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 of
- NSF-PAR ID:
- 10361319
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Physics in Medicine & Biology
- Volume:
- 66
- Issue:
- 3
- ISSN:
- 0031-9155
- Page Range / eLocation ID:
- Article No. 035027
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract -
A new finite element approach is proposed to study the propagation of stress in axons in the central nervous system (CNS) white matter. The axons are embedded in an extra cellular matrix (ECM) and are subjected to tensile loads under purely non-affine kinematic boundary conditions. The axons and the ECM are described by the Ogden hyperelastic material model. The effect of tethering of the axons by oligodendrocytes is investigated using the finite element model. Glial cells are often thought of as the “glue” that hold the axons together. More specifically, oligodendrocytes bond multiple axons to each other and create a myelin sheath that insulates and supports axons in the brainstem. The glial cells create a scaffold that supports the axons and can potentially bind 80 axons to a single oligodendrocyte.more » « less
In this study, the microstructure of the oligodendrocyte connections to axons is modeled using a spring-dashpot approximation. The model allows for the oligodendrocytes to wrap around the outer diameter of the axons at various locations, parameterizing the number of connections, distance between connection points, and the stiffness of the connection hubs. The parameterization followed the distribution of axon-oligodendrocyte connections provided by literature data in which the values were acquired through microtome of CNS white matter. We develop two models: 1) multiple oligodendrocytes arbitrarily tethered to the nearest axons, and 2) a single oligodendrocyte tethered to all the axons at various locations. The results depict stiffening of the axons, which indicates that the oligodendrocytes do aid in the redistribution of stress. We also observe the appearance of bending stresses at inflections points along the tortuous path of the axons when subjected to tensile loading. The bending stresses appear to exhibit a cyclic variation along the length of the undulated axons. This makes the axons more susceptible to damage accumulation and fatigue. Finally, the effect of multiple axon-myelin connections in the central nervous system and the effect of the distribution of these connections in the brain tissue is further investigated at present.
-
Material properties of brain white matter (BWM) show high anisotropy due to the complicated internal three-dimensional microstructure and variant interaction between heterogeneous brain-tissue (axon, myelin, and glia). From our previous study, finite element methods were used to merge micro-scale Representative Volume Elements (RVE) with orthotropic frequency domain viscoelasticity to an integral macro-scale BWM. Quantification of the micro-scale RVE with anisotropic frequency domain viscoelasticity is the core challenge in this study.more » « less
The RVE behavior is expressed by a viscoelastic constitutive material model, in which the frequency-related viscoelastic properties are imparted as storage modulus and loss modulus for the composite comprised of axonal fibers and extracellular glia. Using finite elements to build RVEs with anisotropic frequency domain viscoelastic material properties is computationally very consuming and resource-draining. Additionally, it is very challenging to build every single RVE using finite elements since the architecture of each RVE is arbitrary in an infinite data set. The architecture information encoded in the voxelized location is employed as input data and is consequently incorporated into a deep 3D convolution neural network (CNN) model that cross-references the RVEs’ material properties (output data). The output data (RVEs’ material properties) is calculated in parallel using an in-house developed finite element method, which models RVE samples of axon-myelin-glia composites. This novel combination of the CNN-RVE method achieved a dramatic reduction in the computation time compared with directly using finite element methods currently present in the literature.
-
In the present work, we analyze the applicability of two-step homogenization applied to 3D woven composites with high crimp reinforcement. The available micromechanical homogenization approaches (Hashin, Chamis, Hashin-Shtrikman bounds etc.) were developed and validated for unidirectional composites. These formulas have also been used by the community to homogenize tows in 2D and 3D woven composites including reinforcement architectures with high crimp ratios. However, a rigorous study of their applicability to high-crimp geometries is yet to be performed. We utilize Finite Element Analysis (FEA) to calculate the overall engineering constants (Young’s moduli and shear moduli) of tows having various crimp (𝐶𝑅) and wavelength-to-fiber diameter (𝜆/𝑑) ratios. For this analysis, periodic sinusoidal unit cells following shapes of individual fibers are used. Fiber volume fraction is set to 70% and is the same in all cases. Transversely isotropic carbon fiber and isotropic epoxy matrix are used. The results are compared with overall responses of tows modeled using homogenized tow properties obtained from micromechanics and FEA as well as explicitly modeled tows containing multiple parallel fibers. The results of our analysis show dependence of the overall elastic properties on both crimp ratio and the normalized wavelength. Separation of fiber/tow scales is achieved at 𝜆/𝑑 = 50.more » « less
-
null (Ed.)Healthy aging involves local variations in viscoelastic shear properties of the brain. We employ high-resolution, multi-excitation MRE and a novel anisotropic inversion scheme (iTI) to extract local shear anisotropic moduli in vivo. The ratio of transverse to axial moduli, a new MRE metric, remains greater than 1 along the splenium, body and genu regions of the corpus callosum for both young and old subjects. This metric peaks in the body region and decreases with age throughout the corpus callosum.more » « less
