Cost function tuning improves muscle force estimation computed by static optimization during walking

Muscle force estimation while a dynamic motor task is carried out still presents open questions. In particular, concerning locomotion, although the inverse dynamic based static optimization has been widely accepted as a suitable method to obtain reliable results, appropriate modifications of the object function may improve results. This paper was aimed at analyzing the sensitivity of estimated muscle forces when modifications of the objective function are adopted to better fit EMG signals of healthy subjects. A 7 links and 9 degrees of freedom biomechanical model accounting for 14 lower limb muscles, grouped in 9 equivalent actuators, was developed. Muscle forces were estimated by using the inverse dynamic based static optimization in which the performance criteria was the sum of muscle stresses raised to a certain n power. This exponent was gradually changed (from 2 to 100) and the agreement between force patterns and EMG signals was estimated by both the correlation coefficient and the Coactivation Index. Results suggested that force estimation can be improved by slightly modifying the cost function. In particular, with respect to adopted data, when the exponent belong to the interval between 2.75 and 4, estimated forces better captured general features of EMG signals. Concluding, a more reliable solution can be obtained by suitably tuning the cost function in order to fit EMG signals.