Magnetic resonance elastography: A review

Magnetic resonance elastography (MRE) is a rapidly developing technology for quantitatively assessing the mechanical properties of tissue. The technology can be considered to be an imaging‐based counterpart to palpation, commonly used by physicians to diagnose and characterize diseases. The success of palpation as a diagnostic method is based on the fact that the mechanical properties of tissues are often dramatically affected by the presence of disease processes, such as cancer, inflammation, and fibrosis. MRE obtains information about the stiffness of tissue by assessing the propagation of mechanical waves through the tissue with a special magnetic resonance imaging technique. The technique essentially involves three steps: (1) generating shear waves in the tissue, (2) acquiring MR images depicting the propagation of the induced shear waves, and (3) processing the images of the shear waves to generate quantitative maps of tissue stiffness, called elastograms. MRE is already being used clinically for the assessment of patients with chronic liver diseases and is emerging as a safe, reliable, and noninvasive alternative to liver biopsy for staging hepatic fibrosis. MRE is also being investigated for application to pathologies of other organs including the brain, breast, blood vessels, heart, kidneys, lungs, and skeletal muscle. The purpose of this review article is to introduce this technology to clinical anatomists and to summarize some of the current clinical applications that are being pursued. Clin. Anat. 23:497–511, 2010. © 2010 Wiley‐Liss, Inc.     

Vibration safety limits for magnetic resonance elastography

Magnetic resonance elastography (MRE) has been demonstrated to have potential as a clinical tool for assessing the stiffness of tissue in vivo. An essential step in MRE is the generation of acoustic mechanical waves within a tissue via a coupled mechanical driver. Motivated by an increasing volume of human imaging trials using MRE, the objectives of this study were to audit the vibration amplitude of exposure for our IRB-approved human MRE studies, to compare these values to a conservative regulatory standard for vibrational exposure and to evaluate the applicability and implications of this standard for MRE. MRE displacement data were examined from 29 MRE exams, including the liver, brain, kidney, breast and skeletal muscle. Vibrational acceleration limits from a European Union directive limiting occupational exposure to whole-body and extremity vibrations (EU 2002/44/EC) were adjusted for time and frequency of exposure, converted to maximum displacement values and compared to the measured in vivo displacements. The results indicate that the vibrational amplitudes used in MRE studies are below the EU whole-body vibration limit, and the EU guidelines represent a useful standard that could be readily accepted by Institutional Review Boards to define standards for vibrational exposures for MRE studies in humans.     

磁共振弹性成像的初步实验研究

目的：研究磁共振弹性成像（MRE）技术。方法：研制外部激发装置，设计成像脉冲序列，制作模拟人体软组织的体模。激发装置由序列控制，于体模表面产生低频率剪切波。脉冲序列采用梯度回波序列，在x、y或z轴上施加运动敏感梯度（MSG）。剪切波导致的介质内的周期性移位可使接收信号产生周期性相位位移，从测得的相位位移就能计算出每个体素的移位值，直接显示介质内剪切波的传播。通过调整相位偏置，获得一个完整周期内剪切波的动态传播图像。相位图经局部频率估算法（LFE）处理后计算出量化的弹性模景图。实验采用浓度为1．0％和1．5％不同弹性的琼脂凝胶体模，激发频率分别采用150Hz、200Hz、250Hz和300Hz。结果：MRE的相位图显示了剪切波在体模内的传播，剪切波的波长随激发频率和体模弹性变化。波长与激发频率呈反比，与体模弹性呈正比。剪切波的波长在不同激发频率和不同浓度体模之间呈严格的比例关系。计算出的弹性模量图清楚显示了两种浓度介质的弹性对比。结论：MRE的相位图可显示剪切波在介质内的传播，弹性图可量化和显示介质的弹性模量。     

Three-dimensional analysis of shear wave propagation observed by in vivo magnetic resonance elastography of the brain

