Patterned variability in gait behavior: How can it be measured and what does it mean?

Gait Biometrics: Basic Patterns, Role of Neurological Disorders and Effects of Physical Activity

Volumn , Issue , 2013, Pages 17-43

  Rhea, Christopher K ^a   Kiefer, Adam W ^b,c  

^a UNIVERSITY OF NORTH CAROLINA AT GREENSBORO   (United States)

^b CINCINNATI CHILDREN'S HOSPITAL MEDICAL CENTER   (United States)

^c UNIVERSITY OF CINCINNATI COLLEGE OF MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84953308048     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (123)

1. Adams, J. A. (1971). A closed-loop theory of motor learning. Journal of Motor Behavior, 3, 111-150.
2. Arif, M., Ohtaki, Y., Nagatomi, R., and Inooka, H. (2004). Estimation of the effect of cadence on gait stability in young andelderly people using approximate entropy technique. Measurement Science Review, 4(2), 29-40.
3. Arif, M., Othaki, Y., Nagatomi, R., Ishihara, T., and Inooka, H. (2002). Analysis of the effect of fatigue on walking stability. Proceedings of International Symposium on Micromechatronics and Human Science IEEE, 253-258.
4. Balasubramaniam, R., Riley, M. A. and Turvey, M. T. (2000). Specificity of postural sway to the demands of a precision task. Gait and Posture, 11(1), 12-24.
5. Belair, J., Glass, L., Heiden, U., and Milton, J. (1995). Dynamical disease: Identification, temporal aspects and treatment strategies of human illness. Chaos, 5(1).
6. Berg, K., Wood-Dauphinee, S., Williams, J. I., and Gayton, D. (1989). Measuring balance in the elderly: preliminary development of an instrument. Physiotherapy Canada, 41, 304-311.
7. Bravi, A., Longtin, A. and Seely, A. J. E. (2011). Review and classification of variabilitiy analysis techniques with clinical applications. BioMedical Engineering OnLine, 10, 90.
8. Bruijn, S. M., Bregman, D. J. J., Meijer, O. G., Beek, P. J., and Dieen, J. H. v. (2012). Maximum Lyapunov exponents as predictors of global gait stability: A modeling approach. Medical Engineering and Physics, 34(4), 428-436.
9. Bruijn, S. M., Dieën, J. H. v., Meijer, O. G., and Beek, P. J. (2009). Statistical precision and sensitivity of measures of dynamic gait stability. Journal of Neuroscience Methods, 178 (2), 327-333.
10. Buzzi, U. H., Stergiou, N., Kurz, M. J., Hageman, P. A., and Heidel, J. (2003). Nonlinear dynamics indicates aging affects variability during gait. Clinical Biomechanics, 18, 435-443.
11. Buzzi, U. H. and Ulrich, B. D. (2004). Dynamic stability of gait cycles as a function of speed and system constraints. Motor Control, 8(3), 241-254.
12. Cavanaugh, J. T., Guskiewicz, K. M., Giuliani, C., Marshall, S., Mercer, V. S., and Stergiou, N. (2006). Recovery of postural control after cerebral concussion: New insights using approximate entropy. Journal of Athletic Training, 41(3), 305-313.
13. Costa, M., Goldberger, A. L. and Peng, C. K. (2002). Multiscale entropy analysis of complex physiologic time series. Physical Review Letters, 89(6), 068102.
14. Costa, M., Peng, C.-K., Goldberger, A. L., and Hausdorff, J. M. (2003). Multiscale entropy analysis of human gait dynamics. Physica A, 330, 53-60.
15. Diedrich, F. J. and Warren, W. H. (1995). Why change gaits? Dynamics of the walk-run transition. Journal of Experimental Psychology: Human Perception and Performance, 21 (1), 183-202.
16. Dingwell, J. B. and Cusumano, J. P. (2000). Nonlinear time series analysis of normal and pathological human walking. Chaos, 10(4), 848-863.
17. Dingwell, J. B., Cusumano, J. P., Sternad, D., and Cavanagh, P. R. (2000). Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking. Journal of Biomechanics, 33(10), 1269-1277.
18. Dingwell, J. B. and Kang, H. G. (2007). Differences between local and orbital dynamic stability during human walking. Journal of Biomechanical Engineering, 129(4), 586-593.
19. Dingwell, J. B. and Marin, L. C. (2006). Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. Journal of Biomechanics, 39(3), 444-452.
20. Dingwell, J. B., Robb, R. T., Troy, K. L., and Grabiner, M. D. (2008). Effects of an attention demanding task on dynamic stability during treadmill walking. Journal of Neuro Engineering and Rehabilitation, 5(12).
