INTRODUCTION Sport concussion represents the majority of brain injuries occurring in the United States with 1.6 to 3.8 million cases annually. Understanding the biomechanical properties of this injury will support the development of better diagnostics and preventative techniques. METHODS We monitored all football related head impacts in 78 high school athletes (mean age 16.7 years) from 2005 through 2008 in order to better understand the biomechanical characteristics of concussive impacts. RESULTS Using the Head Impact Telemetry System (HITS), a total of 54,247 impacts were recorded and 13 concussive episodes captured for analysis. A classification and regression tree (CART) analysis of impacts indicated that rotational acceleration (>5582.3 rad/s2), linear acceleration (>96.1 g), and impact location (front, top, back) yielded the highest predictive value of concussion. CONCLUSIONS These threshold values are nearly identical to those reported at the collegiate and professional level. If the HITS were implemented for medical use, sideline personnel can expect to diagnose one of every five athletes with a concussion when the impact exceeds these tolerance levels. Why all athletes did not sustain a concussion when the impacts generated variables in excess of our threshold criteria is not entirely clear, although individual differences between participants may play a role. A similar threshold to concussion in adolescent athletes compared to their collegiate and professional counterparts suggests an equal concussion risk at all levels of play.

In the first part of this series of three papers, we investigate the combined effects of diffusion, spatial variation, and competition ability on the global dynamics of a classical Lotka-Volterra competition-diffusion system. We establish the main results that determine the global asymptotic stability of semitrivial as well as coexistence steady states. Hence a complete understanding of the change in dynamics is obtained immediately. Our results indicate/confirm that, when spatial heterogeneity is included in the model, "diffusion-driven exclusion" could take place when the diffusion rates and competition coefficients of both species are chosen appropriately.

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Part II of this series of three papers, we focus on the joint effects of diffusion and spatial concentration on the global dynamics of a classical Lotka-Volterra competitiondiffusion system. For comparison purposes, we assume that the two species have identical competition abilities and the same amount of total resources throughout this paper. Part II is devoted to the case that the spatial distribution of resources for one species is heterogeneous while that of the other is homogeneous. Our results imply that in this case not only is the former guaranteed to survive, in fact, it will often wipe out the latter, regardless of initial values. Asymptotic behaviors of the stable steady states are also obtained for various limiting cases of the diffusion rates. Mathematics Subject Classification