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Rationale and Objectives: Hydrocephalus (HC) is caused by accumulating cerebrospinal fluid resulting in enlarged ventricles and neurological symptoms. HC can be treated via a shunt in a subset of patients; identifying which individuals will respond through noninvasive imaging would avoid complications from unsuccessful treatments. This preliminary work is a longitudinal study applying MR Elastography (MRE) to HC patients with a focus on normal pressure hydrocephalus (NPH)., Materials and Methods: Twenty-two ventriculomegaly patients were imaged and subsequently received a lumbar drain placement for cerebrospinal fluid (CSF) drainage. NPH lumbar drain responders and NPH syndrome nonresponders were categorized by clinical presentation. Displacement images were acquired using intrinsic activation (IA) MRE and poroelastic inversion recovered shear stiffness and hydraulic conductivity values. A stable IA-MRE inversion protocol was developed to produce unique solutions for both recovered properties, independent of initial estimates., Results: Property images showed significantly increased shear modulus (p = 0.003 in periventricular region, p = 0.005 in remaining cerebral tissue) and hydraulic conductivity (p = 0.04 in periventricular region) in ventriculomegaly patients compared to healthy volunteers. Baseline MRE imaging did not detect significant differences between NPH lumbar drain responders and NPH syndrome nonresponders; however, MRE time series analysis demonstrated consistent trends in average poroelastic shear modulus values over the course of the lumbar drain process in responders (initial increase, followed by a later decrease) which did not occur in nonresponders., Conclusion: These findings are indicative of acute mechanical changes in the brain resulting from CSF drainage in NPH patients., (Copyright © 2020 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.)

Magnetic resonance elastography (MRE) has been developed to noninvasively reconstruct mechanical properties for tissue and tissue-like materials over a frequency range of 10 ~200 Hz. In this work, low frequency (1~1.5 Hz) MRE activations were employed to estimate mechanical property distributions of simulated data and experimental phantoms. Nonlinear inversion (NLI) MRE algorithms based on viscoelastic and poroelastic material models were used to solve the inverse problems and recover images of the shear modulus and hydraulic conductivity. Data from a simulated phantom containing an inclusion with property contrast was carried out to study the feasibility of our low frequency actuated approach. To verify the stability of NLI algorithms for low frequency actuation, different levels of synthetic noise were added to the displacement data. Spatial distributions and property values were recovered well for noise level less than 5%. For the presented experimental phantom reconstructions with regularizations, the computed storage moduli from viscoelastic and poroelastic MRE gave similar results. Contrast was detected between inclusions and background in recovered hydraulic conductivity images. Results and findings confirm the feasibility of future in vivo neuroimaging examinations using natural cerebrovascular pulsations at cardiac frequencies, which can eliminate specialized equipment for high frequency actuation.

Intrinsic activation MR elastography (IA-MRE) is a novel technique which seeks to estimate brain mechanical properties non-invasively and without external mechanical drivers. The method eliminates actuation hardware and patient discomfort while capitalizing on the brain's intrinsic low frequency motion. This study explores low frequency actuation (1 Hz) MR elastography in phantoms and analyzes performance of non-linear inversion (NLI) of viscoelastic and poroelastic mechanical models as a framework for assessing clinical results from IA-MRE. We present results from four gelatin phantoms and report stiffness resolution of 6 mm (two measurement voxels) with a stiffness contrast ratio of 4.21 relative to the background and 9 mm (three measurement voxels) with a lower stiffness contrast ratio of near 1.77. Stiffness edge resolution was also evaluated using edge spread and line spread functions and yielded a stiffness edge response distance of 9 mm. The intraclass correlation coefficient was high (0.93) between mechanical testing and poroelastic estimates, although quantitative agreement was affected by model-data mismatch. Viscoelastic MRE at low frequencies has issues with non-uniqueness due to small inertial forces, and performed worse than poroelastic MRE in terms of inclusion detection and consistency with mechanical testing. These results present the first evaluation of MR elastography using displacement measurements from an actuation frequency less than 5 Hz and support the validity of brain IA-MRE to recover spatially resolved stiffness changes. They provide a baseline of performance in terms of standard metrics for future animal and human brain stiffness studies and analyses based on intrinsic motion.

