Mass-spring-damper modelling of the human body to study running and hopping-an overview

Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine

Volumn 225, Issue 12, 2011, Pages 1121-1135

  Nikooyan, A A ^a   Zadpoor, A A ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

damping; ground reaction force; mechanical modelling; passive and active models; shoe ground model; stiffness

Indexed keywords

ACTIVE MODELS; DAMPING PROPERTY; EXTERNAL LOADS; GOVERNING EQUATIONS OF MOTION; GROUND REACTION FORCES; GROUND STIFFNESS; HUMAN BODIES; MASS SPRING DAMPER; MASS-SPRING-DAMPER MODELS; MECHANICAL MODELLING; MULTI-BODY MODELS; POSSIBLE FUTURES; RESEARCH TRENDS; SOFT TISSUE; STIFFNESS PROPERTIES; PASSIVE AND ACTIVE MODELS; SHOE-GROUND MODELS; STIFFNESS AND DAMPING;

AUTOMOBILE SEATS; DAMPING; EQUATIONS OF MOTION; BIOMECHANICS; BIOPHYSICS; HISTOLOGY; MECHANICAL PROPERTIES; TISSUE;

STIFFNESS;

ALGORITHM; BIOLOGICAL MODEL; BIOMECHANICS; BODY WEIGHT; ELASTICITY; HUMAN; LIMB; NONLINEAR SYSTEM; PHYSIOLOGY; REVIEW; RUNNING; SHOE; SKELETAL MUSCLE; VIBRATION;

ALGORITHMS; BIOMECHANICS; BODY WEIGHT; ELASTICITY; EXTREMITIES; HUMANS; MODELS, BIOLOGICAL; MUSCLE, SKELETAL; NONLINEAR DYNAMICS; RUNNING; SHOES; VIBRATION;

EID: 84857522554     PISSN: 09544119     EISSN: 20413033     Source Type: Journal    
DOI: 10.1177/0954411911424210     Document Type: Review

References (72)

