Three-dimensional subzone-based reconstruction algorithm for MR elastography

Viscoelastic polyacrylamide MR elastography phantoms with tunable damping ratio independent of shear stiffness

Physiologically modeled test samples with known properties and characteristics, or phantoms, are essential for developing sensitive, repeatable, and accurate quantitative MRI techniques. Magnetic resonance elastography (MRE) is one such technique used to estimate tissue mechanical properties, and it is advantageous to use phantoms with independently tunable mechanical properties to benchmark the accuracy of MRE methods. Phantoms with tunable shear stiffness are commonly used for MRE, but tuning the viscosity or damping ratio has proven to be difficult. A promising candidate for MRE phantoms with tunable damping ratio is polyacrylamide (PAA). While pure PAA has very low attenuation, viscoelastic hydrogels have been made by entrapping linear polyacrylamide strands (LPAA) within the PAA network. In this study, we evaluate the use of LPAA/PAA gels as physiologically accurate phantoms with tunable damping ratio, independent of shear stiffness, via MRE. Phantoms were made with 15.3 wt% PAA while the LPAA concentration ranged from 4.5 wt% to 8.0 wt%. MRE was performed at 9.4 T with 400 Hz vibration on all phantoms revealing a strong, positive correlation between damping ratio and LPAA content (p < 0.001). There was no significant correlation between shear stiffness and LPAA content, confirming a constant PAA concentration yielded constant shear stiffness. Rheometry at 10 Hz was performed to verify the damping ratio of the phantoms. Nearly identical slopes for damping ratio versus LPAA content were found from both MRE and rheometry (0.0073 and 0.0075 respectively). Ultimately, this study validates the adaptation of polyacrylamide gels into physiologically-relevant MRE phantoms to enable testing of MRE estimates of damping ratio.

Post-mortem changes of anisotropic mechanical properties in the porcine brain assessed by MR elastography

Knowledge of the mechanical properties of brain tissue in vivo is essential to understanding the mechanisms underlying traumatic brain injury (TBI) and to creating accurate computational models of TBI and neurosurgical simulation. Brain white matter, which is composed of aligned, myelinated, axonal fibers, is structurally anisotropic. White matter in vivo also exhibits mechanical anisotropy, as measured by magnetic resonance elastography (MRE), but measurements of anisotropy obtained by mechanical testing of white matter ex vivo have been inconsistent. The minipig has a gyrencephalic brain with similar white matter and gray matter proportions to humans and therefore provides a relevant model for human brain mechanics. In this study, we compare estimates of anisotropic mechanical properties of the minipig brain obtained by identical, non-invasive methods in the live (in vivo) and dead animals (in situ). To do so, we combine wave displacement fields from MRE and fiber directions derived from diffusion tensor imaging (DTI) with a finite element-based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal alive and at specific times post-mortem. These maps show that white matter is stiffer, more dissipative, and more anisotropic than gray matter when the minipig is alive, but that these differences largely disappear post-mortem, with the exception of tensile anisotropy. Overall, brain tissue becomes stiffer, less dissipative, and less mechanically anisotropic post-mortem. These findings emphasize the importance of testing brain tissue properties in vivo.

Statement of Significance

In this study, MRE and DTI in the minipig were combined to estimate, for the first time, anisotropic mechanical properties in the living brain and in the same brain after death. Significant differences were observed in the anisotropic behavior of brain tissue post-mortem. These results demonstrate the importance of measuring brain tissue properties in vivo as well as ex vivo, and provide new quantitative data for the development of computational models of brain biomechanics.

Estimating the viscoelastic properties of the human brain at 7 T MRI using intrinsic MRE and nonlinear inversion

Intrinsic actuation magnetic resonance elastography (MRE) is a phase-contrast MRI technique that allows for in vivo quantification of mechanical properties of the brain by exploiting brain motion that arise naturally due to the cardiac pulse. The mechanical properties of the brain reflect its tissue microstructure, making it a potentially valuable parameter in studying brain disease. The main purpose of this study was to assess the feasibility of reconstructing the viscoelastic properties of the brain using high-quality 7 T MRI displacement measurements, obtained using displacement encoding with stimulated echoes (DENSE) and intrinsic actuation. The repeatability and sensitivity of the method for detecting normal regional variation in brain tissue properties was assessed as secondary goal. The displacement measurements used in this analysis were previously acquired for a separate study, where eight healthy subjects (27 ± 7 years) were imaged with repeated scans (spatial resolution approx. 2 mm isotropic, temporal resolution 75 ms, motion sensitivity 0.35 mm/2π for displacements in anterior-posterior and left-right directions, and 0.7 mm/2π for feet-head displacements). The viscoelastic properties of the brain were estimated using a subzone based non-linear inversion scheme. The results show comparable consistency to that of extrinsic MRE between the viscoelastic property maps obtained from repeated displacement measurements. The shear stiffness maps showed fairly consistent spatial patterns. The whole-brain repeatability coefficient (RC) for shear stiffness was (mean ± standard deviation) 8 ± 8% relative to the mean whole-brain stiffness, and the damping ratio RC was 28 ± 17% relative to the whole-brain damping ratio. The shear stiffness maps showed similar statistically significant regional trends as demonstrated in a publicly available atlas of viscoelastic properties obtained with extrinsic actuation MRE at 50 Hz. The damping ratio maps showed less consistency, likely due to data-model mismatch of describing the brain as a viscoelastic material under low frequencies. While artifacts induced by fluid flow within the brain remain a limitation of the technique in its current state, intrinsic actuation based MRE allow for consistent and repeatable estimation of the mechanical properties of the brain. The method provides enough sensitivity to investigate regional variation in such properties in the normal brain, which is likely sufficient to also investigate pathological changes.

Clinical application of magnetic resonance elastography in pediatric neurological disorders

Magnetic resonance elastography is a relatively new, rapidly evolving quantitative magnetic resonance imaging technique which can be used for mapping the viscoelastic mechanical properties of soft tissues. MR elastography measurements are akin to manual palpation but with the advantages of both being quantitative and being useful for regions which are not available for palpation, such as the human brain. MR elastography is noninvasive, well tolerated, and complements standard radiological and histopathological studies by providing in vivo measurements that reflect tissue microstructural integrity. While brain MR elastography studies in adults are becoming frequent, published studies on the utility of MR elastography in children are sparse. In this review, we have summarized the major scientific principles and recent clinical applications of brain MR elastography in diagnostic neuroscience and discuss avenues for impact in assessing the pediatric brain.

