- Calcium waves
- Cardiomyocyte
- Eigenvalue analysis
- Stability

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Mathematical Biosciences*,

*236*(2), 97-107. https://doi.org/10.1016/j.mbs.2012.02.005

**Instabilities of the resting state in a mathematical model of calcium handling in cardiac myocytes.** / Tveito, Aslak; Lines, Glenn Terje; Hake, Johan; Edwards, Andrew G.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 236, no. 2, pp. 97-107. https://doi.org/10.1016/j.mbs.2012.02.005

}

TY - JOUR

T1 - Instabilities of the resting state in a mathematical model of calcium handling in cardiac myocytes

AU - Tveito, Aslak

AU - Lines, Glenn Terje

AU - Hake, Johan

AU - Edwards, Andrew G.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - 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 [1] 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 vSERCA as control parameters. In the (ce,vSERCA)-domain we derive an explicit function v*=v*(ce), and we claim that any resting state based on parameters that lie above the curve (i.e. any pair (ce,vSERCA) such that with vSERCA>v*(ce)) is unstable in the sense that small perturbations will grow and can eventually turn into a calcium wave. And conversely; any pair (ce,vSERCA) 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.

AB - 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 [1] 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 vSERCA as control parameters. In the (ce,vSERCA)-domain we derive an explicit function v*=v*(ce), and we claim that any resting state based on parameters that lie above the curve (i.e. any pair (ce,vSERCA) such that with vSERCA>v*(ce)) is unstable in the sense that small perturbations will grow and can eventually turn into a calcium wave. And conversely; any pair (ce,vSERCA) 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.

KW - Calcium waves

KW - Cardiomyocyte

KW - Eigenvalue analysis

KW - Stability

UR - http://www.scopus.com/inward/record.url?scp=84859158547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859158547&partnerID=8YFLogxK

U2 - 10.1016/j.mbs.2012.02.005

DO - 10.1016/j.mbs.2012.02.005

M3 - Article

C2 - 22391458

AN - SCOPUS:84859158547

VL - 236

SP - 97

EP - 107

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 2

ER -