Intervertebral Disc Internal Deformation Measured by Displacements Under Applied Loading with MRI at 3T

Purpose: Noninvasive assessment of tissue mechanical behavior could enable insights into tissue function in healthy and diseased conditions and permit the development of effective tissue repair treatments. Measurement of displacements under applied loading with MRI (dualMRI) has the potential for such biomechanical characterization on a clinical MRI system. Methods: dualMRI was translated from high-field research systems to a 3T clinical system. Precision was calculated using repeated tests of a silicone phantom. dualMRI was demonstrated by visualizing displacements and strains in an intervertebral disc and compared to T 2 measured during cyclic loading. Results: The displacement and strain precisions were 24 mm and 0.3% strain, respectively, under the imaging parameters used in this study. Displacements and strains were measured within the intervertebral disc, but no correlations were found with the T 2 values. Conclusion: The translation of dualMRI to a 3T system unveils the potential for in vivo studies in a myriad of tissue and organ systems. Because of the importance of mechanical behavior to the function of a variety of tissues, it's expected that dual-MRI implemented on a clinical system will be a powerful tool in assessing the interlinked roles of structure, mechanics, and function in both healthy and diseased tissues. Key words: displacement; strain; intervertebral disc; elastography; clinical magnetic resonance imaging The mechanical behavior of a biomaterial is intimately linked to its function, both within natural tissues and biocompatible materials. The material properties and also the loading environment affect the mechanical behavior of tissues, particularly as they relate to healthy and pathological conditions within the body. Noninvasive methods to quantify the mechanical behavior of biomaterials and tissues would permit the measurement of material properties while both preserving the native loading environment and accounting for its influence. Such methods would improve longitudinal studies in animals or humans, greatly reducing the number of animals or human subjects needed for clinical trials, among other benefits. Additionally, these methods could also be implemented to assess tissue quality in patients and monitor the long-term effectiveness of pharmacological or tissue engineering treatments. Some studies have attempted to correlate various relaxometry measures, such as T 2 and T 1r , to mechanical properties in a number of tissues (1,2), motivated by the idea that relaxometry measures correspond to biochemistry and, in turn, are related to mechanical behavior. However, these correlations are based on mechanical tests performed on explanted tissue and do not take advantage of the noninvasive nature of MRI to fully assess tissues within their native environment. Because techniques like displacementencoded MRI can measure displacements and strains noninvasively (3), such a technique for biomechanical characterization of tissue could complement other quantitative MRI techniques (4) for the overall assessment of soft tissue function. The goal of this study was to translate a noninvasive imaging technique that can measure displacements under applied loading with MRI (dualMRI) to a clinical 3T MRI system. Previous efforts in our lab have utilized dualMRI on a high-field MRI scanner, where displacements and strains were measured in explants of healthy cartilage (3) and in intact joints, including tibiofemoral cartilage (5) and degenerated intervertebral discs in animal models (6). Despite the advantages proffered by the higher magnetic field of research MRI systems, these systems are often limited to small volumes and are not approved for clinical use on human subjects. Translation of the dualMRI technique to a clinical scanner would allow for studies of live animals and human subjects, as well as larger tissues and biomaterials that would not be able to fit into the limited confines of a small-bore high-field MRI system. The technical challenge of implementing dualMRI on a living animal or human subject is twofold: (1) the translation of a load-synchronized, displacement-encoded MRI sequence and (2) the development of noninvasive, organ-or joint-specific loading systems capable of repeatable cyclic loading of the tissues of interest. In this article, to address the first of these challenges, we report the translation of dualMRI to a clinical MRI system at 3T, the determination of technique precision using imaging phantoms, and the demonstration of this technique within an intact human intervertebral disc section. We also demonstrate that the displacements and strains measured with dualMRI can be compared to the T 2 distribution of the disc measured under cyclic load. 1231 This research represents a critical step toward the noninvasive in vivo measurement of biomaterial mechanical properties, permitting future studies in clinical and animal research. METHODS Displacement-Encoded Imaging dualMRI was implemented on a 3T clinical MRI system (General Electric Signa HDx, Waukesha, WI) using an eight-channel knee volume coil and a custom pulse sequence After complementary phase-cycled scans were combined for CANSEL (8), a phase difference reconstruction across all channels (9) was used to isolate the overall phase difference between the reference and encoded scans. A sum of squares magnitude reconstruction across all channels was used to compute the signal-to-noise ratio (SNR) of a region-of-interest (ROI) with respect to a region of noise (i.e., air). The displacement in the encoding direction was then computed as a function of the phase difference, as previously described (3,10). Orthogonal in-plane displacements were then smoothed with a Gaussian 5 Â 5 kernel (11) prior to estimation of the Green-Lagrange strain tensor (12). Precision of dualMRI The precision of our dualMRI technique was evaluated across five repeated scan series of a silicone gel phantom (Sylgard 527, Dow Corning, Elizabethtown, KY) that was cyclically loaded with an MRI-compatible loading apparatus (4). Displacement encoding was accomplished with an encoding gradient area of 3.9145 mT ms/mm, equivalent to displacement encoding of 0.33 p/mm, based on pilot studies that showed no more than 63 mm of expected internal deformation. A mixing time (TM) of 600 ms, which included spoiler gradients immediately before acquisition, allowed for the onset of loading prior to data acquisition during the load plateau. TM is limited by the capabilities of the load apparatus (i.e., time required to reach desired load); therefore, the minimum TM allowable by the loading system was chosen to maximize the stimulated echo signal. SSFSE acquisition parameters were as follows: effective echo time (TE) ¼ 62 ms, matrix size ¼ 256 Â 256, spatial resolution ¼ 703 Â 703 mm 2 , and eight averages. The SSFSE sequence was limited by the system software to a field of view of 180 Â 180 mm 2 and slice thickness of 3 mm. Because the acquisition and the loading were synchronized, the effective repetition time was dictated by the 3-s duration loading cycles, during which a load of 18.5 N was applied for 1.5 s, based on