Super-resolution fluorescence microscopy and a mean-field Fokker-Planck equation for the reconstruction of a cell membrane potential

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This talk is part of the public seminar series organised by the Euler Institute (EUL). 

Abstract:
Based on the assumption of stochastic motion of molecules on a cell membrane and the modelling of the ensemble of trajectories by a nonlinear mean-field Fokker-Planck (FP) equation, a new method for the reconstruction of cell membrane
potentials using fluorescence super-resolution microscope images is developed. Central to this method is the formulation of an inverse problem governed by the FP equation and a best-fit functional with a Tikhonov regularization term.
The solution of this problem on a sequence of time windows allows to determine the potential together with an estimate of uncertainty of its reconstruction. Results of numerical experiments successfully validate the proposed reconstruction procedure and demonstrate its applicability in a super-resolution microscope framework.

Biography:
Alfio Borzì is Full Professor (W3) and Chair of Mathematik  ‘Scientific Computing’ at the Institute for Mathematics, University of Würzburg.Trained in Mathematics and Physics, Prof. Borzì's  main field of expertise consists in developing and combining analytical and numerical methods in view of modelling and solving fundamental application problems that are often related to simulation, optimal control and optimisation. His Main research  topics include the Numerical solution of PDE optimization problems, the development and analysis of multigrid methods, analysis of discretization schemes for partial differential equations. Simulation and optimization with uncertainty, simulation and control of quantum systems, Modeling and numerical solution of gas dynamics problems, modeling and simulation of bio-chemical processes,  imaging analysis and inverse and neural networks analysis and application.

Host: Prof. Rolf Krause