Fig 1.
Axonal tractography, corresponding hexahedral brain mesh and the boundary conditions used to investigate the skull flexural effect on axonal deformation.
(a) Axonal tractography of the male model with 9452 axonal tracts, (b) Axonal tractography of the female model with 9771 axonal tracts, (c) High-quality hexahedral mesh of the male brain, (d) High-quality hexahedral mesh of the female brain, (e) Male head model with embedded axonal tracts, and (f) Female model with embedded axonal tracts.
Table 1.
Different anatomic components, material models and corresponding material parameters used in the finite element model.
In this table, ρ is the material density,E is the young's modulus, ν is the poisson ratio, C0 is the speed of sound, S is the linear Hugoniot slope coefficient, Γ0 is the Gruneisen gamma at the reference state, η is the shear viscosity, α is the Ogden material constant, C01 and C10 are the Mooney-Rivlin material constants, K is the bulk modulus, μ is the shear modulus.
Table 2.
Bio-fidelity scale against CORA ratings.
A CORA rating should be greater than 0.26 for a comparison to be acceptable.
Fig 2.
Different loading conditions were used to determine the effect of variation in loading (direction and magnitude) on the axonal response.
(a) ConWep blast loading curves. The different loading magnitudes simulated here include 1500 kPa, 1200 kPa, 900 kPa, 600 kPa, 300 kPa, 200 kPa, 100 kPa, 50 kPa. These blast loads are simulated using the ConWep tool in ABAQUS. (b) Blast loading conditions in comparison to Bowen’s lung threshold curve. This plot shows that all the loading conditions opted here fall below the threshold—indicating that the injury will not result in the death of the subject. (c) Arrangement of detonation points around the head form. This arrangement allows us to study the effect of variation in loading direction on the resulting axonal response. (d) Table shows the different ConWep parameters (Overpressure, ConWep charge, Detonation Distance and Positive Phase Duration) for the corresponding loading values used in this paper.
Table 3.
Different CSF material models used in the past literature.
These different models used include (i) linear elastic, (ii) non-linear hyper-elastic and hyper-viscoelastic, (iii) fluid. Since CSF forms the interface between skull and the brain, the variance in the CSF material description could affect the model predictions.
Table 4.
CORA ratings for the different intracranial pressure validation plots.
Models were subjected to impact loading conditions same as that of the experimental study by Nahum et al. [34].
Table 5.
CORA ratings for the different brain-skull relative displacement validation plots (impact loading–occipital and frontal).
Models were subjected to impact loading conditions, same as that of the experimental study by Hardy et al. [35,36].
Table 6.
CORA ratings for the different brain-skull relative displacement validation plots (impact loading–parietal).
Models were subjected to impact loading conditions, same as that of the experimental study by Hardy et al. [35,36].
Table 7.
CORA ratings for the different intracranial pressure validation plots (blast loading).
Models were subjected to blast loading conditions, same as that of the experimental study by Bir et al.[37].
Table 8.
Table shows the skull flexural displacements for a loading overpressure of 1500 kPa in different directions.
Fig 3.
Results from the parametric study conducted on the female head model.
(i) Axonal deformation in 64 studies, plotted against different blast overpressure magnitudes–(a) Maximum axonal strain rates, (b) Maximum axonal strains. (ii) Axonal deformation in 64 studies plotted against different blast loading directions–(c) Maximum axonal strain rates, (d) Maximum axonal strains.
Fig 4.
Results from the parametric study conducted on the male head model.
(i) Axonal deformation in 64 studies, plotted against different blast overpressure magnitudes–(a) Maximum axonal strain rates, (b) Maximum axonal strains. (ii) Axonal deformation in 64 studies plotted against different blast loading directions–(c) Maximum axonal strain rates, (d) Maximum axonal strains.
Fig 5.
Flexural bending displacements experienced by the skull and the resulting strain rates experienced by the axonal fiber tracts for an overpressure loading of 600 kPa in anterior-posterior direction.
A maximum axonal strain rate of 80 s-1 was observed in this scenario. This figure also emphasizes the fact that embedded element based head model allows for a high-resolution visualization of the model. (i) Flexural displacements of the skull at (a) t = 1 ms. (b) t = 2 ms. (c) t = 3 ms. (d) t = 4 ms. (ii) Strain rates experienced by the axonal fiber tracts (e) t = 1 ms. (f) t = 2 ms. (g) t = 3ms. (h) t = 4ms. Here, the red color cross-sectional view of the skull represents the original skull shape while the blue color cross-sectional view represents the displaced skull’s cross-sectional view.
Table 9.
Table showing the maximum axonal strains and strain rates using different CSF material descriptions.
A frontal blast loading simulation of the model head model was developed with the different CSF material descriptions and used it to tabulate the above results.
Fig 6.
Peak axonal strains and strain rates, for different CSF material models, plotted using a bar graph.
(a) Maximum axonal strains (%) observed for the different simulations, (b) Maximum axonal strain rates observed for the different simulations. The horizontal axis in the above plots show the study number assigned in the Table 3. These are the maximum axonal strains and strain rates plotted for different simulation scenarios. These different simulations varied in terms of CSF material description. This study was developed to determine the range of extreme strains and strain rates possible due to skull flexures. The above results show that the maximum axonal strains span a range of 1.41% to 5.41%; and the maximum axonal strain rates span a range of 128 s-1 to 378 s-1.
Fig 7.
kull thickness across a plane of cross-section for both male and female FE models.
S The variation in skull thickness could be the reason for different flexural behavior across gender.