Contrast detection in fluid-saturated media with magnetic resonance poroelastography

Viscoelastic polyacrylamide MR elastography phantoms with tunable damping ratio independent of shear stiffness

Physiologically modeled test samples with known properties and characteristics, or phantoms, are essential for developing sensitive, repeatable, and accurate quantitative MRI techniques. Magnetic resonance elastography (MRE) is one such technique used to estimate tissue mechanical properties, and it is advantageous to use phantoms with independently tunable mechanical properties to benchmark the accuracy of MRE methods. Phantoms with tunable shear stiffness are commonly used for MRE, but tuning the viscosity or damping ratio has proven to be difficult. A promising candidate for MRE phantoms with tunable damping ratio is polyacrylamide (PAA). While pure PAA has very low attenuation, viscoelastic hydrogels have been made by entrapping linear polyacrylamide strands (LPAA) within the PAA network. In this study, we evaluate the use of LPAA/PAA gels as physiologically accurate phantoms with tunable damping ratio, independent of shear stiffness, via MRE. Phantoms were made with 15.3 wt% PAA while the LPAA concentration ranged from 4.5 wt% to 8.0 wt%. MRE was performed at 9.4 T with 400 Hz vibration on all phantoms revealing a strong, positive correlation between damping ratio and LPAA content (p < 0.001). There was no significant correlation between shear stiffness and LPAA content, confirming a constant PAA concentration yielded constant shear stiffness. Rheometry at 10 Hz was performed to verify the damping ratio of the phantoms. Nearly identical slopes for damping ratio versus LPAA content were found from both MRE and rheometry (0.0073 and 0.0075 respectively). Ultimately, this study validates the adaptation of polyacrylamide gels into physiologically-relevant MRE phantoms to enable testing of MRE estimates of damping ratio.

Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review

MRI-based biomechanical studies can provide a deep understanding of the mechanisms governing liver function, its mechanical performance but also liver diseases. In addition, comprehensive modeling of the liver can help improve liver disease treatment. Furthermore, such studies demonstrate the beginning of an engineering-level approach to how the liver disease affects material properties and liver function. Aimed at researchers in the field of MRI-based liver simulation, research articles pertinent to MRI-based liver modeling were identified, reviewed, and summarized systematically. Various MRI applications for liver biomechanics are highlighted, and the limitations of different viscoelastic models used in magnetic resonance elastography are addressed. The clinical application of the simulations and the diseases studied are also discussed. Based on the developed questionnaire, the papers' quality was assessed, and of the 46 reviewed papers, 32 papers were determined to be of high-quality. Due to the lack of the suitable material models for different liver diseases studied by magnetic resonance elastography, researchers may consider the effect of liver diseases on constitutive models. In the future, research groups may incorporate various aspects of machine learning (ML) into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification.

Poroelastic Mechanical Properties of the Brain Tissue of Normal Pressure Hydrocephalus Patients During Lumbar Drain Treatment Using Intrinsic Actuation MR Elastography

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.

Separation of fluid and solid shear wave fields and quantification of coupling density by magnetic resonance poroelastography

PURPOSE

Biological soft tissues often have a porous architecture comprising fluid and solid compartments. Upon displacement through physiological or externally induced motion, the relative motion of these compartments depends on poroelastic parameters, such as coupling density ( ρ 12 ) and tissue porosity. This study introduces inversion recovery MR elastography (IR-MRE) (1) to quantify porosity defined as fluid volume over total volume, (2) to separate externally induced shear strain fields of fluid and solid compartments, and (3) to quantify coupling density assuming a biphasic behavior of in vivo brain tissue.

THEORY AND METHODS

Porosity was measured in eight tofu phantoms and gray matter (GM) and white matter (WM) of 21 healthy volunteers. Porosity of tofu was compared to values obtained by fluid draining and microscopy. Solid and fluid shear-strain amplitudes and ρ 12 were estimated both in phantoms and in in vivo brain.

RESULTS

T₁ -based measurement of tofu porosity agreed well with reference values (R = 0.99, P < .01). Brain tissue porosity was 0.14 ± 0.02 in GM and 0.05 ± 0.01 in WM (P < .001). Fluid shear strain was found to be phase-locked with solid shear strain but had lower amplitudes in both tofu phantoms and brain tissue (P < .05). In accordance with theory, tofu and brain ρ 12 were negative.

CONCLUSION

IR-MRE allowed for the first time separation of shear strain fields of solid and fluid compartments for measuring coupling density according to the biphasic theory of poroelasticity. Thus, IR-MRE opens horizons for poroelastography-derived imaging markers that can be used in basic research and diagnostic applications.

Nonlinear Inversion MR Elastography With Low-Frequency Actuation

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.

