Characterization of the three-dimensional kinematic behavior of axons in central nervous system white matter

Traumatic injury to axons in white matter of the brain and spinal cord occurs primarily via tensile stretch. During injury, the stress and strain experienced at the tissue level is transferred to the microscopic axons. How this transfer occurs, and the primary constituents dictating this transfer must be better understood to develop more accurate multi-scale models of injury. Previous studies have characterized axon tortuosity and kinematic behavior in 2-dimensions (2-D), where axons have been modeled to exhibit non-affine (discrete), affine (composite-like), or switching behavior. In this study, we characterize axon tortuosity and model axon kinematic behavior in 3-dimensions (3-D). Embryonic chick spinal cords at different development stages were excised and stretched. Cords were then fixed, transversely sectioned, stained, and imaged. 3-D axon tortuosity was measured from confocal images using a custom-built MATLAB script. 2-D kinematic models previously described in Bain et al. (J Biomech Eng 125(6):798, 2003) were extended, re-derived, and validated for the 3-D case. Results showed that 3-D tortuosity decreased with stretch, exhibiting similar trends with changes in development as observed in the 2-D studies. Kinematic parameters also displayed similar general trends. Axons demonstrated more affine behavior with increasing stretch and development. In comparison with 2-D results, a smaller percentage of the populations of 3-D axons were predicted to follow pure non-affine behavior. The data and kinematic models presented herein can be incorporated into multi-scale CNS injury models, which can advance the accuracy of the models and improve the potential to identify axonal injury thresholds.