Nonlinear Dynamical Behavior of the Deep White Matter during Head Impact

Abstract

Traumatic brain injury (TBI) is a major public health concern, affecting as many as 3 million people each year in the U.S. Despite substantial research efforts in recent years, our physical understanding of the cause of injury remains rather limited. In this paper, we characterize the nonlinear dynamical behavior of the brain-skull system through modal analysis and advanced finite-element (FE) simulations. We observe nonlinear behavior in the deep-white-matter (WM) structures near the dural folds, with an energy redistribution of around 30% between the dominant modes. We find evidence of shear-wave redirection near the falx and the tentorium (approximately 15 • in the axial and 8 • in the coronal plane) as a result of geometric nonlinearities. The shift in the falx mode shape, which is perpendicular to the deformation of the brain, causes geometrical nonlinear effects at the falx-brain tissue boundary. This is accompanied by a lateral sliding of the tentorium below the brain tissue, which induces higher local strains at its interface with deep regions of the brain. We observe that deep regions of the brain with high principal strains coincide with the identified nonlinear regions. The onset of nonlinear behavior in brain tissue is closely associated with the previously reported concussion thresholds, suggesting a possible link between the damage mechanism and the underlying nonlinear brain biomechanics.

Convolutional neural network for efficient estimation of regional brain strains

“…Further, the data-driven CNN technique does not address any physics behind brain biomechanical responses. However, as a fast and accurate brain strain response generator, the trained CNN may allow other researchers to efficiently produce impact-response data to explore the physics behind brain strains and concussion in reduced-order models 55 .…”

Low-Rank Representation of Head Impact Kinematics: A Data-Driven Emulator

“…In order to compare the performance of previously proposed biphasic models for angular and linear acceleration impulses (Ji and Zhao, 2014 ; Abderezaei et al, 2019 ) against our low-rank PCA approximation, we reconstruct biphasic triangle (tri) and half-sine (hs) representations of the 537 head impacts described above. First, the maximum absolute value of the angular acceleration profile (α M )—computed by differentiating angular velocity measurements using a first-order forward divided difference method (two points)—was identified, including the time of peak ( t M ).…”

“… Constructing triangular and half-sine biphasic impulses (Ji and Zhao, 2014 ; Abderezaei et al, 2019 ): a representative angular acceleration trace in the coronal plane, magnified to better represent initiation time ( t 0 ), completion time ( t 1 ), time of peak ( t M ), and peak acceleration (α Tri and α HS ). …”

“…However, despite these pioneering efforts, on-field head kinematic measurements are not widely available. As a result, researchers have resorted to simplifying parameterizations of head collisions as idealized biphasic acceleration impulses (Yoganandan et al, 2008 ; Ji and Zhao, 2014 ; Abderezaei et al, 2019 ). These biphasic impulses are commonly represented either by a triangle or half-sine and defined by two parameters: height and width constitute the magnitude and duration of a head impact impulse.…”

A Parametric Study of Mechanical Cross-Coupling in Parallel-Kinematics Piezo-Flexural Nano-Positioning Systems

“…Figure15. The effect of decreasing the dimension of square hole of the frame on the mechanical cross-coupling effect (comparison between Case 1 and 6).…”