Harmonic motion imaging for focused ultrasound (HMIFU): a fully integrated technique for sonication and monitoring of thermal ablation in tissues

FUS (focused ultrasound), or HIFU (high-intensity-focused ultrasound) therapy, a minimally or non-invasive procedure that uses ultrasound to generate thermal necrosis, has been proven successful in several clinical applications. This paper discusses a method for monitoring thermal treatment at different sonication durations (10 s, 20 s and 30 s) using the amplitude-modulated (AM) harmonic motion imaging for focused ultrasound (HMIFU) technique in bovine liver samples in vitro. The feasibility of HMI for characterizing mechanical tissue properties has previously been demonstrated. Here, a confocal transducer, combining a 4.68 MHz therapy (FUS) and a 7.5 MHz diagnostic (pulse-echo) transducer, was used. The therapy transducer was driven by a low-frequency AM continuous signal at 25 Hz, producing a stable harmonic radiation force oscillating at the modulation frequency. A pulser/receiver was used to drive the pulse-echo transducer at a pulse repetition frequency (PRF) of 5.4 kHz. Radio-frequency (RF) signals were acquired using a standard pulse-echo technique. The temperature near the ablation region was simultaneously monitored. Both RF signals and temperature measurements were obtained before, during and after sonication. The resulting axial tissue displacement was estimated using one-dimensional cross correlation. When temperature at the focal zone was above 48 degrees C during heating, the coagulation necrosis occurred and tissue damage was irreversible. The HMI displacement profiles in relation to the temperature and sonication durations were analyzed. At the beginning of heating, the temperature at the focus increased sharply, while the tissue stiffness decreased resulting in higher HMI displacements. This was confirmed by an increase of 0.8 microm degrees C(-1)(r=0.93, p<.005). After sustained heating, the tissue became irreversibly stiffer, followed by an associated decrease in the HMI displacement (-0.79 microm degrees C(-1), r=-0.92, p<0.001). Repeated experiments showed a reproducible pattern of the HMI displacement changes with a temperature at a slope equal to 0.8+/-0.11 and -0.79+/-0.14 microm degrees C(-1), prior to and after lesion formation in seven bovine liver samples, respectively. This technique was thus capable of following the protein-denatured lesion formation based on the variation of the HMI displacements. This method could, therefore, be applied for real-time monitoring of temperature-related stiffness changes of tissues during FUS, HIFU or other thermal therapies.     

Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion

Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.     

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。     

Tissue characterization using magnetic resonance elastography: preliminary results

The well-documented effectiveness of palpation as a diagnostic technique for detecting cancer and other diseases has provided motivation for developing imaging techniques for noninvasively evaluating the mechanical properties of tissue. A recently described approach for elasticity imaging, using propagating acoustic shear waves and phase-contrast MRI, has been called magnetic resonance elastography (MRE). The purpose of this work was to conduct preliminary studies to define methods for using MRE as a tool for addressing the paucity of quantitative tissue mechanical property data in the literature. Fresh animal liver and kidney tissue specimens were evaluated with MRE at multiple shear wave frequencies. The influence of specimen temperature and orientation on measurements of stiffness was studied in skeletal muscle. The results demonstrated that all of the materials tested (liver, kidney, muscle and tissue-simulating gel) exhibit systematic dependence of shear stiffness on shear rate. These data are consistent with a viscoelastic model of tissue mechanical properties, allowing calculation of two independent tissue properties from multiple-frequency MRE data: shear modulus and shear viscosity. The shear stiffness of tissue can be substantially affected by specimen temperature. The results also demonstrated evidence of shear anisotropy in skeletal muscle but not liver tissue. The measured shear stiffness in skeletal muscle was found to depend on both the direction of propagation and polarization of the shear waves.     

