Thermal imaging-based state estimation of a Stefan problem with application to cell thawing

Abstract

The Stefan problem describes the evolution of the interface between two phases of a material undergoing phase change. Its formulation has been applied to model and solve a wide range of science and engineering problems across industries. This article describes observer design of a Stefan problem that arises in cell therapy in which frozen cells need to be thawed before injection. The dynamic model is simulated via a finite difference scheme with the method of lines solved over a moving grid. A Luenberger observer is designed based on the continuous-time moving-boundary moving-grid equations and information from real-time thermal imaging. Simulation and experimental results show that the integrated numerical model and observer can precisely predict the spatiotemporal evolution of thawing with errors of 1%–2% throughout the cell thawing process despite sensor noise, offering a reliable approach for state estimation and monitoring of cell thawing.