Identification of surface tension in mean curvature flow

We study a numerical method for identifying the surface tension in a level set-based mean curvature flow equation. A novel variational problem is formulated to determine the surface tension for which the model best matches a given set of data. An adjoint-based method allows us to compute the gradient of the cost functional of the variational problem with respect to the surface tension. We solve the variational problem using numerical optimization techniques based on this gradient. We demonstrate the effectiveness of the method using a biological example in which the surface tensions of bilayer membranes are determined based on images of vesicle-vesicle adhesion.