MR guided focused ultrasound: technical acceptance measures for a clinical system

Magnetic resonance (MR) guided focused ultrasound (MRgFUS) is a hybrid technique which offers efficient and safe focused ultrasound (FUS) treatments of uterine fibroids under MR guidance and monitoring. As a therapy device, MRgFUS requires systematic testing over a wide range of operational parameters prior to use in the clinical environment. We present technical acceptance tests and data for the first clinical MRgFUS system, ExAblate 2000 (InSightec Inc., Haifa, Israel), that has been FDA approved for treating uterine fibroids. These tests characterize MRgFUS by employing MR temperature measurements in tissue mimicking phantoms. The coronal scan plane is empirically demonstrated to be most reliable for measuring temperature elevations resulting from high intensity ultrasound (US) pulses ('sonications') and shows high sensitivity to changes in sonication parameters. Temperatures measured in the coronal plane were used as a measure of US energy deposited within the focal spot for a range of sonication parameters used in clinical treatments: spot type, spot length, output power, sonication duration, US frequency, and depth of sonication. In addition, MR images acquired during sonications were used to measure effective diameters and lengths of available sonication spot types and lengths. At a constant 60 W output power, the effective spot type diameters were measured to vary between 4.7 +/- 0.3 mm and 6.6 +/- 0.4 mm; treatment temperatures were found to decrease with increasing spot diameter. Prescribing different spot lengths was found to have no effect on the measured length or on measured temperatures. Tests of MRgFUS positioning accuracy determined errors in the direction parallel to the propagation of the US beam to be significantly greater than those in the perpendicular direction; most sonication spots were erroneously positioned towards the FUS transducer. The tests reported here have been demonstrated to be sufficiently sensitive to detect water leakage inside the FUS transducer. The data presented could be used for comparison by those conducting acceptance tests on other clinical MRgFUS systems.     

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.     

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.     

Conformal thermal therapy using planar ultrasound transducers and adaptive closed-loop MR temperature control: demonstration in gel phantoms and ex vivo tissues

MRI-guided transurethral ultrasound therapy offers a minimally invasive approach for the treatment of localized prostate cancer. Integrating a multi-element planar transducer with active MR temperature feedback can enable three-dimensional conformal thermal therapy of a target region within the prostate gland while sparing surrounding normal tissues. Continuous measurement of the temperature distribution in tissue enables dynamic compensation for unknown changes in blood flow and tissue properties during treatment. The main goal of this study was to evaluate the feasibility of using active temperature feedback on a clinical 1.5 T MR imager for conformal thermal therapy. MR thermometry was performed during heating in both gel phantoms and excised tissue with a transurethral heating applicator, and the rotation rate and power were varied based on the thermal measurements. The capability to produce a region of thermal damage that matched a target boundary was evaluated. The influence of a cooling gradient (to simulate cooling of the rectum or urethra) on the desired pattern of thermal damage was also investigated in gel phantoms. Results showed high correlation between the desired target boundary and the 55 degrees C isotherm generated during heating with an average distance error of 0.9 mm +/- 0.4 mm (n = 6) in turkey breasts, 1.4 mm +/- 0.6 mm (n = 4) in gel phantoms without rectal cooling and 1.4 mm +/- 0.6 mm (n = 3) in gel phantoms with rectal cooling. The results were obtained using a temporal update rate of 5 s, a spatial resolution of 3 x 3 x 10 mm for the control point, and a temperature uncertainty of approximately 1 degrees C. The performance of the control algorithm under these conditions was comparable to that of simulations conducted previously by our group. Overall, the feasibility of generating targeted regions of thermal damage with a transurethral heating applicator and active MR temperature feedback has been demonstrated experimentally. This method of treatment appears capable of accounting for unpredictable and varying tissue properties during the treatment.     

Dose distribution measurements by MRI of a phantom containing lung tissue equivalent compartments made of ferrous sulphate gel

Gel dosimetry based on magnetic resonance imaging (MRI) has previously been shown to provide verification of calculated dose distributions in soft tissue equivalent homogeneous phantoms. This study demonstrates how measurements of dose distribution can also be achieved in a phantom containing porous, lung-equivalent, Fricke gel. A phantom was made of Fe2+ infused low-density gel and conventional ferrous sulphate gel, filled in separate compartments in a Perspex container. Absorbed dose measurements were accomplished by MR imaging and by calibrating the proton spin-lattice relaxation rate (R1) versus absorbed dose by means of TLD measurements. This study shows that the production of lung-equivalent low-density (LD) dosimeter gel (mean CT number of -610 HU) is feasible. The MR signal detected in the LD gel dosimeter was substantially more noisy (i.e. displayed larger random fluctuations) than the signal from conventional gel, as expected. A deviation between calculated (TPS) and measured dose of about 3% (6 MV) and 4-7% (15 MV) was found in the LD region of the phantom. These results correspond well with data from other studies of dose distribution in lung-equivalent phantoms. The Fe2+ infused LD gel therefore seems suitable for measurement of absorbed dose distribution in phantoms that contain lung tissue compartments.     

