skip to main content


Title: Numerical Simulation of Stress States in White Matter via a Continuum Model of 3D Axons Tethered to Glia
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.

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.  more » « less

Award ID(s):
1763005
NSF-PAR ID:
10311771
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
International Mechanical Engineering Congress and Exposition, IMECE 2020
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Numerical simulations using non-linear hyper-elastic material models to describe interactions between brain white matter (axons and extra cellular matrix (ECM)) have enabled high-fidelity characterization of stress-strain response. In this paper, a novel finite element model (FEM) has been developed to study mechanical response of axons embedded in ECM when subjected to tensile loads under purely non-affine kinematic boundary conditions. FEM leveraging Ogden hyper-elastic material model is deployed to understand impact of parametrically varying oligodendrocyte-axon tethering and analyze influence of aging material characteristics on stress propagation. In proposed FEM, oligodendrocyte connections to axons are represented via spring-dashpot model, such tethering technique facilitates contact definition at various locations, parameterize connection points and vary stiffness of connection hubs. Two FE submodels are discussed: 1) multiple oligodendrocytes arbitrarily tethered to the nearest axons, and 2) single oligodendrocyte tethered to all axons at various locations. Root mean square deviation (RMSD) were computed between stress-strain plots to depict trends in mechanical response. Axonal stiffness was found to rise with increasing tethering, indicating role of oligodendrocytes in stress redistribution. Finally, stress state results for aging axon material, with varying stiffnesses and number of connections in FEM ensemble have also been discussed to demonstrate gradual softening of tissues.

     
    more » « less
  2. Abstract

    A novel finite element method (FEM) is developed to study mechanical response of axons embedded in extra cellular matrix (ECM) when subjected to harmonic uniaxial stretch under purely non-affine kinematic boundary conditions. The proposed modeling approach combines hyper-elastic (such as Ogden model) and time/frequency domain viscoelastic constitutive models to evaluate the effect of parametrically varying oligodendrocyte-axon tethering under harmonic stretch at 50Hz. A hybrid hyper-viscoelastic material (HVE) model enabled the analysis of repeated uniaxial load on stress propagation and damage accumulation in white matter.

    In the proposed FEM, oligodendrocyte connections to axons are depicted via a spring-dashpot model. This tethering technique facilitates contact definition at various locations, parameterizes connection points and varies stiffness of connection hubs. Results from a home-grown FE submodel configuration of a single oligodendrocyte tethered to axons at various locations are presented. Root mean square deviation (RMSD) are computed between stress-strain plots to depict trends in mechanical response. Steady-state dynamic (SSD) simulations show stress relaxation in axons. Gradual axonal softening under repetitive loads is illustrated employing Prony series - HVE models. Representative von-Mises stress plots indicate that undulated axons experience bending stresses along their tortuous path, suggesting greater susceptibility to damage accumulation and fatigue failure due to repeated strains.

