Three-parameter shear wave inversion in MR elastography of incompressible transverse isotropic media: Application to in vivo lower leg muscles

Sex Differences in Aging-related Myocardial Stiffening Quantitatively Measured with MR Elastography

Purpose To investigate the feasibility of using quantitative MR elastography (MRE) to characterize the influence of aging and sex on left ventricular (LV) shear stiffness. Materials and Methods In this prospective study, LV myocardial shear stiffness was measured in 109 healthy volunteers (age range: 18-84 years; mean age, 40 years ± 18 [SD]; 57 women, 52 men) enrolled between November 2018 and September 2019, using a 5-minute MRE acquisition added to a clinical MRI protocol. Linear regression models were used to estimate the association of cardiac MRI and MRE characteristics with age and sex; models were also fit to assess potential age-sex interaction. Results Myocardial shear stiffness significantly increased with age in female (age slope = 0.03 kPa/year ± 0.01, P = .009) but not male (age slope = 0.008 kPa/year ± 0.009, P = .38) volunteers. LV ejection fraction (LVEF) increased significantly with age in female volunteers (0.23% ± 0.08 per year, P = .005). LV end-systolic volume (LVESV) decreased with age in female volunteers (-0.20 mL/m2 ± 0.07, P = .003). MRI parameters, including T1, strain, and LV mass, did not demonstrate this interaction (P > .05). Myocardial shear stiffness was not significantly correlated with LVEF, LV stroke volume, body mass index, or any MRI strain metrics (P > .05) but showed significant correlations with LV end-diastolic volume/body surface area (BSA) (slope = -3 kPa/mL/m2 ± 1, P = .004, r2 = 0.08) and LVESV/BSA (-1.6 kPa/mL/m2 ± 0.5, P = .003, r2 = 0.08). Conclusion This study demonstrates that female, but not male, individuals experience disproportionate LV stiffening with natural aging, and these changes can be noninvasively measured with MRE. Keywords: Cardiac, Elastography, Biological Effects, Experimental Investigations, Sexual Dimorphisms, MR Elastography, Myocardial Shear Stiffness, Quantitative Stiffness Imaging, Aging Heart, Myocardial Biomechanics, Cardiac MRE Supplemental material is available for this article. Published under a CC BY 4.0 license.

Explorative study using ultrasound time-harmonic elastography for stiffness-based quantification of skeletal muscle function

Time-harmonic elastography (THE) is an emerging ultrasound imaging technique that allows full-field mapping of the stiffness of deep biological tissues. THE's unique ability to rapidly capture stiffness in multiple tissues has never been applied for imaging skeletal muscle. Therefore, we addressed the lack of data on temporal changes in skeletal muscle stiffness while simultaneously covering stiffness of different muscles. Acquiring repeated THE scans every five seconds we quantified shear-wave speed (SWS) as a marker of stiffness of the long head (LHB) and short head (SHB) of biceps brachii and of the brachialis muscle (B) in ten healthy volunteers. SWS was continuously acquired during a 3-min isometric preloading phase, a 3-min loading phase with different weights (4, 8, and 12 kg), and a 9-min postloading phase. In addition, we analyzed temporal SWS standard deviation (SD) as a marker of muscle contraction regulation. Our results (median [min, max]) showed both SWS at preloading (LHB: 1.04 [0.94, 1.12] m/s, SHB: 0.86 [0.78, 0.94] m/s, B: 0.96 [0.87, 1.09] m/s, p < 0.001) and the increase in SWS with loading weight to be muscle-specific (LHB: 0.010 [0.002, 0.019] m/s/kg, SHB: 0.022 [0.017, 0.042] m/s/kg, B: 0.039 [0.019, 0.062] m/s/kg, p < 0.001). Additionally, SWS during loading increased continuously over time by 0.022 [0.004, 0.051] m/s/min (p < 0.01). Using an exponential decay model, we found an average relaxation time of 27 seconds during postloading. Analogously, SWS SD at preloading was also muscle-specific (LHB: 0.018 [0.011, 0.029] m/s, SHB: 0.021 [0.015, 0.027] m/s, B: 0.024 [0.018, 0.037] m/s, p < 0.05) and increased by 0.005 [0.003, 0.008] m/s/kg (p < 0.01) with loading. SWS SD did not change over loading time and decreased immediately in the postloading phase. Taken together, THE of skeletal muscle is a promising imaging technique for in vivo quantification of stiffness and stiffness changes in multiple muscle groups within seconds. Both the magnitude of stiffness changes and their temporal variation during isometric exercise may reflect the functional status of skeletal muscle and provide additional information to the morphological measures obtained by conventional imaging modalities.

In plane quantification ofin vivomuscle elastic anisotropy factor by steered ultrasound pushing beams

Objective.Skeletal muscles are organized into distinct layers and exhibit anisotropic characteristics across various scales. Assessing the arrangement of skeletal muscles may provide valuable biomarkers for diagnosing muscle-related pathologies and evaluating the efficacy of clinical interventions.Approach. In this study, we propose a novel ultrafast ultrasound sequence constituted of steered pushing beams was proposed for ultrasound elastography applications in transverse isotropic muscle. Based on the propagation of the shear wave vertical mode, it is possible to fit the experimental results to retrieve in the same imaging plane, the shear modulus parallel to fibers as well as the elastic anisotropy factor (ratio of Young's moduli times the shear modulus perpendicular to fibers).Main results. The technique was demonstratedin vitroin phantoms andex vivoin fusiform beef muscles. At last, the technique was appliedin vivoon fusiform muscles (biceps brachii) and mono-pennate muscles (gastrocnemius medialis) during stretching and contraction.Significance. This novel sequence provides access to new structural and mechanical biomarkers of muscle tissue, including the elastic anisotropy factor, within the same imaging plane. Additionally, it enables the investigation of multiples parameters during muscle active and passive length changes.

