Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation

Spontaneous sub-cellular calcium release events (SCRE) are conjectured to promote rapid arrhythmias associated with conditions such as heart failure and atrial fibrillation: they can underlie the emergence of spontaneous action potentials in single cells which can lead to arrhythmogenic triggers in tissue. The multi-scale mechanisms of the development of SCRE into arrhythmia triggers, and their dynamic interaction with the tissue substrate, remain elusive; rigorous and simultaneous study of dynamics from the nanometre to the centimetre scale is a major challenge. The aim of this study was to develop a computational approach to overcome this challenge and study potential bi-directional coupling between sub-cellular and tissue-scale arrhythmia phenomena. A framework comprising a hierarchy of computational models was developed, which includes detailed single-cell models describing spatio-temporal calcium dynamics in 3D, efficient non-spatial cell models, and both idealised and realistic tissue models. A phenomenological approach was implemented to reproduce SCRE morphology and variability in the efficient cell models, comprising the definition of analytical Spontaneous Release Functions (SRF) whose parameters may be randomly sampled from appropriate distributions in order to match either the 3D cell models or experimental data. Pro-arrhythmogenic pacing protocols were applied to initiate re-entry and promote calcium overload, leading to the emergence of SCRE. The SRF accurately reproduced the dynamics of SCRE and its dependence on environment variables under multiple different conditions. Sustained re-entrant excitation promoted calcium overload, and led to the emergence of focal excitations after termination. A purely functional mechanism of re-entry and focal activity localisation was demonstrated, related to the unexcited spiral wave core. In conclusion, a novel approach has been developed to dynamically model SCRE at the tissue scale, which facilitates novel, detailed multi-scale mechanistic analysis. It was revealed that complex re-entrant excitation patterns and SCRE may be bi-directionally coupled, promoting novel mechanisms of arrhythmia perpetuation.Author summary: A loss of the regular rhythm of the beating heart, called arrhythmia, can inhibit its pumping function and even lead to sudden death. Understanding the processes by which normal rhythm is interrupted presents a major yet critical research problem. One challenge is the inherent multi-scale dependence of the electrical activity of the heart: behaviour at the microscopic scales (single proteins) can propagate to the macroscopic (whole-heart). Simultaneously studying phenomena at both of these scales is difficult, if not impossible, to perform experimentally. Developing mathematical models of the heart in order to perform variable and controlled simulations of its electrical activity provides the possibility to undertake such multi-scale analysis. However, new approaches are required to simulate the potential role of “spontaneous calcium release”, which occurs at the sub-cellular scale, in triggering arrhythmia events at the whole-heart scale. This study develops an approach to perform such simulations and applies it to study the long-term interactions of these sub-cellular triggers with the complex electrical activity of the most dangerous arrhythmias–tachycardia and fibrillation. The new mechanistic insight has implications for both diagnosis and treatment of the associated disorders.