Reduced-order modeling for cardiac electrophysiology. Application to parameter identification

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium infarctions and long-time simulations. We show in particular that a restitution curve can efficiently be approximated by this approach. The reduced-order model is then used in an inverse problem solved by an evolutionary algorithm. Some attempts are presented to identify ionic parameters and infarction locations from synthetic ECGs.Comment: No. RR-7811 (2011

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

The Role of the Frank–Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis

We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca2+ sensitivity of tension (Ca50), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca2+ to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca50 and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca50 was caused by an inversion in the regional distribution of strain

Modeling Human Atrial Patho-Electrophysiology from Ion Channels to ECG - Substrates, Pharmacology, Vulnerability, and P-Waves

Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This thesis presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF

Modeling Human Atrial Patho-Electrophysiology from Ion Channels to ECG - Substrates, Pharmacology, Vulnerability, and P-Waves

Half of the patients suffering from atrial fibrillation (AF) cannot be treated adequately, today. This book presents multi-scale computational methods to advance our understanding of patho-mechanisms, to improve the diagnosis of patients harboring an arrhythmogenic substrate, and to tailor therapy. The modeling pipeline ranges from ion channels on the subcellular level up to the ECG on the body surface. The tailored therapeutic approaches carry the potential to reduce the burden of AF