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

TL;DR

This paper presents a sensitivity-based optimization method for designing initial conditions in diffusion experiments, significantly improving parameter estimation accuracy, demonstrated through a modified FRAP protocol.

Contribution

It introduces a novel sensitivity-driven approach to optimize initial shape and topology in diffusion parameter identification, with practical application to FRAP experiments.

Findings

Optimized initial conditions enhance parameter estimation accuracy.

Numerical results show increasingly complex optimal shapes.

Modified FRAP protocol improves experimental outcomes.

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 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, 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.