Optimization of the shape (and topology) of the initial conditions for diffusion parameter identification

Abstract

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal experimental design variables and study the optimization of the shape (and topology) of the initial conditions for an inverse problem of a diffusion parameter identification. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on a specific experimental setting of initial conditions. By a numerical optimization, considering radially symmetric shapes only, we find an interesting pattern of increasingly complicated (with respect to connectivity) optimal initial shapes. The proposed modification of the FRAP experimental protocol is rather surprising but entirely realistic and the resulting enhancement of the parameter estimate accuracy is significant.