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Volume 55 Issue 2
Feb.  2023
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Wang Monan, Jiang Guodong, Liu Fengjie. Multi-scale modeling and simulation of skeletal muscle biomechanical properties. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 509-531 doi: 10.6052/0459-1879-22-496
Citation: Wang Monan, Jiang Guodong, Liu Fengjie. Multi-scale modeling and simulation of skeletal muscle biomechanical properties. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(2): 509-531 doi: 10.6052/0459-1879-22-496


doi: 10.6052/0459-1879-22-496
  • Received Date: 2022-10-14
  • Accepted Date: 2022-12-08
  • Available Online: 2022-12-09
  • Publish Date: 2023-02-18
  • Aiming at the problems that there is a certain difference between the muscle fiber microstructure model and the image observed under the microscope, the microscopic component biomechanical model cannot effectively capture the mechanical behavior of skeletal muscle during shear deformation, and the high calculation cost of multi-scale numerical models of skeletal muscle. In this thesis, the mechanical properties of skeletal muscle are studied from the perspectives of experiment, multiscale modeling and simulation. Curved-edge Voronoi polygons are proposed as the cross-section of muscle fibers, and the corresponding representative volume element (RVE) is established at the microscale. A new biomechanical model (MMA model) is proposed, and the MMA model is used as the biomechanical model of muscle fibers and connective tissue, the MMA model adopts complete strain invariants$ {I}_{4}、{I}_{5}、{I}_{6}、{I}_{7} $, so that the shear behavior of skeletal muscle is reflected at the level of material properties. Combine the experimental results of skeletal muscle, the RVE models, the biomechanical models of muscle fibers and connective tissue to establish a multiscale numerical model of skeletal muscle. According to the experimental results, the parameters of the biomechanical model are determined, the multiscale homogenization method are used to realize the connection between the microscale and the macro-scale, and the macroscopic mechanical behavior of skeletal muscle is finally obtained, four deformation forms of Longitudinal stretch, stretch laterally, out-of-plane longitudinal shear and in-plane shear are performed to verify the convergence of the model. This thesis research the effects of model parameters, muscle fiber volume fraction and muscle fiber structure on skeletal muscle on macroscopic mechanical behavior. Combined with experimental data, the effectiveness of the multiscale numerical model is verified. In this paper, the multi-scale numerical model of skeletal muscle can not only be used to study the influence of microscopic factors on the macroscopic mechanical behavior of skeletal muscle, but also to study the influence of diseases on the biomechanical properties of skeletal muscle and to simulate skeletal muscle remodeling and regeneration.


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  • [1]
    陈胜国, 汪华侨. 人体骨骼肌的分布和变异. 解剖学研究, 2013, 35(3): 237-240 (Chen Shengguo, Wang Huaqiao. Distribution and variation of human skeletal muscle. Anatomy Research, 2013, 35(3): 237-240 (in Chinese)
    Janssen I, Heymsfield S, Wang Z, et al. Skeletal muscle mass and distribution in 468 men and women aged 18-88 Yr. Journal of Applied Physiology, 2000, 89(1): 81-88 doi: 10.1152/jappl.2000.89.1.81
    姜宗来. 从生物力学到力学生物学的进展. 力学进展, 2017, 47: 313-336 (Jiang Zonglai. Advances from biomechanics to mechanical biology. Advances in Mechanics, 2017, 47: 313-336 (in Chinese) doi: 10.6052/1000-0992-16-023
