Adam J. Pattison

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.

Time-harmonic magnetic resonance elastography of the normal feline brain

Imaging of the mechanical properties of in vivo brain tissue could eventually lead to non-invasive diagnosis of hydrocephalus, Alzheimers 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.

Contrast detection in fluid‐saturated media with magnetic resonance poroelastography

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., Lamés 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.

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.

Spatially-Resolved Hydraulic Conductivity Estimation Via Poroelastic Magnetic Resonance Elastography

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 tissues 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.

A Dynamic Mechanical Analysis Technique for Porous Media

Dynamic mechanical analysis (DMA) is a common way to measure the mechanical properties of materials as functions of frequency. Traditionally, a viscoelastic mechanical model is applied and current DMA techniques fit an analytical approximation to measured dynamic motion data by neglecting inertial forces and adding empirical correction factors to account for transverse boundary displacements. Here, a finite-element (FE) approach to processing DMA data was developed to estimate poroelastic material properties. Frequency-dependent inertial forces, which are significant in soft media and often neglected in DMA, were included in the FE model. The technique applies a constitutive relation to the DMA measurements and exploits a nonlinear inversion to estimate the material properties in the model that best fit the model response to the DMA data. A viscoelastic version of this approach was developed to validate the approach by comparing complex modulus estimates to the direct DMA results. Both analytical and FE poroelastic models were also developed to explore their behavior in the DMA testing environment. All of the models were applied to tofu as a representative soft poroelastic material that is a common phantom in elastography imaging studies. Five samples of three different stiffnesses were tested from 1-14 Hz with rough platens placed on the top and bottom surfaces of the material specimen under test to restrict transverse displacements and promote fluid-solid interaction. The viscoelastic models were identical in the static case, and nearly the same at frequency with inertial forces accounting for some of the discrepancy. The poroelastic analytical method was not sufficient when the relevant physical boundary constraints were applied, whereas the poroelastic FE approach produced high quality estimates of shear modulus and hydraulic conductivity. These results illustrated appropriate shear modulus contrast between tofu samples and yielded a consistent contrast in hydraulic conductivity as well.

Development of a poroelastic dynamic mechanical analysis technique for biphasic media

Magnetic resonance elastography is a technique where mechanical properties of materials are estimated by fitting a mechanical model to an MRI-acquired displacement field. These models have been primarily limited to viscoelasticity and linear elasticity, and only recently has poroelasticity been utilized as an applied model. To validate these estimates, the same material is measured via an independent dynamic mechanical analysis device. However, these devices only apply analytic viscoelastic models. In some cases, there is a model mismatch if a viscoelastic mechanical analysis is being compared to a poroelastic model in elastography. Thus, a poroelastic dynamic mechanical analysis technique is needed to properly measure porous media and compare the results with the appropriate elastography technique. A finite element technique was implemented on a TA-Q800 Dynamic Mechanical Analysis machine similar to the algorithm used in the corresponding MR elastography method. A viscoelastic version of the finite element code was created to validate the theory and show results similar to those obtained by the analytic DMA solution. Also, differences were seen that can be attributed to inertial forces not accounted for by an analytical solution. A poroelastic algorithm was then applied, showing great promise in the ability to measure properties of porous tissues.

Estimating Hydraulic Conductivity in Vivo Using Magnetic Resonance Elastography

Magnetic resonance elastography (MRE) is an imaging technique that estimates mechanical properties of in vivo tissue. Traditionally, a linear elastic or viscoelastic material model has been used to describe tissue behavior. Recently, a poroelastic algorithm has been developed to better estimate properties of biphasic tissues such as brain, which is 75-80% water. While shear modulus and pore-pressure are usually estimated from this model, hydraulic conductivity may also provide pertinent clinical information. Defined as the rate at which fluid penetrates through pores, estimates of this parameter would be an important biomarker in applications like tumor identification, detection of increased intracranial pressure, diagnosing traumatic brain injury, and drug delivery. Sensitivity analyses have been performed to demonstrate the feasibility of reconstructing this parameter, and hydraulic conductivity has been successfully estimated in simulations. The focus of current work is improving the reliability of this parameter for use in phantoms and in vivo. A robust hydraulic conductivity reconstruction would allow for a wide array of studies testing its applicability to diagnosing disease.

Comparison of Iterative and Direct Inversion MR Elastography Algorithms

Magnetic Resonance Elastography (MRE) is a medical imaging modality which aims to image the mechanical properties of tissue. Tissue stiffness maps can be calculated from measurements of the steady-state mechanical response of the tissue undegoing a low frequency (40-200Hz) mechanical excitation, which are taken using modified magnetic resonance imaging (MRI) sequences. There are two classes of methods to perform this stiffness calculation: Iterative inversion, and Direct inversion. Experiments using gelatin phantoms, consisting of a soft background and stiff inclusion, show that both methods accurately locate the inclusion. Iterative inversion provides better quantitative accuracy when compared to independent measurements using a dynamic mechanical analyzer, however, the computation time is significantly longer than direct inversions (iterative methods take hours, whereas direct inversion take seconds). The decision of which method to use for a given application must be made by weighing up the advantages of fast computation time for direct inversion against the better quantitative accuracy of iterative techniques.

MR elastography of hydrocephalus

Hydrocephalus occurs due to a blockage in the transmission of cerebrospinal fluid (CSF) in either the ventricles or subarachnoid space. Characteristics of this condition include increased intracranial pressure, which can result in neurologic deterioration [1]. Magnetic resonance elastography (MRE) is an imaging technique that estimates the mechanical properties of tissue in vivo. While some investigations of brain tissue have been performed using MRE [2,3,4,5], the effects due to changes in interstitial pressure and fluid content on the mechanical properties of the brain remain unknown. The purpose of this work is to assess the potential of MRE to differentiate between the reconstructed properties of normal and hydrocephalic brains. MRE data was acquired in 18 female feline subjects, 12 of which received kaolin injections resulting in an acute form of hydrocephalus. In each animal, four MRE scans were performed during the process including one pre-injection and three post-injection scans. The elastic parameters were obtained using a subzone-based reconstruction algorithm that solves Naviers equations for linearly elastic materials [6]. The remaining cats were used as controls, injected with saline instead of kaolin. To determine the state of hydrocephalus, ventricular volume was estimated from segmenting anatomical images. The mean ventricular volume of hydrocephalic cats significantly increased (P ⪅ 0.0001) between the first and second scans. The mean volume was not observed to increase (P ⪆ 0.5) for the control cats. Also, there was an observable increase in the recorded elastic shear modulus of brain tissue in the normal and hydrocephalic acquisitions. Results suggest that MRE is able to detect changes in the mechanical properties of brain tissue resulting from kaolin-induced hydrocephalus, indicating the need for further study.