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Klotz T, Bleiler C, Röhrle O. A Physiology-Guided Classification of Active-Stress and Active-Strain Approaches for Continuum-Mechanical Modeling of Skeletal Muscle Tissue. Front Physiol 2021; 12:685531. [PMID: 34408657 PMCID: PMC8365610 DOI: 10.3389/fphys.2021.685531] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 06/30/2021] [Indexed: 11/13/2022] Open
Abstract
The well-established sliding filament and cross-bridge theory explain the major biophysical mechanism responsible for a skeletal muscle's active behavior on a cellular level. However, the biomechanical function of skeletal muscles on the tissue scale, which is caused by the complex interplay of muscle fibers and extracellular connective tissue, is much less understood. Mathematical models provide one possibility to investigate physiological hypotheses. Continuum-mechanical models have hereby proven themselves to be very suitable to study the biomechanical behavior of whole muscles or entire limbs. Existing continuum-mechanical skeletal muscle models use either an active-stress or an active-strain approach to phenomenologically describe the mechanical behavior of active contractions. While any macroscopic constitutive model can be judged by it's ability to accurately replicate experimental data, the evaluation of muscle-specific material descriptions is difficult as suitable data is, unfortunately, currently not available. Thus, the discussions become more philosophical rather than following rigid methodological criteria. Within this work, we provide a extensive discussion on the underlying modeling assumptions of both the active-stress and the active-strain approach in the context of existing hypotheses of skeletal muscle physiology. We conclude that the active-stress approach resolves an idealized tissue transmitting active stresses through an independent pathway. In contrast, the active-strain approach reflects an idealized tissue employing an indirect, coupled pathway for active stress transmission. Finally the physiological hypothesis that skeletal muscles exhibit redundant pathways of intramuscular stress transmission represents the basis for considering a mixed-active-stress-active-strain constitutive framework.
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Affiliation(s)
- Thomas Klotz
- Chair for Continuum Biomechanics and Mechanobiology, Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Sciences (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Christian Bleiler
- Chair for Continuum Biomechanics and Mechanobiology, Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Sciences (SC SimTech), University of Stuttgart, Stuttgart, Germany
| | - Oliver Röhrle
- Chair for Continuum Biomechanics and Mechanobiology, Institute for Modelling and Simulation of Biomechanical Systems, University of Stuttgart, Stuttgart, Germany
- Stuttgart Center for Simulation Sciences (SC SimTech), University of Stuttgart, Stuttgart, Germany
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Barfred T. Achilles Tendon Rupture: Aetiology and Pathogenesis of Subcutaneous Rupture Assessed on the Basis of the Literature and Rupture Experiments on Rats. ACTA ACUST UNITED AC 2014. [DOI: 10.3109/ort.1973.44.suppl-152.01] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
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Buchthal F, Knappeis GG, Lindhard J. Die Struktur der quergestreiften, lebenden Muskelfaser des Frosches in Ruhe und während der Kontraktion1. ACTA ACUST UNITED AC 2012. [DOI: 10.1111/j.1748-1716.1936.tb01463.x] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Asmussen E, Lindhard J. Über die maximale Muskelkontraktion und die Verbreitung des Reizes in der Muskelfaser1. ACTA ACUST UNITED AC 2012. [DOI: 10.1111/j.1748-1716.1935.tb00425.x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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HUIJING PETERA. INTRA-, EXTRA- AND INTERMUSCULAR MYOFASCIAL FORCE TRANSMISION OF SYNERGISTS AND ANTAGONISTS: EFFECTS OF MUSCLE LENGTH AS WELL AS RELATIVE POSITION. J MECH MED BIOL 2011. [DOI: 10.1142/s0219519402000496] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The concepts of intramuscular myofascial force transmission is reintroduced and reviewed on the basis of experiments involving tenotomy and aponeurotomy of dissected rat EDL muscle studied in situ. Results from experiments with measurements of force of EDL muscle, of which the muscle belly was not dissected (i.e. the muscle is surrounded by its natural connective tissue milieu) are discussed. In such experiments, force was measured at proximal as well as distal EDL tendons. Examples of experimental evidence for both extramuscular and intermuscular myofascial force transmission within the rat anterior crural compartment are presented. Evidence is presented also for differential effects of proximal and distal lengthening on myofascial force transmission from EDL, even for the case in which symmetric length changes were imposed on the muscle. It is shown that myofascial force transmission effects are not limited to synergists located within one compartment, but do also play a very substantial role in the interaction between antagonist muscles in neighbouring anterior crural and peroneal compartments.
