Stiffness change of the supraspinatus muscle can be detected by magnetic resonance elastography

Magnetic resonance elastography (MRE) and ultrasound shear wave elastography (SWE) are imaging techniques to measure stiffness of the soft tissue using magnetic resonance imaging (MRI) and ultrasound images, respectively. The purpose of this study was to explore the feasibility of the MRE measurement to evaluate the change in supraspinatus (SSP) muscle stiffness before and after rotator cuff tear, and to compare the result with those of SWE. Six swine shoulders were used. The skin and subcutaneous fat were removed, and the stiffness value of the SSP muscle was measured by MRE and SWE. The MRE measurement was performed with 0.3 T open MRI and the vibration from a pneumatic driver system with active driver to a passive driver to create the shear wave in the tissue. The passive driver was placed on the center of the SSP muscle. The stiffness was estimated from the wave images using local frequency estimation methods. In the SWE measurement, the probe of the ultrasound was placed on the center of the SSP muscle. The shear wave propagation speed was measured at a depth of 1 cm from the surface, and the stiffness was calculated. After those measurements, the rotator cuff tendon was detached from the greater tuberosity, and MRE and SWE measurements were then performed in the same manner again. The differences in the stiffness values were compared between before and after the rotator cuff tendon tear on both the MRE and SWE measurements. The results indicated that stiffness values on MRE and SWE were 9.3 ± 1.8 and 10.0 ± 1.2 kPa respectively before the rotator cuff tear, and 7.3 ± 1.3 and 8.0 ± 0.8 kPa respectively after the tendon detachment. Stiffness values were significantly lower after the tendon detachment on both the MRE and SWE measurements (p < 0.05). Our results demonstrated that stiffness values of the SSP muscle on MRE and SWE were lower after rotator cuff detachment. From this result, MRE may be a feasible method for quantification of the change in rotator cuff muscle stiffness.     

Feasibility of MR elastography of the intervertebral disc

Low back pain (LBP) is a costly and widely prevalent health disorder in the U.S. One of the most common causes of LBP is degenerative disc disease (DDD). There are many imaging techniques to characterize disc degeneration; however, there is no way to directly assess the material properties of the intervertebral disc (IVD) within the intact spine. Magnetic resonance elastography (MRE) is an MRI-based technique for non-invasively mapping the mechanical properties of tissues in vivo. The purpose of this study was to investigate the feasibility of using MRE to detect shear wave propagation in and determine the shear stiffness of an axial cross-section of an ex vivo baboon IVD, and compare with shear displacements from a finite element model of an IVD motion segment in response to harmonic shear vibration. MRE was performed on two baboon lumbar spine motion segments (L3–L4) with the posterior elements removed at a range of frequencies (1000–1500 Hz) using a standard clinical 1.5 T MR scanner. Propagating waves were visualized in an axial cross-section of the baboon IVDs in all three motion-encoding directions, which resembled wave patterns predicted using finite element modeling. The baboon nucleus pulposus showed an average shear stiffness of 79 ± 15 kPa at 1000 Hz. These results suggest that MRE is capable of visualizing shear wave propagation in the IVD, assessing the stiffness of the nucleus of the IVD, and can differentiate the nucleus and annulus regions.     

Magnetic resonance elastography of the supraspinatus muscle: A preliminary study on test-retest repeatability and wave quality with different frequencies and image filtering

