High-frequency oscillations as a consequence of neglected serial damping in Hill-type muscle models

Biological Cybernetics

Volumn 97, Issue 1, 2007, Pages 63-79

  Günther, Michael ^a,b   Schmitt, Syn ^a,c   Wank, Veit ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DAMAGE DETECTION; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; MATHEMATICAL MODELS; VIBRATIONS (MECHANICAL);

CONTRACTILE MACHINERY; HIGH-FREQUENCY VIBRATIONS; HILL-TYPE MUSCLE MODELS; LOADING MASSES;

MUSCLE;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ELECTROSTIMULATION; HIGH FREQUENCY VENTILATION; LOCOMOTION; MECHANICAL STRESS; METHODOLOGY; MUSCLE CONTRACTION; PHYSIOLOGY; SKELETAL MUSCLE; SWINE; TENDON; WEIGHT BEARING;

ANIMALS; ELECTRIC STIMULATION; HIGH-FREQUENCY VENTILATION; LOCOMOTION; MODELS, BIOLOGICAL; MODELS, NEUROLOGICAL; MUSCLE CONTRACTION; MUSCLE, SKELETAL; STRESS, MECHANICAL; SWINE; TENDONS; WEIGHT-BEARING;

EID: 34547291906     PISSN: 03401200     EISSN: 14320770     Source Type: Journal    
DOI: 10.1007/s00422-007-0160-6     Document Type: Article

References (66)