Optical and acoustic properties at 1064 nm of polyvinyl chloride-plastisol for use as a tissue phantom in biomedical optoacoustics

A novel optoacoustic phantom made of polyvinyl chloride-plastisol (PVCP) for optoacoustic studies is described. The optical and acoustic properties of PVCP were measured. Titanium dioxide (TiO2) powder and black plastic colour (BPC) were used to introduce scattering and absorption, respectively, in the phantoms. The optical absorption coefficient (mua) at 1064 nm was determined using an optoacoustic method, while diffuse reflectance measurements were used to obtain the optical reduced scattering coefficient (mu's). These optical properties were calculated to be mua = (12.818 +/- 0.001)ABPC cm(-1) and mu's = (2.6 +/- 0.2)S(TiO2) + (1.4 +/- 0.1) cm(-1), where ABPC is the BPC per cent volume concentration, and S(TiO2) is the TiO2 volume concentration (mg mL(-1)). The speed of sound in PVCP was measured to be (1.40 +/- 0.02) x 10(3) m s(-1) using the pulse echo transmit receive method, with an acoustic attenuation of (0.56 +/- 1.01) f(1.51+/-0.06)MHz (dB cm(-1)) in the frequency range of 0.61-1.25 MHz, and a density, calculated by measuring the displacement of water, of 1.00 +/- 0.04 g cm(-3). The speed of sound and density of PVCP are similar to tissue, and together with the user-adjustable optical properties, make this material well suited for developing tissue-equivalent phantoms for biomedical optoacoustics.     

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.     

Non-invasive quantitative reconstruction of tissue elasticity using an iterative forward approach

A novel iterative approach is presented to estimate Young's modulus in homogeneous soft tissues using vibration sonoelastography. A low-frequency (below 100 Hz) external vibration is applied and three or more consecutive frames of B-scan image data are recorded. The internal vibrational motion of the soft tissue structures is calculated from 2D displacements between pairs of consecutive frames, which are estimated using a mesh-based speckle tracking method. An iterative forward finite element approach has been developed to reconstruct Young's modulus from the measured vibrational motion. This is accomplished by subdividing the 2D image domain into sample blocks in which Young's modulus is assumed to be constant. Because the finite element equations are internally consistent, boundary values other than displacement are not required. The sensitivity of the results to Poisson's ratio and the damping coefficient (viscosity) is investigated. The approach is verified using simulated displacement data and using data from tissue-mimicking phantoms.     

Magnetic resonance acoustic radiation force imaging

Acoustic radiation force impulse imaging is an elastography method developed for ultrasound imaging that maps displacements produced by focused ultrasound pulses systematically applied to different locations. The resulting images are "stiffness weighted" and yield information about local mechanical tissue properties. Here, the feasibility of magnetic resonance acoustic radiation force imaging (MR-ARFI) was tested. Quasistatic MR elastography was used to measure focal displacements using a one-dimensional MRI pulse sequence. A 1.63 or 1.5 MHz transducer supplied ultrasound pulses which were triggered by the magnetic resonance imaging hardware to occur before a displacement-encoding gradient. Displacements in and around the focus were mapped in a tissue-mimicking phantom and in an ex vivo bovine kidney. They were readily observed and increased linearly with acoustic power in the phantom (R2=0.99). At higher acoustic power levels, the displacement substantially increased and was associated with irreversible changes in the phantom. At these levels, transverse displacement components could also be detected. Displacements in the kidney were also observed and increased after thermal ablation. While the measurements need validation, the authors have demonstrated the feasibility of detecting small displacements induced by low-power ultrasound pulses using an efficient magnetic resonance imaging pulse sequence that is compatible with tracking of a dynamically steered ultrasound focal spot, and that the displacement increases with acoustic power. MR-ARFI has potential for elastography or to guide ultrasound therapies that use low-power pulsed ultrasound exposures, such as drug delivery.     

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.     

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.     