The purpose of this study was to determine an optimal condition (vibration frequency and image filtering) for stiffness estimation with high accuracy and stiffness measurement with high repeatability in magnetic resonance elastography (MRE) of the supraspinatus muscle. Nine healthy volunteers underwent two MRE exams separated by at least a 30 min break, on the same day. MRE acquisitions were performed with a gradient-echo type multi-echo MR sequence at 75, 100, and 125 Hz pneumatic vibration. Wave images were processed by a bandpass filter or filter combining bandpass and directional filters (bandpass-directional filter). An observer specified the region of interest (ROI) on clear wave propagation in the supraspinatus muscle, within which the observer measured the stiffness. This study assessed wave image quality according to two indices, as a substitute for the assessment of the accuracy of the stiffness estimation. One is the size of the clear wave propagation area (ROI size used to measure the stiffness) and the other is the qualitative stiffness resolution score in that area. These measurements made by the observer were repeated twice at least one month apart after each MRE exam.This study assessed the intra-examiner and observer repeatability of the stiffness value, ROI size and resolution score in each combination of vibration frequency and image filter. Repeatability of the data was analyzed using the intraclass correlation coefficient (ICC) and 95% limits-of-agreement (LOA) in Bland-Altman analysis. The analyses on intra-examiner and observer repeatability of stiffness indicated that the ICC and 95% LOA were not varied greatly depending on vibration frequency and image filter (intra-examiner repeatability, ICC range, 0.79 to 0.88; 95% LOA range, ±23.95 to ±32.42%, intra-observer repeatability, ICC range, 0.98 to 1.00; 95% LOA range, ±5.10 to ±10.99%). In the analyses on intra-examiner repeatability of ROI size, ICCs were rather low (ranging from: 0.03 to 0.69) while 95% LOA was large in all the combinations of vibration frequency and image filter (ranging from: ±62.66 to ±83.33%). In the analyses on intra-observer repeatability of ROI size, ICCs were sufficiently high in the total combination of vibration frequency and image filter (ranging from 0.80 to 0.87) while the 95% LOAs were better (lower) in the bandpass-directional filter than the bandpass filter (bandpass directional filter vs. bandpass filter, ±28.81 vs. ±54.83% at 75 Hz; ±25.63 vs. ±37.83% at 100 Hz; ±34.51 vs. ±43.36% at 125 Hz). In the analyses on intra-examiner and observer repeatability of resolution score, the mean difference (bias) between the two exams (or observations) was significantly low and there was almost no difference across all the combinations of vibration frequency and image filter (range of bias: −0.11–0.11 and −0.17–0.00, respectively).Additionally, effects of vibration frequency and image filter on wave image quality (ROI size and resolution score) were assessed separately in each exam. Both mean ROI size and resolution score in the bandpass-directional filter were larger than those in the bandpass filter. Among the data in the bandpass-directional filter, mean ROI size was larger at 75 and 100 Hz, and mean resolution score was larger at 100 and 125 Hz. Taking into consideration with the results of repeatability and wave image quality, the present results suggest that optimal vibration frequency and image filter for MRE of the supraspinatus muscles is 100 Hz and bandpass-directional filter, respectively.     

Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials

The authors have recently demonstrated the shear wave interference patterns created by two coherent vibration sources imaged with the vibration sonoelastography technique. If the two sources vibrate at slightly different frequencies omega and omega+deltaomega, respectively, the interference patterns move at an apparent velocity of (deltaomega/2omega)upsilon(shear), where upsilon(shear) is the shear wave speed. We name the moving interference patterns "crawling waves." In this paper, we extend the techniques to inspect biomaterials with nonuniform stiffness distributions. A relationship between the local crawling wave speed and the local shear wave velocity is derived. In addition, a modified technique is proposed whereby only one shear wave source propagates shear waves into the medium at the frequency omega. The ultrasound probe is externally vibrated at the frequency omega-deltaomega. The resulting field estimated by the ultrasound (US) scanner is proven to be an exact representation of the propagating shear wave field. The authors name the apparent wave motion "holography waves." Real-time video sequences of both types of waves are acquired on various inhomogeneous elastic media. The distribution of the crawling/holographic wave speeds are estimated. The estimated wave speeds correlate with the stiffness distributions.     

Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation.

New methods for simulating and analyzing Magnetic Resonance Elastography (MRE) images are introduced. To simulate a two-dimensional shear wave pattern, the wave equation is solved for a field of coupled harmonic oscillators with spatially varying coupling and damping coefficients in the presence of an external force. The spatial distribution of the coupling and the damping constants are derived from an MR image of the investigated object. To validate the simulation as well as to derive the elasticity modules from experimental MRE images, the wave patterns are analyzed using a Local Frequency Estimation (LFE) algorithm based on Gauss filter functions with variable bandwidths. The algorithms are tested using an Agar gel phantom with spatially varying elasticity constants. Simulated wave patterns and LFE results show a high agreement with experimental data. Furthermore, brain images with estimated elasticities for gray and white matter as well as for exemplary tumor tissue are used to simulate experimental MRE data. The calculations show that already small distributions of pathologically changed brain tissue should be detectable by MRE even within the limit of relatively low shear wave excitation frequency around 0.2 kHz.     

Magnetic resonance elastography of the brain in a mouse model of Alzheimer's disease: initial results

The increasing prevalence of Alzheimer's disease (AD) has provided motivation for developing novel methods for assessing the disease and the effects of potential treatments. Magnetic resonance elastography (MRE) is an MRI-based method for quantitatively imaging the shear tissue stiffness in vivo. The objective of this research was to determine whether this new imaging biomarker has potential for characterizing neurodegenerative disease. Methods were developed and tested for applying MRE to evaluate the mouse brain, using a conventional large bore 3.0T MRI system. The technique was then applied to study APP-PS1 mice, a well-characterized model of AD. Five APP-PS1 mice and 8 age-matched wild-type mice were imaged immediately following sacrifice. Brain shear stiffness measurements in APP-PS1 mice averaged 22.5% lower than those for wild-type mice (P = .0031). The results indicate that mouse brain MRE is feasible at 3.0T, and brain shear stiffness has merit for further investigation as a potential new biomarker for Alzheimer's disease.     