Vascular determinants of hippocampal viscoelastic properties in healthy adults across the lifespan

Arterial stiffness and cerebrovascular pulsatility are non-traditional risk factors of Alzheimer's disease. However, there is a gap in understanding the earliest mechanisms that link these vascular determinants to brain aging. Changes to mechanical tissue properties of the hippocampus (HC), a brain structure essential for memory encoding, may reflect the impact of vascular dysfunction on brain aging. We tested the hypothesis that arterial stiffness and cerebrovascular pulsatility are related to HC tissue properties in healthy adults across the lifespan. Twenty-five adults underwent measurements of brachial blood pressure (BP), large elastic artery stiffness, middle cerebral artery pulsatility index (MCAv PI), and magnetic resonance elastography (MRE), a sensitive measure of HC viscoelasticity. Individuals with higher carotid pulse pressure (PP) exhibited lower HC stiffness (β = -0.39, r = -0.41, p = 0.05), independent of age and sex. Collectively, carotid PP and MCAv PI significantly explained a large portion of the total variance in HC stiffness (adjusted R2 = 0.41, p = 0.005) in the absence of associations with HC volumes. These cross-sectional findings suggest that the earliest reductions in HC tissue properties are associated with alterations in vascular function.

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development.

Reverberant magnetic resonance elastographic imaging using a single mechanical driver

Reverberant elastography provides fast and robust estimates of shear modulus; however, its reliance on multiple mechanical drivers hampers clinical utility. In this work, we hypothesize that for constrained organs such as the brain, reverberant elastography can produce accurate magnetic resonance elastograms with a single mechanical driver. To corroborate this hypothesis, we performed studies on healthy volunteers (n= 3); and a constrained calibrated brain phantom containing spherical inclusions with diameters ranging from 4-18 mm. In both studies (i.e. phantom and clinical), imaging was performed at frequencies of 50 and 70 Hz. We used the accuracy and contrast-to-noise ratio performance metrics to evaluate reverberant elastograms relative to those computed using the established subzone inversion method. Errors incurred in reverberant elastograms varied from 1.3% to 16.6% when imaging at 50 Hz and 3.1% and 16.8% when imaging at 70 Hz. In contrast, errors incurred in subzone elastograms ranged from 1.9% to 13% at 50 Hz and 3.6% to 14.9% at 70 Hz. The contrast-to-noise ratio of reverberant elastograms ranged from 63.1 to 73 dB compared to 65 to 66.2 dB for subzone elastograms. The average global brain shear modulus estimated from reverberant and subzone elastograms was 2.36 ± 0.07 kPa and 2.38 ± 0.11 kPa, respectively, when imaging at 50 Hz and 2.70 ± 0.20 kPa and 2.89 ± 0.60 kPa respectively, when imaging at 70 Hz. The results of this investigation demonstrate that reverberant elastography can produce accurate, high-quality elastograms of the brain with a single mechanical driver.

OSCILLATE: A low-rank approach for accelerated magnetic resonance elastography

PURPOSE

MR elastography (MRE) is a technique to characterize brain mechanical properties in vivo. Due to the need to capture tissue deformation in multiple directions over time, MRE is an inherently long acquisition, which limits achievable resolution and use in challenging populations. The purpose of this work is to develop a method for accelerating MRE acquisition by using low-rank image reconstruction to exploit inherent spatiotemporal correlations in MRE data.

THEORY AND METHODS

The proposed MRE sampling and reconstruction method, OSCILLATE (Observing Spatiotemporal Correlations for Imaging with Low-rank Leveraged Acceleration in Turbo Elastography), involves alternating which k-space points are sampled between each repetition by a reduction factor, ROSC. Using a predetermined temporal basis from a low-resolution navigator in a joint low-rank image reconstruction, all images can be accurately reconstructed from a reduced amount of k-space data.

RESULTS

Decomposition of MRE displacement data demonstrated that, on average, 96.1% of all energy from an MRE dataset is captured at rank L = 12 (reduced from a full rank of 24). Retrospectively undersampling data with ROSC  = 2 and reconstructing at low-rank (L = 12) yields highly accurate stiffness maps with voxel-wise error of 5.8% ± 0.7%. Prospectively undersampled data at ROSC  = 2 were successfully reconstructed without loss of material property map fidelity, with average global stiffness error of 1.0% ± 0.7% compared to fully sampled data.

CONCLUSIONS

OSCILLATE produces whole-brain MRE data at 2 mm isotropic resolution in 1 min 48 s.

Relationships between aggression, sensation seeking, brain stiffness, and head impact exposure: Implications for head impact prevention in ice hockey

OBJECTIVES

The objectives of this study were to (1) examine the relationship between the number of head impacts sustained in a season of men's collegiate club ice hockey and behavioral traits of aggression and sensation seeking, and (2) explore the neural correlates of these behaviors using neuroimaging.

DESIGN

Retrospective cohort study.

METHODS

Participants (n = 18) completed baseline surveys to quantify self-reported aggression and sensation-seeking tendencies. Aggression related to playing style was quantified through penalty minutes accrued during a season. Participants wore head impact sensors throughout a season to quantify the number of head impacts sustained. Participants (n = 15) also completed baseline anatomical and magnetic elastography neuroimaging scans to measure brain volumetric and viscoelastic properties. Pearson correlation analyses were performed to examine relationships between (1) impacts, aggression, and sensation seeking, and (2) impacts, aggression, and sensation seeking and brain volume, stiffness, and damping ratio, as an exploratory analysis.

RESULTS

Number of head impacts sustained was significantly related to the number of penalty minutes accrued, normalized to number of games played (r = .62, p < .01). Our secondary, exploratory analysis revealed that number of impacts, sensation seeking, and aggression were related to stiffness or damping ratio of the thalamus, amygdala, hippocampus, and frontal cortex, but not volume.

CONCLUSIONS

A more aggressive playing style was related to an increased number of head impacts sustained, which may provide evidence for future studies of head impact prevention. Further, magnetic resonance elastography may aid to monitor behavior or head impact exposure. Researchers should continue to examine this relationship and consider targeting behavioral modification programs of aggression to decrease head impact exposure in ice hockey.

