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Section: Research Program
Computational Physiology
The objective of Computational Physiology (CP) is to provide models of the major functions of the human body and numerical methods to simulate them. The main applications are in medicine where CP can be used for instance to better understand the basic processes leading to the appearance of a pathology, to model its probable evolution and to plan, simulate, and monitor its therapy.
Quite advanced models have already been proposed to study at the molecular, cellular and organic level a number of physiological systems (see for instance [65] , [62] , [53] , [66] , [59] ). While these models and new ones need to be developed, refined or validated, a grand challenge that we want to address in this project is the automatic adaptation of the model to a given patient by comparing the model with the available biomedical images and signals and possibly also some additional information (e.g. genetic). Building such patient-specific models is an ambitious goal which requires the choice or construction of models with a complexity adapted to the resolution of the accessible measurements and the development of new data assimilation methods coping with massive numbers of measurements and unknowns.
There is a hierarchy of modeling levels for CP models of the human body [54] :
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the first level is mainly geometrical, and addresses the construction of a digital description of the anatomy [49] , essentially acquired from medical imagery;
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the second level is physical, involving mainly the biomechanical modeling of various tissues, organs, vessels, muscles or bone structures [60] ;
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the third level is physiological, involving a modeling of the functions of the major organic systems [61] (e.g. cardiovascular, respiratory, digestive, central or peripheral nervous, muscular, reproductive, hormonal, etc.) or some pathological metabolism (e.g. evolution of cancerous or inflammatory lesions, formation of vessel stenoses, etc.);
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a fourth level would be cognitive, modeling the higher functions of the human brain [40] .
These different levels of modeling are closely related to each other, and several physiological systems may interact with each other (e.g. the cardiopulmonary interaction [63] ). The choice of the resolution at which each level is described is important, and may vary from microscopic to macroscopic, ideally through multiscale descriptions.
Building this complete hierarchy of models is necessary to evolve from a Visible Human project (essentially first level of modeling) to a much more ambitious Physiological Human project (see [61] , [62] ). We will not address all the issues raised by this ambitious project, but instead focus on topics detailed below. Among them, our objective is to identify some common methods for the resolution of the large inverse problems raised by the coupling of physiological models to medical images for the construction of patient-specific models (e.g. specific variational or sequential methods (EKF), dedicated particle filters, etc.). We also plan to develop specific expertise on the extraction of geometrical meshes from medical images for their further use in simulation procedures. Finally, computational models can be used for specific image analysis problems studied in section 3.2 (e.g. segmentation, registration, tracking, etc.). Application domains include