LAGRANGIAN MULTIPLIER / MATRIX PARTITIONING APPROACH FOR THE SOLUTION OF THE MUSCLE LOAD DISTRIBUTION PROBLEM

Abstract

The paper presents a musculoskeletal biomechanical model which resides in the Simulink / MATLAB environment and is suitable for the analysis of sporting activities. The model can be used to calculate ground reaction forces, muscles, joint and skeletal component loadings. The model is currently being used at over 150 research institutions and because of its short learning curve is especially suitable for undergraduate teaching. The calculation of the muscle loading distribution is calculated by minimising an objective function. The optimisation approach implemented uses a Lagrangian multiplier technique and is supplemented by a matrix partitioning method to apply inequality constraints. This technique is capable of calculating the muscle force distribution in near real time using the limited resources of a laptop computer.