previous studies (4,6). The experiment time for all scans within each repeated dualMRI experiment was 10 min. Image acquisition was completed before the load was released within each cycle. Imaging data was processed as described above to calculate in-plane displacements. Precision was computed as the pooled standard deviation across the five repeated scan series of displacement and strain values across 16 points within the imaging phantom (3,5). Precision was calculated for raw displacements and displacements and strains after 10-100 cycles of smoothing (11). dualMRI in an Intact Intervertebral Disc Section To demonstrate the dualMRI technique in a biological specimen, cyclic compression and imaging of a cadaveric intervertebral disc section was synchronized. A cadaveric lumbar spine was obtained from a tissue bank (AlloSource, Centennial, CO) and kept frozen until specimen preparation. The donor was a 22-year-old male and weighed 111 kg, with no medical history of disc degeneration or other spine disease. A spine segment inclusive of the fourth lumbar vertebra (L4) to the fifth lumbar Timing of dualMRI on a 3T MRI system. This schematic shows the timing events for dualMRI in a clinical 3T MRI system (a). Cyclic loading was synchronized with radiofrequency (RF) pulses and gradient actions, including the gradient applied for displacement encoding (G de ). Gradient actions in the readout, phase-encode, and slice-select directions are typical for a singleshot fast spin echo (SSFSE) acquisition and, for brevity, are not shown here. RF transmission pulses are shown in the solid lines and receive action (i.e. acquisition) is shown in dashed lines. Standard MRI scans of an undeformed and deformed imaging phantom (b) are also shown to demonstrate the time points during which the key dualMRI actions were performed. The undeformed image was acquired during the equivalent time point when the phase-cycled RF pulses and displacement encoding gradient, with gradient strength k, were applied. After a mixing time (TM), dualMRI data was acquired using SSFSE during the deformed state. 1232 Chan and Neu vertebra (L5) was excised. The spinal processes and facet joints were removed by transecting the pedicles of the vertebral arch, retaining the vertebral bodies superior and inferior to the L4/L5 intervertebral disc. The L4 and L5 vertebral bodies were partially embedded in polymethylmethacrylate, permitting the full disc segment to be anchored into an MRI-compatible loading apparatus for cyclic compression. Prior to cyclic loading, standard MRI was performed to obtain morphological data. Compression of 450 N was then applied with the MRI-compatible cyclic loading apparatus for 1.5 s during a 3-s cycle. Preconditioning of more than 500 loading cycles (based on pilot studies) was applied prior to dualMRI to ensure that the specimen reached a quasi-steady state deformation response to the cyclic loading (13). Displacement-encoded images were acquired during the load plateau period under quasi-steady state. Parameters for dualMRI were same as for the precision studies above. Displacements within the L4/L5 disc were smoothed to 100 smoothing cycles, and strains were computed. During cyclic loading, standard MRI images were also acquired in the undeformed and deformed configurations for the measurement of nominal change in height and width under cyclic compression. The total experiment time for all dualMRI scans was 20 min, excluding the time necessary for the specimen to achieve quasi-steady state (less than 20 min under this experimental loading regime). T 2 Analysis In addition, to investigate whether any correspondence existed between the presence of mechanical loading and mechanical behavior and the measured T 2 , a known correlate to disc biochemistry (14) and stage of degeneration (15), we estimated T 2 prior to cyclic loading, during cyclic loading immediately after dualMRI, and immediately after the cessation of cyclic loading. T 2 was estimated using a set of fast spin echo acquisitions with variable TE (TEs ¼ 20, 60, 100, 140, 180, and 240 ms) of the same imaging plane as dualMRI. Repetition time was set to 3000 ms, which is approximately four to five times T 1 of human disc (16), to minimize T 1 -weighting. An electronic trigger was used to synchronize the acquisitions for T 2 mapping under cyclic loading. T 2 mapping experiments were performed within 10 min under each loading condition. A least squares fit of an exponential decay curve was used to estimate T 2 at each pixel within the disc ROI before, during and after cyclic loading. Histograms of the T 2 values in each ROI were generated using bins of 5 ms intervals for qualitative comparison. The ROIs were also divided into five regions along the width of the disc, and, separately, into five regions along the height of the disc. Average regional T 2 was computed and compared for each of these sections between loading conditions. Average T 2 values are reported as mean 6 standard deviation. T 2 values were correlated pixel-by-pixel to displacements and strains using linear regression. Statistical significance was defined as P < 0.05. RESULTS dualMRI Precision Displacements measured by dualMRI, displacements after smoothing, and estimated strains were visualized in the silicone phantom FIG. 2. Displacement and strains in a silicone phantom used to evaluate precision. A cyclically loaded silicone phantom was used to validate displacements (a) and strains (b), and determine relationships between displacement and strain precision (c). Including raw displacements, and displacements and strains after 10 and 100 smoothing cycles, depict the influence of displacement smoothing on deformation patterns. Displacements and strains were measured with dualMRI under the same loading conditions that resulted in the undeformed and deformed images in Disc Displacements and Strains at 3T with DualMRI 1233 Intervertebral Disc Displacements and Strains dualMRI on a 3T MRI system permitted the visualization of displacements and strains within the L4/L5 intervertebral disc T 2 Values The average T 2 values across the full disc before, during, and after cyclic loading were 76.8 6 33.7, 80.8 6 33.8, and 80.5 6 34.7 ms, respectively DISCUSSION Translation of dualMRI from research (9.4 T/30 cm bore) to clinical (3.0 T/60 cm bore) MRI systems presented several technical challenges associated with the larger imaging volume and weaker magnetic field, including reduced spatial resolution and faster T 1 decay of the displacement-encoded signal. Despite a reduction in spatial resolution and increased slice thickness, the precision of raw displacement measurement, 95 mm, fell within the ranges of raw displacement precisions measured previously on a research MRI system (4,5). This is most likely because the precision of displacement is tied closely to the SNR (4), which is increased with larger voxel sizes. The displacement and strain fields and precision values after smoothing were also comparable to previous studies 1234 Chan and Neu note that increasing the amount of smoothing could increase bias between the smoothed value and the true value, previous studies with displacement smoothing showed that this bias is often smaller than the precision (11). This validation