zbMATH — the first resource for mathematics

Mathematical model for isometric and isotonic muscle contractions. (English) Zbl 1381.92005
Summary: A new mathematical model is presented to describe both the active and passive mechanics of muscles. In order to account for the active response, a two-layer kinematics that introduces both the visible and rest lengths of the muscle is presented within a rational mechanics framework. The formulation is based on an extended version of the principle of virtual power and the dissipation principle. By using an accurate constitutive description of muscle mobility under activation, details of microscopic processes that lead to muscle contraction are glossed over while macroscopic effects of chemical/electrical stimuli on muscle mechanics are retained. The model predictions are tested with isometric and isotonic experimental data collected from murine extensor digitorum muscle. It is shown that the proposed model captures experimental observations with only three scalar parameters.

92C10 Biomechanics
Full Text: DOI
[1] Ambrosi, D.; Arioli, G.; Nobile, F.; Quarteroni, A., Electromechanical coupling in cardiac dynamics: the active strain approach, SIAM J. Appl. Math., 71, 605-621, (2011) · Zbl 1419.74174
[2] Ambrosi, D.; Guana, F., Stress-modulated growth, Math. Mech. Solids, 12, 319-342, (2007) · Zbl 1149.74040
[3] Chen, H.; Luo, T.; Zhao, X.; Lu, X.; Huo, Y.; Kassab, G. S., Microstructural constitutive model of active coronary media, Biomaterials, 34, 7575-7583, (2013)
[4] Cherubini, C.; Filippi, S.; Nardinocchi, P.; Teresi, L., An electromechanical model of cardiac tissue: constitutive issues and electrophysiological effects, Prog. Biophys. Mol. Biol., 97, 562-573, (2008)
[5] Coleman, B. D.; Noll, W., The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Ration. Mech. Anal., 13, 167-178, (1963) · Zbl 0113.17802
[6] Curatolo, M.; Teresi, L., Modeling and simulation of fish swimming with active muscles, J. Theor. Biol., 409, 18-26, (2016) · Zbl 1405.92012
[7] DiCarlo, A.; Quiligotti, S., Growth and balance, Mech. Res. Commun., 29, 449-456, (2002) · Zbl 1056.74005
[8] Dickinson, M. H.; Farley, C. T.; Full, R. J.; Koehl, M.; Kram, R.; Lehman, S., How animals move: an integrative view, Science, 288, 100-106, (2000)
[9] Dillon, P. F.; Aksoy, M. O.; Driska, S. P.; Murphy, R. A., Myosin phosphorylation and the cross-bridge cycle in arterial smooth muscle, Science, 211, 495-497, (1981)
[10] Germain, P., Sur lapplication de la méthode des puissances virtuelles en mécanique des milieux continus, C. R.Acad. Sci., 274, 1051-1055, (1972) · Zbl 0242.73005
[11] Göktepe, S.; Menzel, A.; Kuhl, E., The generalized Hill model: a kinematic approach towards active muscle contraction, J. Mech. Phys. Solids, 72, 20-39, (2014) · Zbl 1328.74063
[12] Gurtin, M. E., Configurational forces as basic concepts of continuum physics, volume 137, (2008), Springer Science & Business Media
[13] Hill, A. V., The heat of shortening and the dynamic constants of muscle, Proc. R. Soc. London B: Biological Sciences, 126, 136-195, (1938)
[14] Hunter, P. J.; McCulloch, A. D.; Keurs, H. E.D. J.T., Modelling the mechanical properties of cardiac muscle, Prog. Biophys. Mol. Biol., 69, 289-331, (1998)
[15] Keurs, H. E.D. J.T.; Rijnsburger, W. H.; Heuningen, R. V.; Nagelsmit, M. J., Tension development and sarcomere length in rat cardiac trabeculae: evidence of length-dependent activation, Cardiac Dynamics, 25-36, (1980), Springer
