A 3D-geometric model for the deformation of a transversally loaded muscle

Journal of Theoretical Biology

Volumn 298, Issue , 2012, Pages 116-121

  Siebert, Tobias ^a   Günther, Michael ^a,b   Blickhan, Reinhard ^a  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Biomechanics; Cylinder; Ellipsoid; Muscle contraction

Indexed keywords

BIOMECHANICS; DATA SET; DEFORMATION MECHANISM; GEOMETRY; MODEL TEST; MODEL VALIDATION; MUSCLE; THREE-DIMENSIONAL MODELING;

ANISOTROPIC STIFFNESS; ARTICLE; CONNECTIVE TISSUE; CONTROLLED STUDY; MATHEMATICAL MODEL; MUSCLE ISOMETRIC CONTRACTION; MUSCLE LENGTH; MUSCLE STIFFNESS; PREDICTION; PRIORITY JOURNAL; THREE DIMENSIONAL GEOMETRIC MODEL; VALIDATION STUDY; WEIGHT;

ANIMALS; ISOMETRIC CONTRACTION; MODELS, BIOLOGICAL; MUSCLE FIBERS, SKELETAL; MUSCLE, SKELETAL; RATS; WEIGHT-BEARING;

EID: 84856033779     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2012.01.009     Document Type: Article

References (45)

