Abstract
During a single heartbeat, muscle cells in the heart contract and relax. Under healthy conditions, the behaviour of these muscle cells is almost identical from one beat to the next. However, this regular rhythm can be disturbed giving rise to a variety of cardiac arrhythmias including cardiac alternans. Here, we focus on so-called microscopic calcium alternans and show how their complex spatial patterns can be understood with the help of the master stability function. Our work makes use of the fact that cardiac muscle cells can be conceptualised as a network of networks, and that calcium alternans correspond to an instability of the synchronous network state. In particular, we demonstrate how small changes in the coupling strength between network nodes can give rise to drastically different activity patterns in the network.
Highlights
The heart consists of millions of muscle cells called cardiac myocytes (Bers 2002; Eisner et al 2017)
Since for diffusively coupled nodes, the synchronous network state corresponds to the periodic solution of a single calcium release unit (CRU), the mathematical tractability of the master stability function (MSF) significantly depends on the mathematical structure of the ordinary differential equations (ODEs) that describe the behaviour of a CRU
Because diffusive coupling is symmetric and the coupling strength is positive, the eigenvalues λi of the graph Laplacian are real and negative including a zero eigenvalue. The latter corresponds to the periodic orbit of an uncoupled node, which entails that a necessary condition for the existence of a stable synchronous network state is that the periodic orbit of an uncoupled node is linearly stable
Summary
The heart consists of millions of muscle cells called cardiac myocytes (Bers 2002; Eisner et al 2017). Since for diffusively coupled nodes, the synchronous network state corresponds to the periodic solution of a single CRU, the mathematical tractability of the MSF significantly depends on the mathematical structure of the ordinary differential equations (ODEs) that describe the behaviour of a CRU.
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