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

Abstract

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.

MR elastography: Principles, guidelines, and terminology

“…In objects with at least one dimension smaller than about a wavelength (such as in the heart or within tumors), wave behavior depends on geometry as well as the inherent material properties, and such “waveguide effects” can dominate the wave propagation. Consequently, inversion approaches that do not account for this yield biased values 37,71 . This is particularly important in cardiac MRE with typical wall thicknesses around 10 mm.…”

“…54 Taking the curl of the displacement wave field in a homogeneous medium removes longitudinal contributions in theory, leaving behind a wave field that propagates at the true shear wave speed, corresponding to the intrinsic shear modulus. 37,71 However, there are practical difficulties: This requires full 3D data with good resolution in z, causes noise amplification, and low resolution may mean that spatial gradient operators may cross boundaries and yield incorrect results. Alternatively, some inversion approaches (eg, nonlinear inversion) may yield more accurate results near boundaries or in waveguide situations.…”

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

“…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).…”

Advances and Future Direction of Magnetic Resonance Elastography

“…In the Helmholtz equation, the medium is assumed to be infinite. For most soft tissues in which MRE has been performed (e.g., aorta, heart, and spinal cord), the media are bounded in which the propagating mechanical wave becomes complicated due to the relatively small dimensions and the geometry of the object 55 . Additionally, in bounded media, the equation of motion presented in Equation 2 will no longer hold and thus, new equations of motion that take geometry of the medium into account are needed.…”

“…Promising results in different applications were observed. Manduca et al studied the waveguide effects in simulated cardiac MRE data using FEM and reported that inversion without curl processing resulted in biased stiffness values 55 . Moreover, it was observed that 3D inversion on curl-processed MRE data yielded more accurate stiffness estimation when compared to 2D inversion with curl processing, suggesting the importance of 3D MRE inversion.…”