Maximum Lyapunov exponents as predictors of global gait stability: A modelling approach

Medical Engineering and Physics

Volumn 34, Issue 4, 2012, Pages 428-436

  Bruijn, Sjoerd M ^a,b   Bregman, Daan J J ^c   Meijer, Onno G ^b,d   Beek, Peter J ^b   van Dieën, Jaap H ^b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

^c VU UNIVERSITY MEDICAL CENTER   (Netherlands)

^d FUJIAN MEDICAL UNIVERSITY   (China)

Author keywords

Biomechanics; Gait stability; Locomotion; Lyapunov exponents; Modelling; Passive dynamic walking

Indexed keywords

EXTENDED VERSIONS; FINITE-TIME LYAPUNOV EXPONENT; GLOBAL STABILITY; HUMAN GAIT; HUMAN WALKING; LOCAL DYNAMIC STABILITY; LYAPUNOV EXPONENT; MAXIMUM LYAPUNOV EXPONENT; MODELLING; NEAREST NEIGHBOUR; PASSIVE DYNAMIC WALKING; SIMPLEST WALKING MODEL; WEAK CORRELATION;

BIOMECHANICS; BIPED LOCOMOTION; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; PROBABILITY;

SLOPE STABILITY;

ANALYTICAL PARAMETERS; ARTICLE; BIOLOGICAL MODEL; CORRELATION ANALYSIS; DYNAMICS; FOOT; GAIT; GAIT STABILITY; HIP; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MAXIMUM LYAPUNOV EXPONENT; PREDICTION; PRIORITY JOURNAL; PROBABILITY; RIGIDITY; SIMULATION; WALKING AID;

ACCIDENTAL FALLS; FOOT; GAIT; MODELS, BIOLOGICAL; PROBABILITY; TIME FACTORS; WALKING;

EID: 84859774827     PISSN: 13504533     EISSN: 18734030     Source Type: Journal    
DOI: 10.1016/j.medengphy.2011.07.024     Document Type: Article

References (46)