Magnetic resonance elastography with guided pressure waves

Magnetic resonance elastography aims to non-invasively and remotely characterize the mechanical properties of living tissues. To quantitatively and regionally map the shear viscoelastic moduli in vivo, the technique must achieve proper mechanical excitation throughout the targeted tissues. Although it is straightforward, ante manibus, in close organs such as the liver or the breast, which practitioners clinically palpate already, it is somewhat fortunately highly challenging to trick the natural protective barriers of remote organs such as the brain. So far, mechanical waves have been induced in the latter by shaking the surrounding cranial bones. Here, the skull was circumvented by guiding pressure waves inside the subject's buccal cavity so mechanical waves could propagate from within through the brainstem up to the brain. Repeatable, reproducible and robust displacement fields were recorded in phantoms and in vivo by magnetic resonance elastography with guided pressure waves such that quantitative mechanical outcomes were extracted in the human brain.

Mapping heterogenous anisotropic tissue mechanical properties with transverse isotropic nonlinear inversion MR elastography

The white matter tracts of brain tissue consist of highly-aligned, myelinated fibers; white matter is structurally anisotropic and is expected to exhibit anisotropic mechanical behavior. In vivo mechanical properties of tissue can be imaged using magnetic resonance elastography (MRE). MRE can detect and monitor natural and disease processes that affect tissue structure; however, most MRE inversion algorithms assume locally homogenous properties and/or isotropic behavior, which can cause artifacts in white matter regions. A heterogeneous, model-based transverse isotropic implementation of a subzone-based nonlinear inversion (TI-NLI) is demonstrated. TI-NLI reconstructs accurate maps of the shear modulus, damping ratio, shear anisotropy, and tensile anisotropy of in vivo brain tissue using standard MRE motion measurements and fiber directions estimated from diffusion tensor imaging (DTI). TI-NLI accuracy was investigated with using synthetic data in both controlled and realistic settings: excellent quantitative and spatial accuracy was observed and cross-talk between estimated parameters was minimal. Ten repeated, in vivo, MRE scans acquired from a healthy subject were co-registered to demonstrate repeatability of the technique. Good resolution of anatomical structures and bilateral symmetry were evident in MRE images of all mechanical property types. Repeatability was similar to isotropic MRE methods and well within the limits required for clinical success. TI-NLI MRE is a promising new technique for clinical research into anisotropic tissues such as the brain and muscle.

Design, Construction, and Implementation of a Magnetic Resonance Elastography Actuator for Research Purposes

Magnetic resonance elastography (MRE) is a technique for determining the mechanical response of soft materials using applied harmonic deformation of the material and a motion-sensitive magnetic resonance imaging sequence. This technique can elucidate significant information about the health and development of human tissue such as liver and brain, and has been used on phantom models (e.g., agar, silicone) to determine their suitability for use as a mechanical surrogate for human tissues in experimental models. The applied harmonic deformation used in MRE is generated by an actuator, transmitted in bursts of a specified duration, and synchronized with the magnetic resonance signal excitation. These actuators are most often a pneumatic design (common for human tissues or phantoms) or a piezoelectric design (common for small animal tissues or phantoms). Here, we describe how to design and assemble both a pneumatic and a piezoelectric MRE actuator for research purposes. For each of these actuator types, we discuss displacement requirements, end-effector options and challenges, electronics and electronic-driving requirements and considerations, and full MRE implementation. We also discuss how to choose the actuator type, size, and power based on the intended material and use. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Design, construction, and implementation of a convertible pneumatic MRE actuator for use with tissues and phantom models Basic Protocol 2: Design, construction, and implementation of a piezoelectric MRE actuator for localized excitation in phantom models.

Practical and clinical applications of pancreatic magnetic resonance elastography: a systematic review

Magnetic resonance elastography (MRE) is a non-invasive technique suitable for assessing mechanical properties of tissues, i.e., stiffness. MRE of the pancreas is relatively new, but recently an increasing number of studies have successfully assessed pancreas diseases with MRE aiming to differentiate healthy from pathological pancreatic tissue with or without fibrosis. This review will systematically describe the practical and clinical applications of pancreatic MRE. We conducted a systematic literature search with a pre-specified search strategy using PubMed and Embase according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. English peer-reviewed articles applying MRE of the pancreas were included. Two independent reviewers assessed the studies. The literature search yielded 14 studies. The pancreatic stiffness for healthy volunteers ranged from 1.11. to 1.21 kPa at a driver frequency of 40 Hz. In benign tumors, the stiffness values were slightly higher or sometimes even lower (range 0.78 to 2.00 kPa), compared to the healthy pancreas parenchyma whereas, in malignant tumors, the stiffness values tended to be higher (1.42 to 6.06 kPa). The pancreatic stiffness was increased in both acute (median: 1.99 kPa) and chronic pancreatitis (> 1.50 kPa). MRE is a promising technique for detecting and quantifying pancreatic stiffness. It is related to fibrosis and seems to be useful in assessing treatment response and clinical follow-up of pancreatic diseases. However, most of the described practical settings were characterized by a lack of uniformity and inconsistency in reporting standards across studies. Harmonization between centers is necessary to achieve more consensus and optimization of pancreatic MRE protocols.

Magnetic Resonance Elastography Reconstruction for Anisotropic Tissues

Elastography has become widely used clinically for characterising changes in soft tissue mechanics that are associated with altered tissue structure and composition. However, some soft tissues, such as muscle, are not isotropic as is assumed in clinical elastography implementations. This limits the ability of these methods to capture changes in anisotropic tissues associated with disease. The objective of this study was to develop and validate a novel elastography reconstruction technique suitable for estimating the linear viscoelastic mechanical properties of transversely isotropic soft tissues. We derived a divergence-free formulation of the governing equations for acoustic wave propagation through a linearly transversely isotropic viscoelastic material, and transformed this into a weak form. This was then implemented into a finite element framework, enabling the analysis of wave input data and tissue structural fibre orientations, in this case based on diffusion tensor imaging. To validate the material constants obtained with this method, numerous in silico phantom experiments were run which encompassed a range of variations in wave input directions, material properties, fibre structure and noise. The method was also tested on ex vivo muscle and in vivo human volunteer calf muscles, and compared with a previous curl-based inversion method. The new method robustly extracted the transversely isotropic shear moduli (G_⊥^', G_∥^', G^″) from the in silico phantom tests with minimal bias, including in the presence of experimentally realistic levels of noise in either fibre orientation or wave data. This new method performed better than the previous method in the presence of noise. Anisotropy estimates from the ex vivo muscle phantom agreed well with rheological tests. In vivo experiments on human calf muscles were able to detect increases in muscle shear moduli with passive muscle stretch. This new reconstruction method can be applied to quantify tissue mechanical properties of anisotropic soft tissues, such as muscle, in health and disease.

