Modelling muscle wobbling mass dynamics across scales

• Applicants: Dr. Kasper Christensen; Professor Dr. Syn Schmitt
• Subject Area: Mechanics ; Animal Physiology and Biochemistry
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 552918860

Skeletal muscles are the motors of biological locomotion, and probably due to their complex structure, they can withstand repetitive impacts during terrestrial locomotion while contracting. In running, impacts occur when the leg hits the ground, to which the muscle responds by damped oscillations (wobbling mass dynamics). Wobbling mass dynamics are strongly dependent on the muscle mass (inertia), thus animal size; they may interfere, increasingly with animal size, with the force generation at the sarcomere level, and are a determinative factor for ground reaction forces and joint loads. Here, we aim to understand how the muscle responds, both micro- and macroscopically, under real leg impact scenarios across animal species from a body mass of ≈0.1kg to 500kg. Previously, our group developed an experimental setup with which we emulated an impact and directly measured muscle oscillations in isolated muscles. We gained new insights into the dynamic strains and damping properties of the microscopic contractile unit, the sarcomere. We also decomposed the time domain signal of wobbling mass dynamics into characteristic frequency components, and predicted eigenfrequencies, to study what makes up the time domain signal of wobbling mass dynamics. Yet, our earlier findings were limited to the rat (body mass ≈0.4kg) M. gastrocnemius. To expedite knowledge regarding the mechanics of muscular design, we will now first determine rat tendon properties from highly dynamic impact situations and include these in our complex direct-dynamics simulation model of the whole muscle (muscle-tendon-complex). Beyond our previously published analytical, 3-degrees-of-freedom (3DoF) spring-mass model (eigenfrequencies), our enhanced non-linear simulation model must include both distal and proximal tendon stiffness asymmetries, and a number of DoFs that reasonably represents the mass distribution of the muscle belly, and scalability of muscle size. With this, we will explain the measured characteristic wobbling mass frequencies by working out scaling allometries of all muscle tissues that contribute to these characteristic (muscle-induced) frequencies and also calculating (allometrically scaled) eigenfrequencies in larger animals. Furthermore, we will combine non-linear force-strain-rate characteristics of sarcomeres with the gained scaling allometry knowledge to examine, across species, the functional (locomotory) significance of these frequencies. This project will contribute to a better understanding of the relation between skeletal muscle structure and function in daily use, skeletal muscle damage, and muscle regeneration, all by correlating typical external load conditions during legged impacts with internal dynamic processes in the muscle tissue across species of sizes from small to large. An improved understanding of the design of the universal biological actuator ‘muscle’ will also contribute to developing biomimetic robotics actuators and prostheses.

• DFG Programme: Research Grants