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Mathematical modeling & data assimilation for biomedical problems
My research mainly focuses on mathematical modeling and data assimilation for biomedical problems. The first step in my approach is to define biological or medical problems in consultation with experts in those disciplines. When these problems can be solved or at least understood through my areas of expertise – mathematical modeling with differential equations (PDE or ODE), theoretical and numerical study of these models, and data assimilation – collaboration ensues. Aiming for the most complete approach possible, I am developing innovative mathematical tools based mainly on the theoretical or numerical study of PDEs, asymptotic analysis, and data assimilation (including observers) that can address both theoretical and practical aspects. In particular, a first part of my work deals with theoretical aspects of modeling or data assimilation. Another important part of my work is very application oriented, especially when it comes to working with real data. The following figure summarizes the general strategy I used in my research.
Main areas of interest
I have three main areas of interest: Cardiac Electrophysiology, Tumor Growth, and Electroporation Modeling with many interactions between these areas as shown in the figure below.
Illustrative examples
Click on the two links below to access to two illustrative examples of my research:
Publications
An updated list of my publications can be found on my Google Scholar page.
