Applying Multivariate Linear Regression and the Hertz Equation for Development of a Novel Ocular Injury Apparatus

Abstract

Arnav Jain

Soccer is the leading cause of all sports-related ocular injuries in Europe and Israel and leads to blindness at a disproportionately high rate, especially among children [1]. With soccer being the most popular sport in the world, it is surprising the only solution to ocular injuries are sports glasses which can cause direct damage to the eye and impair peripheral vision by 15%, calling for an alternative [2]. This work, based on an imported facial model, focuses on both the qualitative and quantitative aspects of building a personalized, low-cost (through optimizing material needed), superior apparatus to conventional sports glasses. The quantitative side examines a modified and model-validated (through a SRS of thirty unique extrapolated points) multivariate linear regression equation, based on horizontal and vertical rotation angles trained with residual and computer simulation data, that can accurately extrapolate and quantify ocular impact from all horizontal and vertical rotation angles and a modified Hertzian Contact Stress Equation to determine the thickness of the apparatus using the elasticity modulus, impact force, and geometrical facial and soccer- ball features. The qualitative side examines where firstly, ocular impact is most prevalent, and secondly, where most impact is seen from rotating the ball horizontally and vertically through analysis of Pearson’s Correlation Coefficient at the supraorbital, medial canthus, infraorbital, and lateral canthus regions from both regression equations as well as a cost-benefit analysis for comparison with conventional sports glasses. The findings discovered in this work lay the groundwork for future research to build a customized low-cost ocular injury prevention device which can simultaneously ensure complete ocular safety while enhancing athletic performance for over 250,000,000 players [3].

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