Time-dependent parameter identification in a Fokker-Planck equation based magnetization model of large ensembles of nanoparticles

TL;DR

This paper develops a method for identifying time-dependent parameters in a Fokker-Planck model of nanoparticle magnetization, with applications in magnetic particle imaging and dynamic tracking.

Contribution

It introduces a regularization-based approach for parameter identification in a PDE model on a manifold, addressing time-dependent magnetic field and particle orientation.

Findings

Effective reconstruction of magnetic field parameters.

Improved calibration procedures for nanoparticle imaging.

Numerical validation demonstrating method accuracy.

Abstract

In this article, we consider a model motivated by large ensembles of nanoparticles' magnetization dynamics using the Fokker-Planck equation and analyze the underlying parabolic PDE being defined on a smooth, compact manifold without boundary with respect to time-dependent parameter identification using regularization schemes. In the context of magnetic particle imaging, possible fields of application can be found including calibration procedures improved by time-dependent particle parameters and dynamic tracking of nanoparticle orientation. This results in reconstructing different parameters of interest, such as the applied magnetic field and the particles' easy axis. These problems are in particular addressed in the accompanied numerical study.