Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions

We develop a computational approach to locate the source of steady-state gradient diffusing particles from fluxes through narrow windows distributed either on boundary three-dimensional half-space or sphere. This is based solving mixed stationary diffusion equation with Neumann–Green’s function. The method matched asymptotic expansions enables computation probability fluxes. To explore range validity this expansion, we fast analytical-Brownian numerical scheme. scheme accelerates simulation time by avoiding explicit Brownian trajectories in infinite domain. results obtained our derived analytical formulae and agree large parameters. Using representation particle fluxes, show how reconstruct location point source. Furthermore, investigate uncertainty reconstruction due additive fluctuations present also study influence various window configurations: clustered versus uniform distributions recovering position. Finally, discuss possible applications for cell navigation biology.