Section: Application Domains

Applications of the parameter estimation problem to multidisciplinary domains $-$ collaboration with an INSERM team (Rouen University)

For linear systems, the closed-form expressions of the parameters obtained by means of the algebraic parameter estimation problem will continue to provide robust estimates in our multidisciplinary collaborations, in marine biology and human-machine interactions, as it is already the case of existing Non-A results (in collaboration with Loki , Inria Lille - Nord Europe).

For nonlinear systems, a collaboration with biologists and modelers has been developed for a few years already [29]. Our partners are a team from the Applied Mathematical Department of Le Havre University (modelers) and an INSERM team at Rouen University (neurobiologists). The targeted biological problem is the cortical spreading depression, a brain disease likely to occur after cerebrovascular accidents [60]. We seek $-$ ultimately $-$ a mathematical integro-differential model permitting to predict the triggering of this disease for patients arising in the emergency services of hospitals. The key phenomenon to reproduce is a slow depolarization wave of neurons. Our approach is original because it focuses on the role calcium fluxes in neurons and astrocytes.