Breast magnetic resonance elastography: a review of clinical work and future perspectives

This review on magnetic resonance elastography (MRE) of the breast provides an overview of available literature and describes current developments in the field of breast MRE, including new transducer technology for data acquisition and multi-frequency-derived power-law behaviour of tissue. Moreover, we discuss the future potential of breast MRE, which goes beyond its original application as an additional tool in differentiating benign from malignant breast lesions. These areas of ongoing and future research include MRE for pre-operative tumour delineation, staging, monitoring and predicting response to treatment, as well as prediction of the metastatic potential of primary tumours.

Phantom evaluations of nonlinear inversion MR elastography

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.

A numerical framework for interstitial fluid pressure imaging in poroelastic MRE

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.

Gradient-Based Optimization for Poroelastic and Viscoelastic MR Elastography

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.

Investigation of optimal display size for viewing T1-weighted MR images of the brain using a digital contrast-detail phantom

We clarified the relationship between the display size of MRI images and observer performance using a digital contrast-detail (d-CD) phantom. The d-CD phantom was developed using Microsoft Visual Basic 2010 Express. It had a 512 × 512 matrix in size and a total of 100 holes, whose diameter increased stepwise from 4 to 40 pixels with a 4-pixel interval in the vertical direction; the contrast varied stepwise in the horizontal direction. The digital driving level (DDL) of the back-ground, the width of the DDL, and the contrast were adjustable. These parameters were determined on the basis of the actual T1-weighted magnetic resonance (MR) images of the brain. In this study, the DDL, width, and contrast were set to 85, 20, and 1, respectively. The observer performance study was performed for three different display sizes (30 cm × 30 cm as the enlarged size, 16 cm × 16 cm as the original size, and 10 cm × 10 cm as the reduced size) using a 2-megapixel color liquid crystal display monitor, and it was analyzed using Friedman and Wilcoxon statistical tests. The observer performances for the original display (p < 0.01) and the reduced display sizes (p < 0.01) were superior to that observed for the enlarged size, whereas there was no significant difference between the original display and reduced display sizes (p = 0.31). Evaluation with the digital phantom simulating MR imaging also revealed that the original and reduced display sizes were superior to the enlarged display size in observer performance. The d-CD phantom enables a short-term evaluation of observer performance and is useful in analyzing relation-ship between display size and observer performance.

Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography

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.

Ultrasound strain elastography in assessment of cortical mechanical behavior in acute renal vein occlusion: in vivo animal model

To assess the correlation of quantitative ultrasound strain parameters with the severity of cortical edema in renal vein occlusion, we prospectively performed ultrasound strain elastography on a canine acute renal vein occlusion model prior to and following 10, 20, and 40min of renal vein ligation. Strain and strain relaxation time representing the deformation and relaxation of the renal cortices and reference soft tissue were produced by the external compression with the ultrasound transducer and estimated using commercially available 2-D speckle tracking software. Cortical thickness was additionally measured. Repeated-measures analysis of variance was used to examine the difference in cortical thickness, strain ratio (mean cortical strain divided by mean reference tissue strain), and strain relaxation time ratio (cortical relaxation time divided by reference tissue relaxation time) prior to and after renal vein ligation. Pearson's correlation coefficient was applied to test the relationship between strain parameters and the time of the renal vein ligation. There was a strong positive correlation between the duration of renal vein ligation and strain (R(2)=0.97) and strain relaxation time (R(2)=0.98) ratios. Significant differences in strain and strain relaxation time ratios were found at all measured timepoints (all P≪.001). Cortical thickness, however, showed no significant difference between timepoints (P=.065). Our result suggest that strain and strain relaxation time ratios may be used as quantitative markers for the assessment of the renal cortical mechanical behavior in subclinical acute renal vein occlusion.

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.

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 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.

MR elastography in a murine stroke model reveals correlation of macroscopic viscoelastic properties of the brain with neuronal density

The aim of this study was to investigate the influence of neuronal density on viscoelastic parameters of living brain tissue after ischemic infarction in the mouse using MR elastography (MRE). Transient middle cerebral artery occlusion (MCAO) in the left hemisphere was induced in 20 mice. In vivo 7-T MRE at a vibration frequency of 900 Hz was performed on days 3, 7, 14 and 28 (n = 5 per group) after MCAO, followed by the analysis of histological markers, such as neuron counts (NeuN). MCAO led to a significant reduction in the storage modulus in the left hemisphere relative to contralateral values (p = 0.03) without changes over time. A correlation between storage modulus and NeuN in both hemispheres was observed, with correlation coefficients of R = 0.648 (p = 0.002, left) and R = 0.622 (p = 0.003, right). The loss modulus was less sensitive to MCAO, but correlated with NeuN in the left hemisphere (R = 0.764, p = 0.0001). In agreement with the literature, these results suggest that the shear modulus in the brain is reduced after transient ischemic insult. Furthermore, our study provides evidence that the in vivo shear modulus of brain tissue correlates with neuronal density. In diagnostic applications, MRE may thus have diagnostic potential as a tool for image-based quantification of neurodegenerative processes.