Magnetic Resonance Elastography (MRE) detects induced periodic motions in biological tissues allowing maps of tissue mechanical properties to be derived. In-vivo MRE is commonly performed at frequencies of 30-100 Hz using external actuation, however, using cerebro-vascular pulsation at 1 Hz as a form of intrinsic actuation (IA-MRE) eliminates the need for external motion sources and simplifies data acquisition. In this study a hydraulic actuation system was developed to drive 1 Hz motions in gelatin as a tool for investigating the performance limits of IA-MRE image reconstruction under controlled conditions. Quantitative flow (QFLOW) MR techniques were used to phase encode 1 Hz motions as a function of gradient direction using 3D or 4D acquisition; 4D acquisition was twice as fast and yielded comparable motion field and concomitant image reconstruction results provided the motion signal was sufficiently strong. Per voxel motion noise floor corresponded to a displacement amplitude of about 20-30 μm. Signal to noise ratio (SNR) was 94 ± 17 for 3D and dropped to 69 ± 10 for the faster 4D acquisition, but yielded octahedral shear stress and shear modulus maps of high quality that differed by only about 20% on average. QFLOW measurements in gel phantoms were improved significantly by adding Mn(II) to mimic relaxation rates found in brain. Overall, the hydraulic 1 Hz actuation system when coupled with 4D sequence acquisition produced a fast reliable approach for future IA-MRE phantom evaluation and contrast detail studies needed to benchmark imaging performance., (Copyright © 2018 Elsevier Inc. All rights reserved.)

This study evaluated non-linear inversion MRE (NLI-MRE) based on viscoelastic governing equations to determine its sensitivity to small, low contrast inclusions and interface changes in shear storage modulus and damping ratio. Reconstruction parameters identical to those used in recent in vivo MRE studies of mechanical property variations in small brain structures were applied. NLI-MRE was evaluated on four phantoms with contrast in stiffness and damping ratio. Image contrast to noise ratio was assessed as a function of inclusion diameter and property contrast, and edge and line spread functions were calculated as measures of imaging resolution. Phantoms were constructed from silicone, agar, and tofu materials. Reconstructed property estimates were compared with independent mechanical testing using dynamic mechanical analysis (DMA). The NLI-MRE technique detected inclusions as small as 8 mm with a stiffness contrast as low as 14%. Storage modulus images also showed an interface edge response distance of 11 mm. Damping ratio images distinguished inclusions with a diameter as small as 8 mm, and yielded an interface edge response distance of 10 mm. Property differences relative to DMA tests were in the 15%-20% range in most cases. In this study, NLI-MRE storage modulus estimates resolved the smallest inclusion with the lowest stiffness contrast, and spatial resolution of attenuation parameter images was quantified for the first time. These experiments and image quality metrics establish quantitative guidelines for the accuracy expected in vivo for MRE images of small brain structures, and provide a baseline for evaluating future improvements to the NLI-MRE pipeline.

The noninvasive imaging technique of magnetic resonance elastography (MRE) was used to estimate the power law behavior of the viscoelastic properties of the human brain in vivo. The mechanical properties for four volunteers are investigated using shear waves induced over a frequency range of 10-50Hz to produce a displacement field measured by magnetic resonance motion-encoding gradients. The average storage modulus (μ R ) reconstructed with non-linear inversion (NLI) increased from approximately 0.95 to 2.58kPa over the 10-50Hz span; the average loss modulus (μ I ) also increased from 0.29 to 1.25kPa over the range. These increases were modeled by independent power law (PL) relations for μ R and μ I returning whole brain, group mean exponent values of 0.88 and 1.07 respectively. Investigation of these exponents also showed distinctly different behavior in the region of the cerebral falx compared to other brain structures., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

A numerical framework for interstitial fluid pressure imaging (IFPI) in biphasic materials is investigated based on three-dimensional nonlinear finite element poroelastic inversion. The objective is to reconstruct the time-harmonic pore-pressure field from tissue excitation in addition to the elastic parameters commonly associated with magnetic resonance elastography (MRE). The unknown pressure boundary conditions (PBCs) are estimated using the available full-volume displacement data from MRE. A subzone-based nonlinear inversion (NLI) technique is then used to update mechanical and hydrodynamical properties, given the appropriate subzone PBCs, by solving a pressure forward problem (PFP). The algorithm was evaluated on a single-inclusion phantom in which the elastic property and hydraulic conductivity images were recovered. Pressure field and material property estimates had spatial distributions reflecting their true counterparts in the phantom geometry with RMS errors around 20% for cases with 5% noise, but degraded significantly in both spatial distribution and property values for noise levels > 10%. When both shear moduli and hydraulic conductivity were estimated along with the pressure field, property value error rates were as high as 58%, 85% and 32% for the three quantities, respectively, and their spatial distributions were more distorted. Opportunities for improving the algorithm are discussed.

