One-Sided Multidimensional Statistical Significance Testing: A New Method of Calculating the Statistical Significance of Spectra Used to Demonstrate Magnetic Nanoparticle Sensitivity.

Estimating statistical significance of the difference between two spectra or series is a fundamental statistical problem. Multivariate significance tests exist but the limitations preclude their use in many common cases; e.g., one-sided testing, unequal variance and when few repetitions are acquired all of which are required in magnetic spectroscopy of nanoparticle Brownian motion (MSB). We introduce a test, termed the T-S test, that is powerful and exact (exact type I error). It is flexible enough to be one- or two-sided and the one-sided version can specify arbitrary regions where each spectrum should be larger. The T-S test takes the-one or two-sided p-value at each frequency and combines them using Stouffer's method. We evaluated it using simulated spectra and measured MSB spectra. For the single-sided version, mean of the spectrum, A-T, was used as a reference; the T-S test is as powerful when the variance at each frequency is uniform and outperforms when the noise power is not uniform. For the two-sided version, the Hotelling T2 two-sided multivariate test was used as a reference; the two-sided T-S test is only slightly less powerful for large numbers of repetitions and outperforms rather dramatically for small numbers of repetitions. The T-S test was used to estimate the sensitivity of our current MSB spectrometer showing 1 nanogram sensitivity. Using eight repetitions the T-S test allowed 15 pM concentrations of mouse IL-6 to be identified while the mean of the spectra only identified 76 pM.

Distinguishing Nanoparticle Aggregation from Viscosity Changes in MPS/MSB Detection of Biomarkers.

Magnetic particle spectroscopy (MPS) in the Brownian relaxation regime, also termed magnetic spectroscopy of Brownian motion (MSB), can detect and quantitate very low, sub-nanomolar concentrations of molecular biomarkers. MPS/MSB uses the harmonics of the magnetization induced by a small, low-frequency oscillating magnetic field to provide quantitative information about the magnetic nanoparticles' (mNPs') microenvironment. A key application uses antibody-coated mNPs to produce biomarker-mediated aggregation that can be detected using MPS/MSB. However, relaxation changes can also be caused by viscosity changes. To address this challenge, we propose a metric that can distinguish between aggregation and viscosity. Viscosity changes scale the MPS/MSB harmonic ratios with a constant multiplier across all applied field frequencies. The change in viscosity is exactly equal to the multiplier with generality, avoiding the need to understand the signal explicitly. This simple scaling relationship is violated when particles aggregate. Instead, a separate multiplier must be used for each frequency. The standard deviation of the multipliers over frequency defines a metric isolating viscosity (zero standard deviation) from aggregation (non-zero standard deviation). It increases monotonically with biomarker concentration. We modeled aggregation and simulated the MPS/MSB signal changes resulting from aggregation and viscosity changes. MPS/MSB signal changes were also measured experimentally using 100 nm iron-oxide mNPs in solutions with different viscosities (modulated by glycerol concentration) and with different levels of aggregation (modulated by concanavalin A linker concentrations). Experimental and simulation results confirmed that viscosity changes produced small changes in the standard deviation and aggregation produced larger values of standard deviation. This work overcomes a key barrier to using MPS/MSB to detect biomarkers in vivo with variable tissue viscosity.

Toward Localized In Vivo Biomarker Concentration Measurements.

We know a great deal about the biochemistry of cells because they can be isolated and studied. The biochemistry of the much more complex in vivo environment is more difficult to study because the only ways to quantitate concentrations is to sacrifice the animal or biopsy the tissue. Either method disrupts the environment profoundly and neither method allows longitudinal studies on the same individual. Methods of measuring chemical concentrations in vivo are very valuable alternatives to sacrificing groups of animals. We are developing microscopic magnetic nanoparticle (mNP) probes to measure the concentration of a selected molecule in vivo. The mNPs are targeted to bind the selected molecule and the resulting reduction in rotational freedom can be quantified remotely using magnetic spectroscopy. The mNPs must be contained in micrometer sized porous shells to keep them from migrating and to protect them from clearance by the immune system. There are two key issues in the development of the probes. First, we demonstrate the ability to measure concentrations in the porous walled alginate probes both in phosphate buffered saline and in blood, which is an excellent surrogate for the complex and challenging in vivo environment. Second, sensitivity is critical because it allows microscopic probes to measure very small concentrations very far away. We report sensitivity measurements on recently introduced technology that has allowed us to improve the sensitivity by two orders of magnitude, a factor of 200 so far.

3D multislab, multishot acquisition for fast, whole-brain MR elastography with high signal-to-noise efficiency.

