Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002419
pages 143-154


Ciaran K. Simms
Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Ireland
M. Van Loocke
Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Ireland
C. G. Lyons
Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Ireland


The internal loading distribution within the body cannot generally be measured. In contrast, musculoskeletal models have the potential to predict internal stress-strain patterns at all locations within the body. However, this often requires an adequate model of the constitutive behavior of skeletal muscle tissue. Thus far, all attempts at formulating the stress response of skeletal muscle have assumed that the total stress has active and passive components that can be added to yield the total response. In quasi-static applications such as pressure-sore modeling, and in dynamic applications involving transient external loading (especially impact modeling), the passive muscle representation may be more relevant than the active response. This paper summarizes the known passive deformation behavior of skeletal muscle tissue and reviews the constitutive formulations for passive muscle that are included in combined active/passive muscle models. It is shown that none of the existing formulations can adequately represent the asymmetry in the tension/compression stress-strain response, the anisotropy in compression, and the viscoelastic phenomena that have been experimentally observed. To address these shortcomings, a number of modeling developments are proposed. In particular, it is suggested that explicit recognition of the rate dependency of the stress response of skeletal muscle in compression may provide significant benefits. Furthermore, explicit recognition of the high fluid content in skeletal muscle through the development of a poroelastic formulation may be more beneficial than further advances in micromechanical modeling based purely on a solid formulation.


  1. ArItan, S., Oyadiji, S. O., and Bartlett, R. M., A mechanical model representation of the in vivo creep behaviour of muscular bulk tissue. DOI: 10.1016/j.jbiomech.2008.06.004

  2. Audette, M. A., Hayward, V., Astley, O., Doyon, M., McCallister, G. A., and Chinzei, K., APC-based system architecture for real-time finite element-based tool-specific surgical simulation. DOI: 10.1016/j.ics.2004.03.294

  3. Best, T. M., McElhaney, J., Garrett, Jr., W. E., and Myers, B. S., Characterization of the passive responses of live skeletal muscle using the quasi-linear theory of viscoelasticity. DOI: 10.1016/0021-9290(94)90017-5

  4. Blemker, S. S., Pinsky, P. M., and Delp, S. L., A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii. DOI: 10.1016/j.jbiomech.2004.04.009

  5. Boel, M. and Reese, S., Micromechanical modelling of skeletal muscles based on the finite element method. DOI: 10.1007/s00419-009-0378-y

  6. Bosboom, E. M. H., Hesselink, M. K. C., Oomens, C. W. J., Bouten, C. V. C., Drost, M. R., and Baaijens, F. P. T., Passive transverse mechanical properties of skeletal muscle under in vivo compression. DOI: 10.1016/S0021-9290(01)00083-5

  7. Calvo, B., Ramírez, A., Alonso, A., Grasa, J., Soteras, F., Osta, R., and Munoz, M. J., Passive nonlinear elastic behaviour of skeletal muscle: Experimental results and model formulation. DOI: 10.1016/j.jbiomech.2009.08.032

  8. Davis, J., Kaufman, K. R., and Lieber, R. L., Correlation between active and passive isometric force and intramuscular pressure in the isolated rabbit tibialis anterior muscle. DOI: 10.1002/mus.21298

  9. Dkbiology, Muscle contraction—actin and myosin.

  10. Erdemir, A., McLean, S., Herzog, W., and van den Bogert, A. J., Model-based estimation of muscle forces exerted during movements. DOI: 10.1016/j.clinbiomech.2006.09.005

  11. Gielen, A., Oomens, C., Bovendeerd, P., Arts, T., and Janssen, J., A finite element approach for skeletal muscle using a distributed moment model of contraction. DOI: 10.1080/10255840008915267

  12. Hawkins, D. and Bey, M., A comprehensive approach for studying muscle-tendon mechanics. DOI: 10.1115/1.2895704

  13. Hill, A., The series elastic component of muscle. DOI: 10.1098/rspb.1950.0035

  14. Hill, A., First and Last Experiments of Muscle Mechanics.

  15. Huijing, P. A., Epimuscular myofascial force transmission: A historical review and implications for new research, international society of biomechanics muybridge award lecture. DOI: 10.1016/j.jbiomech.2008.09.027

  16. Humphrey, J. and Yin, F., On constitutive relations and finite deformations of passive cardiac tissue: 1. A pseudo-strain energy function. DOI: 10.1161/01.RES.65.3.805

  17. Huxley, A., Muscle contraction and theories of contraction.

  18. Ivancic, P. C., Ito, S., and Panjabi, M. M., Dynamic sagittal flexibility coefficients of the human cervical spine. DOI: 10.1016/j.aap.2006.10.015

  19. Johansson, T., Meier, P., and Blickhan, R., A finite-element model for the mechanical analysis of skeletal muscles. DOI: 10.1006/jtbi.2000.2109

  20. Krause, W., Muscle Tissue.

  21. Lim, Y.-J. and De, S., Real time simulation of nonlinear tissue response in virtual surgery using the point collocation-based method of finite spheres. DOI: 10.1016/j.cma.2006.05.015

  22. Linder-Ganz, E., Shabshin, N., Itzchak, Y., and Gefen, A., Assessment of mechanical conditions in sub-dermal tissues during sitting: A combined experimental-mri and finite element approach. DOI: 10.1016/j.jbiomech.2006.06.020

  23. Linder-Ganz, E., Shabshin, N., Itzchak, Y., Yizhar, Z., Siev-Ner, I., and Gefen, A., Strains and stresses in sub-dermal tissues of the buttocks are greater in paraplegics than in healthy during sitting. DOI: 10.1016/j.jbiomech.2007.10.011

  24. Lissner, H., Lebow, M., and Evans, F., Experimental studies on the relation between acceleration and intracranial pressure changes in man.