21. Diniz, A., Wijnants, M. L., Torre, K., Barreiros, J., Crato, N., Bosman, A. M. T., ... Delignieres, D. (2011). Contemporary theories of 1/f noise in motor control. Human Movement Science, 30, 889-905.
22. Donker, S. F., Ledebt, A., Roerdink, M., Savelsbergh, G. J. P., and Beek, P. J. (2008). Children with cerebral palsy exhibit greater and more regular postural sway than typically developing children. Experimental Brain Research, 184(3), 363-370.
23. Duarte, M. and Zatsiorsky, V. M. (2001). Long-range correlations in human standing. Physics Letters A, 283, 124-128.
24. Eckmann, J., Kamphorst, S. and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhysics Letters, 5(9), 973-977.
25. Fraser, A. M. and Swinney, H. L. (1986). Independent cordinates for strange attractors from mutual information. Physical Review A, 33, 1134-1140.
26. Gates, D. H. and Dingwell, J. B. (2007). Peripheral neuropathy does not alter the fractal dynamics of stride intervals of gait. Journal of Applied Physiology, 102(3), 965-971.
27. Georgoulis, A. D., Moraiti, C., Ristanis, S., and Stergiou, N. (2006). A novel approach to measure variability in the anterior cruciate ligament deficient knee during walking: the use of the approximate entropy in orthopaedics. Journal of Clinical Monitoring and Computing, 20(1), 11-18.
28. Glass, L. (2001). Synchronization and rhythmic processes in physiology. Nature, 410(6825), 277-284.
29. Glass, L. and Mackey, M. C. (1979). Pathological conditions resulting from instabilities in physiological control systems. Annals of the New York Academy of Sciences, 316, 214-235.
30. Goldberger, A. L. (1991). Is the normal heartbeat chaotic or hemostatic. News in Physiological Sciences, 6, 87-91.
31. Goldberger, A. L., Amaral, L. A. N., Hausdorff, J. M., Ivanov, P. C., Peng, C.-K., and Stanley, H. E. (2002). Fractal dynamics in physiology: Alterations with disease and aging. Proceedings from the National Academy of Sciences of The US 99(Suppl. 1), 2466-2476.
32. Goldberger, A. L., Rigney, D. R. and West, B. J. (1990). Chaos and fractals in human physiology. Scientific American, 262, 42-49.
33. Goldberger, A. L. and West, B. J. (1987). Applications of nonlinear dynamics to clinical cardiology. Annals of the New York Academy of Sciences, 504, 195-213.
34. Govindan, R. B., Wilsona, J. D., Eswaran, H., Lowery, C. L., and Preißl, H. (2007). Revisiting sample entropy analysis. Physica A: Statistical Mechanics and its Applications, 376, 158-164.
35. Harbourne, R. T. and Stergiou, N. (2009). Movement Variability and the Use of Nonlinear Tools: Principles to Guide Physical Therapist Practice. Physical Therapy, 89(3), 267-282.
36. Hasson, C. J., Emmerik, R. E. A. V., Caldwell, G. E., Haddad, J. M., Gagnon, J. L., and Hamill, J. (2008). Influence of embedding parameters and noise in center of pressure recurrence quantification analysis. Gait and Posture 27(3), 416-422.
37. Hausdorff, J. M. (2007). Gait dynamics, fractals and falls: Finding meaning in the stride-tostride fluctuations of human walking. Human Movement Science, 26(4), 555-589.
38. Hausdorff, J. M., Cudkowicz, M. E., Firtion, R., Wei, J. Y., and Goldberger, A. L. (1998). Gait variability and basal ganglia disorders: Stride-to-stride variations of gait cycle timing in Parkinson's disease and Huntington's disease. Movement Disorders, 13(3), 428-437.
39. Hausdorff, J. M., Lertratanakul, A., Cudkowicz, M. E., Peterson, A. L., Kaliton, D., and Goldberger, A. L. (2000). Dynamic markers of altered gait rhythm in amyotrophic lateral sclerosis. Journal of Applied Physiology, 88(6), 2045-2053.
40. Hausdorff, J. M., Mitchell, S. L., Firtion, R., Peng, C. K., Cudkowicz, M. E., Wei, J. Y., and Goldberger, A. L. (1997). Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease. Journal of Applied Physiology, 82(1), 262-269.
41. Hausdorff, J. M., Peng, C.-K., Ladin, Z., Wei, J. Y., and Goldberger, A. L. (1995). Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. Journal of Applied Physiology, 78(1), 349-358.
42. Hausdorff, J. M., Purdon, P. L., Peng, C. K., Ladin, Z., Wei, J. Y., and Goldberger, A. L. (1996). Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. Journal of Applied Physiology, 80(5), 1448-1457.
