Numerical simulation of stress states to evaluate oligodendrocyte tethering effect on hyperelastic 3D response of injured axons in brain white matter
Creators: name: Agarwal, Mohit
Publisher: name: No Publisher Supplied
Year: 2022

description: Numerical modeling of Traumatic brain injury (TBI) and central nervous system (CNS) extremities has sprung tremendous interest among researchers to deterministically depict and analyze impact of axonal injuries. Elaborate finite element simulations leveraging non-linear hyper-elastic material models to approximate connections between oligodendrocytes and axons in an extra cellular matrix (ECM) have emerged as prospective solutions to characterize stress-states and investigate stiffness changes corresponding to parametrically varying oligodendrocyte-axons connections. In this study, one such novel finite element model (FEM) has been proposed to study the mechanical response of axons embedded in ECM when subjected to tensile loads under purely non-affine kinematic boundary conditions. The axons and the ECM material characterizations are described by Ogden hyper-elastic material model. Expanding on the previous results, the current work investigates additional tethering scenarios between axons and oligodendrocytes using finite element modeling. It also discusses modifications made in one of the original FE submodel setups and its effect on stress propagation.In the proposed novel FEM, oligodendrocyte connections to axons are represented via the spring-dashpot model (as deployed in our predicate studies). Such tethering technique facilitates contact definition at various locations, parameterize connection points, and vary the stiffness of connection hubs. Such a connection model mimics the tethering between oligodendrocytes and axons, which facilitates inter-axonal bonding and creates a myelin sheath that consequently insulates and supports axons in the brainstem. 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. Detailed FE investigation by parametrically varying connection scenarios enabled comprehensive comparative analysis between proposed submodel efficacy. Root mean square deviation (RMSD) was computed between stress-strain plots to depict trends in mechanical response and bending stresses. Axonal stiffness was found to rise with increasing tethering, indicating the role of oligodendrocytes in stress redistribution. In submodel-2 (single-oligo model), for the same number of connections per axons, RMSD values increased as “K” (oligodendrocyte spring stiffness) values were set higher. RMSD calculations reveal that for a “K” value, sub-model 2 yielded slightly stiffer models compared to submodel-1(multi-oligo model). The current study also addresses potential geometrical limitations in submodel-1 by randomizing and adding connections to ensure greater responsiveness. The stress profile observed from tested FE submodels indicates that Oligodendrocytes do support axons in the extracellular matrix and distribute stresses. High stresses noticed in regions with high tortuosity and bending stresses between all inflection points in the axon paths. Cyclic bending stresses noticed in both sub-models suggest risk of axonal damage accumulation and fatigue failure if subjected to repeated tensile and/or compressive loading.