Continuity equations and super-resolution microscopy for the reconstruction of a cell membrane potential

Continuity equations are fundamental building blocks in the modelling of natural systems at the mesoscopic and macroscopic level. Therefore they are also essential in engineering control mechanisms and in the formulation of inverse problems. In this framework, a central role is played by the Liouville, the Fokker-Planck-Kolmogorov (FPK) and the Boltzmann equations.
In this talk, the focus is on the stochastic motion of molecules on a cell membrane and its modelling by a nonlinear mean-field FPK equation with the purpose to illustrate a new method for the reconstruction of cell membrane potentials based on super-resolution microscope images.
This inverse problem is formulated as an optimization problem governed by the mean-field FPK equation, and the functional to be minimized includes a least-squares error term of the computed and observed particles' densities and a Tikhonov regularization term. This problem is solved on a sequence of time windows to determine the potential together with an estimate of uncertainty of its reconstruction. Results of numerical experiments are presented that successfully validate the proposed reconstruction procedure and demonstrate its applicability in a super-resolution microscopy framework.
This is joint work with Mario Annunziato (U Salerno)
Заседание семинара состоится в Zoom. За ссылкой можно обратиться к В.Ю.Протасову: v-protassov@yandex.ru