Multifrequency inversion in magnetic resonance elastography

Time-harmonic shear wave elastography is capable of measuring viscoelastic parameters in living tissue. However, finite tissue boundaries and waveguide effects give rise to wave interferences which are not accounted for by standard elasticity reconstruction methods. Furthermore, the viscoelasticity of tissue causes dispersion of the complex shear modulus, rendering the recovered moduli frequency dependent. Therefore, we here propose the use of multifrequency wave data from magnetic resonance elastography (MRE) for solving the inverse problem of viscoelasticity reconstruction by an algebraic least-squares solution based on the springpot model. Advantages of the method are twofold: (i) amplitude nulls appearing in single-frequency standing wave patterns are mitigated and (ii) the dispersion of storage and loss modulus with drive frequency is taken into account by the inversion procedure, thereby avoiding subsequent model fitting. As a result, multifrequency inversion produces fewer artifacts in the viscoelastic parameter map than standard single-frequency parameter recovery and may thus support image-based viscoelasticity measurement. The feasibility of the method is demonstrated by simulated wave data and MRE experiments on a phantom and in vivo human brain. Implemented as a clinical method, multifrequency inversion may improve the diagnostic value of time-harmonic MRE in a large variety of applications.     

Horizontal shear wave scattering from a nonwelded interface observed by magnetic resonance elastography

A method based on magnetic resonance elastography is presented that allows measuring the weldedness of interfaces between soft tissue layers. The technique exploits the dependence of shear wave scattering at elastic interfaces on the frequency of vibration. Experiments were performed on gel phantoms including differently welded interfaces. Plane wave excitation parallel to the planar interface with corresponding motion sensitization enabled the observation of only shear-horizontal (SH) wave scattering. Spatio-temporal filtering was applied to calculate scattering coefficients from the amplitudes of the incident, transmitted and reflected SH-waves in the vicinity of the interface. The results illustrate that acoustic wave scattering in soft tissues is largely dependent on the connectivity of interfaces, which is potentially interesting for imaging tissue mechanics in medicine and biology.     

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.     

Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime

Magnetic resonance elastography (MRE) is used to quantify the viscoelastic shear modulus, G*, of human and animal tissues. Previously, values of G* determined by MRE have been compared to values from mechanical tests performed at lower frequencies. In this study, a novel dynamic shear test (DST) was used to measure G* of a tissue-mimicking material at higher frequencies for direct comparison to MRE. A closed-form solution, including inertial effects, was used to extract G* values from DST data obtained between 20 and 200 Hz. MRE was performed using cylindrical 'phantoms' of the same material in an overlapping frequency range of 100-400 Hz. Axial vibrations of a central rod caused radially propagating shear waves in the phantom. Displacement fields were fit to a viscoelastic form of Navier's equation using a total least-squares approach to obtain local estimates of G*. DST estimates of the storage G' (Re[G*]) and loss modulus G″ (Im[G*]) for the tissue-mimicking material increased with frequency from 0.86 to 0.97 kPa (20-200 Hz, n = 16), while MRE estimates of G' increased from 1.06 to 1.15 kPa (100-400 Hz, n = 6). The loss factor (Im[G*]/Re[G*]) also increased with frequency for both test methods: 0.06-0.14 (20-200 Hz, DST) and 0.11-0.23 (100-400 Hz, MRE). Close agreement between MRE and DST results at overlapping frequencies indicates that G* can be locally estimated with MRE over a wide frequency range. Low signal-to-noise ratio, long shear wavelengths and boundary effects were found to increase residual fitting error, reinforcing the use of an error metric to assess confidence in local parameter estimates obtained by MRE.     

Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.     

Effects of constant frequency noise in magnetic resonance imaging with nonuniform k-space sampling

Magnetic resonance images can be compromised by constant frequency (CF) noise, such as radio frequency (RF) noise. We investigate the effects of CF noise in four imaging methods with non-uniform k-space sampling: single-shot echo-planar imaging (EPI) with sinusoidal readout gradients, phase-encoded echo-planar spectroscopic imaging (EPSI) with sinusoidal readout gradients, projection-reconstruction imaging, and single-shot spiral imaging. The characteristics of the CF artifacts in each imaging method are studied with numerical simulations. CF noise is found to cause artifacts of nonclassic forms in the reconstructed images. Specifically, dashed-line, streak, and spiral patterns of CF noise appear in EPI/EPSI with sinusoidal readout gradients, projection-reconstruction imaging, and spiral imaging, respectively. The analytical expression for dashed-line artifacts is found to be a weighted sum of Bessel functions and is verified with in vivo experiments. The CF artifacts can be removed during post-processing by eliminating the noise spikes in the Fourier domain of the raw data.     