Rotational 3D shear wave elasticity imaging: Effect of knee flexion on 3D shear wave propagation in in vivo vastus lateralis

Skeletal muscle is a complex tissue, exhibiting not only direction-dependent material properties (commonly modeled as a transversely isotropic material), but also changes in observed material properties due to factors such as contraction and passive stretch. In this work, we evaluated the effect of muscle passive stretch on shear wave propagation along and across the muscle fibers using a rotational 3D shear wave elasticity imaging system and automatic analysis methods. We imaged the vastus lateralis of 10 healthy volunteers, modulating passive stretch by imaging at 8 different knee flexion angles (controlled by a BioDex system). In addition to demonstrating the ability of this acquisition and automatic processing system to estimate muscle shear moduli over a range of values, we evaluated potential higher order biomarkers for muscle health that capture the change in muscle stiffness along and across the fibers with changing knee flexion. The median within-subject variability of these biomarkers is found to be <16%, suggesting promise as a repeatable clinical metric. Additionally, we report an unexpected observation: that shear wave signal amplitude along the fibers increases with increasing flexion and muscle stiffness, which is not predicted by transversely isotropic (TI) material simulations. This observation may point to an additional potential biomarker for muscle health or inform other material modeling choices for muscle.

Individual Muscle Force Estimation in the Human Forearm Using Multi-Muscle MR Elastography (MM-MRE)

OBJECTIVE

To establish the sensitivity of magnetic resonance elastography (MRE) to active muscle contraction in multiple muscles of the forearm.

METHODS

We combined MRE of forearm muscles with an MRI-compatible device, the MREbot, to simultaneously measure the mechanical properties of tissues in the forearm and the torque applied by the wrist joint during isometric tasks. We measured shear wave speed of thirteen forearm muscles via MRE in a series of contractile states and wrist postures and fit these outputs to a force estimation algorithm based on a musculoskeletal model.

RESULTS

Shear wave speed changed significantly upon several factors, including whether the muscle was recruited as an agonist or antagonist (p = 0.0019), torque amplitude (p = <0.0001), and wrist posture (p = 0.0002). Shear wave speed increased significantly during both agonist (p = <0.0001) and antagonist (p = 0.0448) contraction. Additionally, there was a greater increase in shear wave speed at greater levels of loading. The variations due to these factors indicate the sensitivity to functional loading of muscle. Under the assumption of a quadratic relationship between shear wave speed and muscle force, MRE measurements accounted for an average of 70% of the variance in the measured joint torque.

CONCLUSION

This study shows the ability of MM-MRE to capture variations in individual muscle shear wave speed due to muscle activation and presents a method to estimate individual muscle force through MM-MRE derived measurements of shear wave speed.

SIGNIFICANCE

MM-MRE could be used to establish normal and abnormal muscle co-contraction patterns in muscles of the forearm controlling hand and wrist function.

Comparison of ultrasound elastography, magnetic resonance elastography and finite element model to quantify nonlinear shear modulus

Objective. The aim of this study is to validate the estimation of the nonlinear shear modulus (A) from the acoustoelasticity theory with two experimental methods, ultrasound (US) elastography and magnetic resonance elastography (MRE), and a finite element method.Approach. Experiments were performed on agar (2%)-gelatin (8%) phantom considered as homogeneous, elastic and isotropic. Two specific setups were built to ensure a uniaxial stress step by step on the phantom, one for US and a nonmagnetic version for MRE. The stress was controlled identically in both imaging techniques, with a water tank placed on the top of the phantom and filled with increasing masses of water during the experiment. In US, the supersonic shear wave elastography was implemented on an ultrafast US device, driving a 6 MHz linear array to measure shear wave speed. In MRE, a gradient-echo sequence was used in which the three spatial directions of a 40 Hz continuous wave displacement generated with an external driver were encoded successively. Numerically, a finite element method was developed to simulate the propagation of the shear wave in a uniaxially stressed soft medium.Main results. Similar shear moduli were estimated at zero stress using experimental methods,μ0US= 12.3 ± 0.3 kPa andμ0MRE= 11.5 ± 0.7 kPa. Numerical simulations were set with a shear modulus of 12 kPa and the resulting nonlinear shear modulus was found to be -58.1 ± 0.7 kPa. A very good agreement between the finite element model and the experimental models (AUS= -58.9 ± 9.9 kPa andAMRE= -52.8 ± 6.5 kPa) was obtained.Significance. These results show the validity of such nonlinear shear modulus measurement quantification in shear wave elastography. This work paves the way to develop nonlinear elastography technique to get a new biomarker for medical diagnosis.

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.

Transversely-isotropic brain in vivo MR elastography with anisotropic damping

Measuring tissue parameters from increasingly sophisticated mechanical property models may uncover new contrast mechanisms with clinical utility. Building on previous work on in vivo brain MR elastography (MRE) with a transversely-isotropic with isotropic damping (TI-ID) model, we explore a new transversely-isotropic with anisotropic damping (TI-AD) model that involves six independent parameters describing direction-dependent behavior for both stiffness and damping. The direction of mechanical anisotropy is determined by diffusion tensor imaging and we fit three complex-valued moduli distributions across the full brain volume to minimize differences between measured and modeled displacements. We demonstrate spatially accurate property reconstruction in an idealized shell phantom simulation, as well as an ensemble of 20 realistic, randomly-generated simulated brains. We characterize the simulated precisions of all six parameters across major white matter tracts to be high, suggesting that they can be measured independently with acceptable accuracy from MRE data. Finally, we present in vivo anisotropic damping MRE reconstruction data. We perform t-tests on eight repeated MRE brain exams on a single-subject, and find that the three damping parameters are statistically distinct for most tracts, lobes and the whole brain. We also show that population variations in a 17-subject cohort exceed single-subject measurement repeatability for most tracts, lobes and whole brain, for all six parameters. These results suggest that the TI-AD model offers new information that may support differential diagnosis of brain diseases.

