Impact response of active muscle: experimentation and modelling

• Applicants: Professor Dr. Syn Schmitt; Professor Dr. Tobias Siebert
• Subject Area: Human Factors, Ergonomics, Human-Machine Systems ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2013 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 234087184

• Final Report Year: 2024

Final Report Abstract

Muscles are essential for biological locomotion. The ingenious construction of the muscle allows them to tolerate impacts during their contractile function. For example, when a leg contacts the ground (touch-down: TD) in terrestrial locomotion, shock-wave accelerations are induced on the skeletal system, which travels to the muscles via their suspensions to the skeleton. In response, damped oscillations (wobbling mass dynamics) superpose the driving muscle contractions. Much is unknown about the muscle in such highly dynamic situations, which leaves fundamental questions regarding the design criteria and functional advantages of the ubiquitous biological actuator muscle unanswered. This particularly applies to the combination of the structure of the drive (work generator: cross-bridge, CB) and the primarily elastic structures in series to it, which both consist of built-in levels of compliance and damping properties (inducing energy dissipation). The current project covers the last funding period. It yielded four publications (plus one submitted manuscript) directly related to the entire project period, plus seven publications strongly influenced by this work, which answer questions that additionally arose during the project processing. As part of the project, a unique experimental setup was developed that enables the investigation of the wobbling mass dynamics of isolated muscles under defined impact conditions. In a combination of experiments emulating leg impacts during locomotion and muscle modelling, we aimed to enhance our understanding of how the universal biological actuator ‘muscle’ is designed and functions in one of the most common situations for terrestrial mammals: legged locomotion. Altogether, we studied fibre strain responses, energy dissipation, and the frequency spectrum of a rat’s muscle-tendon complex, all in response to a legged impact scenario. These experimental findings helped us develop a reductionist analytical model that explains the most dominant (eigen)frequency characteristics in wobbling mass dynamics, and a complex, direct-dynamics simulation model that reproduces wobbling mass kinematics. The knowledge gained also influenced the development of a Hill-type model with incorporated phosphate kinetics, and a geometric-mechanistic model, which explains the shift of force-length maxima with muscle activation. This project and its results will be of interest in biomechanical-related fields such as the advancement of biomimetic robot actuators, prostheses development, injury prevention and rehabilitation, as well as the relation between mechanical loads and physiology of the muscle (regarding e.g. the condition of continuous zero gravity).

Publications

• Contraction dynamics and function of the muscle-tendon complex depend on the muscle fibre-tendon length ratio: a simulation study. Biomechanics and Modeling in Mechanobiology, 15(1), 245-258.
  Mörl, Falk; Siebert, Tobias & Häufle, Daniel
  
• Strain in shock-loaded skeletal muscle and the time scale of muscular wobbling mass dynamics. Scientific Reports, 7(1).
  Christensen, Kasper B.; Günther, Michael; Schmitt, Syn & Siebert, Tobias
  
• Inter-filament spacing mediates calcium binding to troponin: A simple geometric-mechanistic model explains the shift of force-length maxima with muscle activation. Journal of Theoretical Biology, 454, 240-252.
  Rockenfeller, Robert & Günther, Michael
  
• The basic mechanical structure of the skeletal muscle machinery: One model for linking microscopic and macroscopic scales. Journal of Theoretical Biology, 456, 137-167.
  Günther, Michael; Haeufle, Daniel F.B. & Schmitt, Syn
  
• Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model. Frontiers in Physiology, 11.
  Rockenfeller, Robert; Günther, Michael; Stutzig, Norman; Haeufle, Daniel F. B.; Siebert, Tobias; Schmitt, Syn; Leichsenring, Kay; Böl, Markus & Götz, Thomas
  
• A geometry- and muscle-based control architecture for synthesising biological movement. Biological Cybernetics, 115(1), 7-37.
  Walter, Johannes R.; Günther, Michael; Haeufle, Daniel F. B. & Schmitt, Syn
  
• Cross-bridge mechanics estimated from skeletal muscles’ work-loop responses to impacts in legged locomotion. Scientific Reports, 11(1).
  Christensen, Kasper B.; Günther, Michael; Schmitt, Syn & Siebert, Tobias
  
• Rules of nature’s Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed. Journal of Theoretical Biology, 523, 110714.
  Günther, Michael; Rockenfeller, Robert; Weihmann, Tom; Haeufle, Daniel F.B.; Götz, Thomas & Schmitt, Syn
  
• Muscle active force-length curve explained by an electrophysical model of interfilament spacing. Biophysical Journal, 121(10), 1823-1855.
  Rockenfeller, Robert; Günther, Michael & Hooper, Scott L.
  
• Muscle wobbling mass dynamics: eigenfrequency dependencies on activity, impact strength, and ground material. Scientific Reports, 13(1).
  Christensen, Kasper B.; Günther, Michael; Schmitt, Syn & Siebert, Tobias
  
• Compliance at the heart of the muscle
  M. Gunther, K. B. Christensen, D. F. B. Haeufle, S. Schmitt & T. Siebert
  
• Rethinking the physiological cross-sectional area of skeletal muscle reveals the mechanical advantage of pennation. Royal Society Open Science, 11(9).
  Rockenfeller, Robert; Günther, Michael; Clemente, Christofer J. & Dick, Taylor J. M.