43. Hausdorff, J. M., Zemany, L., Peng, C.-K., and Goldberger, A. L. (1999). Maturation of gait dynamics: stride-to-stride variability and its temporal organization in children. Journal of Applied Physiology, 86(3), 1040-1047.
44. Hove, M. J., Suzuki, K., Uchitomi, H., Orimo, S., and Miyake, Y. (2012). Interactive rhythmic auditory stimulation reinstates natural 1/f timing in gait of Parkinson's patients. PLoS ONE, 7(3), e32600.
45. Hurd, W. J. and Snyder-Mackler, L. (2007). Knee instability after acute ACL rupture affects movement patterns during the mid-stance phase of gait. Journal of Orthopaedic Research, 25(10), 1369-1377.
46. Ivanov, P. C., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Rosenblum, M. G., Struzik, Z. R., and Stanley, H. E. (1999). Multifractality in human heartbeat dynamics. Nature, 399, 461-465.
47. Jordan, K., Challis, J. H., Cusumano, J. P., and Newell, K. M. (2009). Stability and the timedependent structure of gait variability in walking and running. Human Movement Science, 28(1), 113-128.
48. Jordan, K., Challis, J. H. and Newell, K. M. (2006). Long range correlations in the stride interval of running. Gait and Posture 24(1), 120-125.
49. Jordan, K., Challis, J. H. and Newell, K. M. (2007a). Speed influences on the scaling behavior of gait cycle fluctuations during treadmill running. Human Movement Science, 26(1), 87-102.
50. Jordan, K., Challis, J. H. and Newell, K. M. (2007b). Walking speed influences on gait cycle variability. Gait and Posture, 26(1), 128-134.
51. Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A., and Stanley, H. E. (2002). Multifractal detrended fluctutation analysis of nonstationary time series. Physica A, 316, 87-114.
52. Kaplan, D. T., Furman, M. I., Pincus, S. M., Ryan, S. M., Lipsitz, L. A., and Goldberger, A. L. (1991). Aging and the complexity of cardiovascular dynamics. Biophysical Journal, 59, 945-949.
53. Katsavelis, D., Mukherjee, M., Decker, L., and Stergiou, N. (2010a). The effect of virtual reality on gait variability. Nonlinear Dynamics, Psychology, and Life Sciences, 14(3), 239-256.
54. Katsavelis, D., Mukherjee, M., Decker, L., and Stergiou, N. (2010b). Variability of lower extremity joint kinematics during backward walking in a virtual environment. Nonlinear Dynamics, Psychology, and Life Sciences., 14(2), 165-178.
55. Kennel, M. B., Brown, R. and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Physical Review A, 45 (6), 3403-3411.
56. Kiefer, A. W., Riley, M. A., Shockley, K., Villard, S., and Van Orden, G. C. (2009). Walking changes the dynamics of cognitive estimates of time intervals. Journal of Experimental Psychology: Human Perception and Performance, 35(5), 1532-1541.
57. Kiefer, A. W., Wallot, S., Gresham, L. J., Kloos, H., Riley, M. A., Shockley, K., and Van Orden, G. C. (under review). Development of coordination in time estimation. Developmental Psychology.
58. King, G. P., Jones, R. and Broomhead, D. S. (1987). Phase portraits from a time series: a singular system approach. Nuclear Physics B, 2, 379-390.
59. Kloos, H. and Van Orden, G. C. (2010). Voluntary behavior in cognitive and motor tasks. Mind and Matter, 8(1), 19-43.
60. Labini, F. S., Meli, A., Ivanenko, Y. P., and Tufarelli, D. (2012). Recurrence quantification analysis of gait in normal and hypovestibular subjects. Gait and Posture, 35, 48-55.
61. Lamoth, C. J. C., Ainsworth, E., Polomski, W., and Haudijk, H. (2010). Variability and stability analysis of walking of transfemoral amputees. Medical Engineering and Physics, 32, 1009-1014.
62. Lindstrom, M., Fellander-Tsai, L., Wredmark, T., and Henriksson, M. (2010). Adaptations of gait and muscle activiation in chronic ACL deficiency. Knee Surgery, Sports Traumatology, Arthroscopy, 18, 106-114.
63. Lipsitz, L. A. (2002). Dynamics of stability: The physiologic basis of functional health and frailty. Journal of Gerontology: Biological Sciences, 57A(3), B115-B125.
64. Lipsitz, L. A. and Goldberger, A. L. (1992). Loss of 'complexity' and aging: potential applications of fractals and chaos theory to senescence. JAMA: The Journal of the American Medicine Association, 267(13), 1806-1809.
65. Mackey, M. C. and Glass, L. (1977). Oscillation and chaos in physiological control systems. Science, 197, 287-289.
