Viscosity Sensing via Single Harmonic Amplitude-Phase Cross-Point Using Field-Swept Magnetic Particle Spectroscopy

Magnetic particle spectroscopy (MPS) is a powerful tool for characterizing magnetic nanoparticles (MNPs) and sensing environmental parameters, such as viscosity and temperature of MNPs suspensions. The single-harmonic method has gained attention in viscosity measurement due to its simplicity and reduced sensitivity to signal-to-noise ratio variations. However, it relies solely on signal amplitude, limiting its sensitivity. This study introduces a novel viscosity estimation method using both the amplitude and phase of a single harmonic. By applying field-swept MPS (FS-MPS), we capture the second harmonic signal of MNP suspensions and analyze the decline cross points (DCPs) in the amplitude and phase spectra during field sweeping. A quantitative relationship between the DCP and viscosity is established. Simulation and experimental results show that, compared to methods relying solely on single-harmonic amplitude, our method improves viscosity detection sensitivity, achieving a precision of 0.09 mPa•s. It is also decoupled from MNP concentration, ensuring robustness against concentration variations. This work provides a new approach for measuring the viscosity of biological microenvironments using single-harmonic MPS.