1. Liu W., Nigg B. M.. A mechanical model to determine the influence of masses and mass distribution on the impact force during running. J. Biomech.. 2000 ; 33 (2). 219-224 (Pubitemid 30009840)
2. Bullimore S. R., Burn J. F.. Ability of the planar spring-mass model to predict mechanical parameters in running humans. J. Theor. Biol.. 2007 ; 248 (4). 686-695 (Pubitemid 47429697)
3. Blickhan R.. The spring-mass model for running and hopping. J. Biomech.. 1989 ; 22 (11-12). 1217-1227 (Pubitemid 20097590)
4. McMahon T. A., Cheng G. C.. The mechanics of running: how does stiffness couple with speed?. J. Biomech.. 1990 ; 23 (Suppl. 1). 65-78
5. Farley C. T., González O.. Leg stiffness and stride frequency in human running. J. Biomech.. 1996 ; 29 (2). 181-186 (Pubitemid 26010598)
6. Dalleau G., Belli A., Bourdin M., Lacour J. R.. The spring-mass model and the energy cost of treadmill running. Eur. J. Appl. Physiol.. 1998 ; 77 (3). 257-263 (Pubitemid 28107795)
7. Heise G. D., Martin P. E.. 'Leg spring' characteristics and the aerobic demand of running. Med. Sci. Sports Exerc.. 1998 ; 30 (5). 750-754 (Pubitemid 28211001)
8. Farley C. T., Glasheen J., McMahon T. A.. Running springs: speed and animal size. J. Exp. Biol.. 1993 ; 185 (1). 71-86
9. Arampatzis A., Brüggemann G.-P., Metzler V.. The effect of speed on leg stiffness and joint kinetics in human running. J. Biomech.. 1999 ; 32 (12). 1349-1353 (Pubitemid 29490880)
10. Ferris D. P., Louie M., Farley C. T.. Running in the real world: adjusting leg stiffness for different surfaces. Proc. R. Soc. B, Biol. Sci.. 1998 ; 265 (1400). 989-994 (Pubitemid 28271728)
11. Kerdok A. E., Biewener A. A., McMahon T. A., Weyand P. G., Herr H. M.. Energetics and mechanics of human running on surfaces of different stiffnesses. J. Appl. Physiol.. 2002 ; 92 (2). 469-478 (Pubitemid 34671009)
12. Dutto D. J., Smith G. A.. Changes in spring-mass characteristics during treadmill running to exhaustion. Med. Sci. Sports Exerc.. 2002 ; 34 (8). 1324-1331 (Pubitemid 34840032)
13. Donelan J. M., Kram R.. Exploring dynamic similarity in human running using simulated reduced gravity. J. Exp. Biol.. 2000 ; 203 (16). 2405-2415
14. He J. P., Kram R., McMahon T. A.. Mechanics of running under simulated low gravity. J. Appl. Physiol.. 1991 ; 71 (3). 863-870
15. Seyfarth A., Geyer H., Gunther M., Blickhan R.. A movement criterion for running. J. Biomech.. 2002 ; 35 (5). 649-655 (Pubitemid 34295770)
16. Farley C. T., Blickhan R., Saito J., Taylor C. R.. Hopping frequency in humans: a test of how springs set stride frequency in bouncing gaits. J. Appl. Physiol.. 1991 ; 71 (6). 2127-2132
17. Hobara H., Inoue K., Gomi K., Sakamoto M., Muraoka T., Iso S., Kanosue K.. Continuous change in spring-mass characteristics during a 400-m sprint. J. Sci. Med. Sport. 2009 ; 13 (2). 256-261
18. Butler R. J., Crowell H. P., Davis I. M.. Lower extremity stiffness: implications for performance and injury. Clin. Biomech.. 2003 ; 18 (6). 511-517 (Pubitemid 36793989)
19. Blum Y., Lipfert S. W., Seyfarth A.. Effective leg stiffness in running. J. Biomech.. 2009 ; 42 (14). 2400-2405
20. Hunter I.. A new approach to modeling vertical stiffness in heel-toe distance runners. J. Sports Sci. Med.. 2003 ; 2: 139-143
21. Bullimore S. R., Burn J. F.. Consequences of forward translation of the point of force application for the mechanics of running. J. Theor. Biol.. 2006 ; 238 (1). 211-219 (Pubitemid 41737809)
22. Cavagna G. A.. Force platforms as ergometers. J. Appl. Physiol.. 1975 ; 39 (1). 174-179
23. Cavagna G. A., Franzetti P., Heglund N. C., Willems P.. The determinants of the step frequency in running, trotting and hopping in man and other vertebrates. J. Physiol.. 1988 ; 399: 81-92
24. McMahon T. A., Valiant G., Frederick E. C.. Groucho running. J. Appl. Physiol.. 1987 ; 62 (6). 2326-2337 (Pubitemid 17124610)
25. Zadpoor A. A., Nikooyan A. A.. The relationship between lower-extremity stress fractures and the ground reaction force: a systematic review. Clin. Biomech.. 2010 ; 26 (1). 23-28
26. Zadpoor A. A., Nikooyan A. A., Arshi A. R.. A model-based parametric study of impact force during running. J. Biomech.. 2007 ; 40 (9). 2012-2021 (Pubitemid 46843003)
