Nonlinear Dynamical Behavior of the Deep White Matter during Head Impact

Javid Abderezaei, Wei Zhao, Carissa L. Grijalva, Gloria Fabris, Songbai Ji, Kaveh Laksari, and Mehmet Kurt

Phys. Rev. Applied 12, 014058 – Published 30 July 2019

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 $15^{\circ}$ in the axial and $8^{\circ}$ 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.

Received 18 December 2018
Revised 26 June 2019

DOI:https://doi.org/10.1103/PhysRevApplied.12.014058

Physics Subject Headings (PhySH)

Biomechanics Classical mechanics Shear deformation Strain

Brain Tissues

Chaos & nonlinear dynamics Finite-element method

Interdisciplinary PhysicsPhysics of Living SystemsPolymers & Soft MatterNonlinear Dynamics

Authors & Affiliations

Javid Abderezaei¹, Wei Zhao², Carissa L. Grijalva³, Gloria Fabris¹, Songbai Ji², Kaveh Laksari³, and Mehmet Kurt ^1,4,*

¹Department of Mechanical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA
²Department of Biomedical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609-2280, USA
³Department of Biomedical Engineering, University of Arizona, Tucson, Arizona 85721-0020, USA
⁴Translational and Molecular Imaging Institute, Icahn School of Medicine at Mount Sinai, New York, New York 10029, USA

^*mkurt@stevens.edu

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Vol. 12, Iss. 1 — July 2019

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Images

Figure 1
Finite-element simulation of the brain using the WHIM. (a) The brain anatomical features in the WHIM model [27]. (b) A half-sine rotational acceleration pulse with varying amplitude ( $α = 1 - 10 krad / s^{2}$ ) and duration ( $Δ t = 5 - 25 ms$ ), imposed at the center of gravity of the head.
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Figure 2
Brain tissue does not exhibit global nonlinear behavior. (a) The energy contribution of the first three POMs corresponding to varying amplitudes and durations in the coronal plane: the negligible change of 2.7% in the energy redistribution of the first POM is an indication of weak global nonlinearity. (b) The high correlation between the brain’s dominant mode shape at minimum and maximum acceleration levels. A midsagittal section is shown as a reference.
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Figure 3
The existence of local nonlinearity in the human brain. (a) By varying the acceleration amplitude and duration in the coronal plane, the normalized dominant mode shape $[v_{1} (x, y, z, α, Δ t)]$ corresponding to each acceleration level is compared with the linear baseline $[v_{1} (x, y, z, α_{ref}, Δ t_{ref})]$ and a nonlinear region is identified $(Δ v_{1} > 50 %)$ . (b) The energy redistribution of approximately 30% in the first three POMs of the nonlinear regions in the deep WM is an indication of local nonlinearity. (c) The nonlinear region covers approximately 25% of the WM. A comparison of concussion thresholds with the volume of the nonlinear region suggests a possible link with the injury mechanism. In scale-bar legend, NL: nonlinear, WM: white matter.
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Figure 4
The effect of the falx and the tentorium on shear-wave redirection. The dominant mode shape of the falx and the tentorium for $α = 1 krad / s^{2}$ , $Δ t = 5 ms$ and $α = 10 krad / s^{2}$ , $Δ t = 25 ms$ shows that as the rotational acceleration increases, there is a change in the direction of these two structures of the brain, which in turn can cause shear-wave reflection in their surrounding areas. Three different sections of the falx and the tentorium are shown for reference.
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Figure 5
The nonlinear regions of the human brain due to a real-world football head impact that led to LOC. (a) The recorded 3D rotational acceleration of a football athlete who suffered a LOC injury [8]. (b) The POD of the brain deformation showed nonlinear regions similar to those in an ideal coronal rotation.
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Figure 6
The correspondence of the nonlinear regions with the tissue-level TBI metrics. (a) We observe that high-strain regions ( ${CSDM}_{0.35}$ ) of the brain follow the nonlinear regions over the tentorium, signaling a physical correspondence. (b) The nonlinear regions entail several WM tracts of interest in TBI pathology.
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