Formulation of the inverse problem of parameter localization for a dipolar volumetric source of neuronal current (Q2721292)

An inverse problem concerning the determination of a volumetric source for a neuronal current in a brain model is considered. For this aim, the authors provide first a mathematical model for the potential induced in a conducting medium with constant conductivity in terms of some partial differential equations, namely of a Poisson equation with Neumann boundary condition. The appearance of Dirac's delta function on the right-hand side of the equation motivates the consideration of weak solutions involving distributions and Sobolev spaces. The associated Green function is the main auxiliary tool here. Particular attention is devoted to the case of a dipole source.NEWLINENEWLINEFor the entire collection see [Zbl 0948.00027].