Multi–dimensional Debye model for nanoparticle magnetization in magnetic particle imaging

Magnetic particle imaging (MPI) is a new medical modality to safely image the concentration distribution of superparamagnetic iron-oxide nanoparticles (SPIOs). It relies on the nonlinear magnetization response of SPIOs under a time-varying magnetic field to induce an output voltage signal. When the magnetic field is multidimensional, the accuracy of the first-order Debye model decreases in describing the magnetization process. To solve this problem, we propose a multi–dimensional Debye model, which considers each dimensional magnetic field’s contribution to the magnetization of SPIOs. Through various experiments, the proposed multi–dimensional Debye model shows superiority over the first-order Debye model, with a 30% lower root-mean-square error in modeling the magnetization. The multi–dimensional Debye model can accurately analyze the influence of different magnetic fields on the SPIOs. This model can further guide MPI instrument optimization.