Can one see a force? Inferring mechanics from images of cells and tissues
Mechanical forces shape cells and tissues: they drive morphogenesis, act as cues that cells sense and respond to, and determine whether tissues hold together or fail. Measuring these forces where they act, however, remains difficult. The probes that measure them directly, such as indenters, laser cuts, molecular tension sensors and engineered substrates, perturb the system, give local or relative readouts, or require cells to sit on an artificial substrate, and most cannot reach a cell inside a tissue or a living embryo. Images, by contrast, are now abundant: three-dimensional, time-resolved, and down to nanometre resolution. Inferring forces from images is often the only way to map them where they act, inside tissues and embryos.
But images record shapes and deformations, not forces, and turning one into the other means inverting a physical model. In this talk I will discuss when that inversion is possible and what it takes. In a few favourable cases, such as pressurised epithelia, geometry alone determines the forces. In others, such as malaria-infected red blood cells adhering to the endothelium, knowing beforehand how the material responds and being able to register its deformation allow us to recover the forces. In general neither holds: the unknowns, often the material laws themselves, can only be reached by solving the governing equations many times and comparing the result with the data. I will present EchoEx, a differentiable simulation framework built on JAX that makes such inverse problems routine, and illustrate it by inferring the mechanics of the actin cable during zebrafish gastrulation from live imaging.