1. Alexander RMcN (1988) Elastic mechanisms in animal movement. Cambrigde University Press, Cambridge
2. Alexander RMcN (2001) Damper for bad vibrations. Nature 414(6866):855-857
3. Biewener AA (1990) Biomechanics of mammalian terrestrial locomotion. Science 250(4984):1097-1103
4. Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22(11/12):1217-1227
5. Carrion-Vazquez M, Oberhauser AF, Fowler SB, Marszalek PE, Broedel SE, Clarke J, Fernandez JM (1999) Mechanical and chemical unfolding of a single protein: a comparison. Proc Natl Acad Sci USA 96(7):3694-3699
6. Cavagna GA (1970) Elastic bounce of the body. J Appl Physiol 29(3):279-282
7. Chow JW, Darling WG (1999) The maximum shortening velocity of muscle should be scaled with activation. J Appl Physiol 86(3):1025-1031
8. Currey JD (2002) Bones: structure and mechanics. Princeton University Press, Princeton, NJ
9. Davy DT, Audu ML (1987) A dynamic optimization technique for predicting muscle forces in the swing phase of gait. J Biomech 20(2):187-201
10. Denoth J (1985) The dynamic behaviour of a three link model of the human body during impact with the ground. In: Winter DA, Norman RW, Wells RP, Hayes KC, Patla AE (eds) Biomechanics 9-A, vol 5B of International Series on Biomechanics. Human Kinetics Publishers, Champaign, pp 102-106
11. Denoth J, Stüssi E, Csucs G, Danuser G (2002) Single muscle fiber contraction is dictated by inter-sarcomere dynamics. J Theor Biol 216(1):101-122
12. Epstein M, Herzog W (2003) Aspects of skeletal muscle modelling. Philos Trans R Soc Lond B 358(1437):1445-1452
13. Ettema GJ, Meijer K (2000) Muscle contraction history: modified Hill versus an exponential decay model. Biol Cybern 83(6):491-500
14. Gordon AM, Huxley AF, Julian FJ (1966) The variation in isometric tension with sarcomere length in vertebrate muscle fibers. J Physiol 184:170-192
15. Granzier HL, Labeit S (2006) The giant muscle protein titin is an adjustable molecular spring. Exerc Sport Sci Rev 34(2):50-53
16. Gruber K, Ruder H, Denoth J, Schneider K (1998) A comparative study of impact dynamics: wobbling mass model versus rigid body models. J Biomech 31(5):439-444
17. Günther M, Ruder H (2003) Synthesis of two-dimensional human walking: a test of the λ-model. Biol Cybern 89(2):89-106
18. Günther M, Sholukha VA, Keßler D, Wank V, Blickhan R (2003) Dealing with skin motion and wobbling masses in inverse dynamics. J Mech Med Biol 3(3/4):309-335
19. Hatze H (1977) A myocybernetic control model of skeletal muscle. Biol Cybern 25:103-119
20. Hatze H (1981) Myocybernetic control models of skeletal muscle-characteristics and applications. University of South Africa Press, Pretoria
21. Hill AV (1938) The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B 126:136-195
22. Julian FJ (1971) The effect of calcium on the force-velocity relation of briefly glycerinated frog muscle fibres. J Physiol 218:117-145
23. Katz B (1939) The relation between force and speed in muscular contraction. J Physiol 96:45-64
24. Ker RF (1981) Dynamic tensile properties of the plantaris tendon of sheep (Ovis aries). J Exp Biol 93:283-302
25. Ker RF, Wang XT, Pike AV (2000) Fatigue quality of mammalian tendons. J Exp Biol 203(Pt 8):1317-1327
26. Ker RF, Zioupos P (1997) Creep and fatigue damage of mammalian tendon and bone. Comments Theor Biol 4(2-3):151-181
27. Kistemaker DA, van Soest AJ, Bobbert MF (2006) Is equilibrium point control feasible for fast goal-directed single-joint movements? J Neurophysiol 95(5):2898-2912
28. Krause PC, Choi JS, McMahon TA (1995) The force-velocity curve in passive whole muscle is asymmetric about zero velocity. J Biomech 28(9):1035-1043
29. Krieg M (1992) Simulation und Steuerung biomechanischer Mehrkörpersysteme. Master's thesis. Eberhard-Karls-Universität, Tübingen, Germany
30. Lan G, Sun SX (2005) Dynamics of myosin-driven skeletal muscle contraction: I. Steady-state force generation. Biophys J 88(6):4107-4117
31. Lombardi V, Piazzesi G, Ferenczi MA, Thirlwell H, Dobbie I, Irving M (1995) Elastic distortion of myosin heads and repriming of the working stroke in muscle. Nature 374(6522):553-555
32. Lombardi V, Piazzesi G, Reconditi M, Linari M, Lucii L, Stewart A, Sun YB, Boesecke P, Narayanan T, Irving T, Irving M (2004) X-ray diffraction studies of the contractile mechanism in single muscle fibres. Philos Trans R Soc Lond B 359(1452):1883-1893
33. Marszalek PE, Lu H, Li H, Carrion-Vazquez M, Oberhauser AF, Schulten K, Fernandez JM (1999) Mechanical unfolding intermediates in titin modules. Nature 402(6757):100-103
34. McMahon TA, Cheng GC (1990) The mechanics of running: how does stiffness couple with speed? J Biomech 23(Suppl. 1):65-78
35. Meijer K, Grootenboer HJ, Koopman HF, van der Linden BJ, Huijing PA (1998) A Hill type model of rat medial gastrocnemius muscle that accounts for shortening history effects. J Biomech 31(6):555-563
36. Minajeva A, Kulke M, Fernandez JM, Linke WA (2001) Unfolding of titin domains explains the viscoelastic behavior of skeletal myofibrils. Biophys J 80(3):1442-1451