1. Rubenstein L.Z. Falls in older people: epidemiology, risk factors and strategies for prevention. Age Ageing 2006, 35(Suppl. 2):ii37-ii41.
2. Lockhart T.E., Liu J. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 2008, 51(12):1860-1872.
3. Kang H.G., Dingwell J.B. Effects of walking speed: strength and range of motion on gait stability in healthy older adults. J Biomech 2008, 41(14):2899-2905.
4. Kang H.G., Dingwell J.B. Dynamic stability of superior vs. inferior segments during walking in young and older adults. Gait Posture 2009, 30(2):260-263.
5. Kang H.G., Dingwell J.B. Dynamics and stability of muscle activations during walking in healthy young and older adults. J Biomech 2009, 42(14):2231-2237.
6. Fallah Yakhdani H.R., Abbasi Bafghi H., Meijer O.G., Bruijn S.M., van den Dikkenburg N., Stibbe A.B., et al. Stability and variability of gait in knee osteoarthritis before and after replacement surgery. Clin Biomech 2010, 25(3):230-236.
7. Moraiti C., Stergiou N., Ristanis S., Georgoulis A.D. ACL deficiency affects stride-to-stride variability as measured using nonlinear methodology. Knee Surg Sports Traumatol Arthrosc 2007, 15(12):1406-1413.
8. Dingwell J.B., Kang H.G., Marin L.C. The effects of sensory loss and walking speed on the orbital dynamic stability of human walking. J Biomech 2007, 40(8):1723-1730.
9. Dingwell J.B., Cusumano J.P., Sternad D., Cavanagh P.R. Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking. J Biomech 2000, 33(10):1269-1277.
10. Lamoth C.J., Ainsworth E., Polomski W., Houdijk H. Variability and stability analysis of walking of transfemoral amputees. Med Eng Phys 2010, 32(9):1009-1014.
11. Dingwell J.B., Cusumano J.P. Nonlinear time series analysis of normal and pathological human walking. Chaos 2000, 10(4):848-863.
12. Rosenstein M.T., Collins J.J., Deluca C.J. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Physica D 1993, 65(1-2):117-134.
13. Bruijn S.M., Ten Kate W.R.T., Faber G.S., Meijer O.G., Beek P.J., Dieën J.H. Estimating dynamic gait stability using data from non-aligned inertial sensors. Ann Biomed Eng 2010, 38(8):2588-2593.
14. Bruijn S.M., van Dieen J.H., Meijer O.G., Beek P.J. Statistical precision and sensitivity of measures of dynamic gait stability. J Neurosci Methods 2009, 178(2):327-333.
15. Bruijn S.M., van Dieën J.H., Meijer O.G., Beek P.J. Is slow walking more stable?. J Biomech 2009, 42(10):1506-1512.
16. Dingwell J.B., Marin L.C. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J Biomech 2006, 39(3):444-452.
17. Manor B., Li L. Characteristics of functional gait among people with and without peripheral neuropathy. Gait Posture 2009, 30(2):253-256.
18. Segal A.D., Orendurff M.S., Czerniecki J.M., Shofer J.B., Klute G.K. Local dynamic stability in turning and straight-line gait. J Biomech 2008, 41(7):1486-1493.
19. Buzzi U.H., Stergiou N., Kurz M.J., Hageman P.A., Heidel J. Nonlinear dynamics indicates aging affects variability during gait. Clin Biomech (Bristol, Avon) 2003, 18(5):435-443.
20. Stergiou N., Moraiti C., Giakas G., Ristanis S., Georgoulis A.D. The effect of the walking speed on the stability of the anterior cruciate ligament deficient knee. Clin Biomech (Bristol, Avon) 2004, 19(9):957-963.
21. Manor B., Wolenski P., Li L. Faster walking speeds increase local instability among people with peripheral neuropathy. J Biomech 2008, 41(13):2787-2792.
22. Kyvelidou A., Kurz M., Ehlers J., Stergiou N. Aging and partial body weight support affects gait variability. J Neuroeng Rehab 2008, 5(1):22.
23. Dingwell J.B., Cusumano J.P., Cavanagh P.R., Sternad D. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J Biomech Eng 2001, 123(1):27-32.
24. Hof A.L., van Bockel R.M., Schoppen T., Postema K. Control of lateral balance in walking: experimental findings in normal subjects and above-knee amputees. Gait Posture 2007, 25(2):250-258.
25. Dean J.C., Alexander N.B., Kuo A.D. The effect of lateral stabilization on walking in young and old adults. IEEE Trans Biomed Eng 2007, 54(11):1919-1926.
26. Chang M.D., Sejdic E., Wright V., Chau T. Measures of dynamic stability: detecting differences between walking overground and on a compliant surface. Hum Mov Sci 2010, 29(6):977-986.
27. Van Schooten K.S., Sloot L.H., Bruijn S.M., Kingma H., Meijer O.G., Pijnappels M., et al. Assessing gait stability: the sensitivity of trunk kinematics to galvanic vestibular stimulation. Gait Posture 2011, 33(4):656-660.
28. McAndrew P.M., Wilken J.M., Dingwell J.B. Dynamic stability of human walking in visually and mechanically destabilizing environments. J Biomech 2011, 44(4):644-649.
29. Su J.L.S., Dingwell J.B. Dynamic stability of passive dynamic walking on an irregular surface. J Biomech Eng 2007, 129(6):802-810.
30. Garcia M., Chatterjee A., Ruina A., Coleman M. The simplest walking model: stability, complexity, and scaling. J Biomed Eng-Trans ASME 1998, 120(2):281-288.
31. Kurz M.J., Markopoulou K., Stergiou N. Attractor divergence as a metric for assessing walking balance. Nonlinear Dynam Psychol Life Sci 2010, 14(2):151-164.
32. Roos P.E., Dingwell J.B. Influence of simulated neuromuscular noise on the dynamic stability and fall risk of a 3D dynamic walking model. J Biomech 2011, 44(8):1514-1520.
33. Pijnappels M., Van der Burg J.C.E., Reeves N.D., van Dieen J.H. Identification of elderly fallers by muscle strength measures. Eur J Appl Physiol 2008, 102(5):585-592.
34. Wu W.H., Meijer O.G., Bruijn S.M., Hu H., van Dieen J.H., Lamoth C.J.C., et al. Gait in pregnancy-related pelvic girdle pain: amplitudes, timing, and coordination of horizontal trunk rotations. Eur Spine J 2008, 17(9):1160-1169.
35. Huang Y., Bruijn S.M., Lin J., Meijer O.G., Wu W., Abbasi Bafghi H., et al. Gait adaptations in mild symptomatic lumbar disc herniation (LDH): trunk coordination and arm swing. Eur Spine J 2011, 20(3):491-499.
36. Hobbelen D.G.E., Wisse M. A disturbance rejection measure for limit cycle walkers: the gait sensitivity norm. IEEE Trans Robot 2007, 23(6):1213-1224.
37. Mcgeer T. Passive dynamic walking. Int J Robot Res 1990, 9(2):62-82.
38. England S.A., Granata K.P. The influence of gait speed on local dynamic stability of walking. Gait Posture 2007, 25(2):172-178.
39. Zeng X., Eykholt R., Pielke R.A. Estimating the Lyapunov-exponent spectrum from short time series of low precision. Phys Rev Lett 1991, 66(25):3229-3232.
40. Karssen J.G.D., Wisse M. Fall detection in walking robots by multi-way principal component analysis. Robotica 2009, 27:249-257.
41. Sloot L.H., Van Schooten K.S., Bruijn S.M., Kingma H., Pijnappels M., van Dieën J.H. Sensitivity of local dynamic stability of over-ground walking to balance impairment due to galvanic vestibular stimulation. Ann Biomed Eng 2011, 39(5):1563-1569.
42. Norris J.A., Marsh A.P., Granata K.P., Ross S.D. Revisiting the stability of 2D passive biped walking: local behavior. Phys. D: Nonlinear Phenom 2008, 237(23):3038-3045.
43. Kurz M.J., Judkins T.N., Arellano C., Scott-Pandorf M. A passive dynamic walking robot that has a deterministic nonlinear gait. J Biomech 2008, 41(6):1310-1316.
44. Kurz M.J., Judkins T., Scott-Pandorf M., Arellano C. Can passive dynamic walking robots provide insights on nonlinear gait dynamics?. J Sport Exerc Psychol 2007, 29:S102-S103.
45. Schwab A.L., Wisse M. Basin of attraction of the simplest walking model. Proc ASME Des Eng Tech Conf 2001 2001.
46. Bruijn S.M., Beek P.J., Meijer O.G., Dieën J.H. The effects of arm swing on human gait stability. J Exp Biol 2010, 213(Pt. 23):3945-3952.