Abstract
Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics.
Highlights
Cardiac arrhythmias progress through a number of stages before becoming life-threatening
We investigated the role of Ca2+ diffusion in both the cytosol and the sarcoplasmic reticulum (SR) in the formation of microscopic Ca2+ alternans (Tian et al, 2012), which form one of the earliest harbingers of cardiac arrhythmia
Stronger diffusion in the SR leads to an instability via a saddle-node bifurcation, which to date has not been reported for Ca2+ alternans and which generates microscopic Ca2+ alternans that are distinct from the ones driven by a period-doubling bifurcation
Summary
Cardiac arrhythmias progress through a number of stages before becoming life-threatening. One of the earliest indications of a pathological condition are T-wave alternans in the electrocardiogram (ECG) (Qu et al, 2010; 2014). The amplitude of the T-wave in the ECG alternates between large and small values on successive heartbeats. There is compelling evidence that these macroscopic signals emerge from pathologies at the single cell level. Single cell alternans have received substantial attention (Alvarez-Lacalle et al, 2015; Weiss et al, 2006; Shiferaw et al, 2003; Cherry, 2017; Tomek et al, 2018; Alvarez-Lacalle et al, 2013; Groenendaal et al, 2014; Shiferaw et al, 2005; Restrepo et al, 2008; Kanaporis and Blatter, 2017; Edwards and Blatter, 2014; Shkryl et al, 2012; Qu et al, 2016)
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