The Energy of Muscle Contraction. I. Tissue Force and Deformation During Fixed-End Contractions.

James M Wakeling,David S Ryan,Sebastián Domínguez,Nilima Nigam,Ryan Konno,Bart Bolsterlee,Stephanie A Ross

doi:10.3389/fphys.2020.00813

Abstract

During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

Highlights

Most of our understanding of muscle function and performance comes from measurements at small scales such as sarcomeres, single fibres and small muscles
Changes to the tissue shape were governed by the isotropic base material properties and the volumetric strain energies: because there was an asymmetry to the stress across the muscle, this resulted in an asymmetry to the transverse tissue deformation that was dependent on pennation angle (Figure 7)
Even though the contribution of volumetric and base material strain-energy potentials has been largely ignored to date in considerations of whole muscle force and deformation, we suggest that they play an important role in the 3D structure and function of whole-muscle contractions

Summary

Introduction

Most of our understanding of muscle function and performance comes from measurements at small scales such as sarcomeres, single fibres and small muscles. Understanding how the contractile elements interact with the Energy of Muscle Contractions tissue properties of the whole muscle, how deformations may arise in all three dimensions during contraction, and how the dynamics of muscle size influences whole muscle performance may result in muscle behaviours that are not intuitive from the understanding of single fibre function alone. The purpose of this series of papers is to consider contractile mechanisms that are relevant at the whole muscle level, and how these influence the design and performance of skeletal muscle

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Conclusion