Acquisition and reconstruction conditionsin silicofor accurate and precise magnetic resonance elastography

Abstract

Magnetic resonance elastography (MRE) is a non invasive imaging modality, which holds the promise of absolute quantification of the mechanical properties of human tissues in vivo. MRE reconstruction with algebraic inversion of the Helmholtz equation upon the curl of the shear displacement field may theoretically be flawless. However, its performances are challenged by multiple experimental parameters, especially the frequency and the amplitude of the mechanical wave, the voxel size and the signal-to-noise ratio of the MRE acquisition. A point source excitation was simulated and realistic displacement fields were analytically computed to simulate MRE data sets in an isotropic, homogeneous, linearly-elastic, and half-space infinite medium. Acquisition and reconstruction methods were challenged and the joint influence of the aforementioned parameters was studied. For a given signal-to-noise ratio, the conditions on the number of voxels per wavelength were determined for optimizing voxel-wise accuracy and precision in MRE. It was shown that, once data are acquired, the reconstruction quality could even be improved by effective interpolation or decimation so data could eventually fulfill favorable conditions for mechanical characterization of the tissue. Finally, the overall outcome, which is usually computed from the three acquired motion-encoded directions, may further be improved by appropriate averaging strategies that are based on adapted curl of shear displacement field quality-weighting.

An analytical solution to the dispersion‐by‐inversion problem in magnetic resonance elastography

“…However, it has been recognized that intrinsic dispersion recovered by FDO methods is subject to bias. [18][19][20] Specifically, we and others have shown that stiffness is likely to be overestimated at low spatial support due to the discretization of shear waves while it is often underestimated at high spatial support due to noise. 18,19 Because spatial support in MRE is the number of pixels per wavelength (wave number times pixel size or wavelength divided by pixel size), multifrequency MRE examinations automatically result in a variation of spatial support due to the occurrence of different wavelengths.…”

“…A purely elastic material has no dispersion, yielding constant stiffness values over frequency. However, it has been recognized that intrinsic dispersion recovered by FDO methods is subject to bias 18‐20 . Specifically, we and others have shown that stiffness is likely to be overestimated at low spatial support due to the discretization of shear waves while it is often underestimated at high spatial support due to noise 18,19 .…”

Magnetic Resonance Elastography of Rodent Brain

“…The accuracy and precision of MRE reconstruction methods inherently depends on the wavelength and amplitude of the propagating wave, the size of the biological structures, and the spatial resolution and signal-to-noise ratio (SNR) of the MRE acquisition. Therefore, as reported in two studies of the quality of MRE-reconstructed data, MRE experimental parameters have to present: a wavelength-to-pixel-size ratio of 15 to 30 ( 10 ) or 6 to 10 ( 11 ), depending on the reconstruction technique; a minimum phase accrual induced by motion encoding (i.e., wave amplitude) about 10-fold higher than the standard deviation of the phase noise; and, like in morphological MRI, a minimum number of pixels per unit length to image the structure of interest. For rodent MRE, a brain size of about 1 cm implies a working frequency of about 1,000 Hz, i.e., a wavelength of 1 to 2.5 mm.…”

Elastography Validity Criteria Definition Using Numerical Simulations and MR Acquisitions on a Low-Cost Structured Phantom

“…However, OSS is obtained from spatial derivatives of the motion field, which makes it dependent on the processing [16]. The ratio of local shear wavelength λ to pixel size a has also been introduced as an indicator of reconstruction accuracy [17,18], and values were reported for different methods [19,20]. From these studies, the range of optimal λ/a appears to be broad (∼5-20), although best performances are generally achieved in the range 6.7-10, especially at low SNR.…”

“…The displacement fields are then fed into the MRE reconstruction pipeline, which solves the inverse problem and retrieves the mechanical properties for comparison with groundtruth values. Simulations are generally based on analytical formulations [5,14,17,21] or finite element methods (FEM), either with custom-developed tools [22][23][24] or dedicated commercial softwares [20,[24][25][26][27][28][29][30]. Simulations are very useful to assess the error linked to reconstruction algorithms, however they do not suffice to reflect all potential limitations of an MRE experiment (transducer, B 0 and B 1 inhomogeneities, SNR, motion sensitivity, susceptibility issues, and heterogeneity of the material at very small scales).…”