Predictive Helmet Optimization Framework Based on Reduced-Order Modeling of the Brain Dynamics

Sports-related traumatic brain injuries (TBIs) are among the leading causes of head injuries in the world. Use of helmets is the main protective measure against this epidemic. The design criteria for the majority of the helmets often only consider the kinematics of the head. This approach neglects the importance of regional deformations of the brain especially near the deep white matter structures such as the corpus callosum (CC) which have been implicated in mTBI studies. In this work, we develop a dynamical reduced-order model of the skull-brain-helmet system to analyze the effect of various helmet parameters on the dynamics of the head and CC. Here, we show that the optimal head-helmet coupling values that minimize the CC dynamics are different from the ones that minimize the skull and brain dynamics (at some kinematics, up to two times stiffer for the head motion mitigation). By comparing our results with experimental impact tests performed on seven different helmets for five different sports, we found that the football helmets with an absorption of about 65-75% of the impact energy had the best performance in mitigating the head motion. Here, we found that none of the helmets are effective in protecting the CC from harmful impact energies. Our computational results reveal that the origin of the difference between the properties of a helmet mitigating the CC motion vs. the head motion is nonlinear vs. linear dynamics. Unlike the globally linear behavior of the head dynamics, we demonstrate that the CC exhibits nonlinear mechanical response similar to an energy sink. This means that there are scenarios where, at the instant of impact, the CC does not undergo extreme motions, but these may occur with a time delay as it absorbs shock energy from other parts of the brain. These findings hint at the importance of considering tissue level dynamics in designing new helmets.