In vivoestimation of anisotropic mechanical properties of the gastrocnemius during functional loading with MR elastography

Objective.In vivoimaging assessments of skeletal muscle structure and function allow for longitudinal quantification of tissue health. Magnetic resonance elastography (MRE) non-invasively quantifies tissue mechanical properties, allowing for evaluation of skeletal muscle biomechanics in response to loading, creating a better understanding of muscle functional health.Approach. In this study, we analyze the anisotropic mechanical response of calf muscles using MRE with a transversely isotropic, nonlinear inversion algorithm (TI-NLI) to investigate the role of muscle fiber stiffening under load. We estimate anisotropic material parameters including fiber shear stiffness (μ1), substrate shear stiffness (μ2), shear anisotropy (ϕ), and tensile anisotropy (ζ) of the gastrocnemius muscle in response to both passive and active tension.Main results. In passive tension, we found a significant increase inμ1,ϕ,andζwith increasing muscle length. While in active tension, we observed increasingμ2and decreasingϕandζduring active dorsiflexion and plantarflexion-indicating less anisotropy-with greater effects when the muscles act as agonist.Significance. The study demonstrates the ability of this anisotropic MRE method to capture the multifaceted mechanical response of skeletal muscle to tissue loading from muscle lengthening and contraction.

Mechanical behavior of the hippocampus and corpus callosum: An attempt to reconcile ex vivo with in vivo and micro with macro properties

Mechanical properties of brain tissue are very complex and vary with the species, region, method, and dynamic range, and between in vivo and ex vivo measurements. To reconcile this variability, we investigated in vivo and ex vivo stiffness properties of two distinct regions in the human and mouse brain - the hippocampus (HP) and the corpus callosum (CC) - using different methods. Under quasi-static conditions, we examined ex vivo murine HP and CC by atomic force microscopy (AFM). Between 16 and 40Hz, we investigated the in vivo brains of healthy volunteers by magnetic resonance elastography (MRE) in a 3-T clinical scanner. At high-frequency stimulation between 1000 and 1400Hz, we investigated the murine HP and CC ex vivo and in vivo with MRE in a 7-T preclinical system. HP and CC showed pronounced stiffness dispersion, as reflected by a factor of 32-36 increase in shear modulus from AFM to low-frequency human MRE and a 25-fold higher shear wave velocity in murine MRE than in human MRE. At low frequencies, HP was softer than CC, in both ex vivo mouse specimens (p < 0.05) and in vivo human brains (p < 0.01) while, at high frequencies, CC was softer than HP under in vivo (p < 0.01) and ex vivo (p < 0.05) conditions. The standard linear solid model comprising three elements reproduced the observed HP and CC stiffness dispersions, while other two- and three-element models failed. Our results indicate a remarkable consistency of brain stiffness across species, ex vivo and in vivo states, and different measurement techniques when marked viscoelastic dispersion properties combining equilibrium and non-equilibrium mechanical elements are considered.

Estimation of anisotropic properties of CMR patient-specific left ventricle using the virtual field method

Left ventricle (LV) myocardial dysfunction has been recently investigated using the estimation of isotropic myocardial stiffness from magnetic resonance imaging (MRI). However, Myocardium is known to have a 3D complex geometry with anisotropic stiffness. The assessment of the anisotropy properties characterizes structural changes in myocardium as a consequence of heart failure (HF). From image data, the virtual field method (VFM) can determine material stiffness in a non-invasive manner. In the present work, the objective is to compare two inverse identification methods, given the isotropic and anisotropic models in the characterization of properties of myocardium in acute lymphoblastic leukemia (ALL) survivors using VFM and MRI. Two types of VFM approach are presented. Using the first, the virtual displacements (VFs) allow whole-field LV to be imposed into VFM formulation and caused to directly estimate two independent parameters from isotropic constitutive relation. With the second, anisotropic parameters are estimated using piece-wise (Finite element-based) VFM. The resulting values showed significant differences between the subjects in comparative study of leukemia survivors, and variance in estimated parameters by two different VFM approach. This approach would be an efficient tool to characterize early cardiac dysfunction. This work elucidates the benefits and shortcomings of using VFM to determine anisotropic parameters of LV myocardium in linear elastic and of using the FEM application to generate meshes of patient-specific LVs from MRI images.

Fast acquisition of propagating waves in humans with low-field MRI: Toward accessible MR elastography

Most commonly used at clinical magnetic fields (1.5 to 3 T), magnetic resonance elastography (MRE) captures mechanical wave propagation to reconstruct the mechanical properties of soft tissue with MRI. However, in terms of noninvasively assessing disease progression in a broad range of organs (e.g., liver, breast, skeletal muscle, and brain), its accessibility is limited and its robustness is challenged when magnetic susceptibility differences are encountered. Low-field MRE offers an opportunity to overcome these issues, and yet it has never been demonstrated in vivo in humans with magnetic fields <1.5 T mainly because of the long acquisition times required to achieve a sufficient signal-to-noise ratio. Here, we describe a method to accelerate 3D motion-sensitized MR scans at 0.1 T using only 10% k-space sampling combined with a high-performance detector and an efficient encoding acquisition strategy. Its application is demonstrated in vivo in the human forearm for a single motion-encoding direction in less than 1 min.