Algebraic Helmholtz inversion in planar magnetic resonance elastography

Magnetic resonance elastography (MRE) is an increasingly used noninvasive modality for diagnosing diseases using the response of soft tissue to harmonic shear waves. We present a study on the algebraic Helmholtz inversion (AHI) applied to planar MRE, demonstrating that the deduced phase speed of shear waves depends strongly on the relative orientations of actuator polarization, motion encoding direction and image plane as well as on the actuator plate size, signal-to-noise ratio and discretization of the wave image. Results from the numerical calculation of harmonic elastic waves due to different excitation directions and simulated plate sizes are compared to experiments on a gel phantom. The results suggest that correct phase speed can be obtained despite these largely uncontrollable influences, if AHI is based on out-of-plane displacements and the actuator is driven at an optimal frequency yielding an optimal pixel per wavelength resolution in the wave image. Assuming plane waves, the required number of pixels per wavelength depends only on the degree of noise.     

Analysis and improvement of motion encoding in magnetic resonance elastography

Magnetic resonance elastography (MRE) utilizes phase contrast magnetic resonance imaging (MRI), which is phase locked to externally generated mechanical vibrations, to measure the three‐dimensional wave displacement field. At least four measurements with linear‐independent encoding directions are necessary to correct for spurious phase contributions if effects from imaging gradients are non‐negligible. In MRE, three encoding schemes have been used: unbalanced four‐ and six‐point and balanced four‐point (‘tetrahedral’) encoding. The first two sensitize to motion with orthogonal gradients, with the four‐point method acquiring a single reference scan without motion sensitization, whereas three additional scans with inverted gradients are used with six‐point encoding, leading to two‐fold higher displacement‐to‐noise ratio (DNR) and 50% longer scan duration. Balanced four‐point (tetrahedral) encoding encodes along the four diagonals of a cube, with one direction serving as a reference for the other three encoding directions, similar to four‐point encoding. The objective of this work is to introduce a theoretical framework to compare different motion sensitization strategies with respect to their motion encoding efficiency in two fundamental encoding limits, the gradient strength limit and the dynamic range limit, which are both placed in relation to conventional gradient recalled echo (GRE)‐ and spin echo (SE)‐based MRE sequences. We apply the framework to the three aforementioned schemes and show that the motion encoding efficiency of unbalanced four‐ and six‐point encoding schemes in the gradient‐limited regime can be increased by a factor of 1.5 when using all physical gradient channels concurrently. Furthermore, it is demonstrated that reversing the direction of the reference in balanced four‐point (tetrahedral) encoding results in the Hadamard encoding scheme, which leads to increased DNR by compared with balanced four‐point encoding and 2.8 compared with unbalanced four‐point encoding. As an example, we show that optimal encoding can be utilized to reduce the acquisition time of standard liver MRE in vivo from four to two breath holds.     

Automatic estimation of the noise variance from the histogram of a magnetic resonance image

Estimation of the noise variance of a magnetic resonance (MR) image is important for various post-processing tasks. In the literature, various methods for noise variance estimation from MR images are available, most of which however require user interaction and/or multiple (perfectly aligned) images. In this paper, we focus on automatic histogram-based noise variance estimation techniques. Previously described methods are reviewed and a new method based on the maximum likelihood (ML) principle is presented. Using Monte Carlo simulation experiments as well as experimental MR data sets, the noise variance estimation methods are compared in terms of the root mean squared error (RMSE). The results show that the newly proposed method is superior in terms of the RMSE.     

