Annals of Biomedical Engineering

, Volume 45, Issue 6, pp 1560–1571 | Cite as

Linear and Nonlinear Gait Features in Older Adults Walking on Inclined Surfaces at Different Speeds

  • Marcus Fraga Vieira
  • Fábio Barbosa Rodrigues
  • Gustavo Souto de Sá e Souza
  • Rina Márcia Magnani
  • Georgia Cristina Lehnen
  • Adriano O. Andrade


This study evaluated linear and nonlinear gait features in healthy older adults walking on inclined surfaces at different speeds. Thirty-seven active older adults (experimental group) and fifty young adults (control group) walked on a treadmill at 100% and ±20% of their preferred walking speed for 4 min under horizontal (0%), upward (UP) (+8%), and downward (DOWN) (−8%) conditions. Linear gait variability was assessed using the average standard deviation of trunk acceleration between strides (VAR). Gait stability was assessed using the margin of stability (MoS). Nonlinear gait features were assessed by using the maximum Lyapunov exponent, as a measure of local dynamic stability (LDS), and sample entropy (SEn), as a measure of regularity. VAR increased for all conditions, but the interaction effects between treadmill inclination and age, and speed and age were higher for young adults. DOWN conditions showed the lowest stability in the medial–lateral MoS, but not in LDS. LDS was smaller in UP conditions. However, there were no effects of age for either MoS or LDS. The values of SEn decreased almost linearly from the DOWN to the UP conditions, with significant interaction effects of age for anterior–posterior SEn. The overall results supported the hypothesis that inclined surfaces modulate nonlinear gait features and alter linear gait variability, particularly in UP conditions, but there were no significant effects of age for active older adults.


Inclined walking Linear gait variability Nonlinear analysis Maximum Lyapunov exponent Margin of stability Sample entropy 



The authors are thankful to Brazilian governmental agencies: funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant No. 445567/2014-7), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Fundação de Amparo à Pesquisa do Estado de Goiás and Fundação de Amparo à Pesquisa do Estado de Minas Gerais.