Performance of ultrasound based measurement of 3D displacement using a curvilinear probe for organ motion tracking

Three-dimensional (3D) soft tissue tracking is of interest for monitoring organ motion during therapy. Our goal is to assess the tracking performance of a curvilinear 3D ultrasound probe in terms of the accuracy and precision of measured displacements. The first aim was to examine the depth dependence of the tracking performance. This is of interest because the spatial resolution varies with distance from the elevational focus and because the curvilinear geometry of the transducer causes the spatial sampling frequency to decrease with depth. Our second aim was to assess tracking performance as a function of the spatial sampling setting (low, medium or high sampling). These settings are incorporated onto 3D ultrasound machines to allow the user to control the trade-off between spatial sampling and temporal resolution. Volume images of a speckle-producing phantom were acquired before and after the probe had been moved by a known displacement (1, 2 or 8 mm). This allowed us to assess the optimum performance of the tracking algorithm, in the absence of motion. 3D speckle tracking was performed using 3D cross-correlation and sub-voxel displacements were estimated. The tracking performance was found to be best for axial displacements and poorest for elevational displacements. In general, the performance decreased with depth, although the nature of the depth dependence was complex. Under certain conditions, the tracking performance was sufficient to be useful for monitoring organ motion. For example, at the highest sampling setting, for a 2 mm displacement, good accuracy and precision (an error and standard deviation of <0.4 mm) were observed at all depths and for all directions of displacement. The trade-off between spatial sampling, temporal resolution and size of the field of view (FOV) is discussed.     

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.     

Combining ultrasound-based elasticity estimation and FE models to predict 3D target displacement

During minimally invasive surgical procedures (e.g., needle insertion during interventional radiological procedures), needle–tissue interactions and physiological processes cause tissue deformation. Target displacement is caused by soft-tissue deformation, which results in misplacement of the surgical tool (needle). This study presents a technique to predict target displacement in three-dimensions (3D) by combining soft-tissue elasticity estimation using an ultrasound-based acoustic radiation force impulse (ARFI) technique and finite element (FE) models. Three different phantoms with targets are manufactured, and subjected to varying loading and boundary conditions. Ultrasound images are acquired using a 3D probe during loading and unloading of each phantom, and subsequently target displacement is calculated. 3D FE models of the phantoms are developed, and they are used to predict target displacement. The maximum absolute error in target displacement between the experiments and FE analyses is found to be 1.39 mm. This error is less than the smallest tumor diameter (2.0–3.0 mm) which can be detected in breast tissue. This study shows that the combination of soft-tissue elasticity estimation using the ARFI technique and 3D FE models can accurately predict target displacement, and could be used to develop patient-specific plans for surgical interventions.     

Unipolar MR elastography: Theory,numerical analysis and implementation

In MR elastography (MRE), zeroth moment balanced motion‐encoding gradients (MEGs) are incorporated into MRI sequences to induce a phase shift proportional to the local displacement caused by external actuation. To maximize the signal‐to‐noise ratio (SNR), fractional encoding is employed, i.e., the MEG duration is reduced below the wave period. Here, gradients encode primarily the velocity of the motion‐reducing encoding efficiency. Thus, in GRE‐MRE, T₂* decay and motion sensitivity have to be balanced, imposing a lower limit on repetition times (TRs). We propose to use a single trapezoidal gradient, a “unipolar gradient”, to directly encode spin displacement. Such gradients cannot be used in conventional sequences as they exhibit a large zeroth moment and dephase magnetization. By time‐reversing a spoiled SSFP sequence, the spoiling gradient becomes an efficient unipolar MEG. The proposed “unipolar MRE” technique benefits from this approach in three ways: first, displacement encoding is split over multiple TRs increasing motion sensitivity; second, spoiler and MEG coincide, allowing a reduction in TR; third, motion sensitivity of a typical unipolar lobe is of an order of magnitude higher than a bipolar MEG of equal duration. In this work, motion encoding using unipolar MRE is analyzed using the extended phase graph (EPG) formalism with a periodic motion propagator. As an approximation, the two‐transverse TR approximation for diffusion‐weighted SSFP is extended to incorporate cyclic motion. A complex encoding efficiency metric is introduced to compare the displacement fields of unipolar and conventional GRE‐MRE sequences in both magnitude and phase. The derived theoretical encoding equations are used to characterize the proposed sequence using an extensive parameter study. Unipolar MRE is validated against conventional GRE‐MRE in a phantom study showing excellent agreement between measured displacement fields. In addition, unipolar MRE yields significantly increased octahedral shear strain‐SNR relative to conventional GRE‐MRE and allows for the recovery of high stiffness inclusions, where conventional GRE‐MRE fails.