Modelling of knee joint muscles during the swing phase of gait––a forward dynamics approach using MATLAB/Simulink

Abstract

The present study primarily aims to predict the force (both active and passive) of eight main muscle–tendon actuators crossing the knee joint during the swing cycle. The knee-joint model was restricted and simplified to motion in the sagittal plane only. It was largely built in mathematical notation and was simulated using a high-performance computing and programming tool, MATLAB, along with Simulink. The eight muscles––Biceps Femoris Short Head (BFSH), three heads of Vasti (VL, VM and VI), Rectus Femoris (RF) and the Hamstrings (BFLH, SemiM and SemiT) were each modelled as a two-element, lumped-parameter entity, in series with tendon, which was assumed to be elastic with a known stress–strain relationship. The mechanical behaviour of muscle was described by a Hill-type contractile element which models the active force–length characteristic of muscle fascicles, and a parallel-elastic element which models its passive properties. The knee joint model was simulated for a swing period of 0.4 s and the knee flexed to a maximum of approximately 63°, providing safe toe clearance, and eventually extended to about 4° to prepare for the next heel strike. A comparison of the simulation results in this study with reported data warrants confidence in the prediction of muscle and tendon force. Based on further analysis and quantitative comparison of simulation results, functionally and anatomically similar muscles were eventually approximated with a muscle group and fusiform muscle fibres were favoured over pennate fibres in the muscle–tendon model.