A method for multiplexed and volumetric-based magnetic particle spectroscopy bioassay: mathematical study

Magnetic particle spectroscopy (MPS) is an emerging biosensing technique that detects target analytes by exploiting the dynamic magnetic responses of magnetic nanoparticles (MNPs). Due to the ease of synthesis and surface chemical functionalization of MNPs, MPS-based bioassays have gained popularity around the globe. One limiting factor for MPS-based assay is the ability to detect multiple analytes simultaneously in a single run, namely, multiplexed bioassay. Several groups have reported the realization of multiplexed bioassays on surface-based MPS platforms by spatially separating reaction areas by using the unique magnetic responses of different MNPs. In this work, we systematically study the magnetization curves (M-H curves) of different types of MNPs and their relationship to the dynamic magnetic responses when subjected to AC magnetic driving fields. Due to the different structures, sizes, and magnetic properties of each kind of MNP, the resulting harmonics are unique. Thus, concurrent quantification (also called 'colorization') of each type of MNP in a mixture is possible by solving the harmonic matrix function. Our results show that the uniqueness of M-H response curves of selected types of MNP and the signal-to-noise ratio of the system can affect the accuracy of multiplexed, volumetric-based MPS bioassays. The reported method assumes that each type of MNPs nanoparticles does not interact, and that the magnetic response of the mixture is a linear combination of the responses of each kind of MNP. This assumption may not hold for very dense systems where inter-particle interactions become significant and may require more complex models.