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized 'adjoint method' based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation.

Purpose: Descriptions of the structure of brain tissue as a porous cellular matrix support application of a poroelastic (PE) mechanical model which includes both solid and fluid phases. However, the majority of brain magnetic resonance elastography (MRE) studies use a single phase viscoelastic (VE) model to describe brain tissue behavior, in part due to availability of relatively simple direct inversion strategies for mechanical property estimation. A notable exception is low frequency intrinsic actuation MRE, where PE mechanical properties are imaged with a nonlinear inversion algorithm., Methods: This paper investigates the effect of model choice at each end of the spectrum of in vivo human brain actuation frequencies. Repeat MRE examinations of the brains of healthy volunteers were used to compare image quality and repeatability for each inversion model for both 50 Hz externally produced motion and ≈1 Hz intrinsic motions. Additionally, realistic simulated MRE data were generated with both VE and PE finite element solvers to investigate the effect of inappropriate model choice for ideal VE and PE materials., Results: In vivo, MRE data revealed that VE inversions appear more representative of anatomical structure and quantitatively repeatable for 50 Hz induced motions, whereas PE inversion produces better results at 1 Hz. Reasonable VE approximations of PE materials can be derived by equating the equivalent wave velocities for the two models, provided that the timescale of fluid equilibration is not similar to the period of actuation. An approximation of the equilibration time for human brain reveals that this condition is violated at 1 Hz but not at 50 Hz. Additionally, simulation experiments when using the "wrong" model for the inversion demonstrated reasonable shear modulus reconstructions at 50 Hz, whereas cross-model inversions at 1 Hz were poor quality. Attenuation parameters were sensitive to changes in the forward model at both frequencies, however, no spatial information was recovered because the mechanisms of VE and PE attenuation are different., Conclusions: VE inversions are simpler with fewer unknown properties and may be sufficient to capture the mechanical behavior of PE brain tissue at higher actuation frequencies. However, accurate modeling of the fluid phase is required to produce useful mechanical property images at the lower frequencies of intrinsic brain motions.

Poroelastic magnetic resonance elastography is an imaging technique that could recover mechanical and hydrodynamical material properties of in vivo tissue. To date, mechanical properties have been estimated while hydrodynamical parameters have been assumed homogeneous with literature-based values. Estimating spatially-varying hydraulic conductivity would likely improve model accuracy and provide new image information related to a tissue's interstitial fluid compartment. A poroelastic model was reformulated to recover hydraulic conductivity with more appropriate fluid-flow boundary conditions. Simulated and physical experiments were conducted to evaluate the accuracy and stability of the inversion algorithm. Simulations were accurate (property errors were < 2%) even in the presence of Gaussian measurement noise up to 3%. The reformulated model significantly decreased variation in the shear modulus estimate (p << 0.001) and eliminated the homogeneity assumption and the need to assign hydraulic conductivity values from literature. Material property contrast was recovered experimentally in three different tofu phantoms and the accuracy was improved through soft-prior regularization. A frequency-dependence in hydraulic conductivity contrast was observed suggesting that fluid-solid interactions may be more prominent at low frequency. In vivo recovery of both structural and hydrodynamical characteristics of tissue could improve detection and diagnosis of neurological disorders such as hydrocephalus and brain tumors.

