Stochastic order parameter equation of isometric force production revealed by drift-diffusion estimates

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 5, 2006, Pages

  Frank, T D ^a   Friedrich, R ^a   Beek, P J ^b  

^a UNIVERSITY OF MÜNSTER   (Germany)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC NOISE; DIFFUSION; FORCE CONTROL; LINEAR CONTROL SYSTEMS; PARAMETER ESTIMATION; RANDOM PROCESSES;

DETERMINISTIC STABILITY; HUMAN MOTOR CONTROL; ISOMETRIC FORCES; STOCHASTIC ORDER PARAMETER EQUATIONS;

NONLINEAR EQUATIONS;

ADULT; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; EXERCISE; FEMALE; HUMAN; MALE; MECHANICAL STRESS; MUSCLE ISOMETRIC CONTRACTION; PHYSIOLOGY; SENSITIVITY AND SPECIFICITY; SKELETAL MUSCLE; STATISTICAL MODEL; STATISTICS;

ADULT; COMPUTER SIMULATION; EXERTION; FEMALE; HUMANS; ISOMETRIC CONTRACTION; MALE; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MUSCLE, SKELETAL; SENSITIVITY AND SPECIFICITY; STOCHASTIC PROCESSES; STRESS, MECHANICAL;

EID: 33750717870     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.051905     Document Type: Article

References (77)