study therefore shows that, if larger voxel sizes are acceptable for the tissue of interest, displacement precisions of better than half the spatial resolution can be achieved without smoothing, and smoothing can improve displacement and strain precisions up to 24 mm and 0.3%, respectively. Although some spatial resolution may be lost in the translation from research to clinical scanner, the ability to measure displacements and strains noninvasively in larger volumes and potentially living subjects far outweigh the disadvantages of the clinical system. Several of the imaging parameters used in this study were limited by the imaging system, loading device, or image processing software. The effect on SNR by T 2 decay with TE (in fast spin echo acquisitions) and by T 1 decay with TM (in stimulated echo applications) are well known physical phenomena (3,4,10). Accordingly, image acquisition parameters were chosen to minimize TE and TM within the limitations of the chosen acquisition size and the timing of the load system, respectively. The displacement encoding of 0.33 p/mm was selected to avoid excessive phase wrapping and ease computational efforts in unwrapping the phase. Based on pilot studies, we expected internal deformations of no more than 3 mm in absolute value and therefore set the displacement encoding to encode 3 mm as p. Spatial resolution in this study was limited by the field of view and the choice in acquisition matrix size. In preliminary studies, we compared displacement precision for square matrix sizes of 256 Â 256, 384 Â 384, and 512 Â 512. The additional lines of acquisition resulted in longer effective TEs and required longer load plateaus to accommodate the longer total acquisition time, resulting in attenuation of signal and loss of precision. Although a smaller matrix size (i.e., 128 Â 128) could have been chosen for higher SNR and potentially improved FIG. 4. T 2 analysis of a cyclically loaded intervertebral disc. T 2 maps were estimated for an intervertebral disc (a), before (blue), during (red), and after (green) cyclic loading in the same imaging slice as was used for dualMRI. ROIs (mask for disc before loading shown) were divided into five regions along the width (b) and the height (c) and used to compare average regional T 2 and a histogram of T 2 values (binned in 5-ms intervals) across the full disc (d). Although no displacements and strains were significantly correlated to T 2 values (P > 0.05), the relationship with E xy after 100 cycles of smoothing for each pixel within the ROI is shown (e) because it had the highest R 2 of all linear regressions. Disc Displacements and Strains at 3T with DualMRI 1235 displacement precision, we desired a spatial resolution of at least 1 mm and therefore chose 256 Â 256 acquisition matrix. Although the aforementioned parameters are limited by the current system, a detailed, parameterized study of the effects of TE, TM, displacement encoding strength, spatial resolution, and other imaging parameters could be useful in further characterizing this technique. In this study, dualMRI was demonstrated on the clinical MRI system with a clinically relevant human intervertebral disc segment In previous studies, texture correlation has also been used with magnitude-based MRI to measure the internal strain of intervertebral discs (18). This previous study reported a displacement resolution of 1/20th of a pixel or 12 mm after interpolation and smoothing; however, the optimal subset of 61 pixels, equivalent to 5.2 mm in their study, reportedly resulted in loss of local strain detail. Compared to the cyclic loading conditions used in this study for dualMRI, the texture correlation study used a statically loaded disc. Although texture correlation can provide accurate strain measures in tissues that provide enough SNR and texture in magnitude images, phase-contrast techniques, including dualMRI, do not depend on image texture, which is especially an advantage in tissues that tend toward spatial homogeneity in MRI signal intensity. In this study, we also measured T 2 before, during, and after cyclic loading with the goal of directly comparing T 2 and displacements and strains during cyclic loading Although this study presents promising results for displacement and strain precision, there are a number of improvements that can expedite implementation in vivo. The use of surface array coils should be considered for tissues that would be inappropriate for a volume coil, with SNR as a key deciding factor. Although SSFSE is a fast sequence, it is limited in terms of spatial resolution and relies on the assumption of k-space symmetry to "fill" the remainder of k-space in post processing. A number of acquisition sequences could be substituted for SSFSE, although each acquisition technique presents its own advantages and disadvantages. Additionally, as a technique that synchronizes displacement-encoded MRI with externally applied loading, dualMRI requires an MRI-compatible loading system that can consistently load the tissue or tissues of interest in the confines of a clinical MRI system. The loading system should be able to bring the tissue of interest to a quasi-steady state load-deformation response (13) to achieve optimal image quality. Mechanically loading parts of a living animal or human volunteer, without inducing unwanted motion artifacts or causing undue discomfort, poses a strong technical challenge. Although there are a number of developments that remain to be surmounted, this study nonetheless demonstrates for the first time the use of dualMRI on a clinical MRI system, establishing the in vivo potential. CONCLUSIONS dualMRI was translated to a clinical 3T MRI system for the precise measurement of internal tissue deformation. The precision of displacement measurements was below half the spatial resolution of the image acquisition. Strain precisions were below 2% after just 10 smoothing cycles, and more smoothing (i.e., 100 smoothing cycles) permitted strain precisions of 0.3%. The sequence was demonstrated with a controlled loading system, permitting the visualization of displacement and strain fields in a cyclically compressed intervertebral disc. T 2 mapping during cyclic loading also provided an indication of the structural and biochemical characteristics of the disc. A combination of dualMRI and quantitative MRI could 1236 Chan and Neu be used in combination to gain insight into the structure and mechanical function of tissue noninvasively. ACKNOWLEDGMENTS The authors gratefully acknowledge the assistance of Kent Butz and Paull Gossett, in the specimen preparation and the design of the loading apparatus, Aaditya Chandramouli for his assistance in specimen preparation, Gregory Tamer for his technical assistance on the clinical MRI system, and Eric Nauman for advice and access to the cadaveric specimen. The purpose of this study was to compare displacement behavior of cyclically loaded cadaveric human intervertebral discs as measured noninvasively on a clinical 3.0 T and a research 9.4 T MRI system. Intervertebral discs were cyclically compressed at physiologically relevant levels with the same MRIcompatible loading device in the clinical and research systems. Displacement-encoded imaging was synchronized t