37. Pain MTG, Challis JH (2006) The influence of soft tissue movement on ground reaction forces, joint torques and reaction forces in drop landings. J Biomech 39(1):119-124
38. Petrofsky JS, Phillips CA (1981) The influence of temperature, initial length and electrical activity on force-velocity relationship of the medial gastrocnemius muscle of the cat. J Biomech 14(5):297-306
39. Piazzesi G, Lombardi V (1995) A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle. Biophys J 68(5):1966-1979
40. Piazzesi G, Lombardi V (1996) Simulation of the rapid regeneration of the actin-myosin working stroke with a tight coupling model of muscle contraction. J Muscle Res Cell Motil 17(1):45-53
41. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1994) Numerical recipes in C-the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge
42. Proske U, Morgan DL (1987) Tendon stiffness: methods of measurement and significance for the control of movement. A review. J Biomech 20(1):75-82
43. Reconditi M, Linari M, Lucii L, Stewart A, Sun YB, Boesecke P, Narayanan T, Fischetti RF, Irving T, Piazzesi G, Irving M, Lombardi V (2004) The myosin motor in muscle generates a smaller and slower working stroke at higher load. Nature 428(6982):578-581
44. Reinsch CH (1967) Smoothing by spline functions. Numerische Mathematik 10(3):177-183
45. Riemersma DJ, Schamhardt HC (1985) In vitro mechanical properties of equine tendons in relation to cross-sectional area and collagen content. Res Vet Sci 39(3):263-270
46. Rode C, Siebert T, Herzog W, Blickhan R (2006) The effects of parallel and series elastic components on estimated active muscle force (submitted to the J Biomech)
47. Schmalz T (1993a) Biomechanische Modellierung menschlicher Bewegung, vol 26 of Wissenschaftliche Schriftenreihe des Deutschen Sportbundes. Karl Hofmann, Schorndorf, Germany
48. Schmalz T (1993b) Die Nutzung biomechanischer Modelle zur Bestimmung rheologischer Eigenschaften des Muskel-Sehnen-Komplexes. In: Gutewort W, Schmalz T, Weiß T (eds), Symposium Oberhof: Aktuelle Hauptforschungsrichtungen der Biomechanik sportlicher Bewegungen, vol 55, Sankt Augustin, Germany, 1993. Deutsche Vereinigung für Sportwissenschaft (dvs), Academia, pp 102-108
49. Shadwick RE (1990) Elastic energy storage in tendons: mechanical differences related to function and age. J Appl Physiol 68(3):1033-1040
50. Shampine LF, Gordon MK (1975) Computer solution of ordinary differential equations: the initial value problem. W.H. Freeman & Co., San Francisco
51. Siebert T, Wagner H, Blickhan R (2003) Not all oscillations are rubbish: forward simulation of quick-release experiments. J Mech Med Biol 3(1):107-122
52. Stern JT (1974) Computer modeling of gross muscle dynamics. J Biomech 7:411-428
53. Telley IA, Denoth J, Ranatunga KW (2003) Inter-sarcomere dynamics in muscle fibres. A neglected subject? Adv Exp Med Biol 538:481-500
54. Tskhovrebova L, Trinick J (2002) Role of titin in vertebrate striated muscle. Philos Trans R Soc Lond B 357(1418):199-206
55. van Ingen Schenau GJ (1984) An alternative view to the concept of utilization of elastic energy. Hum Mov Sci 3:301-336
56. van Leeuwen JL (1992) Muscle function in locomotion. In: Alexander RMcN (ed) Advances in comparative and environmental physiology, vol 11, chap 7. Springer, Berlin, pp 191-250
57. van Soest AJ (1992) Jumping from structure to control: a simulation study of explosive movements. PhD thesis, Vrije Universiteit, Amsterdam
58. van Soest AJ, Bobbert MF (1993) The contribution of muscle properties in the control of explosive movements. Biol Cybern 69(3):195-204
59. Wakeling JM, Nigg BM (2001) Soft-tissue vibrations in the quadriceps measured with skin mounted transducers. J Biomech 34(4):539-543
60. Wank V (2000) Aufbau und Anwendung von Muskel-Skelett-Modellen. Habilitationsschrift der Friedrich-Schiller-Universität Jena
61. Wank V, Bauer R, Walter B, Kluge H, Fischer MS, Blickhan R, Zwiener U (2000) Accelerated contractile function and improved fatigue resistance of calf muscles in newborn piglets with IUGR. Am J Physiol Regul Integr Comp Physiol 278(2):R304-R310
62. Wank V, Fischer MS, Walter B, Bauer R (2006) Muscle growth and fiber type composition in hind limb muscles during postnatal development in pigs. Cells Tissues Organs 182(3-4):171-181
63. Wilson AM, Goodship AE (1994) Exercise-induced hyperthermia as a possible mechanism for tendon degeneration. J Biomech 27(7):899-905
64. Wilson AM, McGuigan MP, Su A, van den Bogert AJ (2001) Horses damp the spring in their step. Nature 414(6866):895-899
65. Zajac FE (1989) Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In: Bourne JR (ed) CRC critical reviews in biomedical engineering, vol 17. CRC Press, Boca Raton, pp 359-411
66. Zioupos P, Currey JD, Casinos A (2001) Tensile fatigue in bone: are cycles-, or time to failure, or both, important? J Theor Biol 210(3):389-399