Modeling shear modulus distribution in magnetic resonance elastography with piecewise constant level sets

Magnetic resonance elastography (MRE) is designed for imaging the mechanical properties of soft tissues. However, the interpretation of shear modulus distribution is often confusing and cumbersome. For reliable evaluation, a common practice is to specify the regions of interest and consider regional elasticity. Such an experience-dependent protocol is susceptible to intrapersonal and interpersonal variability. In this study we propose to remodel shear modulus distribution with piecewise constant level sets by referring to the corresponding magnitude image. Optimal segmentation and registration are achieved by a new hybrid level set model comprised of alternating global and local region competitions. Experimental results on the simulated MRE data sets show that the mean error of elasticity reconstruction is 11.33% for local frequency estimation and 18.87% for algebraic inversion of differential equation. Piecewise constant level set modeling is effective to improve the quality of shear modulus distribution, and facilitates MRE analysis and interpretation.     

A WAVE MODEL FOR A PNEUMATIC TYRE BELT

A one-dimensional wave equation of an infinite flattened tyre belt is generated. The belt vibration is controlled by bending, tension, shear and the sidewall stiffness. The dispersion relations for two waves in the belt are calculated and used to find both the input impedance and attenuation on a tyre belt of infinite extent. Tension and the sidewall controls the deformation and stiffness below 100Hz. Waves propagate around the belt above this frequency. The wave speeds due to bending and shear were predicted and measured. The model presented here should be valid for the prediction of tyre response above about 400 Hz when for a car tyre the modal behaviour is observed to cease. In this high-frequency region, the tyre at the input appears to be of infinite extent.     

Dynamic analysis of magnetorheological elastomer-based sandwich beam with conductive skins under various boundary conditions

The dynamic analysis of a three-layered symmetric sandwich beam with magnetorheological elastomer (MRE) embedded viscoelastic core and conductive skins subjected to a periodic axial load have been carried out under various boundary conditions. As the skins of the sandwich beam are conductive, magnetic loads are applied to the skins during vibration. Due to the field-dependent shear modulus of MRE material, the stiffness of the MRE embedded sandwich beam can be changed by the application of magnetic fields. Using extended Hamilton’s principle along with generalized Galarkin’s method the governing equation of motion has been derived. The free vibration analysis of the system has been carried out and the results are compared with the published experimental and analytical results which are found to be in good agreement. The parametric instability regions of the sandwich beam have been determined for various boundary conditions. Here, recently developed magnetorheological elastomer based on natural rubber containing iron particles and carbon blacks have been used. The effects of magnetic field, length of MRE patch, core thickness, percentage of iron particles and carbon blacks on the regions of parametric instability for first three modes of vibration have been studied. These results have been compared with the parametric instability regions of the sandwich beam with fully viscoelastic core to show the passive and active vibration reduction of these structures using MRE and magnetic field. Also, the results are compared with those obtained using higher order theory.     

Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers

Magnetic resonance elastography (MRE) is a technique for quantifying the acoustic response of biological tissues to propagating waves applied at low frequencies in order to evaluate mechanical properties. Application-specific MRE drivers are typically required to effectively deliver shear waves within the tissue of interest. Surface MRE drivers with transversely oriented vibrations have often been used to directly generate shear waves. These drivers may have disadvantages in certain applications, such as poor penetration depth and inflexible orientation. Therefore, surface MRE drivers with longitudinally oriented vibrations are used in some situations. The purpose of this work was to investigate and optimize a longitudinal driver system for MRE applications. A cone-like hemispherical distribution of shear waves being generated by these drivers and the wave propagation being governed by diffraction in the near field are shown. Using MRE visualization of the vector displacement field, we studied the properties of the shear wave field created by longitudinal MRE drivers of various sizes to identify optimum shear wave imaging planes. The results offer insights and improvements in both experimental design and imaging plane selection for 2-D MRE data acquisition.     