Indentation Probing of In Vitro Bovine Articular Cartilage: Effects on Chondrocyte Viability and Tissue Biomechanics

Osteoarthritis (OA) consists of a degenerative disease on articular cartilage, which is prone to excessive mechanical loading and frictional resistance that leads to the wear and tear of the tissue. These factors result in the progressive and incurable disease that affects millions of people worldwide. The goal is to characterize chondrocyte viability and the in vitro biomechanical properties of articular cartilage in two confined indentation studies. One study looks at the chondrocyte viability over seven days. The second compares the immediate effects of strain rates on chondrocyte viability and tissue biomechanics. Bovine cartilage explants are harvested, cultured, and then 40% strain indentation tests are conducted at the rates of 80% s-1 & 0.1% s-1 depending on the study. All samples are stained and imaged via confocal microscopy after indentation and twice more during the seven-day study. Tissue micro- and macro-mechanics was assessed by atomic force microscopy and by the indentation test instrument, respectively. At the rate of 80% s-1, chondrocyte viability did not significantly progress over seven days. A statistically significant decrease in chondrocyte viability between 80% s-1 & 0.1% s-1 was noted along with a statistically significant decrease in the stiffness of the indented area. Cartilage damage propagation over seven days did not occur and cartilage mechanics is dependent on strain rate. For developing a more accurate post-injury OA development model, further biomechanical information needs to be elucidated