MR elastography inversion by compressive recovery

Direct inversion (DI) derives tissue shear modulus by inverting the Helmholtz equation. However, conventional DI is sensitive to data quality due to the ill-posed nature of Helmholtz inversion and thus providing reliable stiffness estimation can be challenging. This becomes more problematic in the case of estimating shear stiffness of the lung in which the low tissue density and short T2* result in considerably low signal-to-noise ratio during lung MRE. In the present study, we propose to perform MRE inversion by compressive recovery (MICRo). Such a technique aims to improve the numerical stability and the robustness to data noise of Helmholtz inversion by using prior knowledge on data noise and transform sparsity of the stiffness map. The developed inversion strategy was first validated in simulated phantoms with known stiffness. Next, MICRo was compared to the standard clinical multi-modal DI (MMDI) method forin vivoliver MRE in healthy subjects and patients with different stages of liver fibrosis. After establishing the accuracy of MICRo, we demonstrated the robustness of the proposed technique against data noise in lung MRE with healthy subjects. In simulated phantoms with single-directional or multi-directional waves, MICRo outperformed DI with Romano filter or Savitsky and Golay filter, especially when the stiffness and/or noise level was high. In hepatic MRE application, agreement was observed between MICRo and MMDI. Measuringin vivolung stiffness, MICRo demonstrated its advantages over filtered DI by yielding stable stiffness estimation at both residual volume and total lung capacity. These preliminary results demonstrate the potential value of the proposed technique and also warrant further investigation in a larger clinical population.

Blood lipid markers are associated with hippocampal viscoelastic properties and memory in humans

Age-related memory loss shares similar risk factors as cardiometabolic diseases including elevated serum triglycerides (TGs) and low-density lipoprotein cholesterol (LDL-C) and reduced high-density lipoprotein cholesterol (HDL-C). The mechanisms linking these aberrant blood lipids to memory loss are not completely understood but may be partially mediated by reduced integrity of the hippocampus (HC), the primary brain structure for encoding and recalling memories. In this study, we tested the hypothesis that blood lipid markers are independently associated with memory performance and HC viscoelasticity-a noninvasive measure of brain tissue microstructural integrity assessed by high-resolution magnetic resonance elastography (MRE). Twenty-six individuals across the adult lifespan were recruited (14 M/12 F; mean age: 42 ± 15 y; age range: 22-78 y) and serum lipid profiles were related to episodic memory and HC viscoelasticity. All subjects were generally healthy without clinically abnormal blood lipids or memory loss. Episodic memory was negatively associated with the TG/HDL-C ratio. HC viscoelasticity was negatively associated with serum TGs and the TG/HDL-C ratio, independent of age and in the absence of associations with HC volume. These data, although cross-sectional, suggest that subtle differences in blood lipid profiles in healthy adults may contribute to a reduction in memory function and HC tissue integrity.

Harnessing brain waves: a review of brain magnetic resonance elastography for clinicians and scientists entering the field

Brain magnetic resonance elastography (MRE) is an imaging technique capable of accurately and non-invasively measuring the mechanical properties of the living human brain. Recent studies have shown that MRE has potential to provide clinically useful information in patients with intracranial tumors, demyelinating disease, neurodegenerative disease, elevated intracranial pressure, and altered functional states. The objectives of this review are: (1) to give a general overview of the types of measurements that have been obtained with brain MRE in patient populations, (2) to survey the tools currently being used to make these measurements possible, and (3) to highlight brain MRE-based quantitative biomarkers that have the highest potential of being adopted into clinical use within the next 5 to 10 years. The specifics of MRE methodology strategies are described, from wave generation to material parameter estimations. The potential clinical role of MRE for characterizing and planning surgical resection of intracranial tumors and assessing diffuse changes in brain stiffness resulting from diffuse neurological diseases and altered intracranial pressure are described. In addition, the emerging technique of functional MRE, the role of artificial intelligence in MRE, and promising applications of MRE in general neuroscience research are presented.

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.

SNR Weighting for Shear Wave Speed Reconstruction in Tomoelastography

In tomoelastography, to achieve a final wave speed map by combining reconstructions obtained from all spatial directions and excitation frequencies, the use of weights is inevitable. Here, a new weighting scheme, which maximizes the signal-to-noise ratio (SNR) of the final wave speed map, has been proposed. To maximize the SNR of the final wave speed map, the use of squares of estimated SNR values of reconstructed individual maps has been proposed. Therefore, derivations of the SNR of the reconstructed wave speed maps have become necessary. Considering the noise on the complex MRI signal, the SNR of the reconstructed wave speed map was formulated by an analytical approach assuming a high SNR, and the results were verified using Monte Carlo simulations (MCSs). It has been assumed that the noise remains approximately Gaussian when the image SNR is high enough, despite the nonlinear operations in tomoelastography inversion. Hence, the SNR threshold was determined by comparing the SNR computed by MCSs and analytical approximations. The weighting scheme was evaluated for accuracy, spatial resolution and SNR performances on simulated phantoms. MR elastography (MRE) experiments on two different phantoms were conducted. Wave speed maps were generated for simulated 3D human abdomen MRE data and experimental human abdomen MRE data. The simulation results demonstrated that the SNR-weighted inversion improved the SNR performance of the wave speed map by a factor of two compared to the performance of the original (i.e., amplitude-weighted) reconstruction. In the case of a low SNR, no bias occurred in the wave speed map when SNR weighting was used, whereas 10% bias occurred when the original weighting (i.e., amplitude weighting) was used. Thus, while not altering the accuracy or spatial resolution of the wave speed map with the proposed weighting method, the SNR of the wave speed map has been significantly improved.

MR elastography: Principles, guidelines, and terminology

Magnetic resonance elastography (MRE) is a phase contrast-based MRI technique that can measure displacement due to propagating mechanical waves, from which material properties such as shear modulus can be calculated. Magnetic resonance elastography can be thought of as quantitative, noninvasive palpation. It is increasing in clinical importance, has become widespread in the diagnosis and staging of liver fibrosis, and additional clinical applications are being explored. However, publications have reported MRE results using many different parameters, acquisition techniques, processing methods, and varied nomenclature. The diversity of terminology can lead to confusion (particularly among clinicians) about the meaning of and interpretation of MRE results. This paper was written by the MRE Guidelines Committee, a group formalized at the first meeting of the ISMRM MRE Study Group, to clarify and move toward standardization of MRE nomenclature. The purpose of this paper is to (1) explain MRE terminology and concepts to those not familiar with them, (2) define "good practices" for practitioners of MRE, and (3) identify opportunities to standardize terminology, to avoid confusion.

