The National Institute for Computer Science and Control (INRIA) provides a postdoctoral fellowship on Mathematical modelling of neuronal EEG activity under brain stimulation. We are interested in developing neurostimulation techniques in order to improve the cure of patients suffering from mental disorders. To this end, our aim is to develop dynamic neural models and merging these data to experimentally observed data, such as EEG or BOLD responses. This merge may utilize diverse optimization techniques, such as data assimilation. The latter permits to estimate model parameters adaptively in non-stationary signals, i.e. online in time. A prominent example for a data assimilation technique is Kalman filtering. More detailed, we are looking for collaborators, who are interested in neural population models describing macroscopic brain activity in pathological brain states under neurostimulation. The mathematical analysis of such models typically yields important insights into the origin of the brain activity. Moreover, the merge with experimental data demands a certain understanding of data analysis techniques to prepare the experimental data and identify correctly good biomarkers. It would be advantageous if the candidate has some fundamental expertise in this respect. Finally, the perfect future collaborator has already some expertise in parameter estimation techniques, especially in data assimilation.

Over the past decade we have demonstrated that the fusion of subject-specific structural information of the human brain with mathematical dynamic models allows building biologically realistic brain network models, which have a predictive value, beyond the explanatory power of each approach independently. The network nodes hold neural population models, which are derived using mean field techniques from statistical physics expressing ensemble activity via collective variables. Our hybrid approach fuses data-driven with forward-modeling-based techniques and has been successfully applied to explain healthy brain function and clinical translation including aging, stroke and epilepsy. Here we illustrate the workflow along the example of epilepsy: we reconstruct personalized connectivity matrices of human epileptic patients using Diffusion Tensor weighted Imaging (DTI). Subsets of brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other healthy brain regions and propagate activity through large brain networks. The identification of the EZ is crucial for the success of neurosurgery and presents one of the historically difficult questions in clinical neuroscience. The application of latest techniques in Bayesian inference and model inversion, in particular Hamiltonian Monte Carlo, allows the estimation of the EZ, including estimates of confidence and diagnostics of performance of the inference. The example of epilepsy nicely underwrites the predictive value of personalized large-scale brain network models. The workflow of end-to-end modeling is an integral part of the European neuroinformatics platform EBRAINS and enables neuroscientists worldwide to build and estimate personalized virtual brains.