This paper describes a method to estimate mechanical properties of soft, anisotropic materials from measurements of shear waves with specific polarization and propagation directions. This method is applicable to data from magnetic resonance elastography (MRE), which is a method for measuring shear waves in live subjects or in vitro samples. Here, we simulate MRE data using finite element analysis. A nearly-incompressible, transversely isotropic (ITI) material model with three parameters (shear modulus, shear anisotropy, and tensile anisotropy) is used, which is appropriate for many fibrous, biological tissues. Both slow and fast shear waves travel concurrently through such a material with speeds that depend on the propagation direction relative to fiber orientation. A three-parameter estimation approach based on directional filtering and isolation of slow and fast shear wave components (directional filter inversion, or DFI) is introduced. Wave speeds of each isolated shear wave component are estimated using local frequency estimation (LFE), and material properties are calculated using weighted least squares. Data from multiple finite element simulations are used to assess the accuracy and reliability of DFI for estimation of anisotropic material parameters.
Mechanical anisotropy is an important property of fibrous tissues; for example, the anisotropic mechanical properties of brain white matter may play a key role in the mechanics of traumatic brain injury (TBI). The simplest anisotropic material model for small deformations of soft tissue is a nearly incompressible, transversely isotropic (ITI) material characterized by three parameters: minimum shear modulus (μ), shear anisotropy (ϕ = μ1/μ − 1) and tensile anisotropy (ζ = E1/E2 − 1). These parameters can be determined using magnetic resonance elastography (MRE) to visualize shear waves, if the angle between the shear-wave propagation direction and fiber direction is known. Most MRE studies assume isotropic material models with a single shear (μ) or tensile (E) modulus. In this study, two types of shear waves, “fast” and “slow”, were analyzed for a given propagation direction to estimate anisotropic parameters μ, ϕ, and ζ in two fibrous soft materials: turkey breast ex vivo and aligned fibrin gels. As expected, the speed of slow shear waves depended on the angle between fiber direction and propagation direction. Fast shear waves were observed when the deformations due to wave motion induced stretch in the fiber direction. Finally, MRE estimates of anisotropic mechanical properties in turkey breast were compared to estimates from direct mechanical tests.
The mechanical properties of brain tissue in vivo determine the response of the brain to rapid skull acceleration. These properties are thus of great interest to the developers of mathematical models of traumatic brain injury (TBI) or neurosurgical simulations. Animal models provide valuable insight that can improve TBI modeling. In this study we compare estimates of mechanical properties of the Yucatan mini-pig brain in vivo and ex vivo using magnetic resonance elastography (MRE) at multiple frequencies. MRE allows estimations of properties in soft tissue, either in vivo or ex vivo, by imaging harmonic shear wave propagation. Most direct measurements of brain mechanical properties have been performed using samples of brain tissue ex vivo. It has been observed that direct estimates of brain mechanical properties depend on the frequency and amplitude of loading, as well as the time post-mortem and condition of the sample. Using MRE in the same animals at overlapping frequencies, we observe that porcine brain tissue in vivo appears stiffer than porcine brain tissue samples ex vivo at frequencies of 100 Hz and 125 Hz, but measurements show closer agreement at lower frequencies.
The mechanical properties of brain tissue, particularly those of white matter (WM), need to be characterized accurately for use in finite element (FE) models of brain biomechanics and traumatic brain injury (TBI). Magnetic resonance elastography (MRE) is a powerful tool for non-invasive estimation of the mechanical properties of soft tissues. While several studies involving direct mechanical tests of brain tissue have shown mechanical anisotropy, most MRE studies of brain tissue assume an isotropic model. In this study, an incompressible transversely isotropic (TI) material model parameterized by minimum shear modulus (μ), shear anisotropy parameter (ϕ), and tensile anisotropy parameter (ζ) is applied to analyze MRE measurements of ex vivo porcine white matter (WM) brain tissue. To characterize shear anisotropy, "slow" (pure transverse) shear waves were propagated at 100, 200 and 300Hz through sections of ex vivo brain tissue including both WM and gray matter (GM). Shear waves were found to propagate with elliptical fronts, consistent with TI material behavior. Shear wave fields were also analyzed within regions of interest (ROI) to find local shear wavelengths parallel and perpendicular to fiber orientation. FE simulations of a TI material with a range of plausible shear modulus (μ) and shear anisotropy parameters (ϕ) were run and the results were analyzed in the same fashion as the experimental case. Parameters of the FE simulations which most closely matched each experiment were taken to represent the mechanical properties of that particular sample. Using this approach, WM in the ex vivo porcine brain was found to be mildly anisotropic in shear with estimates of minimum shear modulus (actuation frequencies listed in parenthesis): μ= 1.04 ± 0.12 kPa (at 100Hz), μ= 1.94 ± 0.29 kPa (at 200Hz), and μ= 2.88 ± 0.34 kPa (at 300Hz) and corresponding shear anisotropy factors of ϕ= 0.27 ± 0.09 (at 100Hz), ϕ= 0.29 ± 0.14 (at 200Hz) and ϕ= 0.34 ± 0.13 (at 300Hz). Future MRE studies will focus on tensile anisotropy, which will require both slow and fast shear waves for accurate estimation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.