MR Elastography of the Breast: Evolution of Technique, Case Examples, and Future Directions

Recognizing that breast cancers present as firm, stiff lesions, the foundation of breast magnetic resonance elastography (MRE) is to combine tissue stiffness parameters with sensitive breast MR contrast-enhanced imaging. Breast MRE is a non-ionizing, cross-sectional MR imaging technique that provides for quantitative viscoelastic properties, including tissue stiffness, elasticity, and viscosity, of breast tissues. Currently, the technique continues to evolve as research surrounding the use of MRE in breast tissue is still developing. In the setting of a newly diagnosed cancer, associated desmoplasia, stiffening of the surrounding stroma, and necrosis are known to be prognostic factors that can add diagnostic information to patient treatment algorithms. In fact, mechanical properties of the tissue might also influence breast cancer risk. For these reasons, exploration of breast MRE has great clinical value. In this review, we will: (1) address the evolution of the various MRE techniques; (2) provide a brief overview of the current clinical studies in breast MRE with interspersed case examples; and (3) suggest directions for future research.

Viscoelasticity of reward and control systems in adolescent risk taking

Heightened risk-taking tendencies during adolescence have been hypothesized to be attributable to physiological differences of maturation in key brain regions. The socioemotional system (e.g., nucleus accumbens), which is instrumental in reward response, shows a relatively earlier development trajectory than the cognitive control system (e.g., medial prefrontal cortex), which regulates impulse response. This developmental imbalance between heightened reward seeking and immature cognitive control potentially makes adolescents more susceptible to engaging in risky activities. Here, we assess brain structure in the socioemotional and cognitive control systems through viscoelastic stiffness measured with magnetic resonance elastography (MRE) and volumetry, as well as risk-taking tendencies measured using two experimental tasks in 40 adolescents (mean age ​= ​13.4 years old). MRE measures of regional brain stiffness reflect brain health and development via myelin content and glial matrix makeup, and have been shown to be highly sensitive to cognitive processes as compared to measures of regional brain volume and diffusion weighted imaging metrics. We find here that the viscoelastic and volumetric differences between the nucleus accumbens and the prefrontal cortex are correlated with increased risk-taking behavior in adolescents. These differences in development between the two brain systems can be used as an indicator of those adolescents who are more prone to real world risky activities and a useful measure for characterizing response to intervention.

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.

Artificial neural networks for magnetic resonance elastography stiffness estimation in inhomogeneous materials

PURPOSE

To test the hypothesis that removing the assumption of material homogeneity will improve the spatial accuracy of stiffness estimates made by Magnetic Resonance Elastography (MRE).

METHODS

An artificial neural network was trained using synthetic wave data computed using a coupled harmonic oscillator model. Material properties were allowed to vary in a piecewise smooth pattern. This neural network inversion (Inhomogeneous Learned Inversion (ILI)) was compared against a previous homogeneous neural network inversion (Homogeneous Learned Inversion (HLI)) and conventional direct inversion (DI) in simulation, phantom, and in-vivo experiments.

RESULTS

In simulation experiments, ILI was more accurate than HLI and DI in predicting the stiffness of an inclusion in noise-free, low-noise, and high-noise data. In the phantom experiment, ILI delineated inclusions ≤ 2.25 cm in diameter more clearly than HLI and DI, and provided a higher contrast-to-noise ratio for all inclusions. In a series of stiff brain tumors, ILI shows sharper stiffness transitions at the edges of tumors than the other inversions evaluated.

CONCLUSION

ILI is an artificial neural network based framework for MRE inversion that does not assume homogeneity in material stiffness. Preliminary results suggest that it provides more accurate stiffness estimates and better contrast in small inclusions and at large stiffness gradients than existing algorithms that assume local homogeneity. These results support the need for continued exploration of learning-based approaches to MRE inversion, particularly for applications where high resolution is required.

Hippocampal viscoelasticity and episodic memory performance in healthy older adults examined with magnetic resonance elastography

Episodic memory is particularly sensitive to normative aging; however, studies investigating the structure-function relationships that support episodic memory have primarily been limited to gross volumetric measures of brain tissue health. Magnetic resonance elastography (MRE) is an emerging non-invasive, high-resolution imaging technique that uniquely quantifies brain viscoelasticity, and as such, provides a more specific measure of neural microstructural integrity. Recently, a significant double dissociation between orbitofrontal cortex-fluid intelligence and hippocampal-relational memory structure-function relationships was observed in young adults, highlighting the potential of sensitive MRE measures for studying brain health and its relation to cognitive function. However, the structure-function relationship observed by MRE has not yet been explored in healthy older adults. In this study, we examined the relationship between hippocampal (HC) viscoelasticity and episodic memory in cognitively healthy adults aged 66-73 years (N = 11), as measured with the verbal-paired associates (VPA) subtest from the Wechsler Memory Scale (WMS-R). Given the particular dependence of verbal memory tasks on the left HC, unilateral HC MRE measurements were considered for the first time. A significant negative correlation was found between left HC damping ratio, ξ and VPA recall score (r_s = -0.77, p = 0.009), which is consistent with previous findings of a relationship between HC ξ and memory performance in young adults. Conversely, correlations between right HC ξ with VPA recall score were not significant. These results highlight the utility of MRE to study cognitive decline and brain aging and suggest its possible use as a sensitive imaging biomarker for memory-related impairments.

Reliable preparation of agarose phantoms for use in quantitative magnetic resonance elastography

Agarose phantoms are one type of phantom commonly used in developing in vivo brain magnetic resonance elastography (MRE) sequences because they are inexpensive and easy to work with, store, and dispose of; however, protocols for creating agarose phantoms are non-standardized and often result in inconsistent phantoms with significant variability in mechanical properties. Many magnetic resonance imaging (MRI) and ultrasound studies use phantoms, but often these phantoms are not tailored for desired mechanical properties and as such are too stiff or not mechanically consistent enough to be used in MRE. In this work, we conducted a systematic study of agarose phantom creation parameters to identify those factors that are most conducive to producing mechanically consistent agarose phantoms for MRE research. We found that cooling rate and liquid temperature affected phantom homogeneity. Phantom stiffness is affected by agar concentration (quadratically), by final liquid temperature and salt content in phantoms, and by the interaction of these two metrics each with stir rate. We captured and quantified the implied relationships with a regression model that can be used to estimate stiffness of resulting phantoms. Additionally, we characterized repeatability, stability over time, impact on MR signal parameters, and differences in agar gel microstructure. This protocol and regression model should prove beneficial in future MRE development studies that use phantoms to determine stiffness measurement accuracy.