  1. 1.
    Bauby, C. E., and A. D. Kuo. Active control of lateral balance in human walking. J. Biomech. 33:1433–1440, 2000.CrossRefPubMedGoogle Scholar
  2. 2.
    Berg, W. P., H. M. Alessio, E. M. Mills, and C. Tong. Circumstances and consequences of falls in independent community-dwelling older adults. Age Ageing 26:261–268, 1997.CrossRefPubMedGoogle Scholar
  3. 3.
    Bruijn, S. M., O. G. Meijer, P. J. Beek, and J. H. van Dieën. Assessing the stability of human locomotion: a review of current measures. J. R. Soc. Interface 10:20120999, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  4. 4.
    Bruijn, S. M., J. H. van Dieën, O. G. Meijer, and P. J. Beek. Statistical precision and sensitivity of measures of dynamic gait stability. J. Neurosci. Methods 178:327–333, 2009.CrossRefPubMedGoogle Scholar
  5. 5.
    Bruijn, S. M., J. H. van Dieën, O. G. Meijer, and P. J. Beek. Is slow walking more stable? J. Biomech. 42:1506–1512, 2009.CrossRefPubMedGoogle Scholar
  6. 6.
    Costa, M., C.-K. Peng, A. L. Goldberger, and J. M. Hausdorr. Multiscale entropy analysis of human gait dynamics. Physica A 330:53–60, 2003.CrossRefGoogle Scholar
  7. 7.
    Daley, M. J., and W. L. Spinks. Exercise, mobility and aging. Sports Med. 29:1–12, 2000.CrossRefPubMedGoogle Scholar
  8. 8.
    DeVita, P., and T. Hortobagyi. Age causes a redistribution of joint torques and powers during gait. J. Appl. Physiol. 88:1804–1811, 2000.PubMedGoogle Scholar
  9. 9.
    Dingwell, J. B., J. P. Cusumano, P. R. Cavanagh, and D. Sternad. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J. Biomech. Eng. 123:27–32, 2001.CrossRefPubMedGoogle Scholar
  10. 10.
    Dingwell, J. B., J. P. Cusumano, D. Sternad, and P. R. Cavanagh. Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking. J. Biomech. 33:1269–1277, 2000.CrossRefPubMedGoogle Scholar
  11. 11.
    Dingwell, J. B., and L. C. Marin. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J. Biomech. 39:444–452, 2006.CrossRefPubMedGoogle Scholar
  12. 12.
    Ferraro, R. A., G. Pinto-Zipp, S. Simpkins, and M. Clark. Effects of an inclined walking surface and balance abilities on spatiotemporal gait parameters of older adults. J. Geriatr. Phys. Ther. 8084:1, 2013.Google Scholar
  13. 13.
    Hak, L., H. Houdijk, P. J. Beek, and J. H. Van Dieën. Steps to take to enhance gait stability: the effect of stride frequency, stride length, and walking speed on local dynamic stability and margins of stability. PLoS ONE 8:e82842, 2013.CrossRefPubMedPubMedCentralGoogle Scholar
  14. 14.
    Hak, L., H. Houdijk, F. Steenbrink, A. Mert, P. van der Wurff, P. J. Beek, and J. H. van Dieën. Speeding up or slowing down? Gait adaptations to preserve gait stability in response to balance perturbations. Gait Posture 36:260–264, 2012.CrossRefPubMedGoogle Scholar
  15. 15.
    Hausdorff, J. M., D. A. Rios, and H. K. Edelberg. Gait variability and fall risk in community-living older adults: a 1-year prospective study. Arch. Phys. Med. Rehabil. 82:1050–1056, 2001.CrossRefPubMedGoogle Scholar
  16. 16.
    Hof, A. L., M. G. J. Gazendam, and W. E. Sinke. The condition for dynamic stability. J. Biomech. 38:1–8, 2005.CrossRefPubMedGoogle Scholar
  17. 17.
    Kang, H. G., and J. B. Dingwell. Separating the effects of age and walking speed on gait variability. Gait Posture 27:572–577, 2008.CrossRefPubMedGoogle Scholar
  18. 18.
    Kang, H. G., and J. B. Dingwell. Effects of walking speed, strength and range of motion on gait stability in healthy older adults. J. Biomech. 41:2899–2905, 2008.CrossRefPubMedGoogle Scholar
  19. 19.
    Kang, H. G., and J. B. Dingwell. Dynamic stability of superior vs. inferior segments during walking in young and older adults. Gait Posture 30:260–263, 2009.CrossRefPubMedPubMedCentralGoogle Scholar
  20. 20.
    Kerrigan, D. C., L. W. Lee, J. J. Collins, P. O. Riley, and L. A. Lipsitz. Reduced hip extension during walking: healthy elderly and fallers versus young adults. Arch. Phys. Med. Rehabil. 82:26–30, 2001.CrossRefPubMedGoogle Scholar
  21. 21.
    Leroux, A., J. Fung, and H. Barbeau. Postural adaptation to walking on inclined surfaces: I. Normal strategies. Gait Posture 15:64–74, 2002.CrossRefPubMedGoogle Scholar
  22. 22.
    Lipsitz, L. A. Dynamics of stability: the physiologic basis of functional health and frailty. J. Gerontol. A 57:B115–B125, 2002.CrossRefGoogle Scholar
  23. 23.
    Lockhart, T. E., and J. Liu. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 51:1860–1872, 2008.CrossRefPubMedPubMedCentralGoogle Scholar
  24. 24.
    Lockhart, T. E., J. C. Woldstad, and J. L. Smith. Effects of age-related gait changes on the biomechanics of slips and falls. Ergonomics 46:1136–1160, 2003.CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Manor, B., M. D. Costa, K. Hu, E. Newton, O. Starobinets, H. G. Kang, C. K. Peng, V. Novak, and L. A. Lipsitz. Physiological complexity and system adaptability: evidence from postural control dynamics of older adults. J. Appl. Physiol. 109:1786–1791, 2010.CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Marigold, D. S., and A. E. Patla. Age-related changes in gait for multi-surface terrain. Gait Posture 27:689–696, 2008.CrossRefPubMedGoogle Scholar
  27. 27.
    McIntosh, A. S., K. T. Beatty, L. N. Dwan, and D. R. Vickers. Gait dynamics on an inclined walkway. J. Biomech. 39:2491–2502, 2006.CrossRefPubMedGoogle Scholar
