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White matter (WM) characterization is challenging due to its anisotropic and inhomogeneous microstructure that necessitates multiscale and multi-modality measurements. Shear elastography is one such modality that requires the accurate interpretation of 3D shear strain measurements, which hinge on developing appropriate constitutive tissue models. Finite element methods enable the development of such models by simulating the shear response of representative elemental volumes (REV). We have developed triphasic (axon, myelin, glia), 2D REVs to simulate the influence of the intrinsic viscoelastic property and volume fraction of each phase. This work constitutes the extension of 2D- to 3D-REVs, focusing on the effect of the intrinsic material properties and their 3D representation on the viscoelastic response of the tissue. By lumping the axon and myelin phases, a flexible 3D REV generation and analysis routine is then developed to allow for shear homogenization in both the axial and transverse directions. The 2D and 3D models agree on stress distribution and total deformation when 2D cross-sectional snapshots are compared. We also conclude that the ratio of transverse to axial transverse modulus is larger than one when axon fibers are stiffer than the glial phase.

 

Motivated by the need to interpret the results from a combined use ofin vivobrain Magnetic Resonance Elastography (MRE) and Diffusion Tensor Imaging (DTI), we developed a computational framework to study the sensitivity of single-frequency MRE and DTI metrics to white matter microstructure and cell-level mechanical and diffusional properties. White matter was modeled as a triphasic unidirectional composite, consisting of parallel cylindrical inclusions (axons) surrounded by sheaths (myelin), and embedded in a matrix (glial cells plus extracellular matrix). Only 2D mechanics and diffusion in the transverse plane (perpendicular to the axon direction) was considered, and homogenized (effective) properties were derived for a periodic domain containing a single axon. The numerical solutions of the MRE problem were performed with ABAQUS and by employing a sophisticated boundary-conforming grid generation scheme. Based on the linear viscoelastic response to harmonic shear excitation and steady-state diffusion in the transverse plane, a systematic sensitivity analysis of MRE metrics (effective transverse shear storage and loss moduli) and DTI metric (effective radial diffusivity) was performed for a wide range of microstructural and intrinsic (phase-based) physical properties. The microstructural properties considered were fiber volume fraction, and the myelin sheath/axon diameter ratio. The MRE and DTI metrics are very sensitive to the fiber volume fraction, and the intrinsic viscoelastic moduli of the glial phase. The MRE metrics are nonlinear functions of the fiber volume fraction, but the effective diffusion coefficient varies linearly with it. Finally, the transverse metrics of both MRE and DTI are insensitive to the axon diameter in steady state. Our results are consistent with the limited anisotropic MRE and co-registered DTI measurements, mainly in thecorpus callosum, available in the literature. We conclude that isotropic MRE and DTI constitutive models are good approximations for myelinated white matter in the transverse plane. The unidirectional composite model presented here is used for the first time to model harmonic shear stress under MRE-relevant frequency on the cell level. This model can be extended to 3D in order to inform the solution of the inverse problem in MRE, establish the biological basis of MRE metrics, and integrate MRE/DTI with other modalities towards increasing the specificity of neuroimaging.

 

Finite element analysis is used to study brain axonal injury and develop Brain White Matter (BWM) models while accounting for both the strain magnitude and the strain rate. These models are becoming more sophisticated and complicated due to the complex nature of the BMW composite structure with different material properties for each constituent phase. State-of-the-art studies focus on employing techniques that combine information about the local axonal directionality in different areas of the brain with diagnostic tools such as Diffusion-Weighted Magnetic Resonance Imaging (Diffusion-MRI). The diffusion-MRI data offers localization and orientation information of axonal tracks which are analyzed in finite element models to simulate virtual loading scenarios. Here, a BMW biphasic material model comprised of axons and neuroglia is considered. The model’s architectural anisotropy represented by a multitude of axonal orientations, that depend on specific brain regions, adds to its complexity. During this effort, we develop a finite element method to merge micro-scale Representative Volume Elements (RVEs) with orthotropic frequency domain viscoelasticity to an integrated macro-scale BWM finite element model, which incorporates local axonal orientation. Previous studies of this group focused on building RVEs that combined different volume fractions of axons and neuroglia and simulating their anisotropic viscoelastic properties. Via the proposed model, we can assign material properties and local architecture on each element based on the information from the orientation of the axonal traces. Consecutively, a BWM finite element model is derived with fully defined both material properties and material orientation. The frequency-domain dynamic response of the BMW model is analyzed to simulate larger scale diagnostic modalities such as MRI and MRE. 

Estimating microstructural parameters of skeletal muscle from diffusion MRI (dMRI) signal requires understanding the relative importance of both microstructural and dMRI sequence parameters on the signal. This study seeks to determine the sensitivity of dMRI signal to variations in microstructural and dMRI sequence parameters, as well as assess the effect of noise on sensitivity.

Using a cylindrical myocyte model of skeletal muscle, numerical solutions of the Bloch‐Torrey equation were used to calculate global sensitivity indices of dMRI metrics (FA, RD, MD,,,) for wide ranges of microstructural and dMRI sequence parameters. The microstructural parameters were: myocyte diameter, volume fraction, membrane permeability, intra‐ and extracellular diffusion coefficients, and intra‐ and extracellulartimes. Two separate pulse sequences were examined, a PGSE and a generalized diffusion‐weighted sequence that accommodates a larger range of diffusion times. The effect of noise and signal averaging on the sensitivity of the dMRI metrics was examined by adding synthetic noise to the simulated signal.

Among the examined parameters, the intracellular diffusion coefficient has the strongest effect, and myocyte diameter is more influential than permeability for FA and RD. The sensitivity indices do not vary significantly between the two pulse sequences. Also, noise strongly affects the sensitivity of the dMRI signal to microstructural variations.

With the identification of key microstructural features that affect dMRI measurements, the reported sensitivity results can help interpret dMRI measurements of skeletal muscle in terms of the underlying microstructure and further develop parsimonious dMRI models of skeletal muscle.