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Purpose: The harmonic spectrum of the magnetization of magnetic nanoparticles (MNPs) in the presence of an applied magnetic field can be used to characterize the properties of the microenvironment of the MNPs. The change in temperature and relaxation time has been measured by varying the magnetic field amplitudes or frequency to obtain the harmonic spectrum. However, scaling estimates of temperature or relaxation time are poor if both change simultaneously. In this work, we show that scaling over both the amplitude and frequency of the applied magnetic field allows both the temperature and relaxation to be estimated simultaneously., Methods: The scaling methods previously used to measure temperature and relaxation times individually have been expanded to two dimensions allowing both parameters to be estimated simultaneously. Samples with different temperature and relaxation times were measured using a magnetic nanoparticle spectrometer to verify this two-dimensional scaling method. Simulations were also carried out for a range of nanoparticle sizes, and the best particle sizes were estimated for this two-dimensional method., Results: The two-dimensional scaling method achieved a mean error of 0.83% for relaxation time by considering the temperature variation as well as relaxation time changes. The temperature and viscosity of the MNPs were measured simultaneously with the mean error of 1.03°C and 0.011 mPas. For monodisperse particles with Brownian relaxation, simulation showed that core radius of 16 nm and hydrodynamic radius of 23 nm had best accuracy for the scaling method., Conclusions: The two-dimensional scaling method allows both temperature and relaxation time to be estimated simultaneously. The measurement accuracy can be improved by combining information in ratios and phases of the magnetic harmonics of the magnetization and by choosing the optimal particle sizes., (© 2019 American Association of Physicists in Medicine.)

Purpose: To evaluate the thrombus maturity noninvasively providing the promise of much earlier and more accurate diagnosis of diseases ranging from stroke to myocardial infarction to deep vein thrombosis., Methods: Magnetic spectroscopy of nanoparticle Brownian rotation (MSB), a form of magnetic particle spectroscopy sensitive to Brownian rotation of magnetic nanoparticles, was used for the detection and characterization of blood clots. The nanoparticles' relaxation time was quantified by scaling the MSB spectra in frequency to match the spectra from nanoparticles in a reference state. The nanoparticles' relaxation time, in the bound state, was used to characterize the nanoparticle binding to thrombin on the blood clot. The number of nanoparticles bound to the clot was also estimated. Both the relaxation time and the weight of bound nanoparticles were obtained for clots of several ages, reflecting different stages of development and organization. The impact of clot development was explored using functionalized nanoparticles present during clot formation., Results: The relaxation time of the bound nanoparticles decreases for more mature, organized clots. The number of nanoparticles able to bind the clot diminishes quantitatively with clot age. On mature clots, the nanoparticles bind the thrombin on the surface while for developing clots the nanoparticles bind several thrombin molecules or become trapped in the clot matrix during formation., Conclusions: By estimating the magnetic nanoparticles' relaxation time the clot age and organization can be predicted. The purposed methods are quick and minimally invasive for in vivo applications., (© 2018 American Association of Physicists in Medicine.)

Purpose: Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm., Methods: This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials., Results: In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different., Conclusions: VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower frequencies of intrinsic brain motions.

Purpose: Breast magnetic resonance imaging is highly sensitive but not very specific for the detection of breast cancer. Opportunities exist to supplement the image acquisition with a more specific modality provided the technical challenges of meeting space limitations inside the bore, restricted breast access, and electromagnetic compatibility requirements can be overcome. Magnetic resonance (MR) and microwave tomography (MT) are complementary and synergistic because the high resolution of MR is used to encode spatial priors on breast geometry and internal parenchymal features that have distinct electrical properties (i.e., fat vs fibroglandular tissue) for microwave tomography., Methods: The authors have overcome integration challenges associated with combining MT with MR to produce a new coregistered, multimodality breast imaging platform--magnetic resonance microwave tomography, including: substantial illumination tank size reduction specific to the confined MR bore diameter, minimization of metal content and composition, reduction of metal artifacts in the MR images, and suppression of unwanted MT multipath signals., Results: MR SNR exceeding 40 dB can be obtained. Proper filtering of MR signals reduces MT data degradation allowing MT SNR of 20 dB to be obtained, which is sufficient for image reconstruction. When MR spatial priors are incorporated into the recovery of MT property estimates, the errors between the recovered versus actual dielectric properties approach 5%., Conclusions: The phantom and human subject exams presented here are the first demonstration of combining MT with MR to improve the accuracy of the reconstructed MT images.