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Affiliation(s)
- PETER A. HUIJING
- Instituut voor Fundamentele en Toegepaste Bewegingswetenschappen, Faculteit Bewegingswetenschappen, Vrije Universiteit, Amsterdam, The Netherlands
- Integrated Biomedical Engineering for Restoration of Human Function, Instituut voor Biomedische Technologie, Department of Biomechanical Engineering, Universiteit Twente, Enschede, The Netherlands
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Saltin B, Gollnick PD. Skeletal Muscle Adaptability: Significance for Metabolism and Performance. Compr Physiol 2011. [DOI: 10.1002/cphy.cp100119] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Chapter X: General Summary. Acta Otolaryngol 2009. [DOI: 10.3109/00016485809124392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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References. Acta Otolaryngol 2009. [DOI: 10.3109/00016485809124394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Huijing PA. Muscular Force Transmission Necessitates a Multilevel Integrative Approach to the Analysis of Function of Skeletal Muscle. Exerc Sport Sci Rev 2003; 31:167-75. [PMID: 14571955 DOI: 10.1097/00003677-200310000-00003] [Citation(s) in RCA: 90] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
Muscular force is transmitted not only to tendon but also to other structures. Connections to extramuscular connective tissue of a compartment and to other muscles are stiff enough to transmit force. The concept of myofascial force transmission is reviewed and some functional consequences considered. An approach for analysis is suggested.
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Affiliation(s)
- Peter A Huijing
- Instituut voor Fundamentele en Klinische Bewegingswetenschappen, Faculteit Bewegingswetenschappen, Vrije Universiteit, Amsterdam, The Netherlands.
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Abstract
A state-of-the-art report is presented on recent progress in selected areas of myodynamics, but also on problems that severely hamper the further development of the discipline. Significant advances have been made in elucidating the force-producing interaction between actin and the myosin-S1-subunit, including the localization of the most probable molecular site of power stroke initiation. Concerning the architecture of the myostructures, strong experimental evidence has accumulated for numerous intra-, inter-, and extramuscular pathways for lateral force transmission in addition to the serial sarcomere-to-sarcomere myotendinous path. It is shown that contemporary muscle models are inadequate in most respects and lag far behind the requirements an appropriate myodynamic model should fulfil. A similar comment applies to the current approaches designed to solve the myoskeletal indeterminacy problem. These formulations neglect myodynamic properties and do not allow for the implementation of biologically realistic objective functions. The solutions currently obtained are highly unsatisfactory. New research directions to rectify these situations are suggested, also with regard to the identification of subject-specific myodynamic parameters.
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Affiliation(s)
- H Hatze
- Department of Biomechanics, University of Vienna, Auf der Schmelz 6, A-1150 Wien, Austria.
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Huijing P. Muscular force transmission: a unified, dual or multiple system? A review and some explorative experimental results. Arch Physiol Biochem 1999; 107:292-311. [PMID: 10779826 DOI: 10.1076/13813455199908107041qft292] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Structures contributing to force transmission in muscle are reviewed combining some historical and relatively recently published experimental data. Also, effects of aponeurotomy and tenotomy are reviewed shortly as well as some new experimental results regarding these interventions that reinforce the concept of myofascial force transmission. The review is also illustrated by some new images of single muscle fibres from Xenopus Laevis indicative of such transmission and some data about locations of insertion of human gluteus maximus muscle. From this review and the new material, emerges a line of thought indicating that mechanical connections between muscle fibres and intramuscular connective tissue play an important role in force transmission. New experimental observations are presented for non-spanning muscle (i.c., rat biceps femoris muscle), regarding the great variety of types of intramuscular connections that exist i n addition to myo-tendinous junctions at the perimuscular ends of muscle fibres. Such connections are classified as (1) tapered end connections, (2) Myo-myonal junctions, (3) myo-epimysial junctions and (3) Myo-endomysial junctions. This line of thought is followed up by consideration of a possible role of connections of intra- and extramuscular connective tissue in force transmission out of the muscle. Experimental results of an explorative nature, regarding the interactions of extensor digitorum longus (EDL), tibialis anterior (TA) and hallucis longus (HAL) muscles within a relatively intact dorsal flexor compartment of the rat hind leg, indicate that: (1) length force properties of EDL are influenced by TA activity in a length dependent fashion. Depending on TA length, force exerted by EDL, kept at constant origin insertion distance, is variable and the effect is influenced by EDL length itself as well; (2) Force is transmitted from muscle to extramuscular connective tissue and vice versa. As a consequence force exerted at proximal and distal tendons of a muscle are not always equal. The difference being transmitted by extramuscular connective tissue and may appear at the tendons of other muscles or may be transmitted via connective tissue directly to bone. It is concluded that the system of force transmission from skeletal muscle should be considered as a multiple system.