Comparison of inversion methods in MR elastography: An open-access pipeline for processing multifrequency shear-wave data and demonstration in a phantom, human kidneys, and brain

PURPOSE

Magnetic resonance elastography (MRE) maps the viscoelastic properties of soft tissues for diagnostic purposes. However, different MRE inversion methods yield different results, which hinder comparison of values, standardization, and establishment of quantitative MRE markers. Here, we introduce an expandable, open-access, webserver-based platform that offers multiple inversion techniques for multifrequency, 3D MRE data.

METHODS

The platform comprises a data repository and standard MRE inversion methods including local frequency estimation (LFE), direct-inversion based multifrequency dual elasto-visco (MDEV) inversion, and wavenumber-based (k-) MDEV. The use of the platform is demonstrated in phantom data and in vivo multifrequency MRE data of the kidneys and brains of healthy volunteers.

RESULTS

Detailed maps of stiffness were generated by all inversion methods showing similar detail of anatomy. Specifically, the inner renal cortex had higher shear wave speed (SWS) than renal medulla and outer cortex without lateral differences. k-MDEV yielded higher SWS values than MDEV or LFE (full kidney/brain k-MDEV: 2.71 ± 0.19/1.45 ± 0.14 m/s, MDEV: 2.14 ± 0.16/0.99 ± 0.11 m/s, LFE: 2.12 ± 0.15/0.89 ± 0.06 m/s).

CONCLUSION

The freely accessible platform supports the comparison of MRE results obtained with different inversion methods, filter thresholds, or excitation frequencies, promoting reproducibility in MRE across community-developed methods.

Characterizing Musculoskeletal Tissue Mechanics Based on Shear Wave Propagation: A Systematic Review of Current Methods and Reported Measurements

Developing methods for the non-invasive characterization of the mechanics of musculoskeletal tissues is an ongoing research focus in biomechanics. Often, these methods use the speed of shear wave propagation to characterize tissue mechanics (e.g., shear wave elastography and shear wave tensiometry). The primary purpose of this systematic review was to identify, compare, and contrast current methods for exciting and measuring shear wave propagation in musculoskeletal tissues. We conducted searches in the Web of Science, PubMed, and Scopus databases for studies published from January 1, 1900, to May 1, 2020. These searches targeted both shear wave excitation using acoustic pushes and mechanical taps, and shear wave speed measurement using ultrasound, magnetic resonance imaging, accelerometers, and laser Doppler vibrometers. Two reviewers independently screened and reviewed the articles, identifying 524 articles that met our search criteria. Regarding shear wave excitation, we found that acoustic pushes are useful for exciting shear waves through the thickness of the tissue of interest, and mechanical taps are useful for exciting shear waves in wearable applications. Regarding shear wave speed measurement, we found that ultrasound is used most broadly to measure shear waves due to its ability to study regional differences and target specific tissues of interest. The strengths of magnetic resonance imaging, accelerometers, and laser Doppler vibrometers make them advantageous to measure shear wave speeds for high-resolution shear wave imaging, wearable measurements, and non-contact ex vivo measurements, respectively. The advantages that each method offers for exciting and measuring shear waves indicate that a variety of systems can be assembled using currently available technologies to determine musculoskeletal tissue material behavior across a range of innovative applications.

Full Characterization of in vivo Muscle as an Elastic, Incompressible, Transversely Isotropic Material Using Ultrasonic Rotational 3D Shear Wave Elasticity Imaging

Using a 3D rotational shear wave elasticity imaging (SWEI) setup, 3D shear wave data were acquired in the vastus lateralis of a healthy volunteer. The innate tilt between the transducer face and the muscle fibers results in the excitation of multiple shear wave modes, allowing for more complete characterization of muscle as an elastic, incompressible, transversely isotropic (ITI) material. The ability to measure both the shear vertical (SV) and shear horizontal (SH) wave speed allows for measurement of three independent parameters needed for full ITI material characterization: the longitudinal shear modulus μL , the transverse shear modulus μT , and the tensile anisotropy χE . Herein we develop and validate methodology to estimate these parameters and measure them in vivo, with μL = 5.77±1.00 kPa, μT = 1.93±0.41 kPa (giving shear anisotropy χμ = 2.11±0.92 ), and χE = 4.67±1.40 in a relaxed vastus lateralis muscle. We also demonstrate that 3D SWEI can be used to more accurately characterize muscle mechanical properties as compared to 2D SWEI.

Acoustoelasticity in transversely isotropic soft tissues: Quantification of muscle nonlinear elasticity

Recent developments in the field of elastography aim at developing the quantification of new mechanical properties of tissues, that are complementary to the shear modulus, which is characteristic of the linear elastic properties of a quasi-incompressible medium. In this context, measurement of the elastic nonlinearity of tissues was recently proposed based on acoustoelasticity. Up to now, most of the experimental applications of acoustoelasticity theory using Landau formalism in human tissues have assumed isotropy. However, this strong hypothesis does not hold in all human tissues, such as muscles that are generally considered as transversely isotropic (TI). In this work, after reviewing the constraints imposed by TI symmetry on the linear and nonlinear elastic properties of TI media, the acoustoelasticity theory in TI incompressible media is developed and implemented experimentally on a TI polyvinyl alcohol phantom and on ex vivo muscular tissues. Based on this theory and on the evolutions of the shear wave speed, with respect to uniaxial static stress, the nonlinear elastic parameter A is experimentally quantified. The estimations of A in ex vivo bovine and porcine muscles are on the order of hundreds of kPa. This work paves the way for more thorough muscle mechanical properties characterization as well as for the development of a potential new biomarker.

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.

