Applied mathematics now plays an important role in the biomedical field and especially the neurosciences. The research activity at PhysNum (“Numerical Physics”) has two main themes: pharmacometrics and brain imaging. In particular Jean-Marc Lina and Habib Benali study the multimodal imaging of the spinal cord, Lina and Christophe Grova the multiresolution and multimodal imaging in magneto-electrophysiology, and Benali and Maxime Descoteaux models of the anatomical and functional connectivity of the brain. Grova also studies neurovascular models in epilepsy and Lina studies sparse representations, inverse problems, brain wave synchronization, and scale-invariant processes in electrophysiology. Fahima Nekka and her team conduct research in pharmacometrics, a discipline whose goal is to interpret and describe pharmacological phenomena in a quantitative manner, so as to support rational therapeutic decisions and improvement of patient health. They have developed a whole framework of probabilistic pharmacometrics in which different sources of variability and the nonlinearity of the system are accounted for. The team is working on compliance metrics and ranking and on direct and inverse problems related to patient drug behaviour and the therapeutic effect of drugs. It is conceiving tools that shed new light on drug development and evaluation, revisiting classical concepts in pharmacology and developing models for drug interactions.

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