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Biological systems are complex systems that are regulated at multiple scales, with dynamics ranging from random molecular fluctuations to spatiotemporal wave dynamics and periodic oscillations. To understand the underlying mechanisms and link the dynamics at the molecular scale to those at the tissue and organ scales, research approaches integrating computer modeling and simulation, nonlinear dynamics, and experimental and clinical data have been widely used. In this article, we review how these approaches have been used to investigate the multiscale cardiac excitation dynamics, particularly the genesis of cardiac arrhythmias that can lead to sudden death. The specific topics covered in this review are: i) Mechanisms of formation of intracellular calcium sparks (the bottom panel in Fig.12) and waves (the second lowest panel in Fig.12) in the subcellular scale, which can be described by stochastic transitions between the two stable states of a bistable system and second order phase transition, respectively; ii) Mechanisms of triggered activities in the cellular scale (the second panel from the top of Fig.12) resulting from transmembrane voltage and intracellular calcium cycling and their coupling, some of which can be well described by the bifurcation theories of the nonlinear dynamical system; iii) Mechanisms for the genesis of arrhythmias at the tissue scale (the top panel in Fig.12) induced by the triggered activities, which can be understood as dynamical instability-induced pattern formation in heterogeneous excitable media; and iv) Manifestations of the excitation dynamics and transitions in the whole heart (organ scale) in electrocardiogram to bridge the spatiotemporal wave dynamics to clinical observations. These results indicate that nonlinear dynamics, pattern formation and statistical physics are the fundamental components for establishing a theoretical framework for understanding cardiac arrhythmias.Fig.12. Multiscale excitation dynamics in the heart. From bottom up the results of different scales are illustrated. The bottom panel (CRU scale) illustrates the line scan images of calcium sparks in the single calcium release unit (upper trace, the color indicates the intensity of the spark), and the trace of the total calcium intensity (lower trace). Calcium spark can be described by the Kramer’s transition between the two states of a bistable system (as shown in Fig.4). The second lowest panel (subcellular scale) is a line scan image of calcium waves inside a cell. The formation of a calcium wave is a self-organization process that involves the second-order phase transition, as indicated by the power-law distribution of calcium spark cluster size (see Fig.5). The second top panel (cellular scale) indicates triggered activities (including early after depolarizations and delayed afterdepolarizations) induced by the coupling between calcium wave and voltage in a single cell, some of which can be well described by the bifurcation theories of the nonlinear dynamical system (as discussed in Fig.6). The top panel (tissue and organ scale) shows spontaneous genesis of reentry (spiral wave) via a dynamical instability in whole heart, which will be manifestated as arrhythmias in the electrocardiogram (see Figs.10 and 11).
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Keywords:
- biological physics /
- nonlinear dynamics /
- excitable media /
- arrhythmias /
- multiscale modeling
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