27. Bennell K., Crossley K., Jayarajan J., Walton E., Warden S., Kiss Z. S., Wrigley T.. Ground reaction forces and bone parameters in females with tibial stress fracture. Med. Sci. Sports Exerc.. 2004 ; 36 (3). 397-404 (Pubitemid 38298690)
28. Creaby M. W., Dixon S. J.. External frontal plane loads may be associated with tibial stress fracture. Med. Sci. Sports Exerc.. 2008 ; 40 (9). 1669-1674
29. Crossley K., Bennell K. L., Wrigley T., Oakes B. W.. Ground reaction forces, bone characteristics, and tibial stress fracture in male runners. Med. Sci. Sports Exerc.. 1999 ; 31 (8). 1088-1093 (Pubitemid 29395226)
30. Dixon S. J., Creaby M. W., Allsopp A. J.. Comparison of static and dynamic biomechanical measures in military recruits with and without a history of third metatarsal stress fracture. Clin. Biomech.. 2006 ; 21 (4). 412-419 (Pubitemid 43276395)
31. Divert C., Mornieux G., Baur H., Mayer F., Belli A.. Mechanical comparison of barefoot and shod running. Int. J. Sports Med.. 2005 ; 26 (7). 593-598 (Pubitemid 41291183)
32. Grimston S. K., Engsberg J. R., Kloiber R., Loiber R., Hanley D. A.. Bone mass, external loads, and stress fractures in female runners. J. Appl. Biomech.. 1991 ; 7 (3). 293-302
33. Wheat J. S., Bartlett R. M., Milner C. E., Mullineaux D. R.. The effect of different surfaces on ground reaction forces during running: a single-individual design approach. J. Hum. Mov. Stud.. 2003 ; 44 (5). 353-364 (Pubitemid 36618611)
34. Alexander R. M., Bennett M. B., Ker R. F.. Mechanical properties and function of the paw pads of some mammals. J. Zool.. 1986 ; 209 (3). 405-419
35. Mizrahi J., Susak Z.. In-vivo elastic and damping response of the human leg to impact forces. J. Biomech. Engng, Trans. ASME. 1982 ; 104 (1). 63-66
36. Nevzat Özgüven H., Berme N.. An experimental and analytical study of impact forces during human jumping. J. Biomech.. 1988 ; 21 (12). 1061-1066 (Pubitemid 19012938)
37. Derrick T. R., Caldwell G. E., Hamill J.. Modeling the stiffness characteristics of the human body while running with various stride lengths. J. Appl. Biomech.. 2000 ; 16 (1). 36-51 (Pubitemid 30112185)
38. Kim W., Voloshin A. S., Johnson S. H.. Modeling of heel strike transients during running. Hum. Mov. Sci.. 1994 ; 13 (2). 221-244 (Pubitemid 124013764)
39. Nigg B. M., Liu W.. The effect of muscle stiffness and damping on simulated impact force peaks during running. J. Biomech.. 1999 ; 32 (8). 849-856 (Pubitemid 29287107)
40. Yue Z., Mester J.. A model analysis of internal loads, energetics, and effects of wobbling mass during the whole-body vibration. J. Biomech.. 2002 ; 35 (5). 639-647 (Pubitemid 34292509)
41. Yue Z., Mester J.. A modal analysis of resonance during the whole-body vibration. Stud. Appl. Math.. 2004 ; 112 (3). 293-314 (Pubitemid 38472465)
42. Zadpoor A. A., Nikooyan A. A.. A mechanical model to determine the influence of masses and mass distribution on the impact force during running-a discussion. J. Biomech.. 2006 ; 39 (2). 388-390 (Pubitemid 41729017)
43. Ly Q. H., Alaoui A., Erlicher S., Baly L.. Towards a footwear design tool: influence of shoe midsole properties and ground stiffness on the impact force during running. J. Biomech.. 2010 ; 43 (2). 310-317
44. Klute G., Berge J.. Modelling the effect of prosthetic feet and shoes on the heel-ground contact force in amputee gait. Proc. IMechE, Part H: J. Engineering in Medicine. 2004 ; 218 (3). 173-182
45. Williams M., Lessner H. Biomechanics of human motion. Pennsylvania: Saunders, Philadelphia ; 1966 :
46. ColeG. K.Loading of the joints of the lower extremities during the impact phase in running, Ph.D. dissertation, Department of Mechanical Engineering, The University of Calgary, Calgary, Canada, 1995.
47. Clarys J. P., Marfell-Jones M. J.. Anthropometric prediction of component tissue masses in the minor limb segments of the human body. Hum. Biol.. 1986 ; 58 (5). 761-769 (Pubitemid 17047457)
48. Clauser C. E., McConville J. T., Young J. W. Weight, volume, and center of mass of segments of the human body, Wright-Patterson Air Force Base. Dayton, Ohio: ; 1969 :
49. Hoerler E.. Mechanisches Modell zur Beschreibung des isometrischen und des dynamischen Muskelkraftverlaufs. Jugend und Sport. 1972 ; 29: 271-273
50. Aerts P., De Clercq D.. Deformation characteristics of the heel region of the shod foot during a simulated heel strike: the effect of varying midsole hardness. J. Sports Sci.. 1993 ; 11 (5). 449-461 (Pubitemid 23333888)