Feasibility of Harmonic Motion Imaging Using a Single Transducer: In Vivo Imaging of Breast Cancer in a Mouse Model and Human Subjects

Harmonic motion imaging (HMI) interrogates the mechanical properties of tissues by simultaneously generating and tracking harmonic oscillation using focused ultrasound and imaging transducers, respectively. Instead of using two transducers, the objective of this work is to develop a single transducer HMI (ST-HMI) to both generate and track harmonic motion at "on-axis" to the force for facilitating data acquisition. In ST-HMI, the amplitude-modulated force was generated by modulating excitation pulse duration and tracking of motion was performed by transmitting tracking pulses interleaved between excitation pulses. The feasibility of ST-HMI was performed by imaging two elastic phantoms with three inclusions (N = 6) and comparing it with acoustic radiation force impulse (ARFI) imaging, in vivo longitudinal monitoring of 4T1, orthotropic breast cancer mice (N = 4), and patients (N = 3) with breast masses in vivo. Six inclusions with Young's moduli of 8, 10, 15, 20, 40, and 60 kPa were embedded in a 5 kPa background. The ST-HMI-derived peak-to-peak displacement (P2PD) successfully detected all inclusions with [Formula: see text] of the linear regression between the P2PD ratio of background to inclusion versus Young's moduli ratio of inclusion to background. The contrasts of 10 and 15 kPa inclusions were higher in ST-HMI than ARFI-derived images. In the mouse study, the median P2PD ratio of tumor to non-cancerous tissues was 3.0, 5.1, 6.1, and 7.7 at 1, 2, 3, and 4 weeks post-injection of the tumor cells, respectively. In the clinical study, ST-HMI detected breast masses including fibroadenoma, pseudo angiomatous stromal hyperplasia, and invasive ductal carcinoma with a P2PD ratio of 1.37, 1.61, and 1.78, respectively. These results indicate that ST-HMI can assess the mechanical properties of tissues via generation and tracking of harmonic motion "on-axis" to the ARF. This study is the first step towards translating ST-HMI in clinics.

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.

Enhanced complex local frequency elastography method for tumor viscoelastic shear modulus reconstruction

BACKGROUND AND OBJECTIVES

The Mayo Clinic provides a magnetic resonance (MR) elastography software named MRE Wave, which uses the conventional local frequency elastography (LFE) method. However, MRE Wave is unable to supply complex viscoelasticity maps for elastography. We sought to improve the local frequency estimation algorithm used in LFE, which we refer to as the Enhanced Complex Local Frequency Elastography (EC-LFE) algorithm.

METHODS

The proposed algorithm uses wave equations under the hypotheses of being linear, isotropic, and locally homogeneous. Two 2D simulation models were used to investigate the accuracy and sensitivity of the EC-LFE algorithm for detecting small tumors. The corresponding statistical parameters were the relative root mean square (RMS) error and contrast-to-noise ratio (CNR). EC-LFE was investigated with two different parameter sets, one with an optimally chosen parameter ξ (EC-LFE Adj, for short) and the other with ξ = 0 (EC-LFE0). We compared the MRE Wave and the EC-LFE using series signal-to-noise (SNR) wave data.

RESULTS

The elasticity RMS error of the MRE Wave software was about 1%, and that of the EC-LFE0 and EC-LFE Adj were about 0.2%. The elasticity standard deviation of the MRE Wave software was about 3% of the mean value, and those of the EC-LFE0 and EC-LFE Adj were about 1% of the mean value. The elasticity CNR value of EC-LFE0 reached 1.93 times that of the MRE Wave in the region of small tumors (less than 10-point sampling). The viscosity RMS errors of the EC-LFE0 could be less than 5%.

CONCLUSION

Compared to conventional methods, the EC-LFE was more accurate and sensitive for small tumor detection and exhibited higher noise immunity. The improved algorithm output more parameters and outperformed than the MRE Wave, thereby rendering them more suitable for clinical applications.

Requirements for accurate estimation of shear modulus by magnetic resonance elastography: A computational comparative study

BACKGROUND

Magnetic resonance (MR) elastography is a non-destructive method of measuring biological tissue and is conducive to the early detection of tumors. Researchers usually set different assumptions according to different research objects, then establish and solve wave equations to estimate the shear modulus. Establishing a more reasonable model for a measured object estimates a more accurate shear modulus. Different assumptions of the mathematical model, and the method used to solve the wave equation causes deviation of the estimation.

OBJECTIVE

This study focused on shear modulus deviations caused by differences in calculation methods. The author demonstrated a method to ensure that the measuring range of the selected reconstruction algorithm with selected drive frequency covers the elasticity range of the target tissue. It is hoped to arouse the interest of researchers to introduce new transform domain methods to the field of MR elastography.

METHOD

In linear, isotropic and local homogeneity assumptions, the typical representative of two different calculation methods are algebraic inversion of the differential equation (AIDE) algorithm and local frequency elastography (LFE) algorithm. To compare the accuracy of these calculation methods, the author adopted a digital phantom that can set the parameter values accurately. It is assumed that the phantom tissue was linear and isotropic, and that the driving wave was sinusoidal. The displacement distribution of waves in the tissue was calculated by the finite element simulation method in two different resolutions with the signal-to-noise ratio (SNR) set to 40 dB and the threshold of relative mean error (RME) no more than 10%. The wavelength-to-pixel-size ratios of the two methods under the setting threshold of RME were compared.

RESULTS

The lower threshold of wavelength-to-pixel-size ratio for AIDE was close to 10, while that for LFE was nearly 2 (the limitation of Shannon's law) under the setting precision. Thus, the measuring range of the AIDE method was less than that of LFE at the same experimental conditions.

