1.     In order to understand the brain function and monitor its activity, an accurate mathematical model describing the relevant variables in the brain is important. We are interested in modeling the coupling between the neural activity, the cerebral blood flow and the metabolite.  We develop  new models for the neurovascular coupling and we propose some algorithms to solve the inverse problem, which consists in estimating the model’s parameters and the neural activity from fMRI measurements. Our current objectives include:

a.     consider the energetic aspects (Consumption of Glucose)in the model ;

b.    extract physiological information on some regions of the brain and study the glucose consumption in different situations thanks to the developed model ;

c.     consider a spatiotemporal version of the proposed model ;

d.    study the different regions in the brain and extend the developed model to a network connecting different regions of the brain.