Keywords: biodomain, mechanical-electrical coupling, virtual experiment, arrhythmia, defibrillation, histological reconstruction, fiber tracking

Information: Undoubtedly, a virtual heart simulator, an "in-silico" heart, which is efficient enough to handle parameter studies using a bidomain formulation together with computational grids which account for both accurate gross anatomy and micro-structural details, has the potential to play a pivotal role in unravelling open questions in cardiac electrophysiology by allowing mechanistic inquiries into the nature of mechanisms underlying the formation of arrhythmias and their termination either by electrical shocks, by pharmacological interventions or by surgical modification of conduction pathways.

The development of such a simulation tool poses several mathematical and engineering challenges: 1) Numerical efficiency is absolutely key to successfully deal with the computational workload imposed by systems arising from fine-grained discretizations (1-50 millions of unknowns). These goals will be pursued by employing multilevel-based fast linear solvers and BEM/FEM coupling approaches and space-time adaptive techniques (FEMBEM). 2) The generation of microscopically accurate cardiac tissue models has to be addressed by applying novel strategies for segmentation (FREELEVEL) and multi-modal registration (INVERSE) to allow the fusion of image stacks obtained with different modalities (serial histology and MRI). 3) The quest of finding an ideal defibrillation protocol which significantly lowers defibrillation energy requirements will be addressed by applying, for the first time, optimal control theory to this problem. 4) Experimentally and clinically applied mapping modalities could be significantly improved by a better understanding of the relationship between physical source quantity and electrically or optically recorded signal. Multilevel inverse methods will be employed to investigate this relationship (MGINV). 5) In the long run,to link the electrical activity of the heart to clinical quantities like ejection fraction and blood pressure, the electrical "virtual heart" will be coupled to a model of mechanical contraction and a fluid mechanical model.