Ferrohydrodynamic modeling of magnetic nanoparticle harmonic spectra for magnetic particle imaging

Abstract

Magnetic Particle Imaging (MPI) is an emerging imaging technique that uses magnetic nanoparticles as tracers. In order to analyze the quality of nanoparticles developed for MPI, a Magnetic Particle Spectrometer (MPS) is often employed. In this paper, we describe results for predictions of the nanoparticle harmonic spectra obtained in a MPS using three models: the first uses the Langevin function, which does not take into account finite magnetic relaxation; the second model uses the magnetization equation by Shliomis (Sh), which takes into account finite magnetic relaxation using a constant characteristic time scale; and the third model uses the magnetization equation derived by Martsenyuk, Raikher, and Shliomis (MRSh), which takes into account the effect of magnetic field magnitude on the magnetic relaxation time. We make comparisons between these models and with experiments in order to illustrate the effects of field-dependent relaxation in the MPS. The models results suggest that finite relaxation results in a significant drop in signal intensity (magnitude of individual harmonics) and in faster spectral decay. Interestingly, when field dependence of the magnetic relaxation time was taken into account, through the MRSh model, the simulations predict a significant improvement in the performance of the nanoparticles, as compared to the performance predicted by the Sh equation. The comparison between the predictions from models and experimental measurements showed excellent qualitative as well as quantitative agreement up to the 19th harmonic using the Sh and MRSh equations, highlighting the potential of ferrohydrodynamic modeling in MPI. V C 2015 AIP Publishing LLC.

Theoretical predictions for spatially-focused heating of magnetic nanoparticles guided by magnetic particle imaging field gradients

“…This equation takes into account the effect of field strength on the relaxation time and is valid at moderate to high field amplitudes and frequencies [31, 32], that is, conditions where the magnetic response of the nanoparticles is no longer linear with the applied magnetic field and for particles relaxing by the Brownian mechanism. In our earlier work [33], we have used the MRSh equation to model the properties of magnetic nanoparticles in a magnetic particle spectrometer and have obtained good agreement with experiments. The MRSh equation is…”

Thermal Decomposition Synthesis of Iron Oxide Nanoparticles with Diminished Magnetic Dead Layer by Controlled Addition of Oxygen

“…77, 78 Ongoing work aims to correlate magnetic diameter to nanoparticle performance for MPI and obtain nanoparticles with performance that approaches theoretical predictions. 79 …”

Finite magnetic relaxation inx-space magnetic particle imaging: comparison of measurements and ferrohydrodynamic models

“…Even though there is a lack of quantitative agreement between the models and experiments on the basis of the FWHM, the agreement between the MRSh model and experiments is quite remarkable in terms of PSF shape and peak position without the need of fitting parameters. According to predictions in our earlier work [22], a significant difference between the MRSh and Sh model would be observed with particles having a core diameter greater than 20 nm. Also, we believe that further improvement in the reconstruction algorithm would improve the FWHM predictions.…”

“…The properties of the nanoparticles used in the x-space relaxometer measurements were the same as those reported in our previous work [22] and were the properties used in the simulations (that is, the simulations contained no fitting parameters). The core diameter determined using transmission electron microscopy was 14 nm, with a geometric deviation of ln σ = 0.12 (standard deviation of ln σ = 0.53) according to fitting to a lognormal size distribution.…”

“…Here we make use of the phenomenological magnetization relaxation equation by Martsenyuk, Raikher and Shliomis (herein referred to as MRSh), [21] which takes into account the field-dependent relaxation time, applicable in the case of high fields encountered in MPI. In contrast to our previous work [22] in which we modeled the harmonic spectra of the nanoparticles in a Magnetic Particle Spectrometer (MPS), here we use the x-space reconstruction method to make comparisons between predictions using the Langevin function, the Shliomis equation [23] (herein referred to as Sh), and the MRSh equation and measurements from experiments conducted in a Berkeley x-space relaxometer.…”