A physiologically based, multi-scale model of skeletal muscle structure and function

Frontiers in Physiology

Volumn 3 SEP, Issue , 2012, Pages

  Rohrle O ^a   Davidson, J B ^b   Pullan, A J ^c  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Continuum mechanics; Excitation contraction coupling; Motor unit recruitment; Multi scale; Skeletal muscle mechanics; Tibialis anterior

Indexed keywords

EID: 84867115837     PISSN: None     EISSN: 1664042X     Source Type: Journal    
DOI: 10.3389/fphys.2012.00358     Document Type: Article

References (62)

1. Andreassen, S., and Arendt-Nielsen, L. (1987). Muscle fibre conduction velocity in motor units of the human tibial muscle: a new size principle parameter. J. Physiol. 391, 561-571.
2. Aquilonius, S., Askmark, H., Gillberg, P., Nandedkar, S., Olsson, Y., and Stalberg, E. (1984). Topographical localization of motor endplates in cryosections of whole human muscles. Muscle Nerve 7, 287-293.
3. Bellemare, F., Woods, J. J., Johansson, R., and Bigland-Ritchie, B. (1983). Motor-unit discharge rates in maximal voluntary contractions of three human muscles. J. Neurophysiol. 50, 1380-1392.
4. Blemker, S., Pinsky, P., and Delp, S. (2005). A 3D model of muscle reveals the causes of nonuniform strains in the biceps brachii. J. Bio-mech. 38, 657-665.
5. Bodine-Fowler, S., Garfinkel, A., Roy, R., and Edgerton, V. (1990). Spatial distribution of muscle fibers within the territory of a motor unit. Muscle Nerve 13, 1133-1145.
6. Böl, M., Pipetz, A., and Reese, S. (2009). Finite element model for the simulation of skeletal muscle fatigue. Materwiss. Werksttech. 40, 5-12.
7. Böl, M., and Reese, S. (2008). Micromechanical modelling of skeletal muscles based on the finite element method. Comput. Methods Biomech. Biomed. Engin. 11, 489-504.
8. Böl, M., Weikert, R., and Weichert, C. (2011).A coupled electromechanical model for the excitation-dependent contraction of skeletal muscle. J. Mech. Behav. Biomed. Mater. 4, 1299.
9. Bradley, C. P., Pullan, A. J., and Hunter, P. J. (1997). Geometric modeling of the human torso using cubic hermite elements. Ann. Biomed. Eng. 25, 96-111.
10. Brand, R., Pedersen, D., and Friederich, J. (1986). The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J. Bio-mech. 19, 589-596.
11. Broman, H., De Luca, C. J., and Mambrito, B. (1985). Motor unit recruitment and firing rates interaction in the control of human muscles. Brain Res. 337, 311-319.
12. Bryant, S. H. (1969). Cable properties of external intercostal muscle fibres from myotinic and nonmyotonic goats. J. Physiol. 204, 539-550.
13. Cisi, R., and Kohn, A. (2008). Simulation system of spinal cord motor nuclei and associated nerves and muscles, in a web-based architecture. J. Comput. Neurosci. 25, 520-542.
14. De Luca, C. J., LeFever, R. S., McCue, M. P., and Xenakis, A. P. (1982). Control scheme governing concurrently active human motor units during voluntary contractions. J. Physiol. 329, 129-142.
15. Do, A. D. V., and Thomas, C. K. (2005). Firing rates of motor units during strong dynamic contractions. Muscle Nerve 32, 316-325.
16. Duchateau, J., Semmler, J., and Enoka, R. (2006). Training adaptations in the behaviour of human motor units. J. Appl. Physiol. 101, 1766-1775.
17. Enoka, R. M., and Fuglevand, A. J. (2001). Motor unit physiology:some unresolved issues. Muscle Nerve 24, 4-17.
18. Fernandez, J. W., Buist, M. L., Nickerson, D. P., and Hunter, P. J. (2005). Modellingthe passive andnerveactivated response of the rectus femoris muscle to a flexion loading: a finite element framework. Med. Eng. Phys. 27, 862-870.