Purpose: To develop an acquisition scheme for generating MR elastography (MRE) displacement data with whole-brain coverage, high spatial resolution, and adequate signal-to-noise ratio (SNR) in a short scan time., Theory and Methods: A 3D multislab, multishot acquisition for whole-brain MRE with 2.0 mm isotropic spatial resolution is proposed. The multislab approach allowed for the use of short repetition time to achieve very high SNR efficiency. High SNR efficiency allowed for a reduced acquisition time of only 6 min while the minimum SNR needed for inversion was maintained., Results: The mechanical property maps estimated from whole-brain displacement data with nonlinear inversion (NLI) demonstrated excellent agreement with neuroanatomical features, including the cerebellum and brainstem. A comparison with an equivalent 2D acquisition illustrated the improvement in SNR efficiency of the 3D multislab acquisition. The flexibility afforded by the high SNR efficiency allowed for higher resolution with a 1.6 mm isotropic voxel size, which generated higher estimates of brainstem stiffness compared with the 2.0 mm isotropic acquisition., Conclusion: The acquisition presented allows for the capture of whole-brain MRE displacement data in a short scan time, and may be used to generate local mechanical property estimates of neuroanatomical features throughout the brain., (Copyright © 2013 Wiley Periodicals, Inc.)

The noninvasive measurement of the mechanical properties of brain tissue using magnetic resonance elastography (MRE) has emerged as a promising method for investigating neurological disorders. To date, brain MRE investigations have been limited to reporting global mechanical properties, though quantification of the stiffness of specific structures in the white matter architecture may be valuable in assessing the localized effects of disease. This paper reports the mechanical properties of the corpus callosum and corona radiata measured in healthy volunteers using MRE and atlas-based segmentation. Both structures were found to be significantly stiffer than overall white matter, with the corpus callosum exhibiting greater stiffness and less viscous damping than the corona radiata. Reliability of both local and global measures was assessed through repeated experiments, and the coefficient of variation for each measure was less than 10%. Mechanical properties within the corpus callosum and corona radiata demonstrated correlations with measures from diffusion tensor imaging pertaining to axonal microstructure., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Tissue displacements required for mechanical property reconstruction in magnetic resonance elastography (MRE) are acquired in a magnetic resonance imaging (MRI) scanner, therefore, anatomical information is available from other imaging sequences. Despite its availability, few attempts to incorporate prior spatial information in the MRE reconstruction process have been reported. This paper implements and evaluates soft prior regularization (SPR), through which homogeneity in predefined spatial regions is enforced by a penalty term in a nonlinear inversion strategy. Phantom experiments and simulations show that when predefined regions are spatially accurate, recovered property values are stable for SPR weighting factors spanning several orders of magnitude, whereas inaccurate segmentation results in bias in the reconstructed properties that can be mitigated through proper choice of regularization weighting. The method was evaluated in vivo by estimating viscoelastic mechanical properties of frontal lobe gray and white matter for five repeated scans of a healthy volunteer. Segmentations of each tissue type were generated using automated software, and statistically significant differences between frontal lobe gray and white matter were found for both the storage modulus and loss modulus . Provided homogeneous property assumptions are reasonable, SPR produces accurate quantitative property estimates for tissue structures which are finer than the resolution currently achievable with fully distributed MRE.

Magnetic resonance elastography (MRE) has been introduced in clinical practice as a possible surrogate for mechanical palpation, but its application to study the human brain in vivo has been limited by low spatial resolution and the complexity of the inverse problem associated with biomechanical property estimation. Here, we report significant improvements in brain MRE data acquisition by reporting images with high spatial resolution and signal-to-noise ratio as quantified by octahedral shear strain metrics. Specifically, we have developed a sequence for brain MRE based on multishot, variable-density spiral imaging, and three-dimensional displacement acquisition and implemented a correction scheme for any resulting phase errors. A Rayleigh damped model of brain tissue mechanics was adopted to represent the parenchyma and was integrated via a finite element-based iterative inversion algorithm. A multiresolution phantom study demonstrates the need for obtaining high-resolution MRE data when estimating focal mechanical properties. Measurements on three healthy volunteers demonstrate satisfactory resolution of gray and white matter, and mechanical heterogeneities correspond well with white matter histoarchitecture. Together, these advances enable MRE scans that result in high-fidelity, spatially resolved estimates of in vivo brain tissue mechanical properties, improving upon lower resolution MRE brain studies that only report volume averaged stiffness values., (© 2012 Wiley Periodicals, Inc.)

