title: 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, r(2), 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 (r(2)=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.
authors.affiliation: Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, Canada. s-lee@northwestern.edu
authors.forename: Sabrina S M
authors.initials: SS
authors.lastname: Lee
authors.forename: Allison S
authors.initials: AS
authors.lastname: Arnold
authors.forename: Maria de Boef
authors.initials: Mde B
authors.lastname: Miara
authors.forename: Andrew A
authors.initials: AA
authors.lastname: Biewener
authors.forename: James M
authors.initials: JM
authors.lastname: Wakeling
mesh_terms: D000818:Animals; D004576:Electromyography; D005260:Female; D006041:Goats; D008297:Male; D008954:Models, Biological; D009119:Muscle Contraction / Q000502:physiology; D018482:Muscle, Skeletal / Q000502:physiology*; D015203:Reproducibility of Results; D012420:Running / Q000502:physiology*; D016138:Walking / Q000502:physiology*
keywords: Forces; Hill-type model; Motor unit; Muscle