CONCLUSION

The driving frequency selection range of the spatial frequency domain method is wider than that of the spatial domain method. It is worthwhile for researchers to devote more time to introducing new transformation domain method for MR elastography.

Multi-Excitation Magnetic Resonance Elastography of the Brain: Wave Propagation in Anisotropic White Matter

Magnetic resonance elastography (MRE) has emerged as a sensitive imaging technique capable of providing a quantitative understanding of neural microstructural integrity. However, a reliable method for the quantification of the anisotropic mechanical properties of human white matter is currently lacking, despite the potential to illuminate the pathophysiology behind neurological disorders and traumatic brain injury. In this study, we examine the use of multiple excitations in MRE to generate wave displacement data sufficient for anisotropic inversion in white matter. We show the presence of multiple unique waves from each excitation which we combine to solve for parameters of an incompressible, transversely isotropic (ITI) material: shear modulus, μ, shear anisotropy, ϕ, and tensile anisotropy, ζ. We calculate these anisotropic parameters in the corpus callosum body and find the mean values as μ = 3.78 kPa, ϕ = 0.151, and ζ = 0.099 (at 50 Hz vibration frequency). This study demonstrates that multi-excitation MRE provides displacement data sufficient for the evaluation of the anisotropic properties of white matter.

Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material

This paper describes the propagation of shear waves in a Holzapfel-Gasser-Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (μ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

Exploration of New Contrasts, Targets, and MR Imaging and Spectroscopy Techniques for Neuromuscular Disease - A Workshop Report of Working Group 3 of the Biomedicine and Molecular Biosciences COST Action BM1304 MYO-MRI

Neuromuscular diseases are characterized by progressive muscle degeneration and muscle weakness resulting in functional disabilities. While each of these diseases is individually rare, they are common as a group, and a large majority lacks effective treatment with fully market approved drugs. Magnetic resonance imaging and spectroscopy techniques (MRI and MRS) are showing increasing promise as an outcome measure in clinical trials for these diseases. In 2013, the European Union funded the COST (co-operation in science and technology) action BM1304 called MYO-MRI (www.myo-mri.eu), with the overall aim to advance novel MRI and MRS techniques for both diagnosis and quantitative monitoring of neuromuscular diseases through sharing of expertise and data, joint development of protocols, opportunities for young researchers and creation of an online atlas of muscle MRI and MRS. In this report, the topics that were discussed in the framework of working group 3, which had the objective to: Explore new contrasts, new targets and new imaging techniques for NMD are described. The report is written by the scientists who attended the meetings and presented their data. An overview is given on the different contrasts that MRI can generate and their application, clinical needs and desired readouts, and emerging methods.

Magnetic resonance elastography (MRE) shows significant reduction of thigh muscle stiffness in healthy older adults

Determining the effect of ageing on thigh muscle stiffness using magnetic resonance elastography (MRE) and investigate whether fat fraction and muscle cross-sectional area (CSA) are related to stiffness. Six healthy older adults in their eighth and ninth decade and eight healthy young men were recruited and underwent a 3 T MRI protocol including MRE and Dixon fat fraction imaging. Muscle stiffness, fat fraction and muscle CSA were calculated in ROIs corresponding to the four quadriceps muscles (i.e. vastus lateralis (VL), vastus medialis (VM), vastus intermedius (VI), rectus femoris (RF)), combined quadriceps, combined hamstrings and adductors and whole thigh. Muscle stiffness was significantly reduced (p < 0.05) in the older group in all measured ROIs except the VI (p = 0.573) and RF (p = 0.081). Similarly, mean fat fraction was significantly increased (p < 0.05) in the older group over all ROIs with the exception of the VI (p = 0.059) and VL muscle groups (p = 0.142). Muscle CSA was significantly reduced in older participants in the VM (p = 0.003) and the combined quadriceps (p = 0.001), hamstrings and adductors (p = 0.008) and whole thigh (p = 0.003). Over the whole thigh, stiffness was significantly negatively correlated with fat fraction (r = − 0.560, p = 0.037) and positively correlated with CSA (r = 0.749, p = 0.002). Stepwise regression analysis revealed that age was the most significant predictor of muscle stiffness (p = 0.001). These results suggest that muscle stiffness is significantly decreased in healthy older adults. Muscle fat fraction and muscle CSA are also significantly changed in older adults; however, age is the most significant predictor of muscle stiffness.

Magnetic resonance elastography of skeletal muscle deep tissue injury

The current state-of-the-art diagnosis method for deep tissue injury in muscle, a subcategory of pressure ulcers, is palpation. It is recognized that deep tissue injury is frequently preceded by altered biomechanical properties. A quantitative understanding of the changes in biomechanical properties preceding and during deep tissue injury development is therefore highly desired. In this paper we quantified the spatial-temporal changes in mechanical properties upon damage development and recovery in a rat model of deep tissue injury. Deep tissue injury was induced in nine rats by two hours of sustained deformation of the tibialis anterior muscle. Magnetic resonance elastography (MRE), T₂ -weighted, and T₂ -mapping measurements were performed before, directly after indentation, and at several timepoints during a 14-day follow-up. The results revealed a local hotspot of elevated shear modulus (from 3.30 ± 0.14 kPa before to 4.22 ± 0.90 kPa after) near the center of deformation at Day 0, whereas the T₂ was elevated in a larger area. During recovery there was a clear difference in the time course of the shear modulus and T₂ . Whereas T₂ showed a gradual normalization towards baseline, the shear modulus dropped below baseline from Day 3 up to Day 10 (from 3.29 ± 0.07 kPa before to 2.68 ± 0.23 kPa at Day 10, P < 0.001), followed by a normalization at Day 14. In conclusion, we found an initial increase in shear modulus directly after two hours of damage-inducing deformation, which was followed by decreased shear modulus from Day 3 up to Day 10, and subsequent normalization. The lower shear modulus originates from the moderate to severe degeneration of the muscle. MRE stiffness values were affected in a smaller area as compared with T₂ . Since T₂ elevation is related to edema, distributing along the muscle fibers proximally and distally from the injury, we suggest that MRE is more specific than T₂ for localization of the actual damaged area.