  25. Marjoux, D., Baumgartner, D., Deck, C., and Willinger, R., Head injury prediction capability of the HIC, HIP, SIMon and ULP criteria—new injury criteria for the head. DOI: 10.1016/j.aap.2007.12.006

  26. Martini, F., Fundamentals of Applied Anatomy and Physiology.

  27. Martins, J. A. C., Pires, E. B., Salvado, R., and Dinis, P. B., A numerical model of passive and active behavior of skeletal muscles. DOI: 10.1016/S0045-7825(97)00162-X

  28. McNamara, L. and Prendergast, P., Bone remodelling algorithms incorporating both strain and microdamage stimuli.

  29. Miller, K., Constitutive model of brain tissue suitable for finite element analysis of surgical procedures. DOI: 10.1016/S0021-9290(99)00010-X

  30. Morrow, D. A., Haut Donahue, T. L., Odegard, G. M., and Kaufman, K. R., Transversely isotropic tensile material properties of skeletal muscle tissue. DOI: 10.1016/j.jmbbm.2009.03.004

  31. Muggenthaler, H., von Merten, K., Peldschus, S., Holley, S., Adamec, J., Praxl, N., and Graw, M., Experimental tests for the validation of active numerical human models. DOI: 10.1016/j.forsciint.2007.12.005

  32. Palevski, A., Ittai-Glaich, I., Portnoy, S., Linder-Ganz, E., and Gefen, A., Stress relaxation of porcine gluteus muscle subjected to sudden transverse deformation as related to pressure sore modeling. DOI: 10.1115/1.2264395

  33. Raul, J., Deck, C., Willinger, R., and Ludes, B., Finite-element models of the human head and their applications in forensic practice. DOI: 10.1007/s00414-008-0248-0

  34. Tang, C. Y., Zhang, G., and Tsui, C. P., A 3D skeletal muscle model coupled with active contraction of muscle fibres and hyperelastic behaviour. DOI: 10.1016/j.jbiomech.2009.01.021

  35. Taylor, C. and Humphrey, J., Open problems in computational vascular biomechanics: Hemodynamics and arterial wall mechanics. DOI: 10.1016/j.cma.2009.02.004

  36. Trotter, J. and Purslow, P., Functional morphology of the endomysium in series fibered muscles. DOI: 10.1002/jmor.1052120203

  37. van den Bogert, A. J., Gerritsen, K. G. M., and Cole, G. K., Human muscle modelling from a user's perspective. DOI: 10.1016/S1050-6411(97)00028-X

  38. Van Loocke, M., Lyons, C. G., and Simms, C. K., A validated model of passive muscle in compression. DOI: 10.1016/j.jbiomech.2005.10.016

  39. Van Loocke, M., Lyons, C. G., and Simms, C. K., Viscoelastic properties of passive skeletal muscle in compression: Stress-relaxation behaviour and constitutive modelling. DOI: 10.1016/j.jbiomech.2008.02.007

  40. Van Loocke, M., Lyons, C. G., and Simms, C. K., Viscoelastic properties of passive skeletal muscle in compression: Cyclic behaviour. DOI: 10.1016/j.jbiomech.2009.02.022

  41. Vignos, P. and Lefkowitz, M., A biochemical study of certain skeletal muscle constituents in human progressive muscular dystrophy. DOI: 10.1172/JCI103869

  42. Wu, P. I. K. and Edelman, E. R., Structural biomechanics modulate intramuscular distribution of locally delivered drugs. DOI: 10.1016/j.jbiomech.2008.06.025

  43. Yamada, H., Strength of Biological Materials.

  44. Yucesoy, C. A., Koopman, B. H. F. J. M., Huijing, P. A., and Grootenboer, H. J., Three-dimensional finite element modeling of skeletal muscle using a two-domain approach: Linked fiber-matrix mesh model. DOI: 10.1016/S0021-9290(02)00069-6

  45. Wang, Z., Deurenberg, P., Wang, W., and Heymsfield, S., Proportion of adipose tissue-free body mass as skeletal muscle: Magnitude and constancy in men. DOI: 10.1002/(SICI)1520-6300(1997)9:4<487::AID-AJHB8>3.0.CO;2-T

Articles with similar content:

Jerry Westerweel
Nonlinear viscoelastic analysis of statistically homogeneous random composites
International Journal for Multiscale Computational Engineering, Vol.2, 2004, issue 4
Michal Sejnoha, R. Valenta, Jan Zeman
Nanoscience and Technology: An International Journal, Vol.8, 2017, issue 2
Alexey I. Shveykin, Peter V. Trusov, Nikita S. Kondratev
International Journal of Energetic Materials and Chemical Propulsion, Vol.7, 2008, issue 4
Gary A. Flandro
Biomechanical Basis of Vascular Tissue Engineering
Critical Reviews™ in Biomedical Engineering, Vol.27, 1999, issue 1-2
S. Q. Liu