A Novel Estimation Method for Temperature of Magnetic Nanoparticles Dominated by Brownian Relaxation Based on Magnetic Particle Spectroscopy

This article presents a novel method for estimating the temperature of magnetic nanoparticles (MNPs) based on ac magnetization harmonics of MNPs dominated by Brownian relaxation. The disparity in the ac magnetization response and magnetization harmonic between the Fokker–Planck equation and the Langevin function was analyzed, and we studied the relationship between the magnetization harmonic and the key factors, such as Brownian relaxation time, temperature, magnetic field strength, core size and hydrodynamic size of MNPs, and excitation frequency. We proposed a compensation function for ac magnetization harmonic with consideration of the key factors and the disparity between the Fokker–Planck equation and the Langevin function. Then, a temperature estimation model based on the compensation function and the analytical harmonic expression of the Langevin function was established. By employing the least-squares algorithm, the temperature was successfully calculated. The experimental results show that the temperature error is less than 0.035 K in the temperature range from 310 to 320 K. The temperature estimation model is expected to improve the performance of the MNP thermometer and to be applied to MNP-mediated hyperthermia.