19. Fuglevand, A. J., Winter, D. A., and Patla, A.E.(1993).Modelsof recruitment and rate coding organization in motor unit pools. J. Neurophysiol. 70, 2470-2488.
20. Fukunaga, T., Ichinose, Y., Ito, M., Kawakami, Y., and Fukashiro, S. (1997). Determination of fascicle length and pennation in a contracting human muscle in vivo. J. Appl. Physiol. 82, 354.
21. Grimby, L., and Hannerz, J. (1977). Firing rate and recruitment order of toe extensor motor units in different modes of voluntary contraction. J. Physiol. 264, 865-879.
22. Heckman, C. J. (1994). Computer simulations of the effects of different synaptic input systems on the steady-state input-output structure of the motoneuron pool. J. Neuro-physiol. 71, 1727-1739.
23. Heckman, C. J., and Binder, M. D. (1988). Analysis of effective synaptic currents generated by homonymous ia afferent fibers in motoneurons of the cat. J. Neurophysiol. 60, 1946-1966.
24. Henneman, E., and Olson, C. (1965). Relations between structure and function in the design of skeletal muscles. J. Neurophysiol. 28, 581-598.
25. Henneman, E., Somjen, G., and Carpenter, D. (1965a). Excitability and inhibitibility of motoneurons of different sizes. J. Neurophysiol. 28, 599-620.
26. Henneman, E., Somjen, G., and Carpenter, D. (1965b). Functional significance of cell size in spinal motoneurons. J. Neurophysiol. 28, 560-580.
27. Henriksson-Larsén, K. B., Lexell, J., and Sjöström, M. (1983). Distribution of different fibre types in human skeletal muscles. I. Method for the preparation and analysis of cross-sections of whole tibialis anterior. Histochem. J. 15, 167-178.
28. Hill, A. V. (1938). The heat of shortening and the dynamic constraints of muscle. Proc. R. Soc. Lond. B Biol. Sci. 126, 136-195.
29. Hindmarsh, A. C. (1982). Odepack, a systematized collection of ode solvers. IMACS Trans. Sci. Comput. 1, 55-64.
30. Hodgkin, A., and Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500-544.
31. Holzapfel, G. A. (2004). Nonlinear Solid Mechanics: A Continuum Approach for Engineering. West Sussex: John Wiley and Sons, Ltd.
32. Huxley, A. F. (1957). Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7, 255-318.
33. Johansson, T., Meier, P., and Blickhan, R. (2000). A finite-element model for the mechanical analysis of skeletal muscles. J. Theor. Biol. 206, 131-149.
34. Kamen, G., and Du, D. C. C. (1999). independence of motor unit recruitment and rate modulation during precision force control. Neuroscience 88, 643-653.
35. Kim, J. H. K., Davidson, J. B., Röhrle, O., Soboleva, T. K., and Pullan, A. J. (2007). Anatomically based lower limb nerve model for electrical stimulation. Biomed. Eng. Online 6, 48.
36. Lansdown, D. A., Ding, A., Wadington, M., Hornberger, J. L., and Damon, B. M. (2007). Quantitative diffusion tensor MRI-based fiber tracking of human skeletal muscle. J. Appl. Physiol. 103, 673-681.
37. Lemos, R. R., Rocke, J., Baranoski, G. V. G., Kawakami, Y., and Kurihara, T. (2005). Modeling and simulating the deformation of human skeletal muscle based on anatomy and physiology. Comput. Animat. Virtual Worlds 16, 319-330.
38. Lexell, J., Downham, D., and Sjöström, M. (1986). Distribution of different fibre types in human skeletal muscles. J. Neurol. Sci. 72, 211-222.
39. Lloyd, C., Lawson, J., Hunter, P., and Nielsen, P. (2008). The cellML model repository. Bioinformatics 24, 2122-2123.
40. Maganaris, C. N. (2001). Force-length characteristics of in vivo human skeletal muscle. Acta Physiol. Scand. 172, 279-285.