Analytical solution for converging elliptic shear wave in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary

Dynamic elastography methods-based on optical, ultrasonic, or magnetic resonance imaging-are being developed for quantitatively mapping the shear viscoelastic properties of biological tissues, which are often altered by disease and injury. These diagnostic imaging methods involve analysis of shear wave motion in order to estimate or reconstruct the tissue's shear viscoelastic properties. Most reconstruction methods to date have assumed isotropic tissue properties. However, application to tissues like skeletal muscle and brain white matter with aligned fibrous structure resulting in local transverse isotropic mechanical properties would benefit from analysis that takes into consideration anisotropy. A theoretical approach is developed for the elliptic shear wave pattern observed in transverse isotropic materials subjected to axisymmetric excitation creating radially converging shear waves normal to the fiber axis. This approach, utilizing Mathieu functions, is enabled via a transformation to an elliptic coordinate system with isotropic properties and a ratio of minor and major axes matching the ratio of shear wavelengths perpendicular and parallel to the plane of isotropy in the transverse isotropic material. The approach is validated via numerical finite element analysis case studies. This strategy of coordinate transformation to equivalent isotropic systems could aid in analysis of other anisotropic tissue structures.

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).

Anisotropic composite material phantom to improve skeletal muscle characterization using magnetic resonance elastography

The presence and progression of neuromuscular pathology, including spasticity, Duchenne's muscular dystrophy and hyperthyroidism, has been correlated with changes in the intrinsic mechanical properties of skeletal muscle tissue. Tools for noninvasively measuring and monitoring these properties, such as Magnetic Resonance Elastography (MRE), could benefit basic research into understanding neuromuscular pathologies, as well as translational research to develop therapies, by providing a means of assessing and tracking their efficacy. Dynamic elastography methods for noninvasive measurement of tissue mechanical properties have been under development for nearly three decades. Much of the technological development to date, for both Ultrasound (US)-based and Magnetic Resonance Imaging (MRI)-based strategies, has been grounded in assumptions of local homogeneity and isotropy. Striated skeletal and cardiac muscle, as well as brain white matter and soft tissue in some other organ regions, exhibit a fibrous microstructure which entails heterogeneity and anisotropic response; as one seeks to improve the accuracy and resolution in mechanical property assessment, heterogeneity and anisotropy need to be accounted for in order to optimize both the dynamic elastography experimental protocol and the interpretation of the measurements. Advances in elastography methodology at every step have been aided by the use of tissue-mimicking phantoms. The aim of the present study was to develop and characterize a heterogeneous composite phantom design with uniform controllable anisotropic properties meant to be comparable to the frequency-dependent anisotropic properties of skeletal muscle. MRE experiments and computational finite element (FE) studies were conducted on a novel 3D-printed composite phantom design. The displacement maps obtained from simulation and experiment show the same elliptical shaped wavefronts elongated in the plane where the structure presents higher shear modulus. The model exhibits a degree of anisotropy in line with literature data from skeletal muscle tissue MRE experiments. FE simulations of the MRE experiments provide insight into proper interpretation of experimental measurements, and help to quantify the importance of heterogeneity in the anisotropic material at different scales.

Estimation of transversely isotropic material properties from magnetic resonance elastography using the optimised virtual fields method

Magnetic resonance elastography (MRE) has been used to estimate isotropic myocardial stiffness. However, anisotropic stiffness estimates may give insight into structural changes that occur in the myocardium as a result of pathologies such as diastolic heart failure. The virtual fields method (VFM) has been proposed for estimating material stiffness from image data. This study applied the optimised VFM to identify transversely isotropic material properties from both simulated harmonic displacements in a left ventricular (LV) model with a fibre field measured from histology as well as isotropic phantom MRE data. Two material model formulations were implemented, estimating either 3 or 5 material properties. The 3-parameter formulation writes the transversely isotropic constitutive relation in a way that dissociates the bulk modulus from other parameters. Accurate identification of transversely isotropic material properties in the LV model was shown to be dependent on the loading condition applied, amount of Gaussian noise in the signal, and frequency of excitation. Parameter sensitivity values showed that shear moduli are less sensitive to noise than the other parameters. This preliminary investigation showed the feasibility and limitations of using the VFM to identify transversely isotropic material properties from MRE images of a phantom as well as simulated harmonic displacements in an LV geometry.

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.

Assessing the mechanical properties of anisotropic soft tissues using guided wave elastography: Inverse method and numerical experiments

Determining the mechanical properties of soft biological tissues can be of great importance. For example, the microstructures of many soft tissues, such as those of the human Achilles tendon, have been identified as typical anisotropic materials. This paper proposes an inverse approach that uses guided wave elastography to determine the anisotropic elastic and hyperelastic parameters of thin-walled transversely isotropic biological soft tissues. This approach was developed from the theoretical solutions for the dispersion relations of guided waves, which were derived based on a constitutive model suitable for describing the deformation behavior of such tissues. The properties of these solutions were investigated; in particular, sensitivity to data errors was addressed by introducing the concept of the condition number. To further validate the proposed inverse approach, the guided wave elastography of thin-walled transversely isotropic soft tissues was investigated using numerical experiments. The results indicated that the four constitutive parameters (other than the tensile modulus along the direction of the fibers, E_L) could be determined with a good level of accuracy using this method.