PURPOSE: To develop an acquisition scheme for generating MR elastography (MRE) displacement data with whole-brain coverage, high spatial resolution, and adequate signal-to-noise ratio (SNR) in a short scan time. THEORY AND METHODS: A 3D multislab, multishot acquisition for whole-brain MRE with 2.0 mm isotropic spatial resolution is proposed. The multislab approach allowed for the use of short repetition time to achieve very high SNR efficiency. High SNR efficiency allowed for a reduced acquisition time of only 6 min while the minimum SNR needed for inversion was maintained. RESULTS: The mechanical property maps estimated from whole-brain displacement data with nonlinear inversion (NLI) demonstrated excellent agreement with neuroanatomical features, including the cerebellum and brainstem. A comparison with an equivalent 2D acquisition illustrated the improvement in SNR efficiency of the 3D multislab acquisition. The flexibility afforded by the high SNR efficiency allowed for higher resolution with a 1.6 mm isotropic voxel size, which generated higher estimates of brainstem stiffness compared with the 2.0 mm isotropic acquisition. CONCLUSION: The acquisition presented allows for the capture of whole-brain MRE displacement data in a short scan time, and may be used to generate local mechanical property estimates of neuroanatomical features throughout the brain.

Approaches for modeling magnetic nanoparticle dynamics.

Magnetic nanoparticles are useful biological probes as well as therapeutic agents. Several approaches have been used to model nanoparticle magnetization dynamics for both Brownian as well as Neel rotation. Magnetizations are often of interest and can be compared with experimental results. Here we summarize these approaches, including the Stoner-Wohlfarth approach and stochastic approaches including thermal fluctuations. Non-equilibrium-related temperature effects can be described by a distribution function approach (Fokker-Planck equation) or a stochastic differential equation (Langevin equation). Approximate models in several regimes can be derived from these general approaches to simplify implementation.

Magnetic nanoparticle sensing: decoupling the magnetization from the excitation field.

Remote sensing of magnetic nanoparticles has exciting applications for magnetic nanoparticle hyperthermia and molecular detection. We introduce, simulate, and experimentally demonstrate an innovation-a sensing coil that is geometrically decoupled from the excitation field-for magnetic nanoparticle spectroscopy that increases the flexibility and capabilities of remote detection. The decoupling enhances the sensitivity absolutely; to small amounts of nanoparticles, and relatively; to small changes in the nanoparticle dynamics. We adapt a previous spectroscopic method that measures the relaxation time of nanoparticles and demonstrate a new measurement of nanoparticle temperature that could potentially be used concurrently during hyperthermia.

Local mechanical properties of white matter structures in the human brain.

The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure.

Magnetic resonance elastography of the brain using multishot spiral readouts with self-navigated motion correction.

Magnetic resonance elastography (MRE) has been introduced in clinical practice as a possible surrogate for mechanical palpation, but its application to study the human brain in vivo has been limited by low spatial resolution and the complexity of the inverse problem associated with biomechanical property estimation. Here, we report significant improvements in brain MRE data acquisition by reporting images with high spatial resolution and signal-to-noise ratio as quantified by octahedral shear strain metrics. Specifically, we have developed a sequence for brain MRE based on multishot, variable-density spiral imaging, and three-dimensional displacement acquisition and implemented a correction scheme for any resulting phase errors. A Rayleigh damped model of brain tissue mechanics was adopted to represent the parenchyma and was integrated via a finite element-based iterative inversion algorithm. A multiresolution phantom study demonstrates the need for obtaining high-resolution MRE data when estimating focal mechanical properties. Measurements on three healthy volunteers demonstrate satisfactory resolution of gray and white matter, and mechanical heterogeneities correspond well with white matter histoarchitecture. Together, these advances enable MRE scans that result in high-fidelity, spatially resolved estimates of in vivo brain tissue mechanical properties, improving upon lower resolution MRE brain studies that only report volume averaged stiffness values.

Quantification of magnetic nanoparticles with low frequency magnetic fields: compensating for relaxation effects.

Quantifying the number of nanoparticles present in tissue is central to many in vivo and in vitro applications. Magnetic nanoparticles can be detected with high sensitivity both in vivo and in vitro using the harmonics of their magnetization produced in a sinusoidal magnetic field. However, relaxation effects damp the magnetic harmonics rendering them of limited use in quantification. We show that an accurate measure of the number of nanoparticles can be made by correcting for relaxation effects. Correction for relaxation reduced errors of 50% for larger nanoparticles in high relaxation environments to 2%. The result is a method of nanoparticle quantification suitable for in vivo and in vitro applications including histopathology assays, quantitative imaging, drug delivery and thermal therapy preparation.

Measurement of magnetic nanoparticle relaxation time.

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.

Concurrent quantification of multiple nanoparticle bound states.

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.

Poroelastic Mechanical Properties of the Brain Tissue of Normal Pressure Hydrocephalus Patients During Lumbar Drain Treatment Using Intrinsic Actuation MR Elastography.

