A mathematical analysis of the musculo-skeletal system of the human shoulder joint
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The purpose of this study has been to formulate a mathematical model capable of predicting muscular tension characteristics for muscles in the human shoulder joint. This was done by using the data that were collected through dissection of a cadaver and through physiological information about human skeletal muscles and anatomical characteristics of the human shoulder joint. By using this method, the explicit characterization of the shoulder joint was described in terms of a three dimensional coordinate system. The mathematical equations for the relationships between the electrical signal intensities that are generated from the muscles, and muscular tensions that are exerted by muscles at various postures during abduction of the upper extremity were investigated. General equations that can be applied to various individual persons who have different anthropometric dimensions were developed by using scale factors. Computer programs were developed to determine the muscular tension in muscles in the shoulder joint of various persons and to predict the linear coefficients between electromyographic electrical signal intensities and the muscular tensions of the skeletal muscles. According to the results and the techniques of this study, it was determined that most of the complicated human musculo-skeletal systems can be analyzed mathematically without invasion of the living body.