  28. 28.
    Menz, H. B., S. R. Lord, and R. C. Fitzpatrick. Acceleration patterns of the head and pelvis when walking on level and irregular surfaces. Gait Posture 18:35–46, 2003.CrossRefPubMedGoogle Scholar
  29. 29.
    Minetti, A. E., L. P. Ardigo, and F. Saibene. Mechanical determinants of gradient walking energetics in man. J. Physiol. 472:725–735, 1993.CrossRefPubMedPubMedCentralGoogle Scholar
  30. 30.
    Minetti, A. E., C. Moia, G. S. Roi, D. Susta, and G. Ferretti. Energy cost of walking and running at extreme uphill and downhill slopes. J. Appl. Physiol. 93:1039–1046, 2002.CrossRefPubMedGoogle Scholar
  31. 31.
    Parijat, P., and T. E. Lockhart. Effects of moveable platform training in preventing slip-induced falls in older adults. Ann. Biomed. Eng. 40:1111–1121, 2012.CrossRefPubMedGoogle Scholar
  32. 32.
    Prince, F., D. Winter, P. Stergiou, and S. Walt. Anticipatory control of upper body balance during human locomotion. Gait Posture 2:19–25, 1994.CrossRefGoogle Scholar
  33. 33.
    Ramdani, S., B. Seigle, J. Lagarde, F. Bouchara, and P. L. Bernard. On the use of sample entropy to analyze human postural sway data. Med. Eng. Phys. 31:1023–1031, 2009.CrossRefPubMedGoogle Scholar
  34. 34.
    Americans with Disabilities Act homepage. Retrieved May 07, 2016, from
  35. 35.
    Reynard, F., and P. Terrier. Local dynamic stability of treadmill walking: intrasession and week-to-week repeatability. J. Biomech. 47:74–80, 2014.CrossRefPubMedGoogle Scholar
  36. 36.
    Reynard, F., and P. Terrier. Role of visual input in the control of dynamic balance: variability and instability of gait in treadmill walking while blindfolded. Exp. Brain Res. 233:1031–1040, 2015.CrossRefPubMedGoogle Scholar
  37. 37.
    Reynard, F., P. Vuadens, O. Deriaz, and P. Terrier. Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities. PLoS ONE 9:e100550, 2014.CrossRefPubMedPubMedCentralGoogle Scholar
  38. 38.
    Riva, F., E. Grimpampi, C. Mazzà, and R. Stagni. Are gait variability and stability measures influenced by directional changes? Biomed. Eng. 13:56, 2014.Google Scholar
  39. 39.
    Robinovitch, S. N., F. Feldman, Y. Yang, R. Schonnop, P. M. Leung, T. Sarraf, J. Sims-Gould, and M. Loughin. Video capture of the circumstances of falls in elderly people residing in long-term care: an observational study. Lancet 381:47–54, 2013.CrossRefPubMedGoogle Scholar
  40. 40.
    Rogers, H. L., R. L. Cromwell, and J. L. Grady. Adaptive changes in gait of older and younger adults as responses to challenges to dynamic balance. J. Aging Phys. Act. 16:85–96, 2008.CrossRefPubMedGoogle Scholar
  41. 41.
    Scaglioni-Solano, P., and L. F. Aragón-Vargas. Age-related differences when walking downhill on different sloped terrains. Gait Posture 41:153–158, 2014.CrossRefPubMedGoogle Scholar
  42. 42.
    Secretaria Nacional de Promoção dos Direitos da Pessoa com Deficiência. Retrieved May 07, 2016, from
  43. 43.
    Shupert, C. L., and F. B. Horak. Adaptation of postural control in normal and pathologic aging: implications for fall prevention programs. J. Appl. Biomech. 15:64–74, 1999.CrossRefGoogle Scholar
  44. 44.
    Stergiou, N., and L. M. Decker. Human movement variability, nonlinear dynamics, and pathology: is there a connection? Hum. Mov. Sci. 30:869–888, 2011.CrossRefPubMedPubMedCentralGoogle Scholar
  45. 45.
    Terrier, P., and O. Dériaz. Non-linear dynamics of human locomotion: Effects of rhythmic auditory cueing on local dynamic stability. Front. Physiol. 4:1–13, 2013.CrossRefGoogle Scholar
  46. 46.
    Terrier, P., and F. Reynard. Effect of age on the variability and stability of gait: a cross-sectional treadmill study in healthy individuals between 20 and 69 years of age. Gait Posture 41:170–174, 2015.CrossRefPubMedGoogle Scholar
  47. 47.
    Toebes, M. J. P., M. J. M. Hoozemans, R. Furrer, J. Dekker, and J. H. van Dieën. Associations between measures of gait stability, leg strength and fear of falling. Gait Posture 41:76–80, 2015.CrossRefPubMedGoogle Scholar
  48. 48.
    Tulchin, K., M. Orendurff, and L. Karol. The effects of surface slope on multi-segment foot kinematics in healthy adults. Gait Posture 32:446–450, 2010.CrossRefPubMedGoogle Scholar
  49. 49.
    van Emmerik, R. E. A., S. W. Ducharme, A. Amado, and J. Hamill. Comparing dynamical systems concepts and techniques for biomechanical analysis. J. Sport Heal. Sci. 2016. doi: 10.1016/j.jshs.2016.01.013.Google Scholar
  50. 50.
    Zeni, J. A., J. G. Richards, and J. S. Higginson. Two simple methods for determining gait events during treadmill and overground walking using kinematic data. Gait Posture 27:710–714, 2008.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2017

Authors and Affiliations

  • Marcus Fraga Vieira
    • 1
    • 2
  • Fábio Barbosa Rodrigues
    • 1
  • Gustavo Souto de Sá e Souza
    • 1
  • Rina Márcia Magnani
    • 1
  • Georgia Cristina Lehnen
    • 1
  • Adriano O. Andrade
    • 2
  1. 1.Bioengineering and Biomechanics LaboratoryUniversidade Federal de GoiásGoiâniaBrazil
  2. 2.Posgraduate Program in Electrical and Biomedical Engineering, Center for Innovation and Technology Assessment in HealthUniversidade Federal de UberlândiaUberlândiaBrazil

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