Mechanical properties of the in vivo adolescent human brain

Viscoelastic mechanical properties of the in vivo human brain, measured noninvasively with magnetic resonance elastography (MRE), have recently been shown to be affected by aging and neurological disease, as well as relate to performance on cognitive tasks in adults. The demonstrated sensitivity of brain mechanical properties to neural tissue integrity make them an attractive target for examining the developing brain; however, to date, MRE studies on children are lacking. In this work, we characterized global and regional brain stiffness and damping ratio in a sample of 40 adolescents aged 12-14 years, including the lobes of the cerebrum and subcortical gray matter structures. We also compared the properties of the adolescent brain to the healthy adult brain. Temporal and parietal cerebral lobes were softer in adolescents compared to adults. We found that of subcortical gray matter structures, the caudate and the putamen were significantly stiffer in adolescents, and that the hippocampus and amygdala were significantly less stiff than all other subcortical structures. This study provides the first detailed characterization of adolescent brain viscoelasticity and provides baseline data to be used in studying development and pathophysiology.

MR elastography at 1 Hz of gelatin phantoms using 3D or 4D acquisition

Magnetic Resonance Elastography (MRE) detects induced periodic motions in biological tissues allowing maps of tissue mechanical properties to be derived. In-vivo MRE is commonly performed at frequencies of 30-100 Hz using external actuation, however, using cerebro-vascular pulsation at 1 Hz as a form of intrinsic actuation (IA-MRE) eliminates the need for external motion sources and simplifies data acquisition. In this study a hydraulic actuation system was developed to drive 1 Hz motions in gelatin as a tool for investigating the performance limits of IA-MRE image reconstruction under controlled conditions. Quantitative flow (QFLOW) MR techniques were used to phase encode 1 Hz motions as a function of gradient direction using 3D or 4D acquisition; 4D acquisition was twice as fast and yielded comparable motion field and concomitant image reconstruction results provided the motion signal was sufficiently strong. Per voxel motion noise floor corresponded to a displacement amplitude of about 20-30 μm. Signal to noise ratio (SNR) was 94 ± 17 for 3D and dropped to 69 ± 10 for the faster 4D acquisition, but yielded octahedral shear stress and shear modulus maps of high quality that differed by only about 20% on average. QFLOW measurements in gel phantoms were improved significantly by adding Mn(II) to mimic relaxation rates found in brain. Overall, the hydraulic 1 Hz actuation system when coupled with 4D sequence acquisition produced a fast reliable approach for future IA-MRE phantom evaluation and contrast detail studies needed to benchmark imaging performance.

Encoding and readout strategies in magnetic resonance elastography

Magnetic resonance elastography (MRE) has evolved significantly since its inception. Advances in motion-encoding gradient design and readout strategies have led to improved encoding and signal-to-noise ratio (SNR) efficiencies, which in turn allow for higher spatial resolution, increased coverage, and/or shorter scan times. The purpose of this review is to summarize MRE wave-encoding and readout approaches in a unified mathematical framework to allow for a comparative assessment of encoding and SNR efficiency of the various methods available. Besides standard full- and fractional-wave-encoding approaches, advanced techniques including flow compensation, sample interval modulation and multi-shot encoding are considered. Signal readout using fast k-space trajectories, reduced field of view, multi-slice, and undersampling techniques are summarized and put into perspective. The review is concluded with a foray into displacement and diffusion encoding as alternative and/or complementary techniques.

Relative identifiability of anisotropic properties from magnetic resonance elastography

Although magnetic resonance elastography (MRE) has been used to estimate isotropic stiffness in the heart, myocardium is known to have anisotropic properties. This study investigated the determinability of global transversely isotropic material parameters using MRE and finite-element modeling (FEM). A FEM-based material parameter identification method, using a displacement-matching objective function, was evaluated in a gel phantom and simulations of a left ventricular (LV) geometry with a histology-derived fiber field. Material parameter estimation was performed in the presence of Gaussian noise. Parameter sweeps were analyzed and characteristics of the Hessian matrix at the optimal solution were used to evaluate the determinability of each constitutive parameter. Four out of five material stiffness parameters (Young's modulii E1 and E3 , shear modulus G13 and damping coefficient s), which describe a transversely isotropic linear elastic material, were well determined from the MRE displacement field using an iterative FEM inversion method. However, the remaining parameter, Poisson's ratio, was less identifiable. In conclusion, Young's modulii, shear modulii and damping can theoretically be well determined from MRE data, but Poisson's ratio is not as well determined and could be set to a reasonable value for biological tissue (close to 0.5).

Stiffness and Beyond: What MR Elastography Can Tell Us About Brain Structure and Function Under Physiologic and Pathologic Conditions

Brain magnetic resonance elastography (MRE) was developed on the basis of a desire to "palpate by imaging" and is becoming a powerful tool in the investigation of neurophysiological and neuropathological states. Measurements are acquired with a specialized MR phase-contrast pulse sequence that can detect tissue motion in response to an applied external or internal excitation. The tissue viscoelasticity is then reconstructed from the measured displacement. Quantitative characterization of brain viscoelastic behaviors provides us an insight into the brain structure and function by assessing the mechanical rigidity, viscosity, friction, and connectivity of brain tissues. Changes in these features are associated with inflammation, demyelination, and neurodegeneration that contribute to brain disease onset and progression. Here, we review the basic principles and limitations of brain MRE and summarize its current neuroanatomical studies and clinical applications to the most common neurosurgical and neurodegenerative disorders, including intracranial tumors, dementia, multiple sclerosis, amyotrophic lateral sclerosis, and traumatic brain injury. Going forward, further improvement in acquisition techniques, stable inverse reconstruction algorithms, and advanced numerical, physical, and preclinical validation models is needed to increase the utility of brain MRE in both research and clinical applications.

