Harmonic phase angles used for nanoparticle sensing

Abstract

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.

Concurrent quantification of magnetic nanoparticles temperature and relaxation time

“…Without losing generality, the functional form of the magnetization, , from a magnetic fluid of MNPs in a sinusoidal applied field has been described aswhere is the amplitude of the applied magnetic field, is its frequency, n is the number of mNPs, V h is the hydrodynamic volume, is core volume, is the saturation magnetization, is the temperature of the microenvironment, is Boltzmann's constant, and is the relaxation time. The relaxation time here refers to the generalized relaxation time which may include the effects like Brownian relaxation, Neel relaxation, and the interactions between particles.…”

“…To quantify changes in either the temperature or the relaxation time, scaling methods are used . The MNP magnetization and its harmonics are functions of the products of variables.…”

“…The products lead to uncertainty relationships between pairs of variables that allow changes in an observed variable to be exactly compensated for by a change in the complimentary variable. The functional relationships are quite general and do not depend on a model of the magnetization . For example, the magnetization is a function of the ratio of the amplitude of the applied magnetic field over the temperature so a change in temperature can be compensated by an opposite scaling of the applied field amplitude to produce identical MNP dynamics.…”

Evaluating blood clot progression using magnetic particle spectroscopy

“…The relaxation time can be measured quantitatively from the MSB spectra at frequencies ω m , using scaling methods because the magnetization is a function of the unitless variable ωτ . The MSB spectra of the MNPs before binding were used as the reference with the reference relaxation time τ f .…”

“…Previous efforts have also used magnetic particle spectroscopy (MPS) to characterize blood clot lysis using MNP hyperthermia and to quantify the amount of iron on the clot Recently, magnetic spectroscopy of MNP Brownian rotation (MSB) has been shown to be a useful tool for the detection and characterization of blood clots and hence it has the potential to characterize thrombus to treat DVT more effectively and reduce the risks . MSB is a form of magnetic particle spectroscopy sensitive to Brownian rotation of MNPs, which allows for quantization of binding and temperature effects . For i n vivo applications, to detect and quantitatively characterize blood clot stiffness, age, and the number of MNPs in the microenvironment of the thrombus.…”