降低加肋双层圆柱壳辐射噪声线谱的结构声学设计

为降低双层圆柱壳辐射噪声线谱,从控制内壳振动响应和衰减壳间振动传递率进行结构声学设计。采用机械阻抗理论分析了环肋圆柱壳模态响应控制机理;由环肋振动方程推导分析了环肋径向机械阻抗特性;基于阻抗失配、波形转换原理提出一种阻抗加强环肋,分析了振动波阻抑特性;利用阻尼减振技术,综合考虑肋板的刚度、阻尼特性,设计了金属橡胶层叠肋板;结合数值计算实例,分析了设计双层壳模型的声辐射性能。结果表明:设计的双层加肋圆柱壳结构能有效降低辐射噪声线谱,在分析频段内辐射声压线谱平均降低约6.6 dB。研究结果对研制低噪声水下航行器具有良好的工程价值和应用前景。      

A theoretical approach to local attenuation measurements of shear waves by MRE. Preliminary experimental results

An essential highlight of the presented method is the employment of Magnetic Resonance Elastography (MRE) for local measurements of the attenuation of elastic shear waves introduced into a biological sample. Such a measurement can be accomplished by combining the MRE method with those methods, in which collective displacement of spins is induced by external physical factors, such as variable electric field, strong magnetic field gradient or longitudinal elastic wave. A theoretical basis of the method involving external factors and results of preliminary experiments have been presented in this paper.     

Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data

The crawling wave experiment was developed to capture a shear wave induced moving interference pattern that is created by two harmonic vibration sources oscillating at different but almost the same frequencies. Using the vibration sonoelastography technique, the spectral variance image reveals a moving interference pattern. It has been shown that the speed of the moving interference pattern, i.e., the crawling wave speed, is proportional to the shear wave speed with a nonlinear factor. This factor can generate high-speed artifacts in the crawling wave speed images that do not actually correspond to increased stiffness. In this paper, an inverse algorithm is developed to reconstruct both the crawling wave speed and the shear wave speed using the phases of the crawling wave and the shear wave. The feature for the data is the application to in vitro prostate data, while the features for the algorithm include the following: (1) A directional filter is implemented to obtain a wave moving in only one direction; and (2) an L(1) minimization technique with physics inspired constraints is employed to calculate the phase of the crawling wave and to eliminate jump discontinuities from the phase of the shear wave. The algorithm is tested on in vitro prostate data measured at the Rochester Center for Biomedical Ultrasound and University of Rochester. Each aspect of the algorithm is shown to yield image improvement. The results demonstrate that the shear wave speed images can have less artifacts than the crawling wave images. Examples are presented where the shear wave speed recoveries have excellent agreement with histology results on the size, shape, and location of cancerous tissues in the glands.     

Micro-vibration suppression of equipment supported on a floor incorporating magneto-rheological elastomer core

In this study, magneto-rheological elastomers (MREs) are adopted to construct a smart sandwich beam for micro-vibration control of equipment. The micro-vibration response of a smart sandwich beam with MRE core which supports mass-concentrated equipment under stochastic support-motion excitations is investigated to evaluate the vibration suppression capability. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. A frequency-domain solution method for the stochastic micro-vibration response of the smart sandwich beam supporting mass-concentrated equipment is developed based on the Galerkin method and random vibration theory. First, the displacements of the beam are expanded as series of spatial harmonic functions and the Galerkin method is applied to convert the partial differential equations of motion into ordinary differential equations. With these equations, the frequency-response function matrix of the beam–mass system and the expression of the velocity response spectrum are then obtained, with which the root-mean-square (rms) velocity response in terms of the one-third octave frequency band can be calculated. Finally, the optimization problem of the complex modulus of the MRE core is defined by minimizing the velocity response spectrum and the rms velocity response of the sandwich beam, through altering the applied magnetic fields. Numerical results are given to illustrate the influence of MRE parameters on the rms velocity response and the response reduction capacity of the smart sandwich beam. The proposed method is also applicable to response analysis of a sandwich beam with arbitrary core characterized by a complex shear modulus and subject to arbitrary stochastic excitations described by a power spectral density function, and is valid for a wide frequency range.     

Low frequency ultrasonic propagation through fibre reinforced,polymer composites

This paper concentrates upon mesoscale variations observed in the time-of-flight (TOF) area scans of shear wave propagation through 'identically processed', injection moulded, glass fibre reinforced, polypropylene plaques. The effect of these structural variations on the derived 3D stiffness constants is discussed. Hence the random measurement errors associated with the stiffness constant measurements are differentiated from the intrinsic process-induced spatial variations. Interesting correlations between TOF and received amplitudes of shear wave propagation have been found and our tentative interpretation of these data in terms of mesostructural variations in the reinforcing fibre locations and fibre orientations is presented.     