Many pathologies alter the mechanical properties of tissue. Magnetic resonance elastography (MRE) has been developed to noninvasively characterize these quantities in vivo. Typically, small vibrations are induced in the tissue of interest with an external mechanical actuator. The resulting displacements are measured with phase contrast sequences and are then used to estimate the underlying mechanical property distribution. Several MRE studies have quantified brain tissue properties. However, the cranium and meninges, especially the dura, are very effective at damping externally applied vibrations from penetrating deeply into the brain. Here, we report a method, termed 'intrinsic activation', that eliminates the requirement for external vibrations by measuring the motion generated by natural blood vessel pulsation. A retrospectively gated phase contrast MR angiography sequence was used to record the tissue velocity at eight phases of the cardiac cycle. The velocities were numerically integrated via the Fourier transform to produce the harmonic displacements at each position within the brain. The displacements were then reconstructed into images of the shear modulus based on both linear elastic and poroelastic models. The mechanical properties produced fall within the range of brain tissue estimates reported in the literature and, equally important, the technique yielded highly reproducible results. The mean shear modulus was 8.1 kPa for linear elastic reconstructions and 2.4 kPa for poroelastic reconstructions where fluid pressure carries a portion of the stress. Gross structures of the brain were visualized, particularly in the poroelastic reconstructions. Intra-subject variability was significantly less than the inter-subject variability in a study of six asymptomatic individuals. Further, larger changes in mechanical properties were observed in individuals when examined over time than when the MRE procedures were repeated on the same day. Cardiac pulsation, termed intrinsic activation, produces sufficient motion to allow mechanical properties to be recovered. The poroelastic model is more consistent with the measured data from brain at low frequencies than the linear elastic model. Intrinsic activation allows MRE to be performed without a device shaking the head so the patient notices no differences between it and the other sequences in an MR examination.

Purpose: Nonlinear inversion (NLI) in MR elastography requires discretization of the displacement field for a finite element (FE) solution of the "forward problem", and discretization of the unknown mechanical property field for the iterative solution of the "inverse problem". The resolution requirements for these two discretizations are different: the forward problem requires sufficient resolution of the displacement FE mesh to ensure convergence, whereas lowering the mechanical property resolution in the inverse problem stabilizes the mechanical property estimates in the presence of measurement noise. Previous NLI implementations use the same FE mesh to support the displacement and property fields, requiring a trade-off between the competing resolution requirements., Methods: This work implements and evaluates multiresolution FE meshes for NLI elastography, allowing independent discretizations of the displacements and each mechanical property parameter to be estimated. The displacement resolution can then be selected to ensure mesh convergence, and the resolution of the property meshes can be independently manipulated to control the stability of the inversion., Results: Phantom experiments indicate that eight nodes per wavelength (NPW) are sufficient for accurate mechanical property recovery, whereas mechanical property estimation from 50 Hz in vivo brain data stabilizes once the displacement resolution reaches 1.7 mm (approximately 19 NPW). Viscoelastic mechanical property estimates of in vivo brain tissue show that subsampling the loss modulus while holding the storage modulus resolution constant does not substantially alter the storage modulus images. Controlling the ratio of the number of measurements to unknown mechanical properties by subsampling the mechanical property distributions (relative to the data resolution) improves the repeatability of the property estimates, at a cost of modestly decreased spatial resolution., Conclusions: Multiresolution NLI elastography provides a more flexible framework for mechanical property estimation compared to previous single mesh implementations.

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.

Magnetic resonance elastography (MRE) uses accumulated phases that are acquired at multiple, uniformly spaced relative phase offsets, to estimate harmonic motion information. Heavily wrapped phase occurs when the motion is large and unwrapping procedures are necessary to estimate the displacements required by MRE. Two unwrapping methods were developed and compared in this paper. The first method is a sequentially applied approach. The three-dimensional MRE phase image block for each slice was processed by two-dimensional unwrapping followed by a one-dimensional phase unwrapping approach along the phase-offset direction. This unwrapping approach generally works well for low noise data. However, there are still cases where the two-dimensional unwrapping method fails when noise is high. In this case, the baseline of the corrupted regions within an unwrapped image will not be consistent. Instead of separating the two-dimensional and one-dimensional unwrapping in a sequential approach, an interleaved three-dimensional quality-guided unwrapping method was developed to combine both the two-dimensional phase image continuity and one-dimensional harmonic motion information. The quality of one-dimensional harmonic motion unwrapping was used to guide the three-dimensional unwrapping procedures and it resulted in stronger guidance than in the sequential method. In this work, in vivo results generated by the two methods were compared.

