# Influence of Chinstrap Stiffness on Cerebrospinal Fluid Dynamics and Brain Stress in Helmet Impacts
## 3 Results
This finding emphasizes that intermediate stiffness can paradoxically amplify injury risk, underscoring the importance of balancing elasticity and rigidity in chinstrap design. Figure 11 presents qualitative effective stress distributions across six helmet chinstrap configurations, ranging from highly stretchable (a) to non-stretchable (f), immediately following a simulated pitch impact. The heatmaps visualize stress concentrations (red: maximum stress; blue: zero stress) on brain structures. Across all configurations, stress maxima localize in the cortical sulci (grooves) and brainstem. These regions are vulnerable to shear forces due to tissue heterogeneities (gray-white matter interfaces) and proximity to the cranial base. The sulcal stress maxima suggest heightened shear-strain injury risks, aligning with concussion-related axonal damage patterns. Elevated brainstem stresses correlate with autonomic dysfunction post-concussion (e.g., dizziness, nausea). Notably, no observational differences exist in the spatial distribution or magnitude of stress maxima between the highly stretchable (a), moderately stretchable (b), semi-stretchable (c), and semi-non-stretchable (d) configurations, i.e., peak stresses occur in identical anatomical regions (sulcal depths and brainstem) with comparable spatial extents. Divergence emerges only in minimally stretchable (e) and non-stretchable (f) designs, where stress patterns expand into adjacent cortical folds, perisulcal regions, and the brainstem-cervical junction. This delayed differentiation aligns with the exponential growth in stress peak values shown temporally in Figures 3-9. The progression follows the viscoelastic stress integral (Equation (2)), where stiffer straps progressively limit energy dissipation through elongation. Highly stretchable to semi-non-stretchable strap configurations, Figure 11a-d, absorb 92-58% of impact energy via strap deformation (per Table 1 residuals), delaying force transmission to neuroanatomical structures. Beyond this threshold, as shown in Figure 11e,f, the diminished strap compliance (\(<\)5% elongation) eliminates protective phase lag, enabling the undampened transmission of kinetic energy to the skull base. The resultant inertial forces amplify stress rates through multiplicative coupling in the hydrostatic-viscous stress tensor (Equation (6)), driving exponential peak growth despite near-identical spatial stress patterns at early stiffness levels. In other words, the apparent paradox arises from the interplay between viscoelastic stress relaxation in brain tissue (Equation (2)) and the strain rate dependence of strap materials. Below the critical stiffness threshold (configurations a-d), strap elongation introduces a phase lag between impact energy transmission and tissue stress accumulation. While peak stress values escalate exponentially with [PERSON]'s modulus (Figures 3-9), their spatial distribution remains superficially similar in Figure 11a-d due to the following factors. The sulcal and brainstem regions act as inherent stress concentrators due to anatomical curvature and tissue interfaces. At lower stiffness (a-d), strap elongation delays force transmission, allowing CSF redistribution (via SPH dynamics, Equation (5)) to homogenize stress spatially at the given timepoint (Figure 11: end of impact), even as temporal peaks escalate. The hereditary integral (Equation (2)) dictates that stress accumulates proportionally to the duration of applied strain. Stretchable straps (a-d) reduce strain rates via elongation, allowing viscous dissipation (i.e., the \(\mu\) term in Equation (6)) to blunt peak stress magnitudes at the instant visualized in Figure 11.  
Once straps exceed the viscoelastic compensation threshold (e-f), undampened inertial forces \(F=m\cdot a\) from Equation (4) directly shear CSF-brain interfaces. These forces exceed the SPH particle coupling strength (Equation (1)), generating new stress concentrations in deeper structures, Figure 11e,f, as the energy propagates unhindered.