Assessment of stiffness changes in the ex vivo porcine aortic wall using magnetic resonance elastography

Magnetic resonance elastography (MRE) is a noninvasive phase-contrast technique for estimating the mechanical properties of tissues by imaging propagating mechanical waves within the tissue. In this study, we hypothesize that changes in arterial wall stiffness, experimentally induced by formalin fixation, can be measured using MRE in ex vivo porcine aortas. In agreement with our hypothesis, the significant stiffness increase after sample fixation was clearly demonstrated by MRE and confirmed by mechanical testing. The results indicate that MRE can be used to examine the stiffness changes of the aorta. This study has provided evidence of the effectiveness of using MRE to directly assess the stiffness change in aortic wall. The results offer motivation to pursue MRE as a noninvasive method for the evaluation of arterial wall mechanical properties.     

Influence of composition of carbonyl iron particles on dynamic mechanical properties of magnetorheological elastomers

Magnetorheological elastomers (MRE) are known as smart materials. However, the magnetorheological (MR) effect of MRE is not high enough at present, which limits its engineering applications. Prior studies have shown that magneto-induced shear storage modulus and MR effect were mainly determined by the performance of the ferromagnetic particles. In this paper, MRE samples were prepared by carbonyl iron particles (CIP) of different compositions based on silicon rubber under external magnetic field. Their microstructures were observed using an optical digital microscope and a scanning electron microscope. The dynamic mechanical properties of MRE samples were measured using a modified dynamic mechanical analyzer under varying magnetic field strength and frequency. The results show that the carbon content of CIP have a greater impact on the dynamic mechanical properties of MRE. The magneto-induced shear storage modulus and MR effect can be increased by selecting CIP of low carbon content. In addition, the damping property is also significantly influenced by the carbon content of the CIP. This study is expected to provide guidance for fabrication of high performance MRE.     

Analysis of flexural wave velocity and vibration mode in thin cylindrical shell

The relationship between the flexural wave velocity and the excited vibration mode of a thin cylindrical shell is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, all of these vibration modes are not excited actually. To estimate the excited vibration mode, the concept of "modified bending stiffness" is introduced, and the influence of each stress component upon the modified bending stiffness is analyzed. The excited mode is theoretically discriminated from the nonexcited mode based on the smallness of this modified bending stiffness. The validity of our theory is confirmed by an excellent agreement between theoretical and experimental results on flexural wave velocity.     

Phase preparation in steady-state free precession MR elastography

Strain and motion measurements in balanced steady-state free precession (bSSFP) imaging require high magnetic field homogeneity. This requirement is due to the nonlinear signal response to spin phase variations in bSSFP. Here, a technique that utilizes background gradients for preparing strong in-plane spin phase variations is proposed. As a result, periodic patterns of increased motion sensitivity appear, which are interleaved with bands of low phase-to-noise ratio. Spatial filters commonly used in MR elastography (MRE) remove these bands and leave wave images equivalent to a uniform phase response in bSSFP-MRE. Since phase preparation gradients locally enhance motion sensitivity, the technique can be employed for selectively increasing the wave signal amplitude in MRE. The method is applied without the need for previous shimming, which reduces the examination time. In vivo phase prepared bSSFP-MRE is demonstrated in human liver and heart.     

Effects of gadoxetic acid on liver elasticity measurement by using magnetic resonance elastography

The purpose of this study was to evaluate the effect of gadoxetic acid (Gd-EOB-DTPA) on measurements of liver stiffness by using magnetic resonance elastography (MRE). In this study, 104 consecutive patients (mean age, 67.7±9.4 years) underwent MRE using a 1.5-T MR scanner equipped with a cylindrical passive driver that was placed across the right chest wall for delivering vibrations. Axial gradient-echo images, which were automatically converted to elastograms that represented stiffness (kPa), were acquired using a continuous sinusoidal vibration of 60 Hz. Two raters independently placed a region of interest on the right lobe of the liver on the elastograms obtained before and after Gd-EOB-DTPA was administered. Liver stiffness was measured using these two elastograms and compared using a paired t test and correlation analysis. No significant difference was observed in liver stiffness before and after Gd-EOB-DTPA was administered (Rater 1, P=.1200; Rater 2, P=.3585). The correlation coefficients were 0.986 (Rater 1) and 0.984 (Rater 2), indicating excellent correlation between the stiffness values before and after Gd-EOB-DTPA was administered. Liver stiffness measured by MRE did not differ before and after Gd-EOB-DTPA was administered.