Different anatomic components, material models and corresponding material parameters used in the finite element model.

<p>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.</p

Table showing the maximum axonal strains and strain rates using different CSF material descriptions.

<p>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.</p

Do blast induced skull flexures result in axonal deformation?

<div><p>Subject-specific computer models (male and female) of the human head were used to investigate the possible axonal deformation resulting from the primary phase blast-induced skull flexures. The corresponding axonal tractography was explicitly incorporated into these finite element models using a recently developed technique based on the embedded finite element method. These models were subjected to extensive verification against experimental studies which examined their pressure and displacement response under a wide range of loading conditions. Once verified, a parametric study was developed to investigate the axonal deformation for a wide range of loading overpressures and directions as well as varying cerebrospinal fluid (CSF) material models. This study focuses on early times during a blast event, just as the shock transverses the skull (< 5 milliseconds). Corresponding boundary conditions were applied to eliminate the rotation effects and the resulting axonal deformation. A total of 138 simulations were developed– 128 simulations for studying the different loading scenarios and 10 simulations for studying the effects of CSF material model variance–leading to a total of 10,702 simulation core hours. Extreme strains and strain rates along each of the fiber tracts in each of these scenarios were documented and presented here. The results suggest that the blast-induced skull flexures result in strain rates as high as 150–378 s^-1. These high-strain rates of the axonal fiber tracts, caused by flexural displacement of the skull, could lead to a rate dependent micro-structural axonal damage, as pointed by other researchers.</p></div

CORA ratings for the different brain-skull relative displacement validation plots (impact loading–parietal).

<p>Models were subjected to impact loading conditions, same as that of the experimental study by Hardy et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0190881#pone.0190881.ref035" target="_blank">35</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0190881#pone.0190881.ref036" target="_blank">36</a>].</p

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.

<p>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.</p

Different loading conditions were used to determine the effect of variation in loading (direction and magnitude) on the axonal response.

<p>(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.</p

Table shows the skull flexural displacements for a loading overpressure of 1500 kPa in different directions.

<p>Table shows the skull flexural displacements for a loading overpressure of 1500 kPa in different directions.</p

Results from the parametric study conducted on the female head model.

<p>(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.</p

CORA ratings for the different intracranial pressure validation plots (blast loading).

<p>Models were subjected to blast loading conditions, same as that of the experimental study by Bir et al.[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0190881#pone.0190881.ref037" target="_blank">37</a>].</p

CORA ratings for the different intracranial pressure validation plots.

<p>Models were subjected to impact loading conditions same as that of the experimental study by Nahum et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0190881#pone.0190881.ref034" target="_blank">34</a>].</p