Modeling of microstructural kinematics during simple elongation of central nervous system tissue

Damage to axons and glial cells in the central nervous system (CNS) white matter is a nearly universal feature of traumatic brain injury, yet it is not clear how the tissue mechanical deformations are transferred to the cellular components of the CNS. Defining how cellular deformations relate to the applied tissue deformation field can both highlight cellular populations at risk for mechanical injury, and define the fraction of cells in a specific population that will exhibit damage. In this investigation, microstructurally based models of CNS white matter were developed and tested against measured transformations of the CNS tissue microstructure under simple elongation. Results show that axons in the unstretched optic nerves were significantly wavy or undulated, where the measured axonal path length was greater than the end-to-end distance of the axon. The average undulation parameter--defined as the true axonal length divided by the end-to-end length--was 1.13. In stretched nerves, mean axonal undulations decreased with increasing applied stretch ratio (lambda)--the mean undulation values decreased to 1.06 at lambda = 1.06, 1.04 at lambda = 1.12, and 1.02 at lambda = 1.25. A model describing the gradual coupling, or tethering, of the axons to the surrounding glial cells best fit the experimental data. These modeling efforts indicate the fraction of the axonal and glial populations experiencing deformation increases with applied elongation, consistent with the observation that both axonal and glial cell injury increases at higher levels of white matter injury. Ultimately, these results can be used in conjunction with computational simulations of traumatic brain injury to aid in establishing the relative risk of cellular structures in the CNS white matter to mechanical injury.