Selective spectral displacement projection for multifrequency MRE

We introduce a new motion encoding concept for the displacement vector in multifrequency magnetic resonance elastography (MRE). Selective spectral displacement projection (SDP)-MRE can be applied to a vibration spectrum composed of three frequencies and exploits the filter condition of MRE for selecting one frequency each per spatial motion encoding direction. The selected components are simultaneously encoded in the phase of the MR signal. Therefore, the total MR phase is represented by a sum of phase portions, each corresponding to a distinct spatial projection and vibration frequency. The individual components can be obtained by applying a Fourier-transform to the temporally resolved phase images. SDP-MRE reduces the number of temporally resolved MRE experiments for data acquisition by a factor of 3, while providing similar wave images as found using conventional monofrequency MRE.

The shear modulus of the nucleus pulposus measured using magnetic resonance elastography: a potential biomarker for intervertebral disc degeneration

PURPOSE

This study aims to: (1) measure the shear modulus of nucleus pulposus (NP) in intact human vertebra-disc-vertebra segments using a magnetic resonance elastography setup for a 7T whole-body scanner, (2) quantify the effect of disc degeneration on the NP shear modulus measured using magnetic resonance elastography, and (3) compare the NP shear modulus to other magnetic resonance-based biomarkers of dis degeneration.

METHODS

Thirty intact human disc segments were classified as normal, mild, or severely degenerated. The NP shear modulus was measured using a custom-made setup that included a novel inverse method less sensitive to noisy displacements. T2 relaxation time was measured at 7T. The accuracy of these parameters to classify different degrees of degeneration was evaluated using receiver operating characteristic curves.

RESULTS

The magnetic resonance elastography measure of shear modulus in the NP was able to differentiate between normal, mild degeneration, and severe degeneration. The T2 relaxation time was able to differentiate between normal and mild degeneration, but it could not distinguish between mild and severe degeneration.

CONCLUSIONS

This study shows that the NP shear modulus measured using magnetic resonance elastography is sensitive to disc degeneration and has the potential of being used as a clinical tool to quantify the mechanical integrity of the intervertebral disc.

In vivo measurement of volumetric strain in the human brain induced by arterial pulsation and harmonic waves

Motion-sensitive phase contrast magnetic resonance imaging and magnetic resonance elastography are applied for the measurement of volumetric strain and tissue compressibility in human brain. Volumetric strain calculated by the divergence operator using a biphasic effective-medium model is related to dilatation and compression of fluid spaces during harmonic stimulation of the head or during intracranial passage of the arterial pulse wave. In six volunteers, phase contrast magnetic resonance imaging showed that the central cerebrum expands at arterial pulse wave to strain values of (2.8 ± 1.9)·10(-4). The evolution of volumetric strain agrees well with the magnitude of the harmonic divergence measured in eight volunteers by magnetic resonance elastography using external activation of 25 Hz vibration frequency. Intracranial volumetric strain was proven sensitive to venous pressure altered by abdominal muscle contraction. In eight volunteers, an increase in volumetric strain due to abdominal muscle contraction of approximately 45% was observed (P = 0.0001). The corresponding compression modulus in the range of 9.5-13.5 kPa demonstrated that the compressibility of brain tissue at 25 Hz stimulation is much higher than that of water. This pilot study provides the background for compression-sensitive magnetic resonance imaging with or without external head stimulation. Volumetric strain may be sensitive to fluid flow abnormalities or pressure imbalances between vasculature and parenchyma as seen in hydrocephalus.

Measurement of vibration-induced volumetric strain in the human lung

Noninvasive image-based measurement of intrinsic tissue pressure is of great interest in the diagnosis and characterization of diseases. Therefore, we propose to exploit the capability of phase-contrast MRI to measure three-dimensional vector fields of tissue motion for deriving volumetric strain induced by external vibration. Volumetric strain as given by the divergence of mechanical displacement fields is related to tissue compressibility and is thus sensitive to the state of tissue pressure. This principle is demonstrated by the measurement of three-dimensional vector fields of 50-Hz oscillations in a compressible agarose phantom and in the lungs of nine healthy volunteers. In the phantom, the magnitude of the oscillating divergence increased by about 400% with 4.8 bar excess air pressure, corresponding to an effective-medium compression modulus of 230 MPa. In lungs, the averaged divergence magnitude increased in all volunteers (N = 9) between 7 and 78% from expiration to inspiration. Measuring volumetric strain by MRI provides a compression-sensitive parameter of tissue mechanics, which varies with the respiratory state in the lungs. In future clinical applications for diagnosis and characterization of lung emphysema, fibrosis, or cancer, divergence-sensitive MRI may serve as a noninvasive marker sensitive to disease-related alterations of regional elastic recoil pressure in the lungs.

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.