Multi-frequency inversion in Rayleigh damped Magnetic Resonance Elastography

A Novel Experimental Approach for the Measurement of Vibration-Induced Changes in the Rheological Properties of Ex Vivo Ovine Brain Tissue

Increased incidence of traumatic brain injury (TBI) imposes a growing need to understand the pathology of brain trauma. A correlation between the incidence of multiple brain traumas and rates of behavioural and cognitive deficiencies has been identified amongst people that experienced multiple TBI events. Mechanically, repetitive TBIs may affect brain tissue in a similar way to cyclic loading. Hence, the potential susceptibility of brain tissue to mechanical fatigue is of interest. Although temporal changes in ovine brain tissue viscoelasticity and biological fatigue of other tissues such as tendons and arteries have been investigated, no methodology currently exists to cyclically load ex vivo brain tissue. A novel rheology-based approach found a consistent, initial stiffening response of the brain tissue before a notable softening when subjected to a subsequential cyclic rotational shear. History dependence of the mechanical properties of brain tissue indicates susceptibility to mechanical fatigue. Results from this investigation increase understanding of the fatigue properties of brain tissue and could be used to strengthen therapy and prevention of TBI, or computational models of repetitive head injuries.

Encoding and readout strategies in magnetic resonance elastography

Magnetic resonance elastography (MRE) has evolved significantly since its inception. Advances in motion-encoding gradient design and readout strategies have led to improved encoding and signal-to-noise ratio (SNR) efficiencies, which in turn allow for higher spatial resolution, increased coverage, and/or shorter scan times. The purpose of this review is to summarize MRE wave-encoding and readout approaches in a unified mathematical framework to allow for a comparative assessment of encoding and SNR efficiency of the various methods available. Besides standard full- and fractional-wave-encoding approaches, advanced techniques including flow compensation, sample interval modulation and multi-shot encoding are considered. Signal readout using fast k-space trajectories, reduced field of view, multi-slice, and undersampling techniques are summarized and put into perspective. The review is concluded with a foray into displacement and diffusion encoding as alternative and/or complementary techniques.

Analysis and improvement of motion encoding in magnetic resonance elastography

Magnetic resonance elastography (MRE) utilizes phase contrast magnetic resonance imaging (MRI), which is phase locked to externally generated mechanical vibrations, to measure the three-dimensional wave displacement field. At least four measurements with linear-independent encoding directions are necessary to correct for spurious phase contributions if effects from imaging gradients are non-negligible. In MRE, three encoding schemes have been used: unbalanced four- and six-point and balanced four-point ('tetrahedral') encoding. The first two sensitize to motion with orthogonal gradients, with the four-point method acquiring a single reference scan without motion sensitization, whereas three additional scans with inverted gradients are used with six-point encoding, leading to two-fold higher displacement-to-noise ratio (DNR) and 50% longer scan duration. Balanced four-point (tetrahedral) encoding encodes along the four diagonals of a cube, with one direction serving as a reference for the other three encoding directions, similar to four-point encoding. The objective of this work is to introduce a theoretical framework to compare different motion sensitization strategies with respect to their motion encoding efficiency in two fundamental encoding limits, the gradient strength limit and the dynamic range limit, which are both placed in relation to conventional gradient recalled echo (GRE)- and spin echo (SE)-based MRE sequences. We apply the framework to the three aforementioned schemes and show that the motion encoding efficiency of unbalanced four- and six-point encoding schemes in the gradient-limited regime can be increased by a factor of 1.5 when using all physical gradient channels concurrently. Furthermore, it is demonstrated that reversing the direction of the reference in balanced four-point (tetrahedral) encoding results in the Hadamard encoding scheme, which leads to increased DNR by 2 compared with balanced four-point encoding and 2.8 compared with unbalanced four-point encoding. As an example, we show that optimal encoding can be utilized to reduce the acquisition time of standard liver MRE in vivo from four to two breath holds.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

AIM

The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elastography (MRE)-an imaging technique that allows for the noninvasive visualization of the displacement field throughout an object from externally driven harmonic motion-as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles.