     
    more » « less
  3. In the developing central nervous system, pre-myelinating oligodendrocytes contact and sample candidate nerve axons by extending and retracting process extensions. Some contacts stabilize and mature, leading to the initiation of axon wrapping, myelin sheath formation, and sheath elongation by oligodendrocytes. Although axonal signals influence the overall process of myelination, which precise steps and oligodendrocyte cell behaviors require signaling from axons is incompletely understood. In this study, we investigated whether cell behaviors during the early events of myelination involve input from axons or are mediated by an oligodendrocyte-autonomous myelination program. To address this, we utilized in vivo time-lapse imaging in embryonic and larval zebrafish during the initial hours and days of axon wrapping and myelination. Transgenic reporter lines marked individual axon subtypes or oligodendrocyte membranes. In the larval zebrafish spinal cord, individual axon subtypes supported distinct nascent sheath growth rates and pruning frequencies. Oligodendrocytes ensheathed individual axon subtypes at different rates during a two-day period after initial axon wrapping. When the ratio of oligodendrocytes to target axons was increased by ablating spinal projection axons, local spinal neuron axons supported a constant ensheathment rate despite the increased ratio of oligodendrocytes to target axons. We conclude that properties of individual axon subtypes instruct oligodendrocyte behaviors during initial stages of myelination by differentially controlling nascent sheath growth and stabilization. 
    more » « less
  4. null (Ed.)
    Abstract Background In the developing central nervous system, pre-myelinating oligodendrocytes sample candidate nerve axons by extending and retracting process extensions. Some contacts stabilize, leading to the initiation of axon wrapping, nascent myelin sheath formation, concentric wrapping and sheath elongation, and sheath stabilization or pruning by oligodendrocytes. Although axonal signals influence the overall process of myelination, the precise oligodendrocyte behaviors that require signaling from axons are not completely understood. In this study, we investigated whether oligodendrocyte behaviors during the early events of myelination are mediated by an oligodendrocyte-intrinsic myelination program or are over-ridden by axonal factors. Methods To address this, we utilized in vivo time-lapse imaging in embryonic and larval zebrafish spinal cord during the initial hours and days of axon wrapping and myelination. Transgenic reporter lines marked individual axon subtypes or oligodendrocyte membranes. Results In the larval zebrafish spinal cord, individual axon subtypes supported distinct nascent sheath growth rates and stabilization frequencies. Oligodendrocytes ensheathed individual axon subtypes at different rates during a two-day period after initial axon wrapping. When descending reticulospinal axons were ablated, local spinal axons supported a constant ensheathment rate despite the increased ratio of oligodendrocytes to target axons. Conclusion We conclude that properties of individual axon subtypes instruct oligodendrocyte behaviors during initial stages of myelination by differentially controlling nascent sheath growth and stabilization. 
    more » « less
  5. In the CNS, oligodendrocyte progenitor cells (OPCs) differentiate into mature oligodendrocytes to generate myelin, an essential component for normal nervous system function. OPC differentiation is driven by signaling pathways, such as mTOR, which functions in two distinct complexes: mTOR complex 1 (mTORC1) and mTOR complex 2 (mTORC2), containing Raptor or Rictor, respectively. In the current studies, mTORC2 signaling was selectively deleted from OPCs in PDGFRα-Cre X Rictorfl/flmice. This study examined developmental myelination in male and female mice, comparing the impact of mTORC2 deletion in the corpus callosum and spinal cord. In both regions, Rictor loss in OPCs resulted in early reduction in myelin RNAs and proteins. However, these deficits rapidly recovered in spinal cord, where normal myelin was noted at P21 and P45. By contrast, the losses in corpus callosum resulted in severe hypomyelination and increased unmyelinated axons. The hypomyelination may result from decreased oligodendrocytes in the corpus callosum, which persisted in animals as old as postnatal day 350. The current studies focus on uniquely altered signaling pathways following mTORC2 loss in developing oligodendrocytes. A major mTORC2 substrate is phospho-Akt-S473, which was significantly reduced throughout development in both corpus callosum and spinal cord at all ages measured, yet this had little impact in spinal cord. Loss of mTORC2 signaling resulted in decreased expression of actin regulators, such as gelsolin in corpus callosum, but only minimal loss in spinal cord. The current study establishes a regionally specific role for mTORC2 signaling in OPCs, particularly in the corpus callosum.

    SIGNIFICANCE STATEMENTmTORC1 and mTORC2 signaling has differential impact on myelination in the CNS. Numerous studies identify a role for mTORC1, but deletion of Rictor (mTORC2 signaling) in late-stage oligodendrocytes had little impact on myelination in the CNS. However, the current studies establish that deletion of mTORC2 signaling from oligodendrocyte progenitor cells results in reduced myelination of brain axons. These studies also establish a regional impact of mTORC2, with little change in spinal cord in these conditional Rictor deletion mice. Importantly, in both brain and spinal cord, mTORC2 downstream signaling targets were impacted by Rictor deletion. Yet, these signaling changes had little impact on myelination in spinal cord, while they resulted in long-term alterations in myelination in brain.

     
    more » « less