Viscoelastic power law parameters of in vivo human brain estimated by MR elastography.

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 (µR) reconstructed with non-linear inversion (NLI) increased from approximately 0.95 to 2.58kPa over the 10-50Hz span; the average loss modulus (µI) also increased from 0.29 to 1.25kPa over the range. These increases were modeled by independent power law (PL) relations for µR and µI 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.

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.

Multiresolution MR elastography using nonlinear inversion.

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.

Subzone based magnetic resonance elastography using a Rayleigh damped material model.

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.

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 = µÎ³. 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.

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.

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, 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.