Magnetic particle spectroscopy (MPS) exploits the nonlinear dynamic magnetization of magnetic nanoparticles (MNPs) under an alternating magnetic field (AMF) to characterize both the physical properties of MNPs and their surrounding liquid environment. This technique has gained widespread application not only for characterizing MNPs but also in magnetic bioassays. Over the past 15 years, MPS-based bioassays have been developed into point-of-care devices for in-field applications, with advantages such as being inexpensive, rapid, accurate, and easy to use. However, the widespread deployment of MPS biosensors is hindered by a lack of multiplexing capability. Researchers have proposed MPS-based spatial multiplexing similar to lateral flow assays, but this approach increases the cost of materials and reagents. MPS-based spectral multiplexing, based on the assumption that the collective harmonics of a mixture of MNPs equal the harmonics of each MNP multiplied by their respective quantities, has been theoretically and experimentally demonstrated. Many studies decode the quantities of MNPs from mixtures by solving an overdetermined set of equations of harmonics through least-squares minimization. However, this can lead to decreased accuracy due to lower signal-to-noise ratios (SNRs) in higher-order harmonics. This work demonstrates that the use of a minimum number of equations to solve for unknown MNP quantities—i.e., a truncated set of equations composed of harmonic information from lower-order harmonics with higher SNR—can result in greater multiplexing accuracy. In a surface-based MPS assay mechanism, where Néel relaxations dominate the dynamic magnetizations of MNPs under an AMF, we apply our truncated set of equations to decode the quantities of different types of commercial iron oxide MNPs from a mixture. Several factors affecting multiplexing accuracy are studied, including dipolar interactions between MNPs of the same type and of different types, the choice of harmonics used in the truncated set of equations, and the amplitude and frequency of the AMF. At the end of this work, we compare the multiplexing accuracy of our method with the accuracy of the reported overdetermined system. While our method requires upfront effort in selecting appropriate harmonics for the truncated set of equations, it ultimately yields greater accuracy.

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• Dipolar interaction
• Magnetization dynamics
• Optoelectronics
• Superparamagnetism
• Magnetic nanoparticles
• Medical imaging
• Radio frequency techniques
• Spectroscopy