Purpose: Nonlinear inversion (NLI) in MR elastography requires discretization of the displacement field for a finite element (FE) solution of the "forward problem", and discretization of the unknown mechanical property field for the iterative solution of the "inverse problem". The resolution requirements for these two discretizations are different: the forward problem requires sufficient resolution of the displacement FE mesh to ensure convergence, whereas lowering the mechanical property resolution in the inverse problem stabilizes the mechanical property estimates in the presence of measurement noise. Previous NLI implementations use the same FE mesh to support the displacement and property fields, requiring a trade-off between the competing resolution requirements., Methods: This work implements and evaluates multiresolution FE meshes for NLI elastography, allowing independent discretizations of the displacements and each mechanical property parameter to be estimated. The displacement resolution can then be selected to ensure mesh convergence, and the resolution of the property meshes can be independently manipulated to control the stability of the inversion., Results: Phantom experiments indicate that eight nodes per wavelength (NPW) are sufficient for accurate mechanical property recovery, whereas mechanical property estimation from 50 Hz in vivo brain data stabilizes once the displacement resolution reaches 1.7 mm (approximately 19 NPW). Viscoelastic mechanical property estimates of in vivo brain tissue show that subsampling the loss modulus while holding the storage modulus resolution constant does not substantially alter the storage modulus images. Controlling the ratio of the number of measurements to unknown mechanical properties by subsampling the mechanical property distributions (relative to the data resolution) improves the repeatability of the property estimates, at a cost of modestly decreased spatial resolution., Conclusions: Multiresolution NLI elastography provides a more flexible framework for mechanical property estimation compared to previous single mesh implementations.

Purpose: Nanoparticle relaxation time measurements have many applications including characterizing molecular binding, viscosity, heating, and local matrix stiffness. The methods capable of in vivo application are extremely limited. The hypothesis investigated by the authors was that the relaxation time could be measured quantitatively using magnetic spectroscopy of nanoparticle Brownian motion (MSB)., Methods: The MSB signal (1) reflects the nanoparticle rotational Brownian motion, (2) can be measured from very low nanoparticle concentrations, and (3) is a function of the product of the drive frequency and the relaxation time characterizing Brownian motion. To estimate the relaxation time, the MSB signal was measured at several frequencies. The MSB signal for nanoparticles with altered relaxation time is a scaled version of that for reference nanoparticles with a known relaxation time. The scaling factor linking the altered and reference MSB measurements is the same factor linking the altered and reference relaxation times. The method was tested using glycerol solutions of varying viscosities to obtain continuously variable relaxation times., Results: The measured relaxation time increased with increasing viscosity of the solution in which the nanoparticles resided. The MSB estimated relaxation time matched the calculated relaxation times based on viscosity with 2% average error., Conclusions: MSB can be used to monitor the nanoparticle relaxation time quantitatively through a scale space correlation of the MSB signal as a function of frequency.

Purpose: Recently, the attenuating behavior of soft tissue has been addressed in magnetic resonance elastography by the inclusion of a damping mechanism in the methods used to reconstruct the resulting mechanical property image. To date, this mechanism has been based on a viscoelastic model for material behavior. Rayleigh, or proportional, damping provides a more generalized model for elastic energy attenuation that uses two parameters to characterize contributions proportional to elastic and inertial forces. In the case of time-harmonic vibration, these two parameters lead to both the elastic modulus and the density being complex valued (as opposed to the case of pure viscoelasticity, where only the elastic modulus is complex valued)., Methods: This article presents a description of Rayleigh damping in the time-harmonic case, discussing the differences between this model and the viscoelastic damping models. In addition, the results from a subzone based Rayleigh damped elastography study of gelatin and tofu phantoms are discussed, along with preliminary results from in vivo breast data., Results: Both the phantom and the tissue studies presented here indicate a change in the Rayleigh damping structure, described as Rayleigh composition, between different material types, with tofu and healthy tissue showing lower Rayleigh composition values than gelatin or cancerous tissue., Conclusions: It is possible that Rayleigh damping elastography and the concomitant Rayleigh composition images provide a mechanism for differentiating tissue structure in addition to measuring elastic stiffness and attenuation. Such information could be valuable in the use of Rayleigh damped magnetic resonance elastography as a diagnostic imaging tool.

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.

