Accuracy of gastrocnemius muscles forces in walking and running goats predicted by one-element and two-element Hill-type models

Abstract

Hill-type models are commonly used to estimate muscle forces during human and animal movement—yet the accuracy of the forces estimated during walking, running, and other tasks remains largely unknown. Further, most Hill-type models assume a single contractile element, despite evidence that faster and slower motor units, which have different activation–deactivation dynamics, may be independently or collectively excited. This study evaluated a novel, two-element Hill-type model with “differential” activation of fast and slow contractile elements. Model performance was assessed using a comprehensive data set (including measures of EMG intensity, fascicle length, and tendon force) collected from the gastrocnemius muscles of goats during locomotor experiments. Muscle forces predicted by the new two-element model were compared to the forces estimated using traditional one-element models and to the forces measured in vivo using tendon buckle transducers. Overall, the two-element model resulted in the best predictions of in vivo gastrocnemius force. The coefficient of determination, r2, was up to 26.9% higher and the root mean square error, RMSE, was up to 37.4% lower for the two-element model than for the one-element models tested. All models captured salient features of the measured muscle force during walking, trotting, and galloping (r2=0.26–0.51), and all exhibited some errors (RMSE=9.63–32.2% of the maximum in vivo force). These comparisons provide important insight into the accuracy of Hill-type models. The results also show that incorporation of fast and slow contractile elements within muscle models can improve estimates of time-varying, whole muscle force during locomotor tasks.