Purpose: Recently, the attenuating behavior of soft tissue has been addressed in magnetic resonance elastography by the inclusion of a damping mechanism in the methods used to reconstruct the resulting mechanical property image. To date, this mechanism has been based on a viscoelastic model for material behavior. Rayleigh, or proportional, damping provides a more generalized model for elastic energy attenuation that uses two parameters to characterize contributions proportional to elastic and inertial forces. In the case of time-harmonic vibration, these two parameters lead to both the elastic modulus and the density being complex valued (as opposed to the case of pure viscoelasticity, where only the elastic modulus is complex valued)., Methods: This article presents a description of Rayleigh damping in the time-harmonic case, discussing the differences between this model and the viscoelastic damping models. In addition, the results from a subzone based Rayleigh damped elastography study of gelatin and tofu phantoms are discussed, along with preliminary results from in vivo breast data., Results: Both the phantom and the tissue studies presented here indicate a change in the Rayleigh damping structure, described as Rayleigh composition, between different material types, with tofu and healthy tissue showing lower Rayleigh composition values than gelatin or cancerous tissue., Conclusions: It is possible that Rayleigh damping elastography and the concomitant Rayleigh composition images provide a mechanism for differentiating tissue structure in addition to measuring elastic stiffness and attenuation. Such information could be valuable in the use of Rayleigh damped magnetic resonance elastography as a diagnostic imaging tool.

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.

Imaging of the mechanical properties of in vivo brain tissue could eventually lead to non-invasive diagnosis of hydrocephalus, Alzheimer's disease and other pathologies known to alter the intracranial environment. The purpose of this work is to (1) use time-harmonic magnetic resonance elastography (MRE) to estimate the mechanical property distribution of cerebral tissue in the normal feline brain and (2) compare the recovered properties of grey and white matter. Various in vivo and ex vivo brain tissue property measurement strategies have led to the highly variable results that have been reported in the literature. MR elastography is an imaging technique that can estimate mechanical properties of tissue non-invasively and in vivo. Data was acquired in 14 felines and elastic parameters were estimated using a globo-regional nonlinear image reconstruction algorithm. Results fell within the range of values reported in the literature and showed a mean shear modulus across the subject group of 7-8 kPa with all but one animal falling within 5-15 kPa. White matter was statistically stiffer (p<0.01) than grey matter by about 1 kPa on a per subject basis. To the best of our knowledge, the results reported represent the most extensive set of estimates in the in vivo brain which have been based on MRE acquisition of the three-dimensional displacement field coupled to volumetric shear modulus image reconstruction achieved through nonlinear parameter estimation. However, the inter-subject variation in mean shear modulus indicates the need for further study, including the possibility of applying more advanced models to estimate the relevant tissue mechanical properties from the data., (Copyright © 2010 Elsevier Ltd. All rights reserved.)

Purpose: The clinical efficacy of breast elastography may be limited when the authors employ the assumption that soft tissues exhibit linear, frequency-independent isotropic mechanical properties during the recovery of shear modulus. Thus, the purpose of this research was to evaluate the degradation in performance incurred when linear-elastic MR reconstruction methods are applied to phantoms that are fabricated using viscoelastic materials., Methods: To develop phantoms with frequency-dependent mechanical properties, the authors measured the complex modulus of two groups of cylindrical-shaped gelatin samples over a wide frequency range (up to 1 kHz) with the established principles of time-temperature superposition (TTS). In one group of samples, the authors added varying amounts of agar (1%-4%); in the other group, the authors added varying amounts of sucrose (2.5%-20%). To study how viscosity affected the performance of the linear-elastic reconstruction method, the authors constructed an elastically heterogeneous MR phantom to simulate the case where small viscoelastic lesions were surrounded by relatively nonviscous breast tissue. The breast phantom contained four linear, viscoelastic spherical inclusions (10 mm diameter) that were embedded in normal gelatin. The authors imaged the breast phantom with a clinical prototype of a MRE system and recovered the shear-modulus distribution using the overlapping-subzone-linear-elastic image-reconstruction method. The authors compared the recovered shear modulus to that measured using the TTS method., Results: The authors demonstrated that viscoelastic phantoms could be fabricated by including sucrose in the gelation process and that small viscoelastic inclusions were visible in MR elastograms recovered using a linear-elastic MR reconstruction process; however, artifacts that degraded contrast and spatial resolution were more prominent in highly viscoelastic inclusions. The authors also established that the accuracy of the MR elastograms depended on the degree of viscosity that the inclusion exhibited., Conclusions: The results demonstrated that reconstructing shear modulus from other constitutive laws, such as viscosity, should improve both the accuracy and quality of MR elastograms of the breast.