RATIONALE AND OBJECTIVES: Hydrocephalus (HC) is caused by accumulating cerebrospinal fluid resulting in enlarged ventricles and neurological symptoms. HC can be treated via a shunt in a subset of patients; identifying which individuals will respond through noninvasive imaging would avoid complications from unsuccessful treatments. This preliminary work is a longitudinal study applying MR Elastography (MRE) to HC patients with a focus on normal pressure hydrocephalus (NPH). MATERIALS AND METHODS: Twenty-two ventriculomegaly patients were imaged and subsequently received a lumbar drain placement for cerebrospinal fluid (CSF) drainage. NPH lumbar drain responders and NPH syndrome nonresponders were categorized by clinical presentation. Displacement images were acquired using intrinsic activation (IA) MRE and poroelastic inversion recovered shear stiffness and hydraulic conductivity values. A stable IA-MRE inversion protocol was developed to produce unique solutions for both recovered properties, independent of initial estimates. RESULTS: Property images showed significantly increased shear modulus (p = 0.003 in periventricular region, p = 0.005 in remaining cerebral tissue) and hydraulic conductivity (p = 0.04 in periventricular region) in ventriculomegaly patients compared to healthy volunteers. Baseline MRE imaging did not detect significant differences between NPH lumbar drain responders and NPH syndrome nonresponders; however, MRE time series analysis demonstrated consistent trends in average poroelastic shear modulus values over the course of the lumbar drain process in responders (initial increase, followed by a later decrease) which did not occur in nonresponders. CONCLUSION: These findings are indicative of acute mechanical changes in the brain resulting from CSF drainage in NPH patients.

Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico.

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

Harmonic phase angle as a concentration-independent measure of nanoparticle dynamics.

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.

The performance of steady-state harmonic magnetic resonance elastography when applied to viscoelastic materials.

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.

Contrast detection in fluid-saturated media with magnetic resonance poroelastography.

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.

Simultaneous quantification of multiple magnetic nanoparticles.

Distinct magnetic nanoparticle designs can have unique spectral responses to an AC magnetic field in a technique called the magnetic spectroscopy of Brownian motion (MSB). The spectra of the particles have been measured using desktop spectrometers and in vivo measurements. If multiple particle types are present in a region of interest, the unique spectral signatures allow for the simultaneous quantification of the various particles. We demonstrate such a potential experimentally with up to three particle types. This ability to concurrently detect multiple particles will enable new biomedical applications.

Quantification of magnetic nanoparticles by compensating for multiple environment changes simultaneously.

The quantification of magnetic nanoparticles is important for many applications, especially for in vivo biosensing. The magnetization harmonics used in spectroscopy of magnetic nanoparticles can be used to estimate nanoparticle number or weight. However, other effects such as temperature or relaxation time change can also influence the nanoparticle magnetization. Therefore, it is necessary to compensate for these factors when estimating the amount of magnetic nanoparticles. This paper shows through simulation that a two-dimensional scaling method can be used to improve the accuracy of nanoparticle quantification, especially when multiple effects are present which can influence the nanoparticle magnetization. Finally, an experiment was performed on a Magnetic Spectroscopy of Brownian motion (MSB) apparatus to demonstrate this method, and nanoparticle weight was determined with a mean error of 1.3 ng (1.81%).

Measuring protein biomarker concentrations using antibody tagged magnetic nanoparticles.

Under physiological conditions biomarker concentrations tend to rise and fall over time e.g. for inflammation. Ex vivo measurements provide a snapshot in time of biomarker concentrations, which is useful, but limited. Approaching real time monitoring of biomarker concentration(s) using a wearable, implantable or injectable in vivo sensor is therefore an appealing target. As an early step towards developing an in vivo biomarker sensor, antibody (AB) tagged magnetic nanoparticles (NPs) are used here to demonstrate the in vitro measurement of ~5 distinct biomarkers with high specificity and sensitivity. In previous work, aptamers were used to target a given biomarker in vitro and generate magnetic clusters that exhibit a characteristic rotational signature quite different from free NPs. Here the method is expanded to detect a much wider range of biomarkers using polyclonal ABs attached to the surface of the NPs. Commercial ABs exist for a wide range of targets allowing accurate and specific concentration measurements for most significant biomarkers. We show sufficient detection sensitivity, using an in-house spectrometer to measure the rotational signatures of the NPs, to assess physiological concentrations of hormones, cytokines and other signaling molecules. Detection limits for biomarkers drawn mainly from pain and inflammation targets were: 10 pM for mouse Granzyme B (mGZM-B), 40 pM for mouse interferon-gamma (mIFN-γ), 7 pM for mouse interleukin-6 (mIL-6), 40 pM for rat interleukin-6 (rIL-6), 40 pM for mouse vascular endothelial growth factor (mVEGF) and 250 pM for rat calcitonin gene related peptide (rCGRP). Much lower detection limits are certainly possible using improved spectrometers and nanoparticles.

Nonlinear Inversion MR Elastography With Low-Frequency Actuation.

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.