Closed-form formulas vs. PDE based numerical solution for the FRAP data processing: Theoretical and practical comparison

In this paper we rigorously formulate the inverse problem of model parameter estimation (including the sensitivity analysis), making possible the comparison of different FRAP parameter inference methods. Then, in a study on simulated data, we focus on how three different methods for inference influence the error in parameter estimation. We demonstrate both theoretically and empirically that our new method based on a solution of a general initial-boundary value problem for the Fick diffusion partial differential equation exhibits less bias and narrower confidence intervals of the estimated diffusion parameter, than two closed formula methods.