    Fung YC. Biomechanics: mechanical properties of living tissues. Journal of Biomechanical Engineering, 1981, 103(4): 231-298 doi: 10.1115/1.3138285
    Spencer A. Deformations of Fibre-reinforced Materials. New York: Oxford University Press, 1972
    Gerard JM, Ohayon J, Luboz V, et al. Non-Linear elastic properties of the lingual and facial tissues assessed by indentation technique application to the biomechanics of speech production. Medical Engineering & Physics, 2005, 27(10): 884-892
    陈伟, 吴立军, 严志汉等. 老年健康女性盆底肛提肌有限元模型的建立及意义. 生物医学工程学杂志, 2011, 28(5): 927-931 (Chen Wei, Wu Lijun, Yan Zhihan, et al. Establishment and significance of finite element model of levator anus pelvic floor muscle in elderly healthy women. Journal of Biomedical Engineering, 2011, 28(5): 927-931 (in Chinese)
    Schiavone P, Boudou T, Promayon E, et al. A light sterilizable pipette device for the in vivo estimation of human soft tissues constitutive laws//International Conference of the IEEE Engineering in Medicine & Biology Society, Vancouver, 2008: 4298-4310
    Nazari MA, Perrier P, Chabanas M, et al. Simulation of dynamic orofacial movements using a constitutive law varying with muscle activation. Computer Methods in Biomechanics and Biomedical Engineering, 2010, 13(4): 469-482 doi: 10.1080/10255840903505147
    Nazari MA, Perrier P, Chabanas M, et al. Shaping by stiffening: a modeling study for lips. Motor Control, 2011, 15(1): 141-168 doi: 10.1123/mcj.15.1.141
    Stavness I, Lloyd JE, Fels S. Automatic prediction of tongue muscle activations using a finite element model. Journal of Biomechanics, 2012, 45(16): 2841-2848 doi: 10.1016/j.jbiomech.2012.08.031
    Gindre J, Takaza M, Moerman KM, et al. A structural model of passive skeletal muscle shows two reinforcement processes in resisting deformation. Journal of the Mechanical Behavior of Biomedical Materials, 2013, 22: 84-94 doi: 10.1016/j.jmbbm.2013.02.007
    Voigt W. Ueber die beziehung zwischen den beiden elasticitätsconstanten isotroper körper. Annalen der Physik (Leipzig) , 1889, 274(12): 573-587 doi: 10.1002/andp.18892741206
    Ogden RW. Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue. Biomechanics of Soft Tissue in Cardiovascular Systems, 2003, 441: 65-108
    Al-Dirini RM, Reed MP, Hu J, et al. Development and validation of a high anatomical fidelity fe model for the buttock and thigh of a seated individual. Annals of Biomedical Engineering, 2016, 44(9): 2805-2816 doi: 10.1007/s10439-016-1560-3
    Roux A, Laporte S, Lecompte J, et al. Influence of muscle-tendon complex geometrical parameters on modeling passive stretch behavior with the discrete element method. Journal of Biomechanics, 2016, 49(2): 252-258 doi: 10.1016/j.jbiomech.2015.12.006
    Bosboom EMH, Hesselink MKC, Oomens CWJ, et al. Passive lateral mechanical properties of skeletal muscle under in vivo compression. Journal of Biomechanics, 2001, 34(10): 1365-1368 doi: 10.1016/S0021-9290(01)00083-5
    粟思橙. 基于肌肉主动力的颈部有限元建模研究. [硕士论文]. 长沙: 湖南大学, 2014

    Su Sicheng. Research on Finite Element Modeling of Neck Based on Muscle Initiative. [Master Thesis]. Changsha: Hunan University, 2014 (in Chinese))
    Sengeh DM, Moerman KM, Petron A, et al. Multi-material 3-D viscoelastic model of a transtibial residuum from in-vivo indentation and mri data. Journal of the Mechanical Behavior of Biomedical Materials, 2016, 59: 379-392 doi: 10.1016/j.jmbbm.2016.02.020
    Moerman KM, Simms CK, Nagel T. Control of stretch-compression asymmetry in ogden hyperelasticity with application to soft tissue modelling. Journal of the Mechanical Behavior of Biomedical Materials, 2016, 56: 218-228 doi: 10.1016/j.jmbbm.2015.11.027
