Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic?

Abstract

Force-velocity relationships reported in the literature for functional tasks involving a combination of joint rotations tend to be quasi-linear. The purpose of this study was to explain why they are not hyperbolic, like Hill's relationship. For this purpose, a leg press task was simulated with a musculoskeletal model of the human leg, which had stimulation of knee extensor muscles as only independent input. In the task the ankles moved linearly, away from the hips, against an imposed external force that was reduced over contractions from 95 to 5% of the maximum isometric value. Contractions started at 70% of leg length, and force and velocity values were extracted when 80% of leg length was reached. It was shown that the relationship between leg extension velocity and external force was quasi-linear, while the relationship between leg extension velocity and muscle force was hyperbolic. The discrepancy was explained by the fact that segmental dynamics canceled more and more of the muscle force as the external force was further reduced and velocity became higher. External power output peaked when the imposed external force was ∼50% of maximum, while muscle power output peaked when the imposed force was only ∼15% of maximum; in the latter case ∼70% of muscle power was buffered by the leg segments. According to the results of this study, there is no need to appeal to neural mechanisms to explain why, in leg press tasks, the force-velocity relationship is quasi-linear rather than hyperbolic.