# Influence of Chinstrap Stiffness on Cerebrospinal Fluid Dynamics and Brain Stress in Helmet Impacts
## 3 Results  
To evaluate the neuroprotective efficacy of helmets with chinstrap materials of varying stiffness, the temporal evolution of maximum effective stress within critical brain structures (cerebrum, cerebellum, and brainstem) was analyzed over the impact duration (0-50 ms) and immediate post-impact phase (50-200 ms), analyzing residual stress dissipation through fluid-structure interactions. Stress distributions were calculated using the combined hydrostatic and viscous stress tensor (Equation (6)), with the viscoelastic tissue behavior governed by Equation (2). The computational analysis evaluated six chinstrap designs with progressively increasing stiffness (Figures 3-8), revealing distinct regimes of force transmission and helmet stability. Highly stretchable configurations (Figure 3a) allowed significant helmet displacement through strap elongation, dissipating energy via viscoelastic deformation and reducing intracranial stress by orders of magnitude compared to non-stretchable counterparts. Intermediate stiffness designs (Figures 4-6) entered a critical transition zone where limited strap stretch caused partial decoupling between the chinguard and mandible, amplifying localized stress concentrations at bony interfaces (Figure 6a). Non-stretchable straps (Figures 7 and 8) eliminated protective energy dissipation, transmitting undamped forces directly through the cranial base. Figure 9 demonstrates the biphasic nature of neuroprotection: stretchable materials mitigate stress via dynamic elongation, while \"semi-non-stretchable\" designs induce interfacial instabilities that paradoxically counteract stress reduction despite partial coupling. The optimal stiffness balances strap elasticity to absorb transient impacts with sufficient rigidity to maintain helmet-skull alignment, avoiding force redirection to vulnerable neurovascular regions. Stress time histories (Figures 3b, 4b, 5b, 6b, 7b and 8b) correlate escalating peak magnitudes with reduced strap deformation, underscoring how energy dissipation mechanisms falter as material stiffness approaches non-stretchable thresholds. The overall temporal evolution of normalized peak effective brain stress for all chinstrap stiffness regimes is summarized in Figure 10, which demonstrates the order-of-magnitude reduction in stress transmission for highly stretchable straps compared to intermediate and non-stretchable designs. Table 1 provides a detailed breakdown of metrics for each data point in the dataset, allowing for a clear and quantitative analysis of why certain points, such as \"semi-non-stretchable\", stand out as outliers. By examining the table, we can compare the actual \(y\)-values, predicted \(y\)-values from the trendline equation, and various error metrics to identify deviations from the expected trend. The first column, \(x\), represents the independent variable, while \(y_{\text{actual}}\) is the observed dependent variable from the dataset. The \(y_{\text{predicted}}\) column shows the corresponding values calculated using the trendline equation \(y=e^{1.622x-7.715}\). The residual column, calculated as \(y_{\text{actual}}-y_{\text{predicted}}\), measures the difference between the observed and predicted values. A large residual indicates that the point deviates significantly from the trendline. The independent variable \(x\) in Table 1 is represented symbolically, using qualitative labels such as \"highly stretchable\", \"moderately stretchable\", \"semi-stretchable\", and so on. However, to perform the necessary calculations for predicting \(y\), these symbolic categories are mapped to numerical values on a scale from 0 to 5. This mapping allows the symbolic \(x\) values to be used in the mathematical model. Specifically, \"highly stretchable\" corresponds to \(x=0\), \"moderately stretchable\" to \(x=1\), \"semi-stretchable\" to \(x=2\), \"semi-non-stretchable\" to \(x=3\), \"minimally stretchable\" to \(x=4\), and \"non-stretchable\" to \(x=5\).