Stiffness reconstruction methods for MR elastography

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave-motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

Phantom evaluations of nonlinear inversion MR elastography

This study evaluated non-linear inversion MRE (NLI-MRE) based on viscoelastic governing equations to determine its sensitivity to small, low contrast inclusions and interface changes in shear storage modulus and damping ratio. Reconstruction parameters identical to those used in recent in vivo MRE studies of mechanical property variations in small brain structures were applied. NLI-MRE was evaluated on four phantoms with contrast in stiffness and damping ratio. Image contrast to noise ratio was assessed as a function of inclusion diameter and property contrast, and edge and line spread functions were calculated as measures of imaging resolution. Phantoms were constructed from silicone, agar, and tofu materials. Reconstructed property estimates were compared with independent mechanical testing using dynamic mechanical analysis (DMA). The NLI-MRE technique detected inclusions as small as 8 mm with a stiffness contrast as low as 14%. Storage modulus images also showed an interface edge response distance of 11 mm. Damping ratio images distinguished inclusions with a diameter as small as 8 mm, and yielded an interface edge response distance of 10 mm. Property differences relative to DMA tests were in the 15%-20% range in most cases. In this study, NLI-MRE storage modulus estimates resolved the smallest inclusion with the lowest stiffness contrast, and spatial resolution of attenuation parameter images was quantified for the first time. These experiments and image quality metrics establish quantitative guidelines for the accuracy expected in vivo for MRE images of small brain structures, and provide a baseline for evaluating future improvements to the NLI-MRE pipeline.

Shear Wave Speed Estimation Using Reverberant Shear Wave Fields: Implementation and Feasibility Studies

Elastography is a modality that estimates tissue stiffness and, thus, provides useful information for clinical diagnosis. Attention has focused on the measurement of shear wave propagation; however, many methods assume shear wave propagation is unidirectional and aligned with the lateral imaging direction. Any deviations from the assumed propagation result in biased estimates of shear wave speed. To address these challenges, directional filters have been applied to isolate shear waves with different propagation directions. Recently, a new method was proposed for tissue stiffness estimation involving creation of a reverberant shear wave field propagating in all directions within the medium. These reverberant conditions lead to simple solutions, facile implementation and rapid viscoelasticity estimation of local tissue. In this work, this new approach based on reverberant shear waves was evaluated and compared with another well-known elastography technique using two calibrated elastic and viscoelastic phantoms. Additionally, the clinical feasibility of this technique was analyzed by assessing shear wave speed in human liver and breast tissues, in vivo. The results indicate that it is possible to estimate the viscoelastic properties in each scanned medium. Moreover, a better approach to estimation of shear wave speed was obtained when only the phase information was taken from the reverberant waves, which is equivalent to setting all magnitudes within the bandpass equal to unity: an idealization of a perfectly isotropic reverberant shear wave field.

Numerical simulations of magnetic resonance elastography using finite element analysis with a linear heterogeneous viscoelastic model

Abstract

Magnetic resonance elastography (MRE) is a technique to identify the viscoelastic moduli of biological tissues by solving the inverse problem from the displacement field of viscoelastic wave propagation in a tissue measured by MRI. Because finite element analysis (FEA) of MRE evaluates not only the viscoelastic model for a tissue but also the efficiency of the inversion algorithm, we developed FEA for MRE using commercial software called ANSYS, the Zener model for displacement field of a wave inside tissue, and an inversion algorithm called the modified integral method. The profile of the simulated displacement field by FEA agrees well with the experimental data measured by MRE for gel phantoms. Similarly, the value of storage modulus (i.e., stiffness) recovered using the modified integral method with the simulation data is consistent with the value given in FEA. Furthermore, applying the suggested FEA to a human liver demonstrates the effectiveness of the present simulation scheme.

Graphical abstract

Measurement of anisotropic mechanical properties in porcine brain white matter ex vivo using magnetic resonance elastography

The mechanical properties of brain tissue, particularly those of white matter (WM), need to be characterized accurately for use in finite element (FE) models of brain biomechanics and traumatic brain injury (TBI). Magnetic resonance elastography (MRE) is a powerful tool for non-invasive estimation of the mechanical properties of soft tissues. While several studies involving direct mechanical tests of brain tissue have shown mechanical anisotropy, most MRE studies of brain tissue assume an isotropic model. In this study, an incompressible transversely isotropic (TI) material model parameterized by minimum shear modulus (μ₂), shear anisotropy parameter (ϕ), and tensile anisotropy parameter (ζ) is applied to analyze MRE measurements of ex vivo porcine white matter (WM) brain tissue. To characterize shear anisotropy, "slow" (pure transverse) shear waves were propagated at 100, 200 and 300Hz through sections of ex vivo brain tissue including both WM and gray matter (GM). Shear waves were found to propagate with elliptical fronts, consistent with TI material behavior. Shear wave fields were also analyzed within regions of interest (ROI) to find local shear wavelengths parallel and perpendicular to fiber orientation. FE simulations of a TI material with a range of plausible shear modulus (μ₂) and shear anisotropy parameters (ϕ) were run and the results were analyzed in the same fashion as the experimental case. Parameters of the FE simulations which most closely matched each experiment were taken to represent the mechanical properties of that particular sample. Using this approach, WM in the ex vivo porcine brain was found to be mildly anisotropic in shear with estimates of minimum shear modulus (actuation frequencies listed in parenthesis): μ₂= 1.04 ± 0.12 kPa (at 100Hz), μ₂= 1.94 ± 0.29 kPa (at 200Hz), and μ₂= 2.88 ± 0.34 kPa (at 300Hz) and corresponding shear anisotropy factors of ϕ= 0.27 ± 0.09 (at 100Hz), ϕ= 0.29 ± 0.14 (at 200Hz) and ϕ= 0.34 ± 0.13 (at 300Hz). Future MRE studies will focus on tensile anisotropy, which will require both slow and fast shear waves for accurate estimation.

Artificial neural networks for stiffness estimation in magnetic resonance elastography

PURPOSE

To investigate the feasibility of using artificial neural networks to estimate stiffness from MR elastography (MRE) data.

METHODS

Artificial neural networks were fit using model-based training patterns to estimate stiffness from images of displacement using a patch size of ∼1 cm in each dimension. These neural network inversions (NNIs) were then evaluated in a set of simulation experiments designed to investigate the effects of wave interference and noise on NNI accuracy. NNI was also tested in vivo, comparing NNI results against currently used methods.