1. K. Davids, S. Bennett, and K. Newell, Movement System Variability (Human Kinetics, Champaign, 2006).
2. S. Morrison and K. M. Newell, Exp. Brain Res. EXBRAP 0014-4819 110, 455 (1996).
3. P. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H. J. Freund, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3291 81, 3291 (1998).
4. R. Friedrich, S. Siegert, J. Peinke, S. Lück, M. Seifert, M. Lindemann, J. Raethjen, G. Deuschl, and G. Pfister, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00334-0 271, 217 (2000).
5. J. J. Collins and C. J. De Luca, Exp. Brain Res. EXBRAP 0014-4819 10.1007/BF00229788 95, 308 (1993).
6. J. J. Collins and C. J. De Luca, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.764 73, 764 (1994).
7. M. A. Riley, S. Wong, S. Mitra, and M. T. Turvey, Exp. Brain Res. EXBRAP 0014-4819 10.1007/s002210050211 117, 165 (1997).
8. K. M. Newell, S. M. Slobounov, E. S. Slobounova, and P. C. M. Molenaar, Exp. Brain Res. EXBRAP 0014-4819 113, 158 (1997).
9. R. J. Peterka, Biol. Cybern. BICYAF 0340-1200 10.1007/s004220050587 82, 335 (2000).
10. T. D. Frank, A. Daffertshofer, and P. J. Beek, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.011905 63, 011905 (2001).
11. M. Duarte and V. M. Zatsiorsky, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01)00188-8 283, 124 (2001).
12. A. Priplata, J. Niemi, M. Salen, J. Harry, L. A. Lipsitz, and J. J. Collins, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.238101 89, 238101 (2002).
13. L. Stark, F. W. Campbell, and J. Atwood, Nature (London) NATUAS 0028-0836 182, 857 (1958).
14. S. Usui and L. Stark, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00387209 45, 13 (1982).
15. A. Longtin, J. G. Milton, J. E. Bos, and M. C. Mackey, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.6992 41, 6992 (1990).
16. J. L. Cabrera and J. G. Milton, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.158702 89, 158702 (2002).
17. K. Vasilakov and A. Beuter, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.1993.1196 165, 389 (1993).
18. S. Morrison and K. M. Newell, J. Motor Behav. JMTBAB 0022-2895 30, 323 (1998).
19. A. B. Slifkin and K. M. Newell, J. Exp. Psychol. Hum. Percept. Perform. JPHPDH 0096-1523 25, 837 (1999).
20. P. M. Fitts, J. Exp. Psychol. JEPSAK 0022-1015 47, 381 (1954).
21. G. S. Schöner, H. Haken, and J. A. S. Kelso, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00336995 53, 247 (1986).
22. J. P. Scholz, J. A. S. Kelso, and G. S. Schöner, Phys. Lett. A PYLAAG 0375-9601 123, 390 (1987).
23. C. E. Peper, P. J. Beek, and P. C. W. van Wieringen, J. Exp. Psychol. Hum. Percept. Perform. JPHPDH 0096-1523 10.1037//0096-1523.21.5.1117 21, 1117 (1995).
24. E. L. Amazeen, P. G. Amazeen, P. J. Treffner, and M. T. Turvey, J. Exp. Psychol. Hum. Percept. Perform. JPHPDH 0096-1523 23, 1552 (1997).
25. Y. Chen, M. Ding, and J. A. Scott Kelso, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.4501 79, 4501 (1997).
26. A. Daffertshofer, C. van den Berg, and P. J. Beek, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00044-5 132, 243 (1999).
27. D. Sternad, W. J. Dean, and K. M. Newell, J. Motor Behav. JMTBAB 0022-2895 32, 249 (2000).
28. A. A. Post, C. E. Peper, A. Daffertshofer, and P. J. Beek, Biol. Cybern. BICYAF 0340-1200 10.1007/s004220000177 83, 443 (2000).
29. G. Madison, J. Exp. Psychol. Hum. Percept. Perform. JPHPDH 0096-1523 27, 411 (2001).
30. H. Haken, Synergetics: Introduction and Advanced Topics (Springer, Berlin, 2004).
31. W. Horsthemke and R. Lefever, Noise-induced Transitions (Springer, Berlin, 1984).
32. T. S. Biro and A. Jakovac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.132302 94, 132302 (2005).
33. P. B. Matthews, J. Physiol. (London) JPHYA7 0022-3751 492, 597 (1996).
34. C. M. Harris and D. M. Wolpert, Nature (London) NATUAS 0028-0836 10.1038/29528 394, 780 (1998).
35. M. T. Turvey, Am. Psychol. AMPSAB 0003-066X 45, 938 (1990).
36. P. J. Beek, C. E. Peper, and D. F. Stegeman, Hum. Mov. Sci. HMSCDO 0167-9457 10.1016/0167-9457(95)00028-5 14, 573 (1995).
37. J. A. S. Kelso, Dynamic Patterns-The Self-organization of Brain and Behavior (MIT Press, Cambridge, 1995).
38. H. Haken, Principles of Brain Functioning (Springer, Berlin, 1996).
39. D. Corbetta and B. Vereijken, Int. J. Sport Psychol. 30, 507 (1999).
40. R. Friedrich and J. Peinke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.863 78, 863 (1997).
41. R. Friedrich and J. Peinke, Photochem. Photobiol. PHCBAP 0031-8655 102, 147 (1997).
42. C. Renner, J. Peinke, R. Friedrich, O. Chanal, and B. Chabaud, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.124502 89, 124502 (2002).
43. H. U. Bödeker, M. C. Röttger, A. W. Liehr, T. D. Frank, R. Friedrich, and H. G. Purwins, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67. 056220 67, 056220 (2003).
44. H. U. Bödeker, A. Liehr, M. C. Röttger, T. D. Frank, R. Friedrich, and H. G. Purwins, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/ 1/062 6, 62 (2004).
45. R. Friedrich, J. Peinke, and C. Renner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5224 84, 5224 (2000).
46. C. Renner, J. Peinke, and R. Friedrich, Physica A PHYADX 0378-4371 10.1016/S0378-4371(01)00269-2 298, 499 (2001).
47. G. R. Jafari, S. M. Fazeli, F. Ghasemi, S. M. Vaez Allaei, M. R. Tabar, A. Iraji Zad, and G. Kavei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.226101 91, 226101 (2002).
48. M. Waechter, F. Riess, T. Schimmel, U. Wendt, and J. Peinke, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00317-4 41, 259 (2004).
49. P. Sangpour, G. R. Jafari, O. Akhavan, A. Z. Moshfegh, and M. R. Tabar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.155423 71, 155423 (2005).
50. S. Kriso, R. Friedrich, J. Peinke, and P. Wagner, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00288-8 299, 287 (2002).
51. T. Kuusela, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.031916 69, 031916 (2004).
52. H. Risken, The Fokker-Planck Equation-Methods of Solution and Applications (Springer, Berlin, 1989).
53. M. Kac, in Selected Papers on Noise and Stochastic Processes, edited by, N. Wax, (Dover, New York, 1947), pp. 295-317.
54. H. Larralde, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.027102 69, 027102 (2004).
55. T. D. Frank, Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer, Berlin, 2005).
56. S. Guillouzic, I. L'Heureux, and A. Longtin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.3970 59, 3970 (1999).
57. T. D. Frank, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.011112 72, 011112 (2005).
58. P. Tass, J. Kurths, M. G. Rosenblum, G. Guasti, and H. Hefter, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.R2224 54, R2224 (1996).
59. U. Langenberg, H. Hefter, K. R. Kessler, and J. D. Crooke, Exp. Brain Res. EXBRAP 0014-4819 10.1007/s002210050268 118, 161 (1998).
60. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Beach, New York, 1963), Vol. 1.
61. J. M. Sancho, M. S. Miguel, S. L. Katz, and J. D. Gunton, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.26.1589 26, 1589 (1982).
62. P. Hänggi, T. J. Mroczkowski, F. Moss, and P. V. E. McClintock, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.695 32, 695 (1985).
63. M. Gitterman, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/27/101 32, L293 (1999).
64. K. Patanarapeelert, T. D. Frank, R. Friedrich, P. J. Beek, and I. M. Tang (unpublished).
65. D. F. Hoyt and C. R. Taylor, Nature (London) NATUAS 0028-0836 10.1038/292239a0 292, 239 (1981).
66. R. M. Alexander, Physiol. Rev. PHREA7 0031-9333 69, 1199 (1989).
67. E. Henneman, G. Somjen, and D. O. Carpenter, J. Physiol. (London) JPHYA7 0022-3751 28, 560 (1965).
68. E. Henneman, in Integration in the Nervous System, edited by, H. Asanuma, and, V. J. Wilson, (Igaku Shoin, Tokyo, 1979), pp. 13-25.
69. R. A. Conwit, D. Stashuk, B. Tracy, M. McHugh, W. F. Brown, and E. J. Metter, J. Clin. Neuropsychol ZZZZZZ 0165-0475 110, 1270 (1999).
70. T. D. Frank, P. J. Beek, and R. Friedrich, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.021912 68, 021912 (2003).
71. T. D. Frank, P. J. Beek, and R. Friedrich, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.06.012 328, 219 (2004).
72. T. D. Frank, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.061104 69, 061104 (2004).
73. T. D. Frank and R. Friedrich, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.08.031 347, 65 (2005).
74. T. D. Frank and P. Beek, J. Stat. Mech.: Theory Exp. ZZZZZZ 1742-5468 (2005), P10010.
75. Isometric force is also referred to as static force indicating that it does not involve a limb movement but rather holding a fixed limb position.
76. Correlation time is defined here implicitly by means of the autocorrelation function ζ(t)ζ (t′) =2 τ-1 exp{-|t- t′ |/τ}.
77. This argument assumes that the noise sources of the motor units are uncorrelated.