Integrated Heart - Coupling multiscale and multiphysics models for the simulation of the cardiac function

Mathematical modelling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a complex multiscale system involving interacting phenomena at the molecular, cellular, tissue, and organ levels. This article addresses the numerical modelling of many aspects of heart function, including the interaction of the cardiac electrophysiology system with contractile muscle tissue, the sub-cellular activation-contraction mechanisms, as well as the hemodynamics inside the heart chambers. Resolution of each of these sub-systems requires separate mathematical analysis and specially developed numerical algorithms, which we review in detail. By using specific sub-systems as examples, we also look at systemic stability, and explain for example how physiological concepts such as microscopic force generation in cardiac muscle cells, translate to coupled systems of differential equations, and how their stability properties influence the choice of numerical coupling algorithms. Several numerical examples illustrate three fundamental challenges of developing multiphysics and multiscale numerical models for simulating heart function, namely: (i) the correct upscaling from single-cell models to the entire cardiac muscle, (ii) the proper coupling of electrophysiology and tissue mechanics to simulate electromechanical feedback, and (iii) the stable simulation of ventricular hemodynamics during rapid valve opening and closure

A posteriori error estimator for model adaptivity in electrocardiology

We introduce an a posteriori modeling error estimator for the effective computation of electric potential propagation in the heart. Starting from the Bidomain problem and an extended formulation of the simplified Monodomain system, we build a hybrid model, called Hybridomain, which is dynamically adapted to be either Bi- or Monodomain ones in different regions of the computational domain according to the error estimator. We show that accurate results can be obtained with the adaptive Hybridomain model with a reduced computational cost compared to the full Bidornain model. We discuss the effectivity of the estimator and the reliability of the results on simulations performed on real human left ventricle geometries retrieved from healthy subjects. (C) 2010 Elsevier B.V. All rights reserved

Studies on the dynamics of chaotic multi-wavelet reentrant propagation using a hybrid cellular automaton model of excitable tissue

There is a compelling body of evidence implicating continuous propagation (reentry) sustained by multiple meandering wavelets in the pathology of advanced human atrial fibrillation (AF). This forms the basis for many current therapies such as the Cox MAZE procedure and its derivatives, which aim to create non-conducting lesions in order to "transect" these circuits before they form. Nevertheless, our ability to successfully treat persistent and permanent AF using catheter ablation remains inadequate due to current limitations of clinical mapping technology as well as an incomplete understanding of how to place lesions in order to maximize circuit transection and, more importantly, minimize AF burden. Here, we used a hybrid cellular automaton model to study the dynamics of chaotic, multi-wavelet reentry (MWR) in excitable tissue. First, we used reentry as an exemplar to investigate a hysteretic disease mechanism in a multistable nonlinear system. We found that certain interactions with the environment can cause persistent changes to system behavior without altering its structure or properties, thus leading to a disconnect between clinical symptoms and the underlying state of disease. Second, we developed a novel analytical method to characterize the spatiotemporal dynamics of MWR. We identified a heterogeneous spatial distribution of reentrant pathways that correlated with the spatial distribution of cell activation frequencies. Third, we investigated the impact of topological and geometrical substrate alterations on the dynamics of MWR. We demonstrated a multi-phasic relationship between obstacle size and the fate of individual episodes. Notably, for a narrow range of sizes, obstacles appeared to play an active role in rapidly converting MWR to stable structural reentry. Our studies indicate that reentrant-pathway distributions are non-uniform in heterogeneous media (such as the atrial myocardium) and suggest a clinically measurable correlate for identifying regions of high circuit density, supporting the feasibility of patient-specific targeted ablation. Moreover, we have elucidated the key mechanisms of interaction between focal obstacles and MWR, which has implications for the use of spot ablation to treat AF as some recent studies have suggested