Exploiting elasticity: Modeling the influence of neural control on mechanics and energetics of ankle muscle–tendons during human hopping

Abstract

We present a simplified Hill-type model of the human triceps surae-Achilles tendon complex working on a gravitational–inertial load during cyclic contractions (i.e. vertical hopping). Our goal was to determine the role that neural control plays in governing muscle, or contractile element (CE), and tendon, or series elastic element (SEE), mechanics and energetics within a compliant muscle–tendon unit (MTU). We constructed a 2D parameter space consisting of many combinations of stimulation frequency and magnitude (i.e. neural control strategies). We compared the performance of each control strategy by evaluating peak force and average positive mechanical power output for the system (MTU) and its respective components (CE, SEE), force–length (F–L) and –velocity (F–V) operating point of the CE during active force production, average metabolic rate for the CE, and both MTU and CE apparent efficiency. Our results suggest that frequency of stimulation plays a primary role in governing whole-MTU mechanics. These include the phasing of both activation and peak force relative to minimum MTU length, average positive power, and apparent efficiency. Stimulation amplitude was primarily responsible for governing average metabolic rate and within MTU mechanics, including peak force generation and elastic energy storage and return in the SEE. Frequency and amplitude of stimulation both played integral roles in determining CE F–L operating point, with both higher frequency and amplitude generally corresponding to lower CE strains, reduced injury risk, and elimination of the need for passive force generation in the CE parallel elastic element (PEE).