Simultaneous estimation of magnetic moment and Brownian relaxation time distributions of magnetic nanoparticles based on magnetic particle spectroscopy for biosensing application

Magnetic nanoparticles (MNPs) exhibit unique physicochemical characteristics owing to their comparable dimensions with important biological substances, high surface-to-volume ratios, size-dependent magnetic properties, and temperature sensitivity. In this study, we present a novel method for simultaneously estimating the magnetic moment and Brownian relaxation time distribution of MNPs based on AC magnetization harmonics. We provide a detailed description of the theoretical framework and experimental procedures. The dynamics of MNP magnetization are described using the Fokker-Planck equation, and a matrix equation is established to connect the magnetic moment, Brownian relaxation time, and magnetization harmonics. By employing a non-negative linear least squares algorithm with constraints, the magnetic moment and Brownian relaxation time distributions are inversed, which are then converted into the distributions of core sizes and hydrodynamic sizes. Finally, the estimated core size distribution reconstructed from M-H curves is consistent with the hydrodynamic size distribution measured by dynamic light scattering. This method is particularly useful for facilitating quantitative magnetic immunoassays.