RESULTS

In 4 simulation experiments, NNI performed as well or better than direct inversion (DI) for predicting the known stiffness of the data. Summary NNI results were also shown to be significantly correlated with DI results in the liver (R²  = 0.974) and in the brain (R²  = 0.915), and also correlated with established biological effects including fibrosis stage in the liver and age in the brain. Finally, repeatability error was lower in the brain using NNI compared to DI, and voxel-wise modeling using NNI stiffness maps detected larger effects than using DI maps with similar levels of smoothing.

CONCLUSION

Artificial neural networks represent a new approach to inversion of MRE data. Summary results from NNI and DI are highly correlated and both are capable of detecting biologically relevant signals. Preliminary evidence suggests that NNI stiffness estimates may be more resistant to noise than an algebraic DI approach. Taken together, these results merit future investigation into NNIs to improve the estimation of stiffness in small regions. Magn Reson Med 80:351-360, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

MR elastography of the brain and its application in neurological diseases

Magnetic resonance elastography (MRE) is an imaging technique for noninvasively and quantitatively assessing tissue stiffness, akin to palpation. MRE is further able assess the mechanical properties of tissues that cannot be reached by hand including the brain. The technique is a three-step process beginning with the introduction of shear waves into the tissue of interest by applying an external vibration. Next, the resulting motion is imaged using a phase-contrast MR pulse sequence with motion encoding gradients that are synchronized to the vibration. Finally, the measured displacement images are mathematically inverted to compute a map of the estimated stiffness. In the brain, the technique has demonstrated strong test-retest repeatability with typical errors of 1% for measuring global stiffness, 2% for measuring stiffness in the lobes of the brain, and 3-7% for measuring stiffness in subcortical gray matter. In healthy volunteers, multiple studies have confirmed that stiffness decreases with age, while more recent studies have demonstrated a strong relationship between viscoelasticity and behavioral performance. Furthermore, several studies have demonstrated the sensitivity of brain stiffness to neurodegeneration, as stiffness has been shown to decrease in multiple sclerosis and in several forms of dementia. Moreover, the spatial pattern of stiffness changes varies among these different classes of dementia. Finally, MRE is a promising tool for the preoperative assessment of intracranial tumors, as it can measure both tumor consistency and adherence to surrounding tissues. These factors are important predictors of surgical difficulty. In brief, MRE demonstrates potential value in a number of neurological diseases. However, significant opportunity remains to further refine the technique and better understand the underlying physiology.

A Comparison of Finite Element-Based Inversion Algorithms, Local Frequency Estimation, and Direct Inversion Approach Used in MRE

In quantitative elastography, maps of the mechanical properties of soft tissue, or elastograms, are calculated from the measured displacement data by solving an inverse problem. The model assumptions have a significant effect on elastograms. Motivated by the high sensitivity of imaging results to the model assumptions for in vivo magnetic resonance elastography of the prostate, we compared elastograms obtained with four different methods. Two finite-element method (FEM)-based methods developed by our group were compared with two other commonly used methods, local frequency estimator (LFE) and curl-based direct inversion (c-DI). All the methods assume a linear isotropic elastic model, but the methods vary in their assumptions, such as local homogeneity or incompressibility, and in the specific approach used. We report results using simulations, phantom, and ex vivo and in vivo data. The simulation and phantom studies show, for regions with an inclusion, that the contrast to noise ratio (CNR) for the FEM methods is about three to five times higher than the CNR for the LFE and c-DI and the rms error is about half. The LFE method produces very smooth results (i.e., low CNR) and is fast. c-DI is faster than the FEM methods but it is only accurate in areas where elasticity variations are small. The artifacts resulting from the homogeneity assumption in c-DI is detrimental in regions with large variations. The ex vivo and in vivo results also show similar trends as the simulation and phantom studies. The c-FEM method is more sensitive to noise compared with the mixed-FEM due to higher orders derivatives. This is especially evident at lower frequencies, where the wave curvature is smaller and it is more prone to such error, causing a discrepancy in the absolute values between the mixed-FEM and c-FEM in our in vivo results. In general, the proposed FEMs use fewer simplifying assumptions and outperform the other methods but they are computationally more expensive.

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

Viscoelasticity of subcortical gray matter structures

Viscoelastic mechanical properties of the brain assessed with magnetic resonance elastography (MRE) are sensitive measures of microstructural tissue health in neurodegenerative conditions. Recent efforts have targeted measurements localized to specific neuroanatomical regions differentially affected in disease. In this work, we present a method for measuring the viscoelasticity in subcortical gray matter (SGM) structures, including the amygdala, hippocampus, caudate, putamen, pallidum, and thalamus. The method is based on incorporating high spatial resolution MRE imaging (1.6 mm isotropic voxels) with a mechanical inversion scheme designed to improve local measures in pre-defined regions (soft prior regularization [SPR]). We find that in 21 healthy, young volunteers SGM structures differ from each other in viscoelasticity, quantified as the shear stiffness and damping ratio, but also differ from the global viscoelasticity of the cerebrum. Through repeated examinations on a single volunteer, we estimate the uncertainty to be between 3 and 7% for each SGM measure. Furthermore, we demonstrate that the use of specific methodological considerations-higher spatial resolution and SPR-both decrease uncertainty and increase sensitivity of the SGM measures. The proposed method allows for reliable MRE measures of SGM viscoelasticity for future studies of neurodegenerative conditions. Hum Brain Mapp 37:4221-4233, 2016. © 2016 Wiley Periodicals, Inc.

Observation of direction-dependent mechanical properties in the human brain with multi-excitation MR elastography

Magnetic resonance elastography (MRE) has shown promise in noninvasively capturing changes in mechanical properties of the human brain caused by neurodegenerative conditions. MRE involves vibrating the brain to generate shear waves, imaging those waves with MRI, and solving an inverse problem to determine mechanical properties. Despite the known anisotropic nature of brain tissue, the inverse problem in brain MRE is based on an isotropic mechanical model. In this study, distinct wave patterns are generated in the brain through the use of multiple excitation directions in order to characterize the potential impact of anisotropic tissue mechanics on isotropic inversion methods. Isotropic inversions of two unique displacement fields result in mechanical property maps that vary locally in areas of highly aligned white matter. Investigation of the corpus callosum, corona radiata, and superior longitudinal fasciculus, three highly ordered white matter tracts, revealed differences in estimated properties between excitations of up to 33%. Using diffusion tensor imaging to identify dominant fiber orientation of bundles, relationships between estimated isotropic properties and shear asymmetry are revealed. This study has implications for future isotropic and anisotropic MRE studies of white matter tracts in the human brain.