High-order mesoscale modeling with geometrically conforming gray/white matter interface for traumatic brain injury

Abstract

Background and objective: Brain injury models with a supramillimeter resolution are not feasible to provide spatially detailed strains at or below millimeter scales, especially in regions of convoluted geometry such as at the gray/white matter interface. Furthermore, non-conforming mesh boundaries resulting from discretization errors can lead to inaccurate strain and stress distributions near interfaces, areas typically associated with elevated vulnerabilities in traumatic brain injury (TBI). Conventional approaches using extremely small linear elements are not effective to address the issue because of challenges in generating boundary-conforming meshes and slow convergence.

Methods: In this study, we adapt the Non-Uniform Rational B-Splines (NURBS) and isogeometric analysis (IGA) to develop high-order mesoscale models that smoothly represent complex tissue boundaries with highly resolved strain distributions. We address key challenges for applications to the brain, including the construction of smooth tissue boundaries from voxelized image segmentation and overcoming numerical difficulties arising from near-incompressibility.

Results: Compared to the conventional model using linear elements, the high-order mesoscale model demonstrates superior efficiency by achieving the same accuracy but with two orders of magnitude fewer degrees of freedom and at least one order of magnitude reduction in computational cost. Two-dimensional mesoscale models are constructed at gray/white matter interface to simulate realistic impact loading. The high-order mesoscale models discover strain concentration at the convoluted tissue boundary missing from the global model (e.g., up to 20% difference in magnitude). Notable differences in strain distribution also exist, with a normalized root mean squared error of up to 7.7% for strains sampled near the interface. These strain differences have major implications on downstream axonal injury model simulations.

Conclusion: This study demonstrates the unique potential of leveraging IGA to develop mesoscale brain models with conforming tissue boundaries, and is important for filling a critical gap between global and cellular brain injury models in a multiscale modeling framework. The technique is general and scalable as it is applicable to diverse two- and three-dimensional biomechanical problems, including and beyond brain biomechanics.

Keywords: High-order elements; Isogeometric analysis; Mesoscale modeling; Multiscale modeling; NURBS; Traumatic brain injury.