Dynamic magnetic resonance elastography (MRE) is a non-invasive method for the quantitative determination of the mechanical properties of soft tissues in vivo. In MRE, shear waves are generated in the tissue and visualized using phase-sensitive MR imaging methods. The resulting two-dimensional (2-D) wave images can reveal in-plane elastic properties when possible geometrical biases of the wave patterns are taken into account. In this study, 3-D MRE experiments of in vivo human brain are analyzed to gain knowledge about the direction of wave propagation and to deduce in-plane elastic properties. The direction of wave propagation was determined using a new algorithm which identifies minimal wave velocities along rays from the surface into the brain. It was possible to quantify biases of the elastic parameters due to projections onto coronal, sagittal and transversal image planes in 2-D MRE. It was found that the in-plane shear modulus is increasingly overestimated when the image slice is displaced from narrow slabs of 2-5cm through the center of the brain. The mean shear modulus of the brain was deduced from 4-D wave data with about 3.5kPa. Using the proposed slice positions in 2-D MRE, this shear modulus can be reproduced with an acceptable error within a fraction of the full 3-D examination time.     

Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticity

A novel quantitative sonoelastography technique for assessing the viscoelastic properties of skeletal muscle tissue was developed. Slowly propagating shear wave interference patterns (termed crawling waves) were generated using a two-source configuration vibrating normal to the surface. Theoretical models predict crawling wave displacement fields, which were validated through phantom studies. In experiments, a viscoelastic model was fit to dispersive shear wave speed sonoelastographic data using nonlinear least-squares techniques to determine frequency-independent shear modulus and viscosity estimates. Shear modulus estimates derived using the viscoelastic model were in agreement with that obtained by mechanical testing on phantom samples. Preliminary sonoelastographic data acquired in healthy human skeletal muscles confirm that high-quality quantitative elasticity data can be acquired in vivo. Studies on relaxed muscle indicate discernible differences in both shear modulus and viscosity estimates between different skeletal muscle groups. Investigations into the dynamic viscoelastic properties of (healthy) human skeletal muscles revealed that voluntarily contracted muscles exhibit considerable increases in both shear modulus and viscosity estimates as compared to the relaxed state. Overall, preliminary results are encouraging and quantitative sonoelastography may prove clinically feasible for in vivo characterization of the dynamic viscoelastic properties of human skeletal muscle.     

Magnetic resonance elastography of the lungs: A repeatability and reproducibility study

Lung diseases are one of the leading causes of death worldwide, from which four million people die annually. Lung diseases are associated with changes in the mechanical properties of the lungs. Several studies have shown the feasibility of using magnetic resonance elastography (MRE) to quantify the lungs' shear stiffness. The aim of this study is to investigate the reproducibility and repeatability of lung MRE, and its shear stiffness measurements, obtained using a modified spin echo‐echo planar imaging (SE‐EPI) MRE sequence. In this study, 21 healthy volunteers were scanned twice by repositioning the volunteers to image right lung both at residual volume (RV) and total lung capacity (TLC) to assess the reproducibility of lung shear stiffness measurements. Additionally, 19 out of the 21 volunteers were scanned immediately without moving the volunteers to test the repeatability of the modified SE‐EPI MRE sequence. A paired t‐test was performed to determine the significant difference between stiffness measurements obtained at RV and TLC. Concordance correlation and Bland–Altman's analysis were performed to determine the reproducibility and repeatability of the SE‐EPI MRE‐derived shear stiffness measurements. The SE‐EPI MRE sequence is highly repeatable with a concordance correlation coefficient (CCC) of 0.95 at RV and 0.96 at TLC. Similarly, the stiffness measurements obtained across all volunteers were highly reproducible with a CCC of 0.95 at RV and 0.92 at TLC. The mean shear stiffness of the lung at RV was 0.93 ± 0.22 kPa and at TLC was 1.41 ± 0.41 kPa. TLC showed a significantly higher mean shear stiffness (P = 0.0004) compared with RV. Lung MRE stiffness measurements obtained using the SE‐EPI sequence were reproducible and repeatable, both at RV and TLC. Lung shear stiffness changes across respiratory cycle with significantly higher stiffness at TLC than RV.     

