Leg stiffness adjustment during hopping by dynamic interaction between the muscle and tendon of the medial gastrocnemius

The biomechanics underlying bouncing exercises are characterized by the spring-like behavior of the human leg. This study investigated a specific form of hopping-performed with an extended knee and minimal ground contact duration-to examine how muscle dynamics contribute to leg stiffness adjustment. This constrained hopping pattern allows us to isolate the role of ankle joint, especially plantar flexor muscle-tendon complex (MTC). To quantitatively analyze changes in the MTC of the medial gastrocnemius (MG) muscle, we utilized an MTC model comprising an active spring and a passive spring connected in series, representing a contractile component (CC) and series elastic component (SEC), respectively. We hypothesized that an increase in CC stiffness would coincide with the increase in leg stiffness, thereby enabling hopping at higher frequencies. Joints and MG fascicle dynamics were collected across different hop frequencies. The results showed that the stiffness of the MTC increased with hop frequency and exhibited a strong correlation with the leg stiffness. In addition, with increasing frequency, the fascicle contractions shifted from isometric to concentric. Consequently, a negative CC stiffness was observed, thereby increasing the overall MTC stiffness. Although this result appears to diverge from our initial hypothesis, the effect of negative CC stiffness on MTC stiffness can be understood, from the perspective of two springs in series, as an extension of the very high stiffness effect. This quantitative understanding of the dynamic interaction between the fascicle and tendon provides deeper insight into the adjustment mechanisms underlying bouncing gaits.