Purpose: The clinical efficacy of breast elastography may be limited when the authors employ the assumption that soft tissues exhibit linear, frequency-independent isotropic mechanical properties during the recovery of shear modulus. Thus, the purpose of this research was to evaluate the degradation in performance incurred when linear-elastic MR reconstruction methods are applied to phantoms that are fabricated using viscoelastic materials., Methods: To develop phantoms with frequency-dependent mechanical properties, the authors measured the complex modulus of two groups of cylindrical-shaped gelatin samples over a wide frequency range (up to 1 kHz) with the established principles of time-temperature superposition (TTS). In one group of samples, the authors added varying amounts of agar (1%-4%); in the other group, the authors added varying amounts of sucrose (2.5%-20%). To study how viscosity affected the performance of the linear-elastic reconstruction method, the authors constructed an elastically heterogeneous MR phantom to simulate the case where small viscoelastic lesions were surrounded by relatively nonviscous breast tissue. The breast phantom contained four linear, viscoelastic spherical inclusions (10 mm diameter) that were embedded in normal gelatin. The authors imaged the breast phantom with a clinical prototype of a MRE system and recovered the shear-modulus distribution using the overlapping-subzone-linear-elastic image-reconstruction method. The authors compared the recovered shear modulus to that measured using the TTS method., Results: The authors demonstrated that viscoelastic phantoms could be fabricated by including sucrose in the gelation process and that small viscoelastic inclusions were visible in MR elastograms recovered using a linear-elastic MR reconstruction process; however, artifacts that degraded contrast and spatial resolution were more prominent in highly viscoelastic inclusions. The authors also established that the accuracy of the MR elastograms depended on the degree of viscosity that the inclusion exhibited., Conclusions: The results demonstrated that reconstructing shear modulus from other constitutive laws, such as viscosity, should improve both the accuracy and quality of MR elastograms of the breast.

Purpose: Recent interest in the poroelastic behavior of tissues has led to the development of magnetic resonance poroelastography (MRPE) as an alternative to single-phase MR elastographic image reconstruction. In addition to the elastic parameters (i.e., Lamé's constants) commonly associated with magnetic resonance elastography (MRE), MRPE enables estimation of the time-harmonic pore-pressure field induced by external mechanical vibration., Methods: This study presents numerical simulations that demonstrate the sensitivity of the computed displacement and pore-pressure fields to a priori estimates of the experimentally derived model parameters. In addition, experimental data collected in three poroelastic phantoms are used to assess the quantitative accuracy of MR poroelastographic imaging through comparisons with both quasistatic and dynamic mechanical tests., Results: The results indicate hydraulic conductivity to be the dominant parameter influencing the deformation behavior of poroelastic media under conditions applied during MRE. MRPE estimation of the matrix shear modulus was bracketed by the values determined from independent quasistatic and dynamic mechanical measurements as expected, whereas the contrast ratios for embedded inclusions were quantitatively similar (10%-15% difference between the reconstructed images and the mechanical tests)., Conclusions: The findings suggest that the addition of hydraulic conductivity and a viscoelastic solid component as parameters in the reconstruction may be warranted.

Purpose: The harmonic spectrum of magnetic nanoparticles contains valuable information about the quantity and environment of the particles. Harmonic amplitudes have been used to produce quantitative images and ratios of these amplitudes have been used to monitor changes in the particle environment. Harmonic phase angles have not yet been utilized in these pursuits. The authors explore harmonic phase angle as a concentration-independent means of remotely monitoring the dynamic magnetization of nanoparticles., Methods: A magnetic nanoparticle spectrometer was used to explore the impacts of viscosity and excitation frequency and amplitude on the phase angle of magnetization harmonics. A dynamic model, which accounts for particle relaxation times, was used to model some results., Results: Harmonic phase angle can undergo large changes when a nanoparticle's Brownian motion is altered. Excitation parameters and particle characteristics have a profound effect on the extent of these changes., Conclusions: Phase angle can allow for monitoring of various impacts on a nanoparticle's Brownian motion. When combined with other concentration-independent metrics, such as ratios of harmonic amplitudes, valuable information about the particle's environment can be gathered.

Purpose: Magnetic resonance (MR) technique was used to detect small displacements induced by localized absorption of pulsed 434 MHz microwave power as a potential method for tumor detection., Methods: Phase contrast subtraction was used to separate the phase change due to motion from thermoelastic expansion from other contributions to phase variation such as the bulk temperature rise of the medium and phase offsets from the MR scanner itself. A simple set of experiments was performed where the motion was constrained to be one dimensional which provided controls on the data acquisition and motion extraction procedures. Specifically, the MR-detected motion signal was isolated by altering the direction of the microwave-induced motion and sampling the response with motion encoding gradients in all three directions when the microwave power was turned on and turned off., Results: Successful signal detection, as evidenced by the recording of a systematic alternating (zigzag) phase pattern, occurred only when the motion encoding was in parallel with either the vertical or horizontal direction of the microwave-induced motion on both 10 and 4 mm spatial scales., Conclusions: These results demonstrate, for the first time, that motion associated with thermoelastic expansion from the absorption of pulsed microwave power can be detected with MR.