In vivo articular cartilage deformation: noninvasive quantification of intratissue strain during joint contact in the human knee

The in vivo measurement of articular cartilage deformation is essential to understand how mechanical forces distribute throughout the healthy tissue and change over time in the pathologic joint. Displacements or strain may serve as a functional imaging biomarker for healthy, diseased, and repaired tissues, but unfortunately intratissue cartilage deformation in vivo is largely unknown. Here, we directly quantified for the first time deformation patterns through the thickness of tibiofemoral articular cartilage in healthy human volunteers. Magnetic resonance imaging acquisitions were synchronized with physiologically relevant compressive loading and used to visualize and measure regional displacement and strain of tibiofemoral articular cartilage in a sagittal plane. We found that compression (of 1/2 body weight) applied at the foot produced a sliding, rigid-body displacement at the tibiofemoral cartilage interface, that loading generated subject- and gender-specific and regionally complex patterns of intratissue strains, and that dominant cartilage strains (approaching 12%) were in shear. Maximum principle and shear strain measures in the tibia were correlated with body mass index. Our MRI-based approach may accelerate the development of regenerative therapies for diseased or damaged cartilage, which is currently limited by the lack of reliable in vivo methods for noninvasive assessment of functional changes following treatment

Finite deformation elastography of articular cartilage and biomaterials based on imaging and topology optimization

Tissues and engineered biomaterials exhibit exquisite local variation in stiffness that defines their function. Conventional elastography quantifies stiffness in soft (e.g. brain, liver) tissue, but robust quantification in stiff (e.g. musculoskeletal) tissues is challenging due to dissipation of high frequency shear waves. We describe new development of finite deformation elastography that utilizes magnetic resonance imaging of low frequency, physiological-level (large magnitude) displacements, coupled to an iterative topology optimization routine to investigate stiffness heterogeneity, including spatial gradients and inclusions. We reconstruct 2D and 3D stiffness distributions in bilayer agarose hydrogels and silicon materials that exhibit heterogeneous displacement/strain responses. We map stiffness in porcine and sheep articular cartilage deep within the bony articular joint space in situ for the first time. Elevated cartilage stiffness localized to the superficial zone is further related to collagen fiber compaction and loss of water content during cyclic loading, as assessed by independent T2 measurements. We additionally describe technical challenges needed to achieve in vivo elastography measurements. Our results introduce new functional imaging biomarkers, which can be assessed nondestructively, with clinical potential to diagnose and track progression of disease in early stages, including osteoarthritis or tissue degeneration. </div

