# A modelling perspective on torque–frequency trade-offs in multifunctional lever systems driven by antagonist muscle pairs

## TL;DR

This paper explores how muscle fiber types and recruitment patterns affect the trade-off between movement speed and force in bird beaks.

## Contribution

The study introduces a modeling framework linking muscle fiber types and Henneman's principle to torque-frequency trade-offs in multifunctional lever systems.

## Key findings

- Muscle fiber type strongly influences frequency output in lever systems.
- Henneman's effect causes overdeveloped muscles to recruit slow-twitch fibers, reducing movement frequency.
- Torque imbalance has minimal impact on frequency once it occurs.

## Abstract

Rapid cyclic movements are generated by antagonistic muscle pairs contracting in an alternating pattern. The highest frequencies can be generated in balanced torque-producing systems with specialized muscle fibers. The system's frequency output is expected to change when it becomes more adapted to functions with conflicting mechanical demand, such as increased static torque production in one direction. This study first conceptualized how distinct factors (fiber type, muscle cross-sectional area, moment arm and inertial properties) could influence this torque–frequency trade-off. Special attention is given to Henneman's principle, as many of these systems contain both slow- and fast-twitch muscle fiber, typically organized in motor units, with the smallest, slow-twitch, fiber-rich motor units being recruited first. Next, we used Hill-type muscle models operating a Java sparrow's mandible as a case study for this framework. Our model showed that muscle fiber type strongly affects the frequency output, with a notable role for Henneman's effect causing the overdeveloped muscle to predominantly recruit slow-twitch muscle fibers. This leads to large muscle torque output overlap, which in turn reduces frequency. Once torque imbalance occurs, altering the other variables only slightly changes the frequency, suggesting a dominant role of muscle contractile properties. This means that the conflicting demands of multifunctional musculoskeletal lever systems such as bird beaks are also tightly linked to fiber type and motor unit roles such as endurance and precision of movement.

Summary: Low-inertia musculoskeletal lever systems are primarily constrained in their high-frequency movement output by fiber types and orderly recruitment, whereas mass, muscle cross-sectional area and moment arms have a minimal effect.