In-silico Analysis of Population Variation in Brain Vibration Mechanics

Introduction: : In recent years, vibration analysis has emerged as a novel approach for evaluating the dynamics of the brain in response to external impulse and vibration. Recent experimental and numerical studies have shown that the motion of the brain during impact loading can be decomposed into one or two low-frequency vibration modes [1-3]. Both experimental and computational studies of brain vibration mechanics have been limited to a relatively small sample size of subjects. As a result, it is unclear how the free vibration response of the brain varies with head size, shape, and material properties of the brain across the population. In this study, we performed a large-sample-size computational analysis of the free- and forced-vibration response of the brain, compared the vibration response observed to the existing experimental brain vibration datasets, and evaluated how the resonant vibration frequencies of the brain varied with changes in brain geometry and material properties.

Materials and

Methods: : Two hundred finite element (FE) head models were generated using pre-existing datasets of segmented head magnetic resonance images (MRI) [4], the corresponding FE meshes [5], and spatial maps of brain tissue stiffness measured using magnetic resonance elastography (MRE) [6]. The model generation workflow is shown in Figure 1. MRE tissue stiffness was co-registered onto the brain geometry and then mapped onto the corresponding locations on the FE mesh. Twenty head models (10 male, 10 female) and twenty MRE tissue stiffness maps (10 male, 10 female) were used to generate 200 unique FE head models. For each head model, a free-vibration eigenvalue analysis was performed using the commercial FE solver LS-DYNA (ANSYS Inc., Canonsburg, PA, USA). We then used a k-means classifier to identify similar vibration modes between head models. Multiple linear regression was used to relate the relative changes in head dimensions and material properties to changes in the natural frequencies of the brain.
To evaluate the accuracy of the FE vibration modes, the strain fields associated with each vibration mode were calculated. The strain fields were then compared to experimental strain fields measured via tagged MRI [3]. Finally, the free vibration modes calculated from the FE models were used to determine the response of the brain to external loading using the modal superposition method. The frequency response function (FRF) of each individual head was averaged to estimate the overall population response to external vibration loading to the head.

Results, Conclusions, and Discussions:: Results
We calculated the lowest vibration frequencies of the brain to be approximately 10 Hz, with a 2 Hz variation in the natural frequencies across the population with changes to head geometry and brain material properties. The fundamental vibration modes of the brain consist of tissue rotation in the coronal, sagittal, and transverse planes. We observed significant changes in the natural frequencies of the brain with changes in brain shape (p < 0.05) or stiffness (p < 0.001), while negligible changes were observed with differences in brain volume. The strain fields associated with the FE vibration modes were similar to those measured experimentally by Escarcega et al. [3], as shown in Figure 2. When exposed to outside forces, the amplitude of brain motion was highest around its lowest natural frequencies—consistent with physical intuition—and decayed logarithmically at higher frequencies, as shown in Figure 3.

Discussion
The lowest vibration frequencies calculated in our computational models at approximately 10.5 Hz were higher than the ~6.7 Hz observed experimentally [3]. However, the calculated vibration modes were well correlated to the experimentally observed behavior. Such an outcome suggests that further evaluation of the material modeling and boundary conditions on the brain is necessary to refine the dynamic response of our models. Nonetheless the models developed herein represent, to the authors’ knowledge, the most high fidelity linear vibration model of brain motion to date.

Conclusions
We have demonstrated that the dynamic response of the brain to impulsive loading can be closely mimicked using a linear vibration analysis. We have performed the largest sample size study of vibration behavior to date and calculated a 2–3 Hz range in the natural vibration frequencies of the brain across the population. Our model generation workflow and the results of our vibration analyses represent a significant advancement the modeling tools available to predict brain motion and estimate the risk of traumatic brain injury.

Acknowledgements and/or References (Optional):: References
[1] Laksari, K. et al., Phys Rev Lett 120 (2018).
[2] Rezayaraghi, F. et al., Brain Multiphysics 5 (2023).
[3] Escarcega, J. et al., ASME J Biomech Eng 145.8 (2023).
[4] Aubert-Broche, B. et al., IEEE T Med Imaging, 25.11 (2006).
[5] Tran, A. et al., Proc SPIE, 7.1 (2020).
[6] Hiscox, L. et al., Hum Brain Mapp, 41.18 (2020).