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Affiliation(s)
- P Huijing
- Instituut voor Fundamentele en Klinische Bewegingswetenschappen, Faculteit Bewegingswetenschappen, Vrije Universiteit, Amsterdam, The Netherlands.
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Abstract
Tendon normally fulfills its primary role as a flexible force transmitting element very effectively and yet failure of this passive tissue leads to great disability. As a connective tissue its structure is relatively simple and the peculiar helical arrangement of collagen fibres confers highly non-linear as well as time-dependent mechanical properties. Functional significance cannot be attributed to any facet of mechanical response until the physiological pattern of loading is established. In particular the rate of deformation and the minimum force experienced by tendon in normal locomotion have yet to be elicited. Most published values of maximum forces transmitted by tendon fall short of the measured quasi-static rupture strength. The fact that some estimates exceed this ultimate force illustrates the errors incurred in indirect assessment. Direct measurement techniques, which have now been demonstrated to be practicable, should yield valuable information when applied to tendons susceptible to spontaneous rupture. Other proposed mechanical functions of tendon are clearly of secondary importance. Much has yet to be learned of the response of muscle to rapid loading and extension before these hypotheses can be tested fully. With our scant knowledge of normal tendon function it is indeed fortunate that the techniques of repair and treatment of damaged tendon are rapidly advancing.
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Barfred T. Experimental rupture of the Achilles tendon. Comparison of various types of experimental rupture in rats. ACTA ORTHOPAEDICA SCANDINAVICA 1971; 42:528-43. [PMID: 5169147 DOI: 10.3109/17453677108989070] [Citation(s) in RCA: 37] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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Herberts P. Myoelectric signals in control of prostheses. Studies on arm amputees and normal individuals. ACTA ORTHOPAEDICA SCANDINAVICA 1969:Suppl 124:1+. [PMID: 5373798 DOI: 10.3109/ort.1969.40.suppl-124.01] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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Ljungqvist R. Subcutaneous partial rupture of the Achilles tendon. ACTA ORTHOPAEDICA SCANDINAVICA 1968:Suppl 113:1+. [PMID: 5597225 DOI: 10.3109/ort.1968.39.suppl-113.01] [Citation(s) in RCA: 47] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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Die Grundlagen des Tetanus und Tonus der quergestreiften Skelettmuskelfasern der Wirbeltiere. ACTA ACUST UNITED AC 1950. [DOI: 10.1007/bf02174831] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Sandow A. Studies on the latent period of muscular contraction. Method. General properties of latency relaxation. ACTA ACUST UNITED AC 1944. [DOI: 10.1002/jcp.1030240306] [Citation(s) in RCA: 57] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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BUCHTHAL FRITZ, KNAPPEIS GG. Propagation of Contraction in the Isolated Striated Muscle Fibre. ACTA ACUST UNITED AC 1943. [DOI: 10.1111/j.1748-1716.1943.tb02054.x] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Arbeitsphysiologie. Rev Physiol Biochem Pharmacol 1939. [DOI: 10.1007/bf02322412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Konstante Unterschiede im Aktionsstrombild menschlicher Muskeln bei Willkürinnervation. ACTA ACUST UNITED AC 1937. [DOI: 10.1007/bf01762863] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Schneller H. Physiologische Bedeutung des Ammoniaks im Organismus der Wirbeltiere. ACTA ACUST UNITED AC 1935. [DOI: 10.1007/bf02320724] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Zusammenhänge zwischen physikalischen und chemischen Vorgängen bei der Muskelkontraktion. ACTA ACUST UNITED AC 1935. [DOI: 10.1007/bf02320723] [Citation(s) in RCA: 53] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Hansen E. Über die Sauerstoffschuld bei körperlicher Arbeit. Eur J Appl Physiol 1934. [DOI: 10.1007/bf02010168] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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