[16] Lucantonio, A.; Nardinocchi, P.; Pezzulla, M.; Teresi, L., Multiphysics of bio-hybrid systems: shape control and electro-induced motion, Smart Mater. Struct., 23, 4, 045043, (2014)
[17] Maugin, G. A., Material inhomogeneities in elasticity, (1993), CRC · Zbl 0797.73001
[18] Minozzi, M.; Nardinocchi, P.; Teresi, L.; Varano, V., Growth-induced compatible strains, Math. Mech. Solids, (2015) · Zbl 1371.74044
[19] Murtada, S.; Holzapfel, G. A., Investigating the role of smooth muscle cells in large elastic arteries: a finite element analysis, J. Theor. Biol., 358, 1-10, (2014) · Zbl 1412.92069
[20] Murtada, S. C.; Arner, A.; Holzapfel, G. A., Experiments and mechanochemical modeling of smooth muscle contraction: significance of filament overlap, J. Theor. Biol., 297, 176-186, (2012) · Zbl 1336.92034
[21] Nardinocchi, P.; Teresi, L., Stress driven remodeling of living tissues, Comsol Multiphysics Conference 2005: Proceedings and User Presentations CD, (2006)
[22] Nardinocchi, P.; Teresi, L., On the active response of soft living tissues, J. Elast., 88, 27-39, (2007) · Zbl 1115.74349
[23] Nardinocchi, P.; Teresi, L., Electromechanical modeling of anisotropic cardiac tissues, Math. Mech. Solids, 18, 576-591, (2013)
[24] Nawroth, J. C.; Lee, H.; Feinberg, A. W.; Ripplinger, C. M.; McCain, M. L.; Grosberg, A.; Dabiri, J. O.; Parker, K. K., A tissue-engineered jellyfish with biomimetic propulsion, Nat. Biotechnol., 30, 792-797, (2012)
[25] Quiat, D.; Voelker, K. A.; Pei, J.; Grishin, N. V.; Grange, R. W.; Bassel-Duby, R.; Olson, E. N., Concerted regulation of myofiber-specific gene expression and muscle performance by the transcriptional repressor sox6, Proc. Natl. Acad. Sci., 108, 10196-10201, (2011)
[26] Rodriguez, E.; Hoger, A.; McCulloch, A., Stress dependent finite growth in soft elastic tissues, J. Biomech., 27, 455-464, (1994)
[27] Sharifimajd, B.; Stålhand, J., A continuum model for excitation-contraction of smooth muscle under finite deformations, J. Theor. Biol., 355, 1-9, (2014) · Zbl 1325.92012
[28] Sperringer, J. E.; Grange, R. W., In vitro assays to determine skeletal muscle physiologic function, Skeletal Muscle Regeneration in the Mouse: Methods and Protocols, 271-291, (2016)
[29] Stålhand, J.; Klarbring, A.; Holzapfel, G. A., Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains, Prog. Biophys. Mol. Biol., 96, 465-481, (2008)
[30] Stålhand, J.; Klarbring, A.; Holzapfel, G. A., A mechanochemical 3D continuum model for smooth muscle contraction under finite strains, J. Theor. Biol., 268, 120-130, (2011) · Zbl 1411.92020
[31] Stålhand, J.; McMeeking, R. M.; Holzapfel, G. A., On the thermodynamics of smooth muscle contraction, J. Mech. Phys. Solids, (2016)
[32] Tan, T.; De Vita, R., A structural constitutive model for smooth muscle contraction in biological tissues, Int. J. Non Linear Mech., 75, 46-53, (2015)
[33] Truesdell, C.; Noll, W., The non-linear field theories of mechanics, Handbuch der Physik, III/3, (1965), Berlin-Heidelberg-New York: Springer · Zbl 0779.73004
[34] Virgilio, K. M.; Martin, K. S.; Peirce, S. M.; Blemker, S. S., Multiscale models of skeletal muscle reveal the complex effects of muscular dystrophy on tissue mechanics and damage susceptibility, Interface Focus, 5, 20140080, (2015)
[35] Wolff, A. V.; Niday, A. K.; Voelker, K. A.; Call, J. A.; Evans, N. P.; Granata, K. P.; Grange, R. W., Passive mechanical properties of maturing extensor digitorum longus are not affected by lack of dystrophin, Muscle Nerve, 34, 304-312, (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.