The authors present a method of measuring the temperature of magnetic nanoparticles that can be adapted to provide in vivo temperature maps. Many of the minimally invasive therapies that promise to reduce health care costs and improve patient outcomes heat tissue to very specific temperatures to be effective. Measurements are required because physiological cooling, primarily blood flow, makes the temperature difficult to predict a priori. The ratio of the fifth and third harmonics of the magnetization generated by magnetic nanoparticles in a sinusoidal field is used to generate a calibration curve and to subsequently estimate the temperature. The calibration curve is obtained by varying the amplitude of the sinusoidal field. The temperature can then be estimated from any subsequent measurement of the ratio. The accuracy was 0.3 degree K between 20 and 50 degrees C using the current apparatus and half-second measurements. The method is independent of nanoparticle concentration and nanoparticle size distribution.

We explore the properties of the signal from magnetic nanoparticles. The nanoparticle signal has been used to generate images in magnetic particle imaging (MPI). MPI promises to be one of the most sensitive methods of imaging small numbers magnetic nanoparticles and therefore shows promise for molecular imaging. The nanoparticle signal is generated with a pure sinusoidal magnetic field that repeatedly saturates the nanoparticles creating harmonics in the induced magnetization that are easily isolated from the driving field. Signal from a selected position is isolated using a static magnetic field to completely saturate all of the particles outside a voxel enabling an image to be formed voxel by voxel. The signal produced by the magnetization of the nanoparticles contains only odd harmonics. However, it is demonstrated experimentally that with the addition of a static magnetic field bias even harmonics are introduced which increase the total signal significantly. Further, the distribution of signal among the harmonics depends on the static bias field so that information might be used to localize the nanoparticle distribution. Finally, the field required to completely saturate nanoparticles can be quite large and theory predicts that the field required is determined by the smallest nanoparticles in the sample.

An objective contrast-detail analysis was performed in this study to assess the low contrast detectability of a clinical prototype harmonic magnetic resonance elastographic imaging system. Elastographic imaging was performed on gelatin phantoms containing spherical inclusions of varying size and modulus contrast. The results demonstrate that lesions as small as 5 mm can be detected with a minimum modulus contrast of 14 dB. However, the shear modulus of such small lesions was not accurately recovered. In general, the shear modulus of larger focal lesions was accurately (i.e., within 25% of the true value) recovered. The minimum modulus contrast needed to detect focal lesions was observed to decrease with increasing lesion size.

Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.

The determination of the elastic property distribution in heterogeneous gel samples with a finite element based reconstruction scheme is considered. The algorithm operates on small overlapping subzones of the total field to allow for a high degree of spatial discretization while maintaining computational tractability. By including a Maxwellian-type viscoelastic property in the model physics and optimizing the spatial distribution of this property in the same manner as elasticity, a Young's modulus image is obtained which reasonably reflects the true distribution within the gel. However, the image lacks the clarity and accuracy expected based on simulation experience. Preliminary investigations suggest that transient effects in the data are the cause of a significant mismatch between the inversion model, which assumes steady-state conditions, and the actual displacements as measured by a phase contrast MR technique.

We have developed a multiscale algorithm for elastic (or molded) alignment of images. There is a wide array of medical applications of elastic (as opposed to strictly rigid) alignment: Subtraction of previous images from current ones to identify changes is perhaps the most obvious. We present preliminary results of this molding technique on a variety of images, and conclude with some closing remarks about this and future directions and goals of this work.

Principal-components analysis is used to obtain a set of parameters for dual-energy radiography that completely describes the attenuation coefficient of any tissue over a given energy range. These parameters are the weighted averages of the densities of the elements present in a substance. Principal-components (PC) parameters are calculated for several soft tissues from measured attenuation coefficients published by Phelps et al. The calculated PC parameters are compared to the more conventional dual-energy representations of the attenuation coefficient: (1) the electron density/effective atomic number (or Compton/photoelectric) representation and (2) the equivalent water/equivalent aluminum thickness representation. The principal-components parameters represent the attenuation coefficients more accurately, and are more stable than the currently used parameters. In addition, these new parameters are sensitive to differences in the chemical composition and density, whereas the previous representations are primarily sensitive to changes in the density. It is concluded that the principal-components method provides a more sensitive and accurate indicator of changes in tissue composition than previous characterizations of the linear attenuation coefficient. The principal-components method provides a means for improving the accuracy of the characterization of tissues in dual-energy computed tomographic imaging and in dual-energy digital radiography.