1. Almqvist G., Berndt B. Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the Ladies Diary. Am. Math. Mon. 1988, 95:585-608.
2. Azizi E., Roberts T.J. Biaxial strain and variable stiffness in aponeuroses. J. Physiol. 2009, 587(Pt 17):4309-4318.
3. Baskin R., Paolini P. Volume change and pressure development in muscle during contraction. Am. J. Physiol. 1967, 213(4):1025-1030.
4. Böl M., Reese S. Micromechanical modelling of skeletal muscles based on the finite element method. Comput. Methods Biomech. Biomed. Eng. 2008, 11(5):489-504.
5. Boriek A., Zhu D., Zeller M., Rodarte J. Inferences on force transmission from muscle fiber architecture of the canine diaphragm. Am. J. Physiol.-Regul. Integrative Comp. Physiol. 2001, 280(1):R156-R165.
6. Callister R., Callister R., Peterson E. Design and control of the head retractor muscle in a turtle, Pseudemys (Trachemys) scripta: I. Architecture and histochemistry of single muscle fibers. J. Comp. Neurol. 1992, 325(3):405-421.
7. Cull-Candy S., Miledi R., Nakajima Y., Uchitel O. Visualization of satellite cells in living muscle fibres of the frog. Proc. R. Soc. London B 1980, 209(1177):563-568.
8. Eldred E., Garfinkel A., Hsu E., Ounjian M., Roy R., Edgerton V. The physiological cross-sectional area of motor units in the cat tibialis anterior. Anat. Rec. 1993, 235(3):381-389.
9. Eldred E., Ounjian M., Roy R., Edgerton V. Tapering of the intrafascicular endings of muscle fibers and its implications to relay of force. Anat. Rec. 1993, 236(2):390-398.
10. Epstein M., Herzog W. Theoretical Models of Skeletal Muscle-Biological and Mathematical Considerations 1998, Wiley & Sons, Chichester.
11. Huijing P., Baan G. Extramuscular myofascial force transmission within the rat anterior tibial compartment: proximo-distal differences in muscle force. Acta Physiol. Scand. 2001, 173(3):297-311.
12. Iwamoto M., Miki K., Yang K.H. Development of a finite element model of the human shoulder to investigate the mechanical responses and injuries in side impact. JSME Int. J. Ser. C 2001, 44(4):1072-1081.
13. Johansson T., Meier P., Blickhan R. A finite-element model for the mechanical analysis of skeletal muscles. J. Theor. Biol. 2000, 206(1):131-149.
14. Kardel T. Niels Stensen's geometrical theory of muscle contraction (1667): a reappraisal. J. Biomech. 1990, 23(10):953-965.
15. Lee D., Glueck M., Khan A., Fiume E., Jackson K. A survey of modeling and simulation of skeletal muscle. ACM Trans. Graphics 2010, 28(4):1-13.
16. Linder-Ganz E., Yarnitzky G., Yizhar Z., Siev-Ner I., Gefen A. Real-time finite element monitoring of sub-dermal tissue stresses in individuals with spinal cord injury: toward prevention of pressure ulcers. Ann. Biomed. Eng. 2009, 37(2):387-400.
17. Mackerle J. Finite element crash simulations and impact-induced injuries: an addendum. A Bibliography (1998-2002). Shock Vib. Dig. 2003, 6:321-334.
18. McMahon T.A. Muscles, Reflexes, and Locomotion 1984, Princeton University Press, Princeton, NJ.
19. Meier P., Blickhan R. FEM-simulation of skeletal muscle: the influence of inertia during activation and deactivation. Skeletal Muscle Mechanics: From Mechanisms to Function 2000, 207-223. Wiley & Sons, Chichester, (Chapter 12). W. Herzog (Ed.).
20. Otten E., Hulliger M. A finite-elements approach to the study of functional architecture in skeletal muscle. Zoology 1995, 98:233-241.
21. Ounjian M., Roy R., Eldred E., Garfinkel A., Payne J., Armstrong A., Toga A., Edgerton V. Physiological and developmental implications of motor unit anatomy. J. Neurobiol. 1991, 22(5):547-559.
22. Pogogeff I., Murray M. Form and behavior of adult mammalian skeletal muscle in vitro. Anat. Rec. 1946, 95(3):321-335.
23. Ramanujan S. Modular equations and approximations to π. Q. J. Math. (Oxford) 1914, 45:355-372.
24. Ramanujan S. Notebooks 2 volumes 1957, Tata Institute of Fundamental Research, Bombay.
25. Ramanujan S. Collected Papers 1962, Chelsea, New York.
26. Richmond F., MacGillis D., Scott D. Muscle-fiber compartmentalization in cat splenius muscles. J. Neurophysiol. 1985, 53(4):868-885.
27. Röhrle O., Pullan A. Three-dimensional finite element modelling of muscle forces during mastication. J. Biomech. 2007, 40(15):3363-3372.
28. Scheepers F., Parent R., Carlson W., May S. Anatomy-based modeling of the human musculature. Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques. Annual Conference Series. ACM SIGGRAPH 1997, 163-172. Addison-Wesley. T. Whitted (Ed.).
29. Segal S., Cunningham S., Jacobs T. Motor nerve topology reflects myocyte morphology in hamster retractor and epitrochlearis muscles. J. Morphol. 2000, 246(2):103-117.
30. Siebert T., Rode C., Herzog W., Till O., Blickhan R. Nonlinearities make a difference: comparison of two common Hill-type models with real muscle. Biol. Cybern. 2008, 98(2):133-143.
31. Siebert T., Sust M., Thaller S., Tilp M., Wagner H. An improved method to determine neuromuscular properties using force laws - From single muscle to applications in human movements. Hum. Movement Sci. 2007, 26(2):320-341.
32. Siebert, T., Till, O., Blickhan, R., 2010. Muscle force is influenced by lateral muscle loading: experiment and simulation. In: 6th World Congress of Biomechanics (WCB). Singapore, p. 444.
33. Siebert, T., Till, O., Blickhan, R. Work partitioning of transversally loaded muscle: experimentation and simulation. Comput. Methods Biomech. Biomed. Eng., submitted for publication.
34. Stensen (Stenonis), N., 1667. Elementorum Myologiæ Specimen, seu Muscili Descriptio Geometrica, vol. 2. Stellae, Florence, pp. 61-111.
35. (see Kardel, T., 1990. Niels Stensen's geometrical theory of muscle contraction (1667): a reappraisal. J. Biomech. 23 (10), 953-965).
36. Swammerdam, J., 1663. Earliest known experimental evidence for volume constancy of skeletal muscle during contraction. After McMahon, T.A., 1984. Muscles, Reflexes, and Locomotion. Princeton University Press, Princeton, NJ; first published by quotation not before 1669.
37. see also Kardel, T., 1990. Niels Stensen's geometrical theory of muscle contraction (1667): a reappraisal. J.
38. van Leeuwen J., Spoor C. Modelling mechanically stable muscle architectures. Philos. Trans. R. Soc. London B 1992, 336(1277):275-292.
39. Van Loocke M., Lyons C.G., Simms C.K. Viscoelastic properties of passive skeletal muscle in compression: stress-relaxation behaviour and constitutive modelling. J. Biomech. 2008, 41(7):1555-1566.
40. van Rooij L., Bours R., van Hoof J., Mihm J., Ridella S., Bass C., Crandall J. The development, validation and application of a finite element upper extremity model subjected to air bag loading. Stapp Car Crash J. 2003, 47:55-78.
41. Verver M., van Hoof J., Oomens C., Wismans J., Baaijens F. A finite element model of the human buttocks for prediction of seat pressure distributions. Comput. Methods Biomech. Biomed. Eng. 2004, 7(4):193-203.
42. Wagner H., Siebert T., Ellerby D., Marsh R., Blickhan R. ISOFIT: a model-based method to measure muscle-tendon properties simultaneously. Biomech. Modeling Mechanobiol. 2005, 4(1):10-19.
43. Woittiez R., Huijing P., Boom H., Rozendal R. A three-dimensional muscle model: a quantified relation between form and function of skeletal muscles. J. Morphol. 1984, 182(1):95-113.
44. Yaniv Y., Juhaszova M., Wang S., Fishbein K., Zorov D., Sollott S. Analysis of mitochondrial 3D-deformation in cardiomyocytes during active contraction reveals passive structural anisotropy of orthogonal short axes. PLoS One 2011, 6(7).
45. Young M., Paul A., Rodda J., Duxson M., Sheard P. Examination of intrafascicular muscle fiber terminations: implications for tension delivery in series-fibered muscles. J. Morphol. 2000, 245(2):130-145.