A transition model for finite element simulation of kinematics of central nervous system white matter

Mechanical damage to axons is a proximal cause of deficits following traumatic brain injury and spinal cord injury. Axons are injured predominantly by tensile strain, and identifying the strain experienced by axons is a critical step toward injury prevention. White matter demonstrates complex nonlinear mechanical behavior at the continuum level that evolves from even more complex, dynamic, and composite behavior between axons and the "glial matrix" at the microlevel. In situ, axons maintain an undulated state that depends on the location of the white matter and the stage of neurodevelopment. When exposed to tissue strain, axons do not demonstrate pure affine or non-affine behavior, but instead transition from non-affine-dominated kinematics at low stretch levels to affine kinematics at high stretch levels. This transitional and predominant kinematic behavior has been linked to the natural coupling of axons to each other via the glial matrix. In this paper, a transitional kinematic model is applied to a micromechanics finite element model to simulate the axonal behavior within a white matter tissue subjected to uniaxial tensile stretch. The effects of the transition parameters and the volume fraction of axons on axonal behavior is evaluated and compared to previous experimental data and numerical simulations.