Purpose: Recent interest in the poroelastic behavior of tissues has led to the development of magnetic resonance poroelastography (MRPE) as an alternative to single-phase MR elastographic image reconstruction. In addition to the elastic parameters (i.e., Lamé's constants) commonly associated with magnetic resonance elastography (MRE), MRPE enables estimation of the time-harmonic pore-pressure field induced by external mechanical vibration., Methods: This study presents numerical simulations that demonstrate the sensitivity of the computed displacement and pore-pressure fields to a priori estimates of the experimentally derived model parameters. In addition, experimental data collected in three poroelastic phantoms are used to assess the quantitative accuracy of MR poroelastographic imaging through comparisons with both quasistatic and dynamic mechanical tests., Results: The results indicate hydraulic conductivity to be the dominant parameter influencing the deformation behavior of poroelastic media under conditions applied during MRE. MRPE estimation of the matrix shear modulus was bracketed by the values determined from independent quasistatic and dynamic mechanical measurements as expected, whereas the contrast ratios for embedded inclusions were quantitatively similar (10%-15% difference between the reconstructed images and the mechanical tests)., Conclusions: The findings suggest that the addition of hydraulic conductivity and a viscoelastic solid component as parameters in the reconstruction may be warranted.

Magnetic resonance poroelastography (MRPE) is introduced as an alternative to single-phase model-based elastographic reconstruction methods. A 3-D finite element poroelastic inversion algorithm was developed to recover the mechanical properties of fluid-saturated tissues. The performance of this algorithm was assessed through a variety of numerical experiments, using synthetic data to probe its stability and sensitivity to the relevant model parameters. Preliminary results suggest the algorithm is robust in the presence of noise and capable of producing accurate assessments of the underlying mechanical properties in simulated phantoms. Furthermore, a 3-D time-harmonic motion field was recorded for a poroelastic phantom containing a single cylindrical inclusion and used to assess the feasibility of MRPE image reconstruction from experimental data. The elastograms obtained from the proposed poroelastic algorithm demonstrate significant improvement over linearly elastic MRE images generated using the same data. In addition, MRPE offers the opportunity to estimate the time-harmonic pressure field resulting from tissue excitation, highlighting the potential for its application in the diagnosis and monitoring of disease processes associated with changes in interstitial pressure.

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz-1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases.

Motion estimation is an essential step common to all magnetic resonance elastography (MRE) methods. For dynamic techniques, the motion is obtained from a sinusoidal fit of the image phase at multiple, uniformly spaced relative phase offsets, phi, between the motion and the motion encoding gradients (MEGs). Generally, eight values of phi sampled at the Nyquist interval pi/4 over [0, 2pi). We introduce a method, termed reduced motion encoding (RME), that reduces the number of phi required, thereby reducing the imaging time for an MRE acquisition. A frequency-domain algorithm was implemented using the discrete Fourier transform (DFT) to derive the general least-squares solution for the motion amplitude and phase given an arbitrary number of phi. A closed form representation of the condition number of the transformation matrix which is used for estimating motion was introduced to determine the sensitivity to noise for different sampling patterns of phi. Simulation results confirmed the minimum error sampling patterns suggested from the condition number maps. The minimum noise in the motion estimate is obtained when the sampled phi are essentially evenly distributed over the range [0, pi) with an interval pi/n, where n is the number of phi sampled, or alternatively with an interval 2pi/n over the range [0, 2pi) which represents the Nyquist interval. Simulations also show that the noise level decreases as n increases as expected. The decrease in noise is the largest when n is small and it becomes less significant as n increases. The algorithm also makes it possible to estimate the motion from only two values of phi, which cannot be accomplished with traditional methods because sampling at the Nyquist interval is indeterminate. Finally, noise levels in motion estimated from phantom studies and in vivo results taken with different n agreed with that predicted by simulation and condition number calculations.