In vivo elasticity measurements of extremity skeletal muscle with MR elastography

MR elastography (MRE) has been shown to be capable of non-invasively measuring tissue elasticity even in deep-lying regions. Although limited studies have already been published examining in vivo muscle elasticity, it is still not clear over what range the in vivo elasticity values vary. The present study intends to produce further information by examining four different skeletal muscles in a group of 12 healthy volunteers in the age range of 27-38 years. The examinations were performed in the biceps brachii, the flexor digitorum profundus, the soleus and the gastrocnemius. The average shear modulus was determined to be 17.9 (+/- 5.5), 8.7 (+/- 2.8), 12.5 (+/- 7.3) and 9.9 (+/- 6.8) kPa for each muscle, respectively. To ascertain the reproducibility of the examination, the stiffness measurements in two volunteers were repeated seven times for the biceps brachii. These examinations yielded a mean shear modulus of 11.3 +/-.7 and 13.3 +/- 4.7 kPa for the two subjects. For elasticity reconstruction, an automated reconstruction algorithm is introduced which eliminates variation due to subjective manual image analysis. This study yields new information regarding the expected variation in muscle elasticity in a healthy population, and also reveals the expected variability of the MRE technique in skeletal muscle.     

Frequency-dependent viscoelastic parameters of mouse brain tissue estimated by MR elastography

Viscoelastic properties of mouse brain tissue were estimated non-invasively, in vivo, using magnetic resonance elastography (MRE) at 4.7 T to measure the dispersive properties of induced shear waves. Key features of this study include (i) the development and application of a novel MR-compatible actuation system which transmits vibratory motion into the brain through an incisor bar, and (ii) the investigation of the mechanical properties of brain tissue over a 1200 Hz bandwidth from 600-1800 Hz. Displacement fields due to propagating shear waves were measured during continuous, harmonic excitation of the skull. This protocol enabled characterization of the true steady-state patterns of shear wave propagation. Analysis of displacement fields obtained at different frequencies indicates that the viscoelastic properties of mouse brain tissue depend strongly on frequency. The average storage modulus (G') increased from approximately 1.6 to 8 kPa over this range; average loss modulus (G″) increased from approximately 1 to 3 kPa. Both moduli were well approximated by a power-law relationship over this frequency range. MRE may be a valuable addition to studies of disease in murine models, and to pre-clinical evaluations of therapies. Quantitative measurements of the viscoelastic parameters of brain tissue at high frequencies are also valuable for modeling and simulation of traumatic brain injury.     

Magnetic Resonance Elastography of kidneys: SE‐EPI MRE reproducibility and its comparison to GRE MRE

The purpose of this study is 1) to demonstrate reproducibility of spin echo‐echo planar imaging (SE‐EPI) magnetic resonance elastography (MRE) to estimate kidney stiffness; and 2) to compare SE‐EPI MRE and gradient recalled echo (GRE) MRE‐derived stiffness estimations in various anatomical regions of the kidney. Kidney MRE was performed on 33 healthy subjects (8 for SE‐EPI MRE reproducibility and 25 for comparison with GRE MRE; age range: 22–66 years) in a 3 T MRI scanner. To demonstrate SE‐EPI MRE reproducibility, subjects were scanned for the first scan and then asked to leave the scan room and repositioned again for the second (repeat) scan. Similar set‐up was used for GRE MRE as well. The displacement data was then processed to obtain overall stiffness estimates of the kidney. Concordance correlation analyses were performed to determine SE‐EPI MRE reproducibility and agreement between GRE MRE and SE‐EPI MRE derived stiffness. A high concordance correlation (ρ_c = 0.95; p‐value<0.0001) was obtained for SE‐EPI MRE reproducibility. Good concordance correlation was observed (ρ_c = 0.84; p < 0.0001 for both kidneys, ρ_c = 0.91; p < 0.0001 for right kidney and ρ_c = 0.78; p < 0.0001 for left kidney) between GRE MRE and SE‐EPI MRE derived stiffness measurements. Paired t‐test results showed that stiffness value of medulla was significantly (p < 0.0001) greater than cortex using SE‐EPI MRE as well as GRE MRE. SE‐EPI MRE was reproducible and good agreement was observed in MRE‐derived stiffness measurements obtained using SE‐EPI and GRE sequences. Therefore, SE‐EPI can be used for kidney MRE applications.     

