A comparison of direct and iterative finite element inversion techniques in dynamic elastography

Honarvar, Mohammad; Rohling, Robert; Salcudean, Septimiu E.

doi:10.1088/0031-9155/61/8/3026

Cited by 36 publications

(27 citation statements)

References 38 publications

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“…On the other hand, these techniques are potentially more resistant to noise, since they only take first derivatives of the wave field. MRE inversion techniques that solve the full equation of motion and explicitly account for the pressure term should handle waveguide effects correctly in principle, although this has not yet been demonstrated to our knowledge.…”

Section: Discussionmentioning

confidence: 97%

Waveguide effects and implications for cardiac magnetic resonance elastography: A finite element study

et al. 2018

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Magnetic resonance elastography (MRE) is increasingly being applied to thin or small structures in which wave propagation is dominated by waveguide effects, which can substantially bias stiffness results with common processing approaches. The purpose of this work was to investigate the importance of such biases and artifacts on MRE inversion results in: (i) various idealized 2D and 3D geometries with one or more dimensions that are small relative to the shear wavelength; and (ii) a realistic cardiac geometry. Finite element models were created using simple 2D geometries as well as a simplified and a realistic 3D cardiac geometry, and simulated displacements acquired by MRE from harmonic excitations from 60 to 220 Hz across a range of frequencies. The displacement wave fields were inverted with direct inversion of the Helmholtz equation with and without the application of bandpass filtering and/or the curl operator to the displacement field. In all geometries considered, and at all frequencies considered, strong biases and artifacts were present in inversion results when the curl operator was not applied. Bandpass filtering without the curl was not sufficient to yield accurate recovery. In the 3D geometries, strong biases and artifacts were present in 2D inversions even when the curl was applied, while only 3D inversions with application of the curl yielded accurate recovery of the complex shear modulus. These results establish that taking the curl of the wave field and performing a full 3D inversion are both necessary steps for accurate estimation of the shear modulus both in simple thin-walled or small structures and in a realistic cardiac geometry when using simple inversions that neglect the hydrostatic pressure term. In practice, sufficient wave amplitude, signal-to-noise ratio, and resolution will be required to achieve accurate results.

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Section: Discussionmentioning

confidence: 97%

Waveguide effects and implications for cardiac magnetic resonance elastography: A finite element study

et al. 2018

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“…This implementation was later used in a study on bandpass sampling and was extended to employ mesh adaptation . Honarvar et al solved the mixed displacement‐pressure and time‐harmonic form using Gauss–Newton and Levenburg–Marquardt. This implementation was also used for comparison with heterogeneous direct methods …”

Section: Methodsmentioning

confidence: 99%

“…Honarvar et al solved the mixed displacement‐pressure and time‐harmonic form using Gauss–Newton and Levenburg–Marquardt. This implementation was also used for comparison with heterogeneous direct methods …”

Section: Methodsmentioning

confidence: 99%

“…Similar results were reported between the mixed and curl forms, although, since removing the pressure term reduces the number of unknowns, the curl form is computationally faster . The mixed form was later compared with an iterative method . Computation times of 15 minutes were reported for the curl form for 3D data and 35 minutes for the mixed form (computed on 15×15×15 overlapping subdomains of a 140×46×30 ROI with a MATLAB implementation, but CPU information was not reported).…”

Section: Methodsmentioning

confidence: 99%

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Stiffness reconstruction methods for MR elastography

2018

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Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave‐motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

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“…Magnetic resonance elastography (MRE) allows the in vivo determination of local tissue shear stiffness using time-resolved measurements of shear wave-induced signal phase shifts. 1 Recent technological advances in the field have focused on the development of actuator systems, [2][3][4][5] wave inversion algorithms, [6][7][8][9] improved image acquisition 10,11 and motion encoding techniques. [12][13][14][15] Fundamentally, a key metric for the optimization of MRE is the displacement-to-noise ratio (DNR).…”

Section: Introductionmentioning

confidence: 99%

Analysis and improvement of motion encoding in magnetic resonance elastography

et al. 2018

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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.

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A comparison of direct and iterative finite element inversion techniques in dynamic elastography

Cited by 36 publications

References 38 publications

Waveguide effects and implications for cardiac magnetic resonance elastography: A finite element study

Waveguide effects and implications for cardiac magnetic resonance elastography: A finite element study

Stiffness reconstruction methods for MR elastography

Analysis and improvement of motion encoding in magnetic resonance elastography

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