Applying stochastic Langevin function with coupled Brownian–Néel relaxations to study the dynamic magnetizations of nanoparticle tracers in magnetic particle imaging

Abstract Magnetic particle imaging (MPI) is a new imaging technique that utilizes biologically safe iron oxide nanoparticle tracers for medical imaging. Although in the preclinical stage, MPI has shown strong potential for applications such as cell tracking, angiography, cancer imaging, etc. With the ever-growing research interest in MPI and the increasing desire to apply it in clinical medical imaging, the design of tracers, MPI systems, image reconstruction algorithms, and other related components has become increasingly critical. To date, most of the theoretical studies in MPI rely on the static Langevin function to describe the magnetization responses of superparamagnetic iron oxide nanoparticle (SPION) tracers. However, under a fast-changing excitation field (usually tens of kHz), the magnetic relaxation time of SPION tracers is no longer negligible, thus, the static Langevin function is inaccurate in explaining the tracers’ magnetic signals in MPI. Herein, we apply a stochastic Langevin function with coupled Brownian–Néel relaxation models to study the dynamic magnetization responses of SPION tracers in MPI. The time domain magnetization responses ( M – t curve), dynamic magnetization-field hysteresis loops ( M – H curve), and point spread functions are modeled for different SPION tracer designs with varying physical and magnetic properties. Our results show that larger magnetic core sizesreduce the MPI spatial resolution. Conversely, thicker non-magnetic coatings on tracers do not significantly affect the spatial resolution. The increased anisotropy diminishes the MPI resolution, and a higher saturation magnetization favors higher MPI resolution.