Parameter Estimation and Quantification of Magnetic Nanoparticles Based on Improved Particle Swarm Optimization

Magnetic Relaxometry (MRX) is a promising technique for probing the magnetic properties of nanoparticles with considerable potential in biomedical applications. It magnetizes magnetic nanoparticles through a direct current magnetic field to obtain measurable Néel relaxation signals when magnetic nanoparticles are combined with specific cells or antibodies. It employs highly sensitive magnetic sensors to record relaxation signals following nanoparticle magnetization, from which intrinsic parameters and quantitative information can be extracted, and ultimately completes mass detection. The essential step in MRX-based mass detection is to establish the calibration relationship between the relaxation signal amplitude reflecting the magnetic moment and the corresponding mass of magnetic nanoparticles. In this article, we present a parameter estimation and quantification framework that integrates an improved Particle Swarm Optimization (PSO) algorithm with the Moment Superposition Model (MSM) as the objective function. The proposed method effectively combines experimental data with a theoretical model, enabling accurate determination of key intrinsic parameters, including saturation magnetization and magnetic anisotropy. Building on these reliable estimating parameters, the proposed PSO algorithm is further applied to quantify nanoparticle mass. Validation through simulations and experimental data confirms the robustness of the method, with the final mass detection error reaching the microgram level. These results highlight its potential for precise characterization of magnetic nanoparticles in biomedical contexts.