    Holzapfel GA, Gasser TC, Ogden RW. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity, 2000, 61(1/3): 1-48 doi: 10.1023/A:1010835316564
    Hernández B, Pena E, Pascual G, et al. Mechanical and histological characterization of the abdominal muscle. A Previous Step to Modelling Hernia Surgery. J Mech Behav Biomed Mater, 2011, 4(3): 392-404
    Böl M, Weikert R, Weichert C. A coupled electromechanical model for the excitation-dependent contraction of skeletal muscle. Journal of the Mechanical Behavior of Biomedical Materials, 2011, 4(7): 1299-1310 doi: 10.1016/j.jmbbm.2011.04.017
    Wu T, Hung APL, Hunter P, et al. Modelling facial expressions: a framework for simulating nonlinear soft tissue deformations using embedded 3D muscles. Finite Elements in Analysis and Design, 2013, 76: 63-70 doi: 10.1016/j.finel.2013.08.002
    Calvo B, Ramírez A, Alonso A, et al. Passive nonlinear elastic behaviour of skeletal muscle: experimental results and model formulation. Journal of Biomechanics, 2010, 43(2): 318-325 doi: 10.1016/j.jbiomech.2009.08.032
    Spyrou LA, Agoras M, Danas K. A homogenization model of the voigt type for skeletal muscle. Journal of Theoretical Biology, 2017, 414: 50-61 doi: 10.1016/j.jtbi.2016.11.018
    Spyrou LA, Brisard S, Danas K. Multiscale modeling of skeletal muscle tissues based on analytical and numerical homogenization. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 92: 97-117 doi: 10.1016/j.jmbbm.2018.12.030
    Sharafi B, Blemker SS. A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry. Journal of Biomechanics, 2010, 43: 3207-3213 doi: 10.1016/j.jbiomech.2010.07.020
    Sharafi B, Blemker SS. A mathematical model of force transmission from intrafascicularly terminating muscle fibers. Journal of Biomechanics, 2011, 44(11): 2031-2039 doi: 10.1016/j.jbiomech.2011.04.038
    Jiménez FL. Modeling of soft composites under three-dimensional loading. Composites Part B-Engineering, 2014, 59: 173-180 doi: 10.1016/j.compositesb.2013.11.020
    Virgilio KM, Martin KS, Peirce SM, et al. Multiscale models of skeletal muscle reveal the complex effects of muscular dystrophy on tissue mechanics and damage susceptibility. Interface Focus, 2015, 5(2): 20140080 doi: 10.1098/rsfs.2014.0080
    Kuravi R, Leichsenring K, Böl M, et al. 3D finite element models from serial section histology of skeletal muscle tissue-the role of micro-architecture on mechanical behaviour. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 113: 104109 doi: 10.1016/j.jmbbm.2020.104109
    Valentin T, Simms C. An inverse model of the mechanical response of passive skeletal muscle: implications for microstructure. Journal of Biomechanics, 2020, 99: 109483 doi: 10.1016/j.jbiomech.2019.109483
    Kuravi R, Leichsenring K, Trostorf R, et al. Predicting muscle tissue response from calibrated component models and histology-based finite element models. Journal of the Mechanical Behavior of Biomedical Materials, 2021, 117: 104375 doi: 10.1016/j.jmbbm.2021.104375
    Bleiler C, Ponte CP, Rohrle O. A microstructurally-based, multi-Scale, continuum-mechanical model for the passive behaviour of skeletal muscle tissue. Journal of the Mechanical Behavior of Biomedical Materials, 2019, 97: 171-186 doi: 10.1016/j.jmbbm.2019.05.012
    王礼立. 高应变率下材料动态力学性能. 力学与实践, 1982, 1: 9-19 (Wang Lili. Dynamic mechanical properties of materials under high strain rate. Mechanics in Engineering, 1982, 1: 9-19 (in Chinese)
    Nemat-Nasser S, Lori MSKD. Micromechanics: overall properties of heterogeneous materials. Journal of Applied Mechanics, 1996, 63(2): 561 doi: 10.1115/1.2788912
