In MR elastography (MRE), periodic tissue motion is phase encoded using motion-encoding gradients synchronized to an externally applied periodic mechanical excitation. Conventional methods result in extended scan time for quality phase images, thus limiting the broad application of MRE in the clinic. For practical scan times, researchers have been relying on one-dimensional or two-dimensional motion-encoding, low-phase sampling and a limited number of slices, and artifact-prone, single-shot, echo planar imaging (EPI) readout. Here, we introduce a rapid multislice pulse sequence capable of three-dimensional motion encoding that is also suitable for simultaneously encoding motion with multiple frequency components. This sequence is based on a gradient-recalled echo (GRE) sequence and exploits the principles of fractional encoding. This GRE MRE pulse sequence was validated as capable of acquiring full three-dimensional motion encoding of isotropic voxels in a large volume within less than a minute. This sequence is suitable for monofrequency and multifrequency MRE experiments. In homogeneous paraffin phantoms, the eXpresso sequence yielded similar storage modulus values as those obtained with conventional methods, although with markedly reduced variances (7.11 ± 0.26 kPa for GRE MRE versus 7.16 ± 1.33 kPa for the conventional spin-echo EPI sequence). The GRE MRE sequence obtained better phase-to-noise ratios than the equivalent spin-echo EPI sequence (matched for identical acquisition time) in both paraffin phantoms and in vivo data in the liver (59.62 ± 11.89 versus 27.86 ± 3.81, 61.49 ± 14.16 versus 24.78 ± 2.48 and 58.23 ± 10.39 versus 23.48 ± 2.91 in the X, Y and Z components, respectively, in the case of liver experiments). Phase-to-noise ratios were similar between GRE MRE used in monofrequency or multifrequency experiments (75.39 ± 14.93 versus 86.13 ± 18.25 at 28 Hz, 71.52 ± 24.74 versus 86.96 ± 30.53 at 56 Hz and 95.60 ± 36.96 versus 61.35 ± 26.25 at 84Hz, respectively).

This article presents a new approach to magnetic resonance elastography of the prostate using transperineal mechanical excitation. This approach is validated using a prostate elasticity phantom and in vivo studies of healthy volunteers. It is demonstrated that the transperineal approach can generate shear wave amplitudes on the order of 6–30 μm in the mid‐gland region. The driver was implemented using an electromagnetic actuator with a hydraulic transmission system. The magnetic resonance elastography acquisition time has been reduced significantly by using a “second harmonic” approach. Displacement fields are processed using the established three‐dimensional local frequency estimation algorithm. The three‐dimensional curl‐based direct inversion was used to calculate the local wavelength. The traveling wave expansion algorithm was used to reconstruct the wave damping image for one case. Using the proposed method, it was possible to resolve lesions of 0.5 cc in the phantom study. Repeatability experiments were performed and analyzed. The results from this study indicate that transperineal magnetic resonance elastography—without an endorectal coil—is a suitable candidate for a patient study involving multiparametric magnetic resonance imaging of prostate cancer, where magnetic resonance elastography may provide additional information for improved diagnosis and image‐based surveillance. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.

The purpose of this work was to assess trans-perineal prostate magnetic resonance elastography (MRE) for (1) repeatability in phantoms/volunteers and (2) diagnostic power as correlated with histopathology in prostate cancer patients. The three-dimensional (3D) displacement field was obtained using a fractionally encoded gradient echo sequence using a custom-made transducer. The repeatability of the method was assessed based on three repeat studies and by changing the driving frequency by 3% in studies on a phantom and six healthy volunteers. Subsequently, 11 patients were examined with MRE prior to radical prostatectomy. The areas under the receiver operating characteristic curves were calculated using a windowed voxel-to-voxel approach by comparing the 2D registered slides, masked with the Gleason score. For the repeatability study, the average intraclass correlation coefficient for elasticity images was 99% for repeat phantom studies, 98% for ±6 Hz phantom studies, 95% for volunteer repeat studies with 2 min acquisition time, 82% for ±2 Hz volunteer studies with 2 min acquisition time and 73% for repeat volunteer studies with 8 min acquisition time. For the patient study, the average elasticity was 8.2 ± 1.7 kPa in the prostate capsule, 7.5 ± 1.9 kPa in the peripheral zone (PZ), 9.7 ± 3.0 kPa in the central gland (CG) and 9.0 ± 3.4 kPa in the transition zone. In the patient study, cancerous tissue with Gleason score at least 3 + 3 was significantly (p < 0.05) different from normal tissue in 10 out of 11 cases with tumors in the PZ, and 6 out of 9 cases with tumors in the CG. However, the overall case-averaged area under the curve was 0.72 in the PZ and 0.67 in the CG. Cancerous tissue was not always stiffer than normal tissue. The inversion algorithm was sensitive to (i) vibration amplitude and displacement nodes and (ii) misalignment of the 3D wave field due to subject movement.

In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.

Our aim is to develop a clinically viable, fast-acquisition, prostate MR elastography (MRE) system with transperineal excitation. We developed a new actively shielded electromagnetic transducer, designed to enable quick deployment and positioning within the scanner. The shielding of the transducer was optimized using simulations. We also employed a new rapid pulse sequence that encodes the three-dimensional displacement field in the prostate gland using a fractionally encoded steady-state gradient echo sequence, thereby shortening the acquisition time to a clinically acceptable 8-10 min. The methods were tested in two phantoms and seven human subjects (six volunteers and one patient with prostate cancer). The MRE acquisition time for 24 slices, with an isotropic resolution of 2 mm and eight phase offsets, was 8 min, and the total scan, including positioning and set-up, was performed in 15-20 min. The phantom study demonstrated that the transducer does not interfere with the acquisition process and that it generates displacement amplitudes that exceed 100 µm even at frequencies as high as 300 Hz. In the in vivo human study, average wave amplitudes of 30 µm (46 µm at the apex) were routinely achieved within the prostate gland at 70 Hz. No pain or discomfort was reported. Results in a single patient suggest that MRE can identify cancer tumors, although this result is preliminary. The proposed methods allow the integration of prostate MRE with other multiparametric MRI methods. The results of this study clearly motivate the clinical evaluation of transperineal MRE in patients.

In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques.

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

We consider the inverse problem of continuum mechanics with the tissue deformation described by a mixed displacement-pressure finite element formulation. The mixed formulation is used to model nearly incompressible materials by simultaneously solving for both elasticity and pressure distributions. To improve numerical conditioning, a common solution to this problem is to use regularization to constrain the solutions of the inverse problem. We present a sparsity regularization technique that uses the discrete cosine transform to transform the elasticity and pressure fields to a sparse domain in which a smaller number of unknowns is required to represent the original field. We evaluate the approach by solving the dynamic elastography problem for synthetic data using such a mixed finite element technique, assuming time harmonic motion, and linear, isotropic and elastic behavior for the tissue. We compare our simulation results to those obtained using the more common Tikhonov regularization. We show that the sparsity regularization is less dependent on boundary conditions, less influenced by noise, requires no parameter tuning and is computationally faster. The algorithm has been tested on magnetic resonance elastography data captured from a CIRS elastography phantom with similar results as the simulation.