Non-invasive measurement of brain viscoelasticity using magnetic resonance elastography

The purpose of this work was to develop magnetic resonance elastography (MRE) for the fast and reproducible measurement of spatially averaged viscoelastic constants of living human brain. The technique was based on a phase-sensitive echo planar imaging acquisition. Motion encoding was orthogonal to the image plane and synchronized to intracranial shear vibrations at driving frequencies of 25 and 50 Hz induced by a head-rocker actuator. Ten time-resolved phase-difference wave images were recorded within 60 s and analyzed for shear stiffness and shear viscosity. Six healthy volunteers (six men; mean age 34.5 years; age range 25-44 years) underwent 23-39 follow-up MRE studies over a period of 6 months. Interindividual mean +/- SD shear moduli and shear viscosities were found to be 1.17 +/- 0.03 kPa and 3.1 +/- 0.4 Pas for 25 Hz and 1.56 +/- 0.07 kPa and 3.4 +/- 0.2 Pas for 50 Hz, respectively (P < or = 0.01). The intraindividual range of shear modulus data was 1.01-1.31 kPa (25 Hz) and 1.33-1.77 kPa (50 Hz). The observed modulus dispersion indicates a limited applicability of Voigt's model to explain viscoelastic behavior of brain parenchyma within the applied frequency range. The narrow distribution of data within small confidence intervals demonstrates excellent reproducibility of the experimental protocol. The results are necessary as reference data for future comparisons between healthy and pathological human brain viscoelastic data.     

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.     

Influence of thoracolumbar fascia stretching on lumbar back muscle stiffness: A supersonic shear wave elastography approach

The lumbar paraspinal muscle compartment (PMC) is a stabilizing system of the spine whose efficiency depends on its elastic properties, which may be quantifiable by supersonic shear wave elastography (SWE). The thoracolumbar fascia (TLF) encapsulates the lumbar paraspinal muscles (LPM) and creates a PMC. Tensioning of the TLF via the stretching of the latissimus dorsi is supposed to increase stiffness within the PMC. The aims of this study were (1) to test the reliability of SWE in the multifidus and the erector spinae (ES) in prone and sited position; (2) to investigate the role of the tensioning of the pTLF, via stretching of the latissimus dorsi (LD), on LPM stiffness. Stiffness of ES and multifidus was measured using SWE at L3–L4 in procubitus and seated position in 15 participants. Stretching of LD was performed with arm elevation. Parametric paired tests, multiple analyses of variance, and intraclass correlation were used for statistical analysis. Reliability estimates were fair to excellent. Reliability was greater in ES than the multifidus, greater in seated position than during rest. Stiffness was greater in the ES than in multifidus, and in seated position than at rest. Tensioning of the TLF via LD stretching did not generate significant LPM stiffness changes. SWE is a reliable tool for assessing stiffness in the LPM. Reliability of SWE protocols is improved during seated position. Tensioning of the TLF via LD stretching did not influence LPM stiffness. Clin. Anat. 32:73–80, 2019. © 2018 Wiley Periodicals, Inc.     

Post-processing noise removal algorithm for magnetic resonance imaging based on edge detection and wavelet analysis

A post-processing noise suppression technique for biomedical MRI images is presented. The described procedure recovers both sharp edges and smooth surfaces from a given noisy MRI image; it does not blur the edges and does not introduce spikes or other artefacts. The fine details of the image are also preserved. The proposed algorithm first extracts the edges from the original image and then performs noise reduction by using a wavelet de-noise method. After the application of the wavelet method, the edges are restored to the filtered image. The result is the original image with less noise, fine detail and sharp edges. Edge extraction is performed by using an algorithm based on Sobel operators. The wavelet de-noise method is based on the calculation of the correlation factor between wavelet coefficients belonging to different scales. The algorithm was tested on several MRI images and, as an example of its application, we report the results obtained from a spin echo (multi echo) MRI image of a human wrist collected with a low field experimental scanner (the signal-to-noise ratio, SNR, of the experimental image was 12). Other filtering operations have been performed after the addition of white noise on both channels of the experimental image, before the magnitude calculation. The results at SNR = 7, SNR = 5 and SNR = 3 are also reported. For SNR values between 5 and 12, the improvement in SNR was substantial and the fine details were preserved, the edges were not blurred and no spikes or other artefacts were evident, demonstrating the good performances of our method. At very low SNR (SNR = 3) our result is worse than that obtained by a simpler filtering procedure.     

Which factors influence liver stiffness measured by real-time two dimensional shear wave elastography in patients on maintenance hemodialysis?

