Programmation GPU du solveur LS-DYNA pour la simulation électrique du cœur

La modélisation et la simulation du cœur constituent un outil prometteur afin de mieux diagnostiquer, planifier et vérifier les thérapies, au point que le cœur soit devenu l'organe virtuel le plus sophistiqué jamais développé. L'utilisation de méthodes numériques précises et rapides est cruciale pour simuler avec réalisme les phénomènes bioélectriques dans le cœur. Le solveur monodomaine [1,2], qui permet de résoudre les équations de propagation de l'excitation électrique dans le tissu cardiaque, est largement utilisé pour ces simulations. Cependant, ces calculs sont souvent coûteux en temps et en ressources, en particulier lorsqu'ils sont effectués sur de grands domaines ou des maillages fins.

L'objectif de ce stage est d'implémenter une version GPU du solveur monodomaine dans le logiciel LS-DYNA [3], afin d'accélérer significativement les temps de calcul [4]. Cette accélération est essentielle pour rendre possible la quantification d'incertitudes des paramètres des modèles ainsi que des analyses de sensibilités aux paramètres, dans des temps raisonnables. La programmation sera réalisée en Fortran, et les performances de la nouvelle implémentation seront évaluées à l'aide de cas tests représentatifs des situations rencontrées en modélisation cardiaque.

Qualifications :

• Niveau Master en ingénierie, mathématiques appliqués, ingénierie biomédicale ou équivalent
• Bonnes bases en programmation openGL et fortran, en compilation, et environnement linux
• Capacités rédactionnelles et en communication en français et en anglais
• Un attrait pour la recherche biomédicale est très souhaité

GPU Programming of the LS-DYNA Solver for Cardiac Electrical Simulation

Cardiac modeling and simulation have become promising tools for improving diagnosis, treatment planning, and therapy validation, making the heart the most sophisticated virtual organ ever developed. The use of accurate and fast numerical methods is crucial to realistically simulate bioelectrical phenomena in the heart. The monodomain solver [1,2], which solves the equations governing the propagation of electrical excitation in cardiac tissue, is widely used for such simulations. However, these computations are often time- and resource-intensive, especially when applied to large domains or fine meshes.

The goal of this internship is to implement a GPU-accelerated version of the monodomain solver within the LS-DYNA software [3], in order to significantly reduce computation times [4]. his acceleration is essential to enable uncertainty quantification of model parameters as well as sensitivity analyses within reasonable timeframes. Programming will be performed in Fortran, and the performance of the new implementation will be evaluated using test cases representative of situations encountered in cardiac modeling.

Qualifications:

• Master's level in Engineering, Applied Mathematics, Biomedical Engineering, or equivalent
• Solid background in OpenGL and Fortran programming, compiling, and Linux environments
• Strong writing and communication skills in both French and English
• A strong interest in biomedical research is highly desirable

Bibliography:

[1] Boulakia, M., Cazeau, S., Fernández, M. A., Gerbeau, J. F., & Zemzemi, N. (2010). Mathematical modeling of electrocardiograms: a numerical study. Annals of biomedical engineering, 38, 1071-1097.

[2] Wikipedia contributors. (2024, September 16). Monodomain model. Wikipedia. https://en.wikipedia.org/wiki/Monodomain_model

[3] https://lsdyna.ansys.com/

[4] Mena, A., Ferrero, J. M., & Matas, J. F. R. (2015). GPU accelerated solver for nonlinear reaction-diffusion systems. Application to the electrophysiology problem. Computer Physics Communications, 196, 280-289.

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