    Wisdom KM, Delp SL, Kuhl E. Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomech Model Mechanobiol, 2015, 14(2): 195-215 doi: 10.1007/s10237-014-0607-3
    Kanit T, Forest S, Galliet I, et al. Determination of the size of the representative volume element for random composites: statistical and numerical approach. International Journal of Solids and Structures, 2003, 40(13-14): 3647-3679 doi: 10.1016/S0020-7683(03)00143-4
    武鹏伟. 非均质材料微—宏观非线性分析的多尺度研究. [硕士论文]. 杭州: 浙江工业大学, 2016

    Wu Pengwei. Multi-scale study of micro-macroscopic nonlinear analysis of heterogeneous materials. [Master Thesis]. Hangzhou: Zhejiang University of Technology, 2016 (in Chinese))
    李庆, 杨晓翔. 周期性边界条件下炭黑增强橡胶基复合材料有效弹性性能数值模拟. 福州大学学报(自然科学版), 2013, 41(1): 97-103 (Li Qing, Yang Xiaoxiang. Numerical simulation of effective elastic properties of carbon black reinforced rubber matrix composites under periodic boundary conditions. Journal of Fuzhou University (Natural Science Edition, 2013, 41(1): 97-103 (in Chinese)
    Xia Z, Zhang Y, Ellyin F. A unified periodical boundary conditions for representative volume elements of composites and applications. International Journal of Solids and Structures, 2003, 40(8): 1907-1921 doi: 10.1016/S0020-7683(03)00024-6
    Xu R, Bouby C, Zahrouni H, et al. 3D modeling of shape memory alloy fiber reinforced composites by multiscale finite element method. Composite Structures, 2018, 200: 408-419 doi: 10.1016/j.compstruct.2018.05.108
    Holzapfel GA. Nonlinear solid mechanics: a continuum approach for engineering. Chichester: John Wiley & Sons, 2000, 37: 489-490
    Flory PJ. Thermodynamic relations for high elastic materials. Transactions of the Faraday Society, 1961, 57(5): 829-838
    Nolan DR, Gower AL, Destrade M, et al. A robust anisotropic hyperelastic formulation for the modelling of soft tissue. Journal of the Mechanical Behavior of Biomedical Materials, 2014, 39: 48-60 doi: 10.1016/j.jmbbm.2014.06.016
    Nolan DR, Mcgarry JP. On the compressibility of arterial tissue. Annals of Biomedical Engineering, 2016, 44(4): 993-1007 doi: 10.1007/s10439-015-1417-1
    Klisch SM. A bimodular polyconvex anisotropic strain energy function for articular cartilage. Journal of Biomechanical Engineering, 2007, 129(2): 250-258 doi: 10.1115/1.2486225
    Schrder J, Neff P. Invariant formulation of hyperelastic lateral isotropy based on polyconvex free energy functions. International Journal of Solids & Structure, 2003, 40(2): 401-445
    Sun W, Chaikof EL, Levenston ME. Numerical approximation of tangent Moduli for finite element implementations of nonlinear hyperelastic material models. Journal of Biomechanical Engineering, 2008, 130(6): 061003
    Bazant ZP, Gattu M, Vorel J. Work conjugacy error in commercial finite-element codes: its magnitude and how to compensate for it. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2012, 468(2146): 3047-3058 doi: 10.1098/rspa.2012.0167
    Böl M, Iyer R, Dittmann J, et al. Investigating the passive mechanical behaviour of skeletal muscle fibres: micromechanical experiments and bayesian hierarchical modelling. Acta Biomaterialia, 2019, 92: 277-289 doi: 10.1016/j.actbio.2019.05.015
    Purslow PP. Muscle fascia and force transmission. Journal of Bodywork and Movement Therapies, 2010, 14(4): 411-417 doi: 10.1016/j.jbmt.2010.01.005
    Morrow DA, Haut Donahue TL, Odegard GM, et al. Laterally isotropic stretch material properties of skeletal muscle tissue. Journal of the Mechanical Behavior of Biomedical Materials, 2010, 3(1): 124-129 doi: 10.1016/j.jmbbm.2009.03.004
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