Behzad Babaei1, Daniel Fovargue2, David Nordsletten2,3, and Lynne Bilston1,4
1Neuroscience Research Australia, Sydney, Australia, 2King's College London, London, United Kingdom, 3Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States, 4Prince of Wales Clinical School, University of New South Wales, Randwick, Australia
Synopsis
MR elastography is well established for measuring the
mechanical properties of soft tissues in a broad range of clinical populations.
However, unlike liver tissue, which is generally considered to be isotropic,
muscle is significantly anisotropic, with stiffer mechanical behaviour along
the muscle fibre directions. Identifying anisotropic properties is challenging
due to the need to track fibre directions and additional numerical difficulties
in estimating properties. Here, we describe a novel finite element inversion
method for estimating anisotropic mechanical properties of ex vivo tissue data,
and validate this method using three sets of simulated data.
Introduction
MR elastography
(MRE) has gained substantial use clinically, most commonly for noninvasively
detecting liver fibrosis. There has been considerable interest in extending its
use to neural and musculoskeletal tissues, however these tissues do not obey
the fundamental assumption of most elastography inversion methods, namely
isotropy (similar mechanical behaviour in all directions). There has been
growing interest in anisotropic MRE methods, but since the governing equations
for wave propagation in anisotropic materials include higher-order derivatives,
this poses additional numerical challenges for inversion algorithms. In
addition, there is a need to identify the local fiber directions (e.g. for
muscles or white matter) using DTI or other approaches, and integrate these
into the MRE inversion methods. This study describes and validates a novel
finite element inversion method and analysis pipeline for anisotropic MRE.Methods
A novel anisotropic finite element (FE) inversion
method was developed by extending an existing divergence free isotropic FE
method 1 to solve the transversely anisotropic wave
equation. This method enables the combination of multiple input datasets to
ensure that adequate wave coverage from different sources fully characterises
wave propagation2. The method was validated using simulated data,
and then trialled on data from the ex vivo muscle tissue data. Simulated
anisotropic elastography data sets were generated using custom finite element
software, with a region that has anisotropic viscoelastic properties defined (Gparallel=4kPa, Gperpendicular=2kPa,
G"=0.5kPa) embedded within an isotropic
region (G’=3kPa, G"=0.5kPa).
Displacement data from these simulations was exported and fed into the new
inversion software, along with the known anisotropy symmetry axes. Shear moduli
parallel and perpendicular to the anisotropic symmetry axes were calculated and
compared to the simulation inputs. Next, experimental MRE and DTI data was
collected from samples of bovine muscle tissue, using the eXpresso technique
(Bovine:F=50Hz, TR/TE=130/9.21ms, 9 slices, voxel size=2mm isotropic3. DTI data was collected with matching geometry
(32 directions, b factor=500, TR/TE=3600/60ms). An analysis pipeline was
developed to denoise the DTI data using an LPCA method, register the DTI data
to anatomical images and magnitude images from the MRE acquisitions using
Elastix, and then perform the anisotropic MRE inversion. Results
Simulation results (Figure 1) show that the new
anisotropic inversion method accurately reproduces the input shear moduli, both
in the anisotropic region (with constant vertical fibre direction) and the
isotropic surrounding region. The simulation of Figure 1 was repeated with varying
fibre directions along all 3 dimensions for the anisotropic region (Figure 2). 10%
noise was added to the ideal simulation of Figure 2, and the simulation was
reconstructed, as shown in Figure 3. Experimental
data from the bovine muscle tissue was successfully analysed (Figure 4), and
provided anisotropic material properties similar to previous studies on similar
samples 4.Discussion
This new finite element inversion method provides
quantitatively correct anisotropic shear moduli for both isotropic and
anisotropic regions within a simulated domain, a major step forward in
anisotropic MRE. The capacity to input more than one dataset with differing
wave propagation directions, such as from multiple wave sources enables more
robust parameter estimation, although this is not essential for accurate
estimation of properties in skeletal muscles if the vibration sources used
sufficiently probe all tissue directions. Conclusion
Our new anisotropic finite element inversion
method is able to robustly extract validated anisotropic viscoelastic
mechanical properties from experimental MRE and matched DTI datasets. It is
suitable for use in human studies of muscles, and may also have application for
other anisotropic soft tissues, such as white matter in the brain. Acknowledgements
B. Babaei and D. Fovargue contributed equally to this work. This work was supported by a Discovery grant from the Australian Research Council. LEB is supported by an NHMRC senior research fellowship.References
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