Cell nucleus elastography with the adjoint-based inverse solver

Background and Objectives: The mechanics of the nucleus depends on cellular structures and architecture, and impact a number of diseases. Nuclear mechanics is yet rather complex due to heterogeneous distribution of dense heterochromatin and loose euchromatin domains, giving rise to spatially variable stiffness properties. Methods: In this study, we propose to use the adjoint-based inverse solver to identify for the first time the nonhomogeneous elastic property distribution of the nucleus. Inputs of the inverse solver are deformation fields measured with microscopic imaging in contracting cardiomyocytes. Results: The feasibility of the proposed method is first demonstrated using simulated data. Results indicate accurate identification of the assumed heterochromatin region, with a maximum relative error of less than 5%. We also investigate the influence of unknown Poisson's ratio on the reconstruction and find that variations of the Poisson's ratio in the range [0.3-0.5] result in uncertainties of less than 15% in the identified stiffness. Finally, we apply the inverse solver on actual deformation fields acquired within the nuclei of two cardiomyocytes. The obtained results are in good agreement with the density maps obtained from microscopy images. Conclusions: Overall, the proposed approach shows great potential for nuclear elastography, with promising value for emerging fields of mechanobiology and mechanogenetics

Transient and Microscale Deformations and Strains Measured under Exogenous Loading by Noninvasive Magnetic Resonance

Characterization of spatiotemporal deformation dynamics and material properties requires non-destructive methods to visualize mechanics of materials and biological tissues. Displacement-encoded magnetic resonance imaging (MRI) has emerged as a noninvasive and non-destructive technique used to quantify deformation and strains. However, the techniques are not yet applicable to a broad range of materials and load-bearing tissues. In this paper, we visualize transient and internal material deformation through the novel synchrony of external mechanical loading with rapid displacement-encoded MRI. We achieved deformation measurements in silicone gel materials with a spatial resolution of 100 µm and a temporal resolution (of 2.25 ms), set by the repetition time (TR) of the rapid MRI acquisition. Displacement and strain precisions after smoothing were 11 µm and 0.1%, respectively, approaching cellular length scales. Short (1/2 TR) echo times enabled visualization of in situ deformation in a human tibiofemoral joint, inclusive of multiple variable T2 biomaterials. Moreover, the MRI acquisitions achieved a fivefold improvement in imaging time over previous technology, setting the stage for mechanical imaging in vivo. Our results provide a general approach for noninvasive and non-destructive measurement, at high spatial and temporal resolution, of the dynamic mechanical response of a broad range of load-bearing materials and biological tissues

Strains in stratified agarose constructs as determined by displacement-encoded MRI

Osteoarthritis (OA) is a debilitating disease for which no satisfactory treatment exists. Tissue engineering-based strategies have shown considerable potential for repair. Agarose is frequently used as a scaffold material, as chondrocytes maintain their phenotype and cells remain responsive to mechanical stimuli. To improve the mechanical quality of tissue engineered cartilage, recent studies aimed to reproduce the depth-dependent structure of healthy cartilage. One approach to achieve this is by applying depth-dependent mechanical stimuli via cyclically sliding a glass cylinder over the cell-seeded agarose construct [1,2]. The different strains applied to the surface and the deeper regions are expected to induce stratified matrix synthesis and therefore stratified tissue stiffness. Consequently, with the same external stimuli, the internal strain distribution may alter with ongoing tissue development. Such effect is important to understand in order to optimize mechanical loading regimes for cartilage tissue engineering

Displacements and strains determined by noninvasive DENSE-FISP.

<p>An MRI-compatible loading apparatus cyclically loads a silicone gel phantom within a 9.4T MRI system by compressing the phantom against a fixed platform and then retracting after the load plateau (<i>A</i>). The unloaded phantom was imaged using standard MRI (<i>B</i>) prior to displacement-encoded MRI. In the representative images, displacements (<i>C</i>) and strains computed from smoothed displacements, after 25 smoothing cycles, (<i>D</i>) were found to be heterogeneous.</p