Mechanics of ultrasound elastography

Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.

MR elastography measurement of the effect of passive warmup prior to eccentric exercise on thigh muscle mechanical properties

Purpose

To investigate the effect of warmup by application of the thermal agent Deep Heat (DH) on muscle mechanical properties using magnetic resonance elastography (MRE) at 3T before and after exercise‐induced muscle damage (EIMD).

Materials and Methods

Twenty male participants performed an individualized protocol designed to induce EIMD in the quadriceps. DH was applied to the thigh in 50% of the participants before exercise. MRE, T₂‐weighted MRI, maximal voluntary contraction (MVC), creatine kinase (CK) concentration, and muscle soreness were measured before and after the protocol to assess EIMD effects. Five participants were excluded: four having not experienced EIMD and one due to incidental findings.

Results

Total workload performed during the EIMD protocol was greater in the DH group than the control group (P < 0.03), despite no significant differences in baseline MVC (P = 0.23). Shear stiffness |G*| increased in the rectus femoris (RF) muscle in both groups (P < 0.03); however, DH was not a significant between‐group factor (P =  0.15). MVC values returned to baseline faster in the DH group (5 days) than the control group (7 days). Participants who displayed hyperintensity on T₂‐weighted images had a greater stiffness increase following damage than those without: RF; 0.61 kPa vs. 0.15 kPa, P < 0.006, vastus intermedius; 0.34 kPa vs. 0.03 kPa, P = 0.06.

Conclusion

EIMD produces increased muscle stiffness as measured by MRE, with the change in |G*| significantly increased when T₂ hyperintensity was present. DH did not affect CK concentration or soreness; however, DH participants produced greater workload during the EIMD protocol and exhibited accelerated MVC recovery.

Level of Evidence: 1

Technical Efficacy: Stage 2

J. Magn. Reson. Imaging 2017;46:1115–1127.

Requirements for accurate estimation of anisotropic material parameters by magnetic resonance elastography: A computational study

PURPOSE

To establish the essential requirements for characterization of a transversely isotropic material by magnetic resonance elastography (MRE).

THEORY AND METHODS

Three methods for characterizing nearly incompressible, transversely isotropic (ITI) materials were used to analyze data from closed-form expressions for traveling waves, finite-element (FE) simulations of waves in homogeneous ITI material, and FE simulations of waves in heterogeneous material. Key properties are the complex shear modulus μ₂ , shear anisotropy ϕ=μ1/μ2-1, and tensile anisotropy ζ=E1/E2-1.

RESULTS

Each method provided good estimates of ITI parameters when both slow and fast shear waves with multiple propagation directions were present. No method gave accurate estimates when the displacement field contained only slow shear waves, only fast shear waves, or waves with only a single propagation direction. Methods based on directional filtering are robust to noise and include explicit checks of propagation and polarization. Curl-based methods led to more accurate estimates in low noise conditions. Parameter estimation in heterogeneous materials is challenging for all methods.

CONCLUSIONS

Multiple shear waves, both slow and fast, with different propagation directions, must be present in the displacement field for accurate parameter estimates in ITI materials. Experimental design and data analysis can ensure that these requirements are met. Magn Reson Med 78:2360-2372, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Magnetic resonance elastography of slow and fast shear waves illuminates differences in shear and tensile moduli in anisotropic tissue

Mechanical anisotropy is an important property of fibrous tissues; for example, the anisotropic mechanical properties of brain white matter may play a key role in the mechanics of traumatic brain injury (TBI). The simplest anisotropic material model for small deformations of soft tissue is a nearly incompressible, transversely isotropic (ITI) material characterized by three parameters: minimum shear modulus (µ), shear anisotropy (ϕ=µ1µ-1) and tensile anisotropy (ζ=E1E2-1). These parameters can be determined using magnetic resonance elastography (MRE) to visualize shear waves, if the angle between the shear-wave propagation direction and fiber direction is known. Most MRE studies assume isotropic material models with a single shear (µ) or tensile (E) modulus. In this study, two types of shear waves, "fast" and "slow", were analyzed for a given propagation direction to estimate anisotropic parameters µ, ϕ, and ζ in two fibrous soft materials: turkey breast ex vivo and aligned fibrin gels. As expected, the speed of slow shear waves depended on the angle between fiber direction and propagation direction. Fast shear waves were observed when the deformations due to wave motion induced stretch in the fiber direction. Finally, MRE estimates of anisotropic mechanical properties in turkey breast were compared to estimates from direct mechanical tests.

Estimation of material parameters from slow and fast shear waves in an incompressible, transversely isotropic material

This paper describes a method to estimate mechanical properties of soft, anisotropic materials from measurements of shear waves with specific polarization and propagation directions. This method is applicable to data from magnetic resonance elastography (MRE), which is a method for measuring shear waves in live subjects or in vitro samples. Here, we simulate MRE data using finite element analysis. A nearly incompressible, transversely isotropic (ITI) material model with three parameters (shear modulus, shear anisotropy, and tensile anisotropy) is used, which is appropriate for many fibrous, biological tissues. Both slow and fast shear waves travel concurrently through such a material with speeds that depend on the propagation direction relative to fiber orientation. A three-parameter estimation approach based on directional filtering and isolation of slow and fast shear wave components (directional filter inversion, or DFI) is introduced. Wave speeds of each isolated shear wave component are estimated using local frequency estimation (LFE), and material properties are calculated using weighted least squares. Data from multiple finite element simulations are used to assess the accuracy and reliability of DFI for estimation of anisotropic material parameters.