Application of a biomechanical model and combinatorial optimization to determine lower limb joints torsional stiffness in human landing

Abstract

Lower limb joint’s torsional stiffness is directly related to the individual’s performance and probability of injury when landing. There are various methods of calculating ankle, knee, and hip joint’s torsional stiffness in which the reliability of the achieved values by them are highly controversial. The purpose of this research is to provide a new method of calculating lower limb joint’s active torsional stiffness based on the body’s four-degrees-of-freedom biomechanical model. For this purpose, a group of subjects performs single-leg landing protocol from the box. In this method, the biomechanical model’s equations of motion are derived in the sagittal plane and are combined with a combinatorial optimization algorithm, which consists of genetic and simulated annealing. By the use of acquired data from the force plate and motion analysis system, combinatorial genetic algorithm–simulated annealing algorithm tries to minimize the differences between the model’s ground reaction force (GRF_Model) and the GRF_Experimental for each subject and thereby the joint’s torsional stiffness values are obtained. Results show that calculating lower limb joint’s torsional stiffness using the proposed method has good ability in simulating the GRF_Experimental in the model. Also, the obtained values by the proposed method have moderate to good reliability and desirable variability in the measurements. Comparing the obtained stiffness values with the values of three conventional computation method in the literature shows that those common methods’ results have high computational errors, low reliability, and high variability in the measurement. Also, their ability to produce GRF_Model similar to the GRF_Experimental is weaker than the proposed method in single-leg landing protocol.