Pde-Constrained Optimization For Nuclear Mechanics

We propose an image based PDE-constrained optimisation framework to compute the dynamical quantities of a cell nucleus undergoing deformation. It allows retrieving the displacement, strain and stress at each pixel of the nuclear domain, as well as the traction force on the boundary. It is based on a mechanical model of the nuclear components and a pair of images documenting the deformation of the cell nucleus. To test our approach, we provide a warping method that produces a second image from an initial one along with the expected mechanical quantities. Both quantitative and qualitative analysis conclude for a significant and consistent improvement of our method over optical flow techniques.