ϕ-FEM : development of a Finite Element Method for the design of real-time digital twins in surgery

Michel Duprez

320 k €

ϕ-FEM is a recently proposed finite element method for the efficient numerical solution of partial differential equations posed in domains of complex shapes, using simple regular meshes. The main goal of this project is to further develop ϕ-FEM turning it into a tool for efficient, patient-specific and real-time simulations of human organs. To reach this objective, we shall adapt ϕ-FEM to the equations appropriate to biomechanics, provide an efficient implementation for it allowing for the use of actual organ geometries, and finally combine it with convolution neural networks to make it real time after training. The ultimate, long-term, goal is thus to contribute to the construction of digital twins of organs able to guide the surgical act in real time using information acquired before the operation and to reduce the costs of a medical doctors’ training by working on visual organs. The innovation of ϕ-FEM lies in its ability to combine the ease of implementation of classical immersed boundary methods with the accuracy of more recent CutFEM/XFEM approaches. It incorporates, by its very construction, the popular description of geometry by Level Set functions, which can represent the real geometry with whatever accuracy desired which makes this approach numerically less expensive than classical finite element methods. The ϕ-FEM paradigm will also be used to develop efficient registration algorithms. Our results will be integrated into the open-source SOFA platform developed in the MIMESIS team to facilitate dissemination.

New Trends in Control and Stabilization: Constraints and Non-local terms

Sylvain Ervedoza

300 k €

Le but de ce projet est de contribuer au développement de nouvelles directions en théorie du contrôle pour des équations aux dérivées partielles, motivées par des modèles issus de l'écologie et de la biologie. On s'intéressera notamment à deux aspects. Le premier est lié aux contraintes tolérées sur les contrôles et/ou les trajectoires contrôlées, par exemple des contraintes de positivité, qui apparaissent naturellement lorsque l'état modélise une température. Le deuxième aspect concerne les questions de contrôlabilité et de stabilisation de problèmes faisant intervenir des opérateurs non-locaux, que ce soit des opérateurs intégraux en espace, pour prendre en compte des phénomènes dépendant de la masse totale de la population par exemple, des termes de retard ou de mémoire comme pour les fluides visco-élastiques, souvent utilisés pour modéliser le sang, ou plus généralement pour des modèles décrits par des systèmes couplant des effets hyperboliques et paraboliques.

Understanding Keloid Disorders: A multi-scale in vitro/in vivo/in silico approach towards digital twins of skin organoids on the chip

Raluca Efimi et Stéphane Bordas

575 k €

La modélisation mathématique biologiques à différentes échelles: cellulaire, assemblage cellulaire, et tissulaire. Le projet S-keloid vise à modéliser le rôle de facteurs mécaniques et inflammatoires environnant les cellules, et les interfaces entre tissus sains et pathologiques associés au développement anormal de la fibrose chéloïdienne. Des modèles expérimentaux cellulaires 3D seront mis en culture sous contraintes (mécanique et inflammatoire) simulant lʼenvironnement du tissu chéloïdien in vivo, et une modélisation mathématique de ces systèmes sera proposée. A partir dʼessais à lʼéchelle tissulaire, et grâce à une approche multi-échelle, les champs de contraintes mécaniques seront intégrés dans le modèle mathématiques 3D. L'identification, l'optimisation puis lʼapplication de paramètres à plusieurs échelles garantira le réalisme des modèles et des prévisions quantitatives et qualitatives de lʼévolution de la maladie chéloïde.

NEw Methods for BIological Control of the Arboviruses

Pierre-Alexandre Bliman

15 k €

The present project is concerned with new strategies to control the spread of established diseases (such as e.g. dengue, chikungunya and Zika) and potentially emerging or reemerging diseases (e.g. Mayaro, Oropouche and Yellow fever) transmitted by mosquitoes Aedes aegypti and Aedes albopictus. Due especially to the widespread resistance to the insecticides traditionally used to control the vectors, the use of sterile insect (SIT – Sterile Insect Technique), of transgenic mosquitoes (RIDL – Release of Insect carrying Dominant Lethal gene) and/or of mosquitoes infected with the bacterium Wolbachia (which drastically reduces their vector competence), are considered as viable control alternatives. These biological control techniques envisage either the elimination of the vector in a locality (SIT or RIDL), or its local substitution by a population refractory to the arboviruses transmitted by these species (Wolbachia). How to achieve the releases on a large scale in order to maximize their effect is still a source of some central questions that we aim to study here. We will focus more specifically on the issues related to spatial spreading of the treatment, on observer techniques for estimating the number of mosquitoes during the releases, and on optimal and non-optimal control approaches. An important modeling effort will also be conducted on some key issues: we will assess the effects of the chemical and mechanical control methods on the success of the above techniques; the consequences of inter and intra-species competition in larval phase (an important issue so far overlooked); the questions raised by the use of self-propagating genetic mechanisms and the definition of associated efficacy measures; and develop genome scale model of Wolbachia in order to identify in the parasite-host relationship, crucial biological factors that could dynamically affect the dissemination.