Nonlinear Spectroscopic Characterization and Volterra Series Inspired Modeling of Magnetic Nanoparticles

Magnetic nanoparticles (MNPs) have emerging applications as tracer agents in medical diagnosis and for image guidance in surgery and targeted drug delivery. A critical component of the translation of MNPs into clinical use is an accurate understanding of the induced magnetic response to applied time-varying (ac) and static (dc) magnetic fields. Here, we propose a way of obtaining a Volterra series inspired model to predict the nonlinear behavior of MNPs in a single characterization step. For this purpose, we built an apparatus measuring the nonlinear responses of MNPs to frequencies from 1 to 5 kHz, applied ac magnetic fields from 1 to 5 mT, and applied dc magnetic fields from -5 to 5 mT. Using these characterization data, we then fit a reduced Volterra series inspired model to the nonlinear dynamic responses of the first seven harmonic frequencies of the ac excitation (R 2 > 0.99). This model could offer a practical alternative to physical modeling for MNP imaging methods, such as nonlinear susceptibility magnitude imaging (nSMI). Volterra series modeling as demonstrated in this paper could overcome the need for empirical calibration of the MNP response to external magnetic fields before imaging. This approach would eliminate one of the critical barriers to the translation of nSMI into clinical use.