METHODS

Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multistep process for which custom scaffolding was designed and built. A customized spin-echo-based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite-element method.

RESULTS

Both complex shear moduli show a significant frequency dependence (p 0.001) in keeping with previous work.

CONCLUSION

The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies.

SIGNIFICANCE

On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g., a cylinder representing a blood vessel. This study demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies.

Multi-frequency Rayleigh damped elastography: in silico studies

Rayleigh damping (RD) is commonly used to model energy attenuation for analyses of structures subjected to dynamic loads. In time-harmonic Magnetic Resonance Elastography (MRE), the RD model was shown to be non-identifiable at a single frequency data due to the ill-posed nature of the imaginary components describing energy dissipation arising from elastic and inertial forces. Thus, parametrisation or multi-frequency (MF) input data is required to overcome the fundamental identifiability issue of the model. While parametrisation allows improved accuracy of the identified parameters, simultaneous inversion using MF input data is a prerequisite for theoretical identifiably of the model. Furthermore, to establish good practical identifiability, frequencies should be separated over a wide range to produce different dynamic response. This research investigates the effects on practical identifiability of the RD model using MF data over different combinations of frequencies in noise-free heterogenous simulated geometry and compares the outcomes to reconstruction result based on single frequency input data. We tested eight frequencies in silico for a phantom type geometry comprises three independent material regions characterised by different mechanical properties. Combinations of two near or well separated frequencies are used to test the separation necessary to obtain accurate results, while the use of four or eight simultaneous frequencies is used to assess robustness. Results confirm expected non-identifiability of the RD model given single frequency input data. Practical identifiability of the RD parameters improved as more input frequencies were used for simultaneous inversion and when two frequencies were well separated. Best quality reconstruction results were achieved using full range data comprising eight available frequencies over a wide range. The main outcome is that high quality motion data over at least two frequencies over a wide range is required for establishing minimal practical identifiability of the model, while quality of the practical identifiability increases proportionally with more input frequencies used. Further simulation studies are required to determine acceptable signal-to-noise ratio (SNR) thresholds in motion data for accurate inversion of the RD parameters.

Parametric-based brain Magnetic Resonance Elastography using a Rayleigh damping material model

The three-parameter Rayleigh damping (RD) model applied to time-harmonic Magnetic Resonance Elastography (MRE) has potential to better characterise fluid-saturated tissue systems. However, it is not uniquely identifiable at a single frequency. One solution to this problem involves simultaneous inverse problem solution of multiple input frequencies over a broad range. As data is often limited, an alternative elegant solution is a parametric RD reconstruction, where one of the RD parameters (μI or ρI) is globally constrained allowing accurate identification of the remaining two RD parameters. This research examines this parametric inversion approach as applied to in vivo brain imaging. Overall, success was achieved in reconstruction of the real shear modulus (μR) that showed good correlation with brain anatomical structures. The mean and standard deviation shear stiffness values of the white and gray matter were found to be 3±0.11kPa and 2.2±0.11kPa, respectively, which are in good agreement with values established in the literature or measured by mechanical testing. Parametric results with globally constrained μI indicate that selecting a reasonable value for the μI distribution has a major effect on the reconstructed ρI image and concomitant damping ratio (ξd). More specifically, the reconstructed ρI image using a realistic μI=333Pa value representative of a greater portion of the brain tissue showed more accurate differentiation of the ventricles within the intracranial matter compared to μI=1000Pa, and ξd reconstruction with μI=333Pa accurately captured the higher damping levels expected within the vicinity of the ventricles. Parametric RD reconstruction shows potential for accurate recovery of the stiffness characteristics and overall damping profile of the in vivo living brain despite its underlying limitations. Hence, a parametric approach could be valuable with RD models for diagnostic MRE imaging with single frequency data.