Inverse problems for image-based characterisation of cellular mechanics: how do cells move?
Aleix Boquet

Meeting • 23 February 2021

Abstract
While intracellular mechanics are essential to biological function, standard physical probes are too invasive to provide physiologically relevant insight. To measure the internal biophysical quantities necessary to the study of cell migration with microscopy imaging alone, we propose combining optical flow and continuum models into a single Bayesian PDE-constrained framework. This formulation transforms pixel intensity directly into physical measurements in the context of probability distributions. In particular, the posterior mean is an inverse problem that tracks image movement while satisfying a physical model, thus yielding estimates of the variables therein; whereas the posterior covariance derives measurement error out of image noise. To make this approach tractable, we exploit the dual space via the adjoint method, and rely on the compactness of the Hessian to work with low-rank approximations while assuring scale-independent convergence. We first test our method by reformulating image-based techniques in other domains such as traction force microscopy and elastography, increasing the accuracy of their measurements and providing error bounds, as well as generalising their boundary conditions. We then use our framework to study the cytoplasm in cell videos via fluid dynamics, obtaining unprecedented estimates of intracellular pressure gradients and forces that reconcile and extend multiple reports on cell migration.