JCJC - Jeunes chercheuses & jeunes chercheurs

MOdèles et Méthodes Mathématiques en Electrocardiologie – MOMME

Submission summary

Scientific background and objectives The project is driven by a kernel team of 3 researchers in Nantes (in mathematics), with an associated researcher in Sophia-Antipolis (in imaging). It aims at building a mathematical model for the electro-physiological behavior of the human heart in real situations, and mathematical methods for its numerical simulation. Results might be confronted to clinical data, providing a feedback on modeling and computing. Considering our work in the fields of applied mathematics or imaging for cardiac modeling during a post-doctoral, PHD, ATER or permanent position, we decided to gather our knowledges in order to better understand and model the electrical behavior of the heart inside the torso, for practical use . Cardiologists detect many pathologies from the very sparse data (mainly electrocardiogram, ECG) and simple representations (electrical dipoles) they have of the electrical behavior of the heart. Yet very complex mathematical models of the muscle tissue are now known and lead to expensive and complex computations. Additionally, at a higher level of complexity, the heart is a network of different kind of tissues (atria, ventricles, sinus node, atrioventricular node, special conduction network); and this part is not well understood, although it is essential for the activation sequence. At last, it is not clear whether realistic tissue models or realistic models of the organ (eg as a network) are the most important in ECG simulations. Several teams address the problem of simulating realistic and complex models of excitable tissues. But fast and accurate computing remains a difficult scientific computing challenge. This project intent to develop new methods to solve this problem, but also a hierarchy of simpler models and faster methods to compute the action potential (AP) propagation (monodomain, level-sets and Eikonal eqs). The second main issue of this project is the development of a model integrating the AP propagation ones to account for the whole organ in ECG simulations. Therefore, a collaborative work of mathematical modeling, scientific computing and medical imaging is necessary. The project has various issues of different nature, mainly concerning 1) nonlocal systems of reaction-diffusion equations; front propagation modeling through Hamilton-Jacobi equations; 2) numerical analysis for finite volumes schemes; fast marching and similar techniques; and at last fast multipole methods; 3) parallel computing, preconditioning and iterative solvers; 4) segmentation of moving images, registration of measure devices in images. Description, methodology The project is planned on 4 years with the help of post-doctoral researchers for the last 3 years. Starting from an original finite volumes method (PhD thesis of C. Pierre), the following problems will be considered: a) develop time-stepping methods, preconditioning and parallel computing in the current code, b) understand the limits of the available modeling levels (bidomain, monodomain, Eikonal), finding links between them, in order to adjust the numerical tools to the desired level of complexity of applications, c) use fast methods for simpler models, specifically high-order methods on 3D unstructured grids for Eikonal eqs, d) use a generic idealized model of the heart to understand the activation sequence and ECG patterns; be able to adjust it to images and measures, and therefore interact with applied scientists (clinicians, bioengineers). The discussion on modeling aspects, the choice of numerical methods to apply, the specification of useful test-cases is a common aspect to be discussed by the whole team, based on the personal work and experience of the members in analysis, approximation, scientific computing, imaging. Post-doctoral researchers will have very specific 1-year tasks: (1) parallel preconditioning and time-stepping methods, (2) integral equations, fast multipole methods and computing of the ECG and (3) front-tracking using fast-sweeping methods. Expected results Based on an analytical model of the anatomy that may be fitted to images and on an existing finite volumes code for a model of the ventricles, we plan to develop a hierarchical framework of models for the whole heart and torso and implement their numerical solutions into the current code. This ought to provide an experimental software tool usable both to understand activation sequences and ECG patterns and for practical purpose, that our collaborators from the Cardiac MR Research Group, Guy's Hospital, King's College, London are interested in. Mathematical results are expected concerning every of the issues 1) to 4) above; in the fields of analysis, numerical analysis and scientific computing.

Project coordination

Yves COUDIERE (Université)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

Help of the ANR 125,000 euros
Beginning and duration of the scientific project: - 48 Months

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