Viscoelasticity-based MR elastography of skeletal muscle

An in vivo multifrequency magnetic resonance elastography (MRE) protocol was developed for studying the viscoelastic properties of human skeletal muscle in different states of contraction. Low-frequency shear vibrations in the range of 25-62.5 Hz were synchronously induced into the femoral muscles of seven volunteers and measured in a cross-sectional view by encoding the fast-transverse shear wave component parallel to the muscle fibers. The so-called springpot model was used for deriving two viscoelastic constants, μ and α, from the dispersion functions of the complex shear modulus in relaxed and in loaded muscle. Representing the shear elasticity parallel to the muscle fibers, μ increased in all volunteers upon contraction from 2.68 ± 0.23 kPa to 3.87 ± 0.50 kPa. Also α varied with load, indicating a change in the geometry of the mechanical network of muscle from relaxation (α = 0.253 ± 0.009) to contraction (α = 0.270 ± 0.009). These results provide a reference for a future assessment of muscular dysfunction using rheological parameters.     

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.     

An octahedral shear strain-based measure of SNR for 3D MR elastography

A signal-to-noise ratio (SNR) measure based on the octahedral shear strain (the maximum shear strain in any plane for a 3D state of strain) is presented for magnetic resonance elastography (MRE), where motion-based SNR measures are commonly used. The shear strain, γ, is directly related to the shear modulus, μ, through the definition of shear stress, τ = μγ. Therefore, noise in the strain is the important factor in determining the quality of motion data, rather than the noise in the motion. Motion and strain SNR measures were found to be correlated for MRE of gelatin phantoms and the human breast. Analysis of the stiffness distributions of phantoms reconstructed from the measured motion data revealed a threshold for both strain and motion SNR where MRE stiffness estimates match independent mechanical testing. MRE of the feline brain showed significantly less correlation between the two SNR measures. The strain SNR measure had a threshold above which the reconstructed stiffness values were consistent between cases, whereas the motion SNR measure did not provide a useful threshold, primarily due to rigid body motion effects.     

In vivo brain viscoelastic properties measured by magnetic resonance elastography

Magnetic resonance elastography (MRE) is a non-invasive imaging technique used to visualise and quantify mechanical properties of tissue, providing information beyond what can be currently achieved with standard MR sequences and could, for instance, provide new insight into pathological processes in the brain. This study uses the MRE technique at 3 T to extract the complex shear modulus for in vivo brain tissue utilizing a full three-dimensional approach to reconstruction, removing contributions of the dilatational wave by application of the curl operator. A calibrated phantom is used to benchmark the MRE measurements, and in vivo results are presented for healthy volunteers. The results provide data for in vivo brain storage modulus (G'), finding grey matter (3.1 kPa) to be significantly stiffer than white matter (2.7 kPa). The first in vivo loss modulus (G') measurements show no significant difference between grey matter (2.5 kPa) and white matter (2.5 kPa).     