51. Cavagna G. A.. Elastic bounce of the body. J. Appl. Physiol.. 1970 ; 29 (3). 279-282
52. Santello M.. Review of motor control mechanisms underlying impact absorption from falls. Gait Posture. 2005 ; 21 (1). 85-94 (Pubitemid 41569256)
53. Lafortune M. A., Hennig E. M., Lake M. J.. Dominant role of interface over knee angle for cushioning impact loading and regulating initial leg stiffness. J. Biomech.. 1996 ; 29 (12). 1523-1529 (Pubitemid 26381863)
54. Bates B. T., Osternig L. R., Sawhill J. A., James S. L.. An assessment of subject variability, subject-shoe interaction, and the evaluation of running shoes using ground reaction force data. J. Biomech.. 1983 ; 16 (3). 181-191 (Pubitemid 13003309)
55. Clarke T. E., Frederick E. C., Cooper L. B.. The effects of shoe cushioning upon ground reaction forces in running. Int. J. Sports Med.. 1983 ; 4 (4). 247-251 (Pubitemid 14209119)
56. De Wit B., De Clercq D., Aerts P.. Biomechanical analysis of the stance phase during barefoot and shod running. J. Biomech.. 2000 ; 33 (3). 269-278
57. Dixon S. J., Collop A. C., Batt M. E.. Surface effects on ground reaction forces and lower extremity kinematics in running. Med. Sci. Sports Exerc.. 2000 ; 32 (11). 1919-1926
58. Lieberman D. E., Venkadesan M., Werbel W. A., Daoud A. I., D'Andrea S., Davis I. S., Mang'Eni R. O., Pitsiladis Y.. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature. 2010 ; 463 (7280). 531-535
59. Nigg B. M., Stefanyshyn D., Cole G., Stergiou P., Miller J.. The effect of material characteristics of shoe soles on muscle activation and energy aspects during running. J. Biomech.. 2003 ; 36 (4). 569-575 (Pubitemid 36207587)
60. Wakeling J. M., Liphardt A. M., Nigg B. M.. Muscle activity reduces soft-tissue resonance at heel-strike during walking. J. Biomech.. 2003 ; 36 (12). 1761-1769 (Pubitemid 37393255)
61. Wakeling J. M., Nigg B. M.. Modification of soft tissue vibrations in the leg by muscular activity. J. Appl. Physiol.. 2001 ; 90 (2). 412-420 (Pubitemid 32118897)
62. Wakeling J. M., Nigg B. M., Rozitis A. I.. Muscle activity in the lower extremity damps the soft-tissue vibrations which occur in response to pulsed and continuous vibrations. J. Appl. Physiol.. 2002 ; 93 (3). 1093-1103 (Pubitemid 34919684)
63. Wakeling J. M., Pascual S. A., Nigg B. M.. Altering muscle activity in the lower extremities by running with different shoes. Med. Sci. Sports Exerc.. 2002 ; 34 (9). 1529-1532 (Pubitemid 35006829)
64. Wakeling J. M., Von Tscharner V., Nigg B. M., Stergiou P.. Muscle activity in the leg is tuned in response to ground reaction forces. J. Appl. Physiol.. 2001 ; 91 (3). 1307-1317 (Pubitemid 32803927)
65. Nikooyan A. A., Zadpoor A. A.. A model-based parametric study of soft tissue vibrations during running. Proceedings of the Annual Symposium of the IEEE-EMBS Benelux Chapter ; Heeze, The Netherlands ;. 49.
66. Zadpoor A. A., Nikooyan A. A.. Modeling muscle activity to study the effects of footwear on the impact forces and vibrations of the human body during running. J. Biomech.. 2010 ; 43 (2). 186-193
67. Lewis R., Torczon V.. Pattern search algorithms for bound constrained minimization. SIAM J. Optim.. 1999 ; 9 (4). 1082-1099 (Pubitemid 129489318)
68. Nikooyan A. A., Zadpoor A. A.. An improved cost function for modeling of muscle activity during running. J. Biomech.. 2011 ; 44 (5). 984-987
69. Nikooyan A. A., Veeger H. E. J., Westerhoff P., Graichen F., Bergmann G., van der Helm F. C. T.. Validation of the Delft Shoulder and Elbow Model using in-vivo glenohumeral joint contact forces. J. Biomech.. 2010 ; 43 (15). 3007-3014
70. Scheys L., Jonkers I., Schutyser F., Pans S., Spaepen A., Suetens P.. Image based methods to generate subject-specific musculoskeletal models for gait analysis. International Congress Series. 2005 ; 1281: 62-67 (Pubitemid 43693670)
71. Kawamura A., Chi Z.. One-leg jumping with virtual spring principle. Proceedings of the 8th IEEE-RAS International Conference on Humanoid Robots ; Daejeon, Korea ;. 34.
72. Tamaddoni S. H., Alasty A., Meghdari A., Sohrabpour S., Salarieh H.. Spring-mass jumping of underactuated biped robots. Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference ; Las Vegas, Nevada ;. 1923.