Harmonic phase angles used for nanoparticle sensing.

A series of techniques have been developed to use magnetic nanoparticles as biosensors to characterize their local microenvironment. Two approaches have been used to obtain quantitative information: model based approaches and scaling based approaches. We have favored scaling based approaches, because approximations made in models can lead to limitations in the accuracy. Currently all the scaling approaches use harmonic ratios to retrieve physical parameters like temperature, viscosity and relaxation time. In this work, we showed that the phase angle of the signal at a single harmonic frequency is an alternative to the ratio. The phase angle is nanoparticle density-independent, and can be used to improve sensitivity, enabling us to measure smaller biomedical effects. With the phase angle as an example, we showed that scaling methods are general and do not depend on specific approximations. We showed that the same scaling techniques can be used with both the phase angle and harmonic ratio because they both depend on the same combinations of physical parameters. Using the phase angle improves the precision and using the combination of phase angles and harmonic ratio provides the best precision.