Simultaneous multislice rapid magnetic resonance elastography of the liver

To design and validate a rapid Simultaneous Multi‐slice (SMS) Magnetic Resonance Elastography technique (MRE), which combines SMS acquisition, in‐plane undersampling and an existing rapid Magnetic Resonance Elastography (MREr) scheme to allow accelerated data acquisition in healthy volunteers and comparison against MREr. SMS‐MREr sequence was developed by incorporating SMS acquisition scheme into an existing MREr sequence that accelerates MRE acquisition by acquiring data during opposite phases of mechanical vibrations. The MREr sequence accelerated MRE acquisition by acquiring data during opposite phases of mechanical vibrations. Liver MRE was performed on 23 healthy subjects using MREr and SMS‐MREr sequences, and mean stiffness values were obtained for manually drawn regions of interest. Linear correlation and agreement between MREr‐ and SMS‐MREr‐based stiffness values were investigated. SMS‐MREr reduced the scan time by half relative to MREr, and allowed acquisition of four‐slice MRE data in a single 17‐second breath‐hold. Visual comparison suggested agreement between MREr and SMS‐MREr elastograms. A Pearson's correlation of 0.93 was observed between stiffness values derived from MREr and SMS‐MREr. Bland–Altman analysis demonstrated good agreement, with ?0.08 kPa mean bias and narrow limits of agreement (95% CI: 0.23 to ?0.39 kPa) between stiffness values obtained using MREr and SMS‐MREr. SMS can be combined with other fast MRE approaches to achieve further acceleration. This pushes the limit on the acceleration that can be achieved in MRE acquisition, and makes it possible to conduct liver MRE exams in a single breath‐hold.     

The link between tissue elasticity and thermal dose in vivo

The objective of this study was to investigate in vivo the relationship between stiffness and thermal dose. For this purpose, shear wave elastography (SWE)--a novel ultrasound-based technique for real-time mapping of the stiffness of biological soft tissues--is performed in temperature-controlled experiments. Experiments were conducted on nine anesthetized rats. Their right leg was put in a thermo-regulated waterbath. The right leg of each animal was heated at one particular temperature between 38 °C and 48.5 °C for 15 min to 3 h. Shear waves were generated in the muscle using the acoustic radiation force induced by a linear ultrasonic probe. The shear wave propagation was imaged in real time by the probe using an ultrafast scanner prototype (10,000 frames s?1). The local tissue stiffness was derived from the shear wave speed. Two optical fiber sensors were inserted into the muscle to measure in situ the temperature. Stiffness was found to increase strongly during the experiments. When expressed as a function of the thermal dose, the stiffness curves were found to be the same for all experiments. A thermal dose threshold was found at 202 min for an eightfold stiffness increase. Finally, the time-temperature relationship was established for different stiffness ratios. The slope of the time-temperature relationship based on stiffness measurements was found identical to the one obtained for cell death in the seminal paper on the thermal dose by Sapareto and Dewey in 1984 (Int. J. Radiat. Oncol. Biol. Phys. 10 787-800). The present results highlight the stiffness increase as a good indicator of thermal necrosis. SWE imaging can be used in vivo for necrosis threshold determination in thermal therapy.     

Effects of frequency- and direction-dependent elastic materials on linearly elastic MRE image reconstructions

The mechanical model commonly used in magnetic resonance elastography (MRE) is linear elasticity. However, soft tissue may exhibit frequency- and direction-dependent (FDD) shear moduli in response to an induced excitation causing a purely linear elastic model to provide an inaccurate image reconstruction of its mechanical properties. The goal of this study was to characterize the effects of reconstructing FDD data using a linear elastic inversion (LEI) algorithm. Linear and FDD phantoms were manufactured and LEI images were obtained from time-harmonic MRE acquisitions with variations in frequency and driving signal amplitude. LEI responses to artificially imposed uniform phase shifts in the displacement data from both purely linear elastic and FDD phantoms were also evaluated. Of the variety of FDD phantoms considered, LEI appeared to tolerate viscoelastic data-model mismatch better than deviations caused by poroelastic and anisotropic mechanical properties in terms of visual image contrast. However, the estimated shear modulus values were substantially incorrect relative to independent mechanical measurements even in the successful viscoelastic cases and the variations in mean values with changes in experimental conditions associated with uniform phase shifts, driving signal frequency and amplitude were unpredictable. Overall, use of LEI to reconstruct data acquired in phantoms with FDD material properties provided biased results under the best conditions and significant artifacts in the worst cases. These findings suggest that the success with which LEI is applied to MRE data in tissue will depend on the underlying mechanical characteristics of the tissues and/or organs systems of clinical interest.     