41. Maganaris, C. N., Baltzopoulos, V., Ball, D., and Sargeant, A. J. (2001). In vivo specific tension of human skeletal muscle. J. Appl. Physiol. 90, 865-872.
42. McNeil, C. J., Doherty, T. J., Stashuk, D. W., and Rice, C. L. (2005). Motor unit number estimates in the tibialis anterior muscle of young, old, and very old men. Muscle Nerve 31, 461-467.
43. McNulty, P. A., and Cresswell, A. G. (2004). Recruitment of single human low-threshold motor units with increasing load at different muscle lengths. J. Electromyogr. Kinesiol. 14, 369-377.
44. Miller, A. E. J., MacDougall, J. D., Tarnopolsky, M. A., and Sale, D. G. (1993). Gender differences in strength and muscle fiber characteristics. Eur. J. Appl. Physiol. 66, 254-262.
45. Monti, R., Roy, R., Hodgson, J., and Edgerton, V. (1999). Transmission of forces within mammalian skeletal muscles. J. Biomech. 32, 371-380.
46. Monti, R. J., Roy, R. R., and Edgerton, V. R. (2001). Role of motor unit structure in defining function. Muscle Nerve 24, 848-866.
47. Oomens, C. W. J., Maenhout, M., Van Oijen, C. H., Drost, M. R., and Baaijens, F. P. (2003). Finite element modelling of contracting skeletal muscle. Philos. Trans. R. Soc. B Biol. Sci. 358, 1453-1460.
48. Petzold, L. R. (1983). Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J. Sci. Stat. Comput. 4, 136-148.
49. Polgar, J., Johnson, M. A., Weightman, D., and Appleton, D. (1973). Data on fibre size in thirty-six human muscles: an autopsy study. J. Neurol. Sci. 19, 307-318.
50. Pullan, A. J., Buist, M. L., and Cheng, L. K. (2005). Mathematically Mod-elling the Electrical Activity of the Heart. Singapore: World Scientific Publishing Co. Pte. Ltd.
51. Röhrle, O. (2010). Simulating the electro-mechanical behavior of skeletal muscles. Comput. Sci. Eng. 12, 48-58.
52. Röhrle, O., Davidson, J. B., and Pullan, A. J. (2008). Bridging scales: a three-dimensional electromechanical finite element model of skeletal muscle. SIAM J. Sci. Comput. 30, 2882-2904.
53. Röhrle, O., and Pullan, A. J. (2007). Three-dimensional finite element modelling of muscle forces during mastication. J. Biomech. 40, 3363-3372.
54. Roy, R., Garfinkel, A., Ounjian, M., Payne, J., Hirahara, A., Hsu, E., and Edgerton, V. (1995). Threedimensional structure of cat tibialis anterior motor units. Muscle Nerve 18, 1187-1195.
55. Rush, S., Abildskov, J. A., and McFee, R. (1963). Resistivity of body tissues at low frequencies. Circ. Res. 12, 40-50.
56. Schwann, H. P., and Kay, C. F. (1957). The conductivity of living tissues. Ann. N. Y. Acad. Sci. 65, 1007-10013.
57. Shorten, P. R., O'Callaghan, P., Davidson, J. B., and Soboleva, T. K. (2007). A mathematical model of fatigue in skeletal muscle force contraction. J. Muscle Res. Cell. Motil. 28, 293-313.
58. Sjöström, M., Lexell, J., Eriksson, A., and Taylor, C. C. (1991). Evidence of fibre hyperplasia in human skeletal muscles from healthy young men? Eur. J. Appl. Physiol. 62, 301-304.
59. Spitzer, V. M., and Whitlock, D. G. (1998). National Library of Med-icine: Atlas of the Visible Human Male -Reverse Engineering of the Human Body. Sudbury, MA: Jones and Bartlett Publishers.
60. Winters, J. M., and Stark, L. (1987). Muscle models: what is gained and what is lost by varying model complexity. Biol. Cybern. 55, 403-420.
61. Wuerker, R., McPhedran, A., and Henneman, E. (1965). Properties of motor units in a heterogeneous pale muscle (m. gastrocnemius) of the cat. J. Neurophysiol. 28, 85-99.
62. Yao, W., Fuglevand, A. J., and Enoka, R. M. (2000). Motor-unit synchronization increases EMG amplitude and decreases force steadiness of simulated contractions. J. Neurophysiol. 83, 441-452.