White matter tract-oriented deformation is dependent on real-time axonal fiber orientation

Abstract

Traumatic axonal injury (TAI) is a critical public health issue with its pathogenesis remaining largely elusive. Finite element (FE) head models are promising tools to bridge the gap between mechanical insult and localized brain response and resultant injury. In particular, the FE-derived deformation along the direction of white matter (WM) tracts (i.e., tract-oriented strain) has been shown to be an appropriate predictor for TAI. However, the evolution of fiber orientation in time during the impact and its potential influence on tract-oriented strain remained unknown. To address this question, the present study leveraged an embedded element approach to track real-time fiber orientation during impacts. A new scheme to calculate the tract-oriented strain was proposed by projecting the strain tensors from pre-computed simulations along the temporal fiber direction instead of its static counterpart directly obtained from diffuse tensor imaging. The results revealed that incorporating the real-time fiber orientation not only altered the direction but also amplified the magnitude of the tract-oriented strain, resulting in a generally more extended distribution and a larger volume ratio of WM exposed to high deformation along fiber tracts. Results of this study provide important insights into how best to incorporate fiber orientation in head injury models and derive the WM tract-oriented deformation from computational simulations, which is important for furthering our understanding of the underlying mechanisms of TAI.

Towards a comprehensive delineation of white matter tract-related deformation

“…When focusing on MPS and MTOS, enhanced performance on injury discrimination was noted for MTOS with respect to MPS, correlating well with the findings in previous computational studies [25,38,40,41,47,74]. However, possibly because of the lack of consensus of brain mechanics, substantial differences existed among the previous studies, particularly on the brain materials (e.g., isotropic vs. anisotropic, heterogeneous vs. homogeneous) and the computation of tract-oriented strain (e.g., time-variant fiber orientation vs. time-invariant fiber orientation) [49]. The current study was unique since we simulated the brain as an isotropic and homogenous structure and leveraged an embedded element approach to monitor the real-time fiber orientation during head impacts.…”

“…Given that the deformation of WM fiber tracts is directly dependent on the real-time fiber orientation, an embedded element method was implemented in the FE model to monitor the temporal evaluation of fiber orientation (Fig. 1D-F) following the approach presented earlier [49].…”

“…, and 3 v , respectively. Details about the transformation of the strain tensor from the global coordinate system to the skull-fixed coordinate system are available in the previous publications from our group [42,49] as well as others [25]. Given that the deformation of the fiber tracts is dependent on the fiber orientation, a specific tract-aligned coordinate system, i.e., the tract-aligned coordinate system (1) (…”

“…Consequently, the real-time fiber orientation during head impacts was reflected by the temporal direction of the truss element and was updated at each timestep of the simulation. Details regarding the coupling protocol between DTI and WM element and the implementation of the embedded element method for tracking the real-time fiber orientation are available in [37] and [49], respectively.…”

“…As reflected by our modeling choice that no relative motion between the truss elements and their master elements were permitted [49], these analytical solutions in Table 1 were attained based on the assumption that the displacements across the fiber tracts and surrounding matrix was continuous, similar to the assumption in the aforementioned in vitro models [51][52][53] and other computational studies [29,30,40,41,46,74,75,91]. This assumption was partially verified by one in vitro model, in which no evident movement of soma/neurite with respect to the surrounding matrix was observed in the rat [53].…”