Mechanistic Insights into Human Brain Impact Dynamics through Modal Analysis

Although concussion is one of the greatest health challenges today, our physical understanding of the cause of injury is limited. In this Letter, we simulated football head impacts in a finite element model and extracted the most dominant modal behavior of the brain’s deformation. We showed that the brain’s deformation is most sensitive in low frequency regimes close to 30 Hz, and discovered that for most subconcussive head impacts, the dynamics of brain deformation is dominated by a single global mode. In this Letter, we show the existence of localized modes and multimodal behavior in the brain as a hyperviscoelastic medium. This dynamical phenomenon leads to strain concentration patterns, particularly in deep brain regions, which is consistent with reported concussion pathology.

Figure 1

Brain deformation due to a football head impact that led to loss of consciousness: (a) Propagation of the first displacement mode oscillating at 28 Hz. (b) Propagation of the third displacement mode oscillating at 42 Hz showing out of phase oscillation with mode 1 (Supplemental Material [45], videos S3–S5). (c) Anterior-posterior displacement traces of two brain nodes; one at the interface between white and gray matter (node 1) and one from the cerebellum region (node 2). (d) Fourier modes of the displacement traces of the brain nodes superimposed on the energy amplitude of the DMD modes, showing close agreement.

Figure 2

Overall temporal characteristics of brain deformation: (a) Average modal amplitudes of all displacement modes of all the simulated case, showing amplification at 28 Hz. Modes in the axial direction show a greater bandwidth than those in the sagittal and coronal directions. (b) Average accumulated modal energy for all simulated cases which correlates with the explained variance using each mode, showing exponential convergence to 100% variance. (c) Strain values derived from each mode normalized by the peak rotational acceleration of the corresponding head kinematics.

Figure 3

Dynamic ranges of brain modes indicate multimodal behavior for higher input amplitudes: (a) Football data from Stanford mouthguard and NFL data from Ref. [52] are compared against the best linear fit calculated by using the global dominant mode [Fig. 4]. Multimodal behavior is observed for higher strain values, where a single mode fails to predict the peak principal strain. The dynamic range of football cases reveals a transition towards a multimodal behavior at higher strain values. (b) The dynamic ranges of individual football simulations significantly increase as they are further away from the single mode prediction.

Figure 4

Dominant frequencies of brain structures: (a) Schematic of the FE model of the head showing various parts of the brain. (b) Strain values derived from each mode normalized by the peak rotational acceleration of the corresponding head kinematics. Here, we superimpose regional dominant frequencies for each brain part for the LOC case (red circles) and the average and standard deviations (blue solid dots) for all cases. Brain part abbreviations: corpus callosum (CC), gray matter (GM), brain stem (BS), midbrain (MB), white matter (WM), thalamus (TH), corpus callosum, cerebellum (CB). (c) Structural distribution of the dominant frequency of brain regions for the LOC case, indicating out of phase oscillation due to significant discrepancy between regions especially in the periventricular region. (d) Structural distribution of dominant frequencies for an average head impact case, which indicates a lower dynamic range.