Negative stiffness in calf muscles enhances high-speed hopping

Researchers at the University of Tokyo reveal the way our legs adapt to fast movements. When people hop at high speeds, key muscle fibers in the calf shorten rather than lengthen as forces increase, which they call "negative stiffness." This counterintuitive process helps the leg become stiffer, allowing for faster motion. The findings could improve training, rehabilitation, and even the design of prosthetic limbs or robotic exoskeletons.

When you hop, run or jump, your legs behave like springs, absorbing and returning energy with each step. But what happens to your muscles and tendons to make this possible? Associate Professor Daisuke Takeshita and doctoral student Kazuki Kuriyama from the Department of Life Sciences sought to investigate how muscles and tendons work together during bouncing movements, specifically hopping, as it serves as a proxy for common activities like running.

"Human movements like hopping and running are often characterized by a spring-mass model, where the leg acts as a spring supporting the body mass as it bounces off the ground," said Takeshita.

In our study, we specifically examined hopping under constrained conditions, instructing participants to maintain extended knees and minimize ground contact time. These constraints were crucial as they allowed us to isolate the role of ankle joint mechanics and focus on what's known as the plantarflexor muscle-tendon dynamics."

Daisuke Takeshita, Associate Professor, Department of Life Sciences, University of Tokyo

Through this, Takeshita and Kuriyama discovered that muscle fibers behave differently depending on the hopping frequency. During slow hopping, muscle fibers maintain nearly constant length. However, during fast hopping, they actively shorten even as force increases, displaying what they call negative stiffness. This counterintuitive behavior enhances the overall stiffness of the leg, allowing for faster movements.

"Our findings provide a new framework for understanding muscle function during various activities," said Kuriyama. "Rather than viewing muscles as simply generators of force, we've shown that they actively modulate the mechanical properties of the leg through their dynamic interaction with tendons. This perspective opens new avenues for research in sports science, rehabilitation medicine and biomechanical engineering."

To carry out this investigation, the pair first had to integrate different sensing apparatus which don't normally go together for this kind of purpose. They built a synchronized measurement system including ultrasound imaging with motion capture and force plate data, all synchronized to ensure corresponding data points were well aligned in order to understand the correct sequence of events unfolding beneath the skin.

"The ultrasound imaging portion was particularly demanding. After collecting the images, Kuriyama manually digitized the muscle fiber data from thousands of ultrasound frames," said Takeshita. "This process was incredibly time-consuming and labor-intensive, requiring meticulous attention to detail to accurately track the subtle changes in muscle fiber length throughout each hopping cycle. Each stage of the research process required carefully designed solutions to unique problems, making the entire journey from data collection to interpretation a significant challenge that demanded both technical innovation and conceptual creativity."

The action of hopping helped the researchers design appropriate observational experiments, as the activity is naturally spatially constrained and has fewer variables than something less bound. But they do intend to take their ideas out of the lab and on to the running track one day, as this will allow them to study more generally how lower leg muscles work their magic and propel athletes forward. And this kind of study could feed into the body of knowledge which athletes and trainers draw from to provide more effective training, which in turn can help those involved in rehabilitation. These future directions will help bridge the gap between basic biomechanical principles observed in simplified laboratory tasks and the complex, real-world movements that humans perform in daily life and athletic activities.