AimTo evaluate liver stiffness (LS) by real-time two-dimensional shear wave elastography (RT 2D-SWE) and to assess its correlation with the mean arterial pressure (MAP) in patients on maintenance hemodialysis (MHD). The secondary aim was to identify biological and biochemical parameters associated with elevated LS.MethodsThis study enrolled patients treated with MHD in the Split University Hospital from December 2017 through February 2018. LS was measured after a HD session using RT 2D-SWE. Mean arterial pressure was measured before RT-2D-SWE was performed.ResultsThe study enrolled 47 patients with the mean ± standard deviation age of 68.48 ± 14.33 years. Arterial hypertension was diagnosed in 70.2% of patients. Liver stiffness >7 kPa, suggesting clinically relevant fibrosis, was found in 59.5% of patients. Arterial pressure was significantly correlated with LS (ρ = 0.38, P = 0.008). C-reactive protein (ρ = 0.548, P = 0.023), parathyroid hormone (ρ = 0.507, P = 0.038), and total bilirubin (ρ = 0.423, P = 0.020) were correlated with elevated LS.ConclusionMean arterial pressure is correlated with increased LS in patients on MHD. Our results emphasize the importance of proper regulation of arterial blood pressure and indicate that LS should always be interpreted in combination with laboratory parameters. Further prospective studies with larger series are needed.

Chronic kidney disease (CKD) is an important public health problem. The number of CKD patients in the world has increased from approximately 10 000 patients in 1973 to 703 243 in 2015 (1,2). All CKD stages and end stage renal disease (ESRD) are associated with high morbidity, increased health care utilization, and mortality (3). Patients on long-term maintenance hemodialysis (MHD) have an increased risk for hepatitis B and C viral infection and chronic liver inflammation. Acute or chronic liver inflammation is frequently followed by a development of liver fibrosis (LF) (4-6). The clinical presentation of LF differs from that of cirrhosis. Mild LF, as well as early stage liver cirrhosis, are asymptomatic in most patients, which points to the importance of an early diagnosis. Appropriate staging of LF is important for prognosis and for therapeutic decision-making.Percutaneous liver biopsy is still the gold standard for the evaluation and staging of LF (7). It is an invasive procedure with substantial limitations and very serious potential side effects, primarily, post procedural bleeding. The risk is even higher in dialysis patients who have a bleeding tendency due to platelet dysfunction caused by uremic state. Not less important, liver biopsy carries the risk of pneumothorax and hematothorax (8,9). Another limitation is the possibility of a significant sampling error, since the biopsy specimen represents only 1/50 000 the size of the liver parenchyma (10,11). Due to these limitations, many non-invasive tools for the assessment of LF have been recently investigated, showing promising results (11,12). The most frequently applied novel methods, using ultrasound waves for tissue elasticity measurement, are transient elastography and two-dimensional real-time shear wave elastography (RT-2D-SWE) (13,14). RT 2D-SWE is a fast, quantitative method for assessing LF by measuring liver stiffness (LS) in real time. Acoustic push pulses induce shear waves, and their speed is observed as color image in the region of interest (ROI). Velocity (m/s) is determined by measuring the waves passing through the examined tissue. These values are converted into tissue elasticity expressed in kilopascals (Young’s module) (15). 2D-SWE has demonstrated high resolution and excellent reproducibility for assessing LF (16-19).LS can be affected by different parameters. LS values are elevated in healthy people with BMI>30 kg/m², and in patients with viral hepatitis, primary biliary cholangitis, alcoholic liver disease, and cholestatic liver diseases independent of the degree of fibrosis (20-23). LS correlates significantly with portal pressure and arterial pressure (24-27), and is affected by volume overload: either due to heart failure or liver failure with ascites (11,28). To avoid volume overload, LS measurement should be performed following a hemodialysis (HD) session (29-31). It remains unexplored to what extend blood pressure contributes to LS (25). Little is known about biological and biochemical factors associated with LS changes in ESRD patients on MHD. To the best of our knowledge, most such studies have been conducted on patients with underlying liver disease (32,33). Only a few have focused on factors that influence LS (measured by transient elastography) and fibrosis in HD population (28). In dialysis patients, active chronic inflammation possibly affects the liver and changes LS (34). Another pathophysiological mechanism could be chronic hepatic congestion with subsequent idiopathic noncirrhotic portal hypertension (35). This study aims to investigate the correlation between the mean arterial pressure (MAP) and LS in patients on MHD. The secondary aim was to identify biological and biochemical parameters correlated with elevated LS. Finally, we hypothesized that MAP influenced LS and that C-reactive protein (CRP), parathyroid hormone (PTH), and total bilirubin correlate with the LS value.     

Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography

A quasistatic magnetic resonance elastography (MRE) method for the evaluation of breast cancer is proposed. Using a phase contrast, stimulated echo MRI approach, strain imaging in phantoms and volunteers is presented. First-order assessment of tissue biomechanical properties based on inverse strain mapping is outlined and demonstrated. The accuracy of inverse strain imaging is studied through simulations in a two-dimensional model and in an anthropomorphic, three-dimensional finite-element model of the breast. To improve the accuracy of modulus assessment by elastography, inverse methods are discussed as an extension to strain imaging, and simulations quantify MRE in terms of displacement signal/noise required for robust inversion. A direct inversion strategy providing information on tissue modulus and pressure distribution is described along with a novel iterative method utilizing a priori knowledge of tissue geometry. It is shown that through the judicious choice of information from previous contrast-enhanced MRI breast images, MRE data acquisition requirements can be significantly reduced while maintaining robust modulus reconstruction in the presence of strain noise. An experimental apparatus for clinical breast MRE and preliminary images of a normal volunteer are presented.     

Value of whole breast magnetic resonance elastography added to MRI for lesion characterization

The purpose of this work was to assess the diagnostic value of magnetic resonance elastography (MRE) in addition to MRI to differentiate malignant from benign breast tumors, and the feasibility of performing MRE on the whole breast. MRE quantified biomechanical properties within the entire breast (50 slices) using an 11 min acquisition protocol at an isotropic image acquisition resolution of 2 × 2 × 2 mm³. Fifty patients were included. Finally, 43 patients (median age 52) with a suspect breast lesion detected by mammography and/or ultrasound were examined by MRI and MRE at 1.5 T. The viscoelastic parameters, i.e. elasticity (G_d), viscosity (G_l), the magnitude of the complex shear modulus , and the phase angle , were measured via MRE and correlated with MRI Breast Imaging—Reporting and Data System (BI‐RADS) score, histological type, and histological grade. Stroma component and angiogenesis were also correlated with viscoelastic properties. In the 43 lesions, G_d decreased and y increased with the MRI BI‐RADS score (p_Gd = 0.02, p_y = 0.002), whereas (G_l) and y were increased in malignant lesions (p_Gl = 0.045, p_y = 0.0004). The area under the curve increased from 0.84 for MRI BI‐RADS alone to 0.92 with the MRI BI‐RADS and y (AUC increase +0.08; 95% CI (?0.003; 0.16)). Lesion characterization using the y parameter increased the diagnostic accuracy. The phase angle y was found to have a significant role (p = 0.01) in predicting malignancy independently of the MRI BI‐RADS. Interestingly, histological analysis showed no correlation between viscoelastic parameters and percentage and type of stroma, CD34 quantification of vessels, or histological grade. The combination of MRE and MRI improves the diagnostic accuracy for breast lesions in the studied cohort. In particular, the phase angle y was found to have a significant role in predicting malignancy in addition to BI‐RADS.     

Interactive multidimensional display of magnetic resonance imaging data

Acquisition of multiparametric images in multiple planes often requires unacceptably long scanning times. The ability to display high quality planar cuts in arbitrary planes from single plane (eg, transaxial, coronal, or sagittal plane) images would alleviate the need to acquire images in multiple planes. The need to display data from three-dimensional volume acquisitions also poses a problem to the radiologist. We have developed an interactive multidimensional display tool for magnetic resonance data. The tool presents three orthogonal planes (such as transaxial, coronal, and sagittal) simultaneously and allows the user to interactively roam through the data set. The user can select any arbitrary oblique plane and obtain the corresponding reformations. Additionally the tool allows the correlated display of sets of differently acquired data. This tool offers an effective means for the display of isotropic data and reformatted planar data. The ability to interact directly with the data allows increased transference of information to the radiologist and referring physician.