Overhauser‐enhanced magnetic resonance elastography

Magnetic resonance elastography (MRE) is a powerful technique to assess the mechanical properties of living tissue. However, it suffers from reduced sensitivity in regions with short T₂ and T₂* such as in tissue with high concentrations of paramagnetic iron, or in regions surrounding implanted devices. In this work, we exploit the longer T₂* attainable at ultra‐low magnetic fields in combination with Overhauser dynamic nuclear polarization (DNP) to enable rapid MRE at 0.0065 T. A 3D balanced steady‐state free precession based MRE sequence with undersampling and fractional encoding was implemented on a 0.0065 T MRI scanner. A custom‐built RF coil for DNP and a programmable vibration system for elastography were developed. Displacement fields and stiffness maps were reconstructed from data recorded in a polyvinyl alcohol gel phantom loaded with stable nitroxide radicals. A DNP enhancement of 25 was achieved during the MRE sequence, allowing the acquisition of 3D Overhauser‐enhanced MRE (OMRE) images with (1.5 × 2.7 × 9) mm³ resolution over eight temporal steps and 11 slices in 6 minutes. In conclusion, OMRE at ultra‐low magnetic field can be used to detect mechanical waves over short acquisition times. This new modality shows promise to broaden the scope of conventional MRE applications, and may extend the utility of low‐cost, portable MRI systems to detect elasticity changes in patients with implanted devices or iron overload. Copyright © 2016 John Wiley & Sons, Ltd.     

正电子发射断层成像/CT观察健康人空腹时不同器官对18F脱氧葡萄糖的摄取

背景：既往国内外研究中,主要针对肿瘤患者体内葡萄糖的摄取情况,而关于正常人在空腹状态下不同器官对葡萄糖的摄取作用研究很少。 目的：正电子发射断层成像/CT观察健康人在空腹状态下不同器官对¹⁸F脱氧葡萄糖的摄取情况,分析空腹时脑、肝、肾、心脏和骨骼肌组织在糖代谢中的相关性。 方法：31例健康成年人空腹抽血测肝肾功能、血糖和血脂,并行正电子发射断层成像/CT检查,测脑、心脏、肝、肾脏和骨骼肌的18F脱氧葡萄糖的平均标准摄入值以及最大标准摄入值。 结果与结论：空腹时脑皮质18F脱氧葡萄糖的平均标准摄入值约是心脏和肾脏的两三倍,是肝脏的4倍左右,是骨骼肌的15倍。肝脏平均标准摄入值与肾脏和骨骼肌的平均标准摄入值呈显著正相关(r=0.406,0.391,P=0.023,0.030),但肝脏的平均标准摄入值与心和脑的平均标准摄入值无相关性。结果提示空腹状态下脑组织对葡萄糖摄取最多,骨骼肌最少,心脏、肝脏和肾脏居中;空腹状态下肝脏与肾脏和骨骼肌之间对葡萄糖的代谢存在显著相关性。     

Calculation of shear stiffness in noise dominated magnetic resonance elastography data based on principal frequency estimation

Magnetic resonance elastography (MRE) is a non-invasive phase-contrast-based method for quantifying the shear stiffness of biological tissues. Synchronous application of a shear wave source and motion encoding gradient waveforms within the MRE pulse sequence enable visualization of the propagating shear wave throughout the medium under investigation. Encoded shear wave-induced displacements are then processed to calculate the local shear stiffness of each voxel. An important consideration in local shear stiffness estimates is that the algorithms employed typically calculate shear stiffness using relatively high signal-to-noise ratio (SNR) MRE images and have difficulties at an extremely low SNR. A new method of estimating shear stiffness based on the principal spatial frequency of the shear wave displacement map is presented. Finite element simulations were performed to assess the relative insensitivity of this approach to decreases in SNR. Additionally, ex vivo experiments were conducted on normal rat lungs to assess the robustness of this approach in low SNR biological tissue. Simulation and experimental results indicate that calculation of shear stiffness by the principal frequency method is less sensitive to extremely low SNR than previously reported MRE inversion methods but at the expense of loss of spatial information within the region of interest from which the principal frequency estimate is derived.