Quantification of magnetic nanoparticles with low frequency magnetic fields: compensating for relaxation effects.

Quantifying the number of nanoparticles present in tissue is central to many in vivo and in vitro applications. Magnetic nanoparticles can be detected with high sensitivity both in vivo and in vitro using the harmonics of their magnetization produced in a sinusoidal magnetic field. However, relaxation effects damp the magnetic harmonics rendering them of limited use in quantification. We show that an accurate measure of the number of nanoparticles can be made by correcting for relaxation effects. Correction for relaxation reduced errors of 50% for larger nanoparticles in high relaxation environments to 2%. The result is a method of nanoparticle quantification suitable for in vivo and in vitro applications including histopathology assays, quantitative imaging, drug delivery and thermal therapy preparation.