Research Collaboration Visit to the Auckland Bioengineering Institute, New Zealand.

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Despite over a century's study, the mechanisms of cardiac arrhythmias are poorly understood. Even modern experimental methods do not provide sufficient temporal and spacial resolution to trace down fine details of fibrillation development in samples of cardiac tissue, not to mention the heart in vivo. Advances in human genetics provide information on the impact of certain genes on cellular activity, but do not explain the resultant mechanisms by which fibrillation arises. Thus, for some genetic cardiac diseases, the first presenting symptom is death.Combination of mathematical modelling and the latest realistic computer simulations of electrical activity in the heart have much advanced our understanding of heart fibrillation and sudden cardiac death, and the impact of in-silico modelling, or indeed in-silico "testing", is expected to increase significantly as we approach the ultimate goal of the whole-heart modelling. Biophysically and anatomically realistic simulation of cardiac action potential propagation through the heart is computationally expensive due to the huge number of equations per cell and the vast spacial and temporal scales required. Therefore any insights that can be obtained through generic mathematical model analysis is very valuable, as it tends to reveal generic mechanisms, unlike direct computer simulations, which provide answers valid only for a specific choice of parameters and initial conditions and depend on the computer model accuracy. Note that despite of the decades of steady progress, computer models still have qualitative rather than quantitative predictive power on the macroscopic scale, e.g. where whole heart or a whole chamber of the heart are concerned. Our recent progress in asymptotic analysis of dissipative vortices dynamics has revealed a new phenomenon of the vortices interaction with sharp variations of thickness in excitable layer. Such interaction of cardiac re-entry with sharp anatomical features, as e.g. pectinate muscles and terminal crest in atria, can cause considerable displacement of established localisation of re-entry compared to where it was first localised. The asymptotic theory prediction of the vortices drift caused by interaction with sharp thickness variations in a layer has been confirmed in experiments with Belousov-Zhabotinski reaction, and verified in computer simulations with a variety of cell excitation models, from extremely simplified "conceptual" models to realistic ionic kinetics models, and for tissue geometries from artificial idealised geometries to a realistic anatomy of human atria. A better underestanding of this phenomenon may have significant implications in clinics, say for chosing an individual ablation strategy for treatment of atrial fibrillation.Validation of the identified new phenomenon has so far been done only on a single model of human atrium, and understanding of to what extent the effect is universal requires extensive testing on a wide variety of cardiac MRI anatomy models, before experimental testing and clinical implications can be considered. The aim of the proposed project is to visit the Auckland Bioengineering Institute (ABI), New Zealand, which is an international leader in the heart and cardiovascular system research that combines instrumentation development, experimental measurements and modelling. ABI cardiovascular magnetic resonance (CMR) imaging group obtains most detail models of heart geometry and tissue microstructure. This visit will forge a closer collaboration than it is feasible from a distance, and provide a possibility of exhaustive testing of the new phenomenon in the most up-to-date anatomically and biophysically realistic models. An extra benefit will be provided by the applicant's participation in Cardiac Physiome Workshop (23 August 2016, Seoul, Korea), which will be a unique opportunity to discuss our recent findings and future directions of research with the world leaders in the field.