Harmonic phase angle as a concentration‐independent measure of nanoparticle dynamics

Rauwerdink, Adam M.; Weaver, John B.

doi:10.1118/1.3426294

Cited by 48 publications

(56 citation statements)

References 29 publications

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“…11 Multiplying Eq. (6) by x, and integrating the second-derivative term by parts twice and the first-derivative term by parts transforms the FP into…”

Section: Iid Effective-field Fp Approximationmentioning

confidence: 99%

“…Along with the applications, and largely preceding them, there is an accumulated wealth of modeling work in the literature, both to help understand and to predict the experimental results. 6,[9][10][11][12][13][14]16 A starting point is the equation of motion of the magnetic moment of the nanoparticle under the influence of thermal torques in addition to relaxation and external magnetic field effects. This is the famous Langevin stochastic differential equation with random variables describing the thermal torquing.…”

Section: Introductionmentioning

confidence: 99%

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Modeling the Brownian relaxation of nanoparticle ferrofluids: Comparison with experiment

et al. 2013

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Purpose:The authors investigate the ability of current models for magnetic nanoparticles immersed in dilute ferrofluids and external sinusoidal magnetic fields to explain recent experiments in which the relaxation effects are dominated by viscous damping. Methods: The Fokker-Planck (FP) equation appropriate for the nanoparticle magnetic moment distribution corresponding to the underlying stochastic Langevin model is numerically studied and solutions compared to experimental results. The FP equation is solved using an expansion in Legendre polynomials. The polydisperse properties of the ferrofluids are incorporated into the analysis. Results: By using a FP approach that includes polydispersion, the authors obtain good agreement with recent experimental results using ferrofluids containing nanoparticles with average hydrodynamic diameters in the 40-120 nm range. Conclusions: For nanoparticles used in recent magnetic spectroscopy experiments, the FP approach can be used to accurately model experimental data in the situation where Brownian relaxation effects are dominant and the ferrofluids are dilute.

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“…11 Multiplying Eq. (6) by x, and integrating the second-derivative term by parts twice and the first-derivative term by parts transforms the FP into…”

Section: Iid Effective-field Fp Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling the Brownian relaxation of nanoparticle ferrofluids: Comparison with experiment

et al. 2013

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“…In the frequency domain, this response can be analyzed using the amplitude and phase of the magnetization harmonics. 9,10 As the proportion of nanoparticles that undergo Brownian relaxation increases, the influence of the physical environment on the magnetization also increases. We demonstrate this experimentally in Fig.…”

Section: Iiia Nanoparticle Selectionmentioning

confidence: 99%

“…Magnetic spectroscopy of nanoparticle Brownian motion ͑MSB͒ is a method of measuring characteristics of nanoparticles that affect their Brownian motion. 8 The harmonic spectrum of a particle's magnetization can be influenced by a number of physical parameters including temperature, 9 viscosity, 10 and binding. 11 The magnetic harmonics measured in MSB are also used in magnetic particle imaging ͑MPI͒, which images the concentration of magnetic nanoparticles with high speed, resolution, and sensitivity.…”

Section: Introductionmentioning

confidence: 99%

Concurrent quantification of multiple nanoparticle bound states

Rauwerdink

Weaver

2011

Medical Physics

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Purpose:The binding of nanoparticles to in vivo targets impacts their use for medical imaging, therapy, and the study of diseases and disease biomarkers. Though an array of techniques can detect binding in vitro, the search for a robust in vivo method continues. The spectral response of magnetic nanoparticles can be influenced by a variety of changes in their physical environment including viscosity and binding. Here, the authors show that nanoparticles in these different environmental states produce spectral responses, which are sufficiently unique to allow for simultaneous quantification of the proportion of nanoparticles within each state. Methods: The authors measured the response to restricted Brownian motion using an array of magnetic nanoparticle designs. With a chosen optimal particle type, the authors prepared particle samples in three distinct environmental states. Various combinations of particles within these three states were measured concurrently and the authors attempted to solve for the quantity of particles within each physical state. Results: The authors found the spectral response of the nanoparticles to be sufficiently unique to allow for accurate quantification of up to three bound states with errors on the order of 1.5%. Furthermore, the authors discuss numerous paths for translating these measurements to in vivo applications. Conclusions: Multiple nanoparticle environmental states can be concurrently quantified using the spectral response of the particles. Such an ability, if translated to the in vivo realm, could provide valuable information about the fate of nanoparticles in vivo or improve the efficacy of nanoparticle based treatments.

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“…There have been studies on relaxation in MPI [22], [27] but to date no one has studied the effect of relaxation on image reconstruction or resolution.…”

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confidence: 99%

Relaxation in x-space Magnetic Particle Imaging

Croft

Goodwill

Ferguson

et al. 2012

Springer Proceedings in Physics

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Magnetic particle imaging (MPI) is a new imaging modality that noninvasively images the spatial distribution of superparamagnetic iron oxide nanoparticles (SPIOs). MPI has demonstrated high contrast and zero attenuation with depth, and MPI promises superior safety compared to current angiography methods, X-ray, computed tomography, and magnetic resonance imaging angiography. Nanoparticle relaxation can delay the SPIO magnetization, and in this work we investigate the open problem of the role relaxation plays in MPI scanning and its effect on the image. We begin by amending the x-space theory of MPI to include nanoparticle relaxation effects. We then validate the amended theory with experiments from a Berkeley x-space relaxometer and a Berkeley x-space projection MPI scanner. Our theory and experimental data indicate that relaxation reduces SNR and asymmetrically blurs the image in the scanning direction. While relaxation effects can have deleterious effects on the MPI scan, we show theoretically and experimentally that x-space reconstruction remains robust in the presence of relaxation. Furthermore, the role of relaxation in x-space theory provides guidance as we develop methods to minimize relaxation-induced blurring. This will be an important future area of research for the MPI community.

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Harmonic phase angle as a concentration‐independent measure of nanoparticle dynamics

Cited by 48 publications

References 29 publications

Modeling the Brownian relaxation of nanoparticle ferrofluids: Comparison with experiment

Modeling the Brownian relaxation of nanoparticle ferrofluids: Comparison with experiment

Concurrent quantification of multiple nanoparticle bound states

Relaxation in x-space Magnetic Particle Imaging

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