66. Mackey, M. C. and Milton, J. G. (1987). Dynamical diseases. Annals of the New York Academy of Sciences, 504, 16-32.
67. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. New York: Freeman.
68. Marwan, N. (2011). How to avoid potential pitfalls in recurrence plot based data analysis. International Journal of Bifurcation and Chaos, 21, 1003.
69. Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Physics Reports 438(5-6), 237-329.
70. Mazaheri, M., Negahban, H., Salavati, M., Sanjari, M. A., and Parnianpour, M. (2010). Reliability of recurrence quantification analysis measures of the center of pressure during standing in individuals with musculoskeletal disorders. Medical Engineering and Physics 32(7), 808-812.
71. Moraiti, C. O., Stergiou, N., Ristanis, S., and Georgoulis, A. D. (2007). ACL deficiency affects stride-to-stride variability as measured using nonlinear methodology. Knee Surgery, Sports Traumatology, Arthroscopy, 15(12), 1406-1413.
72. Moraiti, C. O., Stergiou, N., Ristanis, S., Vasiliadis, H. S., Patras, K., Lee, C., and Georgoulis, A. D. (2009). The effect of anterior cruciate ligament reconstruction on stride-to-stride variability. Arthroscopy, 25(7), 742-749.
73. Negahban, H., Salavati, M., Mazaheri, M., Sanjari, M. A., Hadian, M. R., and Parnianpour, M. (2010). Non-linear dynamical features of center of pressure extracted by recurrence quantification analysis in people with unilateral anterior cruciate ligament injury. Gait and Posture, 31(4), 450-455.
74. Newell, K. M. (1986). Constraints on the development of coordination. In: M. G. Wade and H. T. A. Whiting (Eds.), Motor skill acquisition in children: Aspects of coordination and control (pp. 341-360). Amsterdam: Martinies NIJHOS.
75. Olmo, M. F. d. and Cudeiro, J. (2005). Temporal variability of gait in Parkinson disease: Effects of a rehabilitation programme based on rhythmic sound cues. Parkinsonism and Related Disorders, 11, 25-33.
76. Osternig, L. R., Caster, B. L. and James, C. R. (1995). Contralateral hamstring (biceps femoris) coactivation patterns and anterior cruciate ligament dysfunction. Medicine and Science in Sports and Exercise, 27(6), 805-808.
77. Pellechia, G. L. and Shockley, K. (2005). Application of recurrence quantification analysis: Influence of cognitive activity on postural fluctuations. In: M. A. Riley and G. C. Van Orden (Eds.), Tutorials in contemporary nonlinear methods for the behavioral sciences (pp. 95-141): NSF.
78. Peng, C. K., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Sciortino, F., Simons, M., and Stanley, H. E. (1992). Long-range correlations in nucleotide sequences. Nature, 356, 168-170.
79. Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L. (1994). Mosaic organization of DNA necleotides. Physical Review E, 49(2), 1685-1689.
80. Peng, C. K., Havlin, S., Stanley, H. E., and Goldberger, A. L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos, 5(1), 82-87.
81. Peng, C. K., Mietus, J., Hausdorff, J. M., Havlin, S., Stanley, H. E., and Goldberger, A. L. (1993). Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Physical Review Letters, 79(9), 1343-1346.
82. Perlmutter, S., Lin, F. and Makhsous, M. (2010). Quantitative analysis of static sitting posture in chronic stroke. Gait and Posture, 32(1), 53-56.
83. Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. US, 88(6), 2297-2301.
84. Ramdani, S., Bouchara, F. and Lagarde, J. (2009). Influence of noise on the sample entropy algorithm. Chaos, 19(1), 013123.
85. Reeves, N. P., Narendra, K. S. and Cholewicki, J. (2007). Spine stability: the six blind men and the elephant. Clinical Biomechanics, 22(3), 266-274.
86. Rhea, C. K., Kiefer, A. W., D'Andrea, S. E., Warren, W. H., and Aaron, R. K. (2010). Approximate entropy of stride-to stride intervals following ACL injury. Paper presented at the American Society for Biomechanics, Providence, RI.
87. Rhea, C. K., Kiefer, A. W., Gerin-Lajoie, M., Warren, W. H., and Aaron, R. K. (under review). Constraining knee motion changes the dynamic structure of the direction of travel in a functional mobility task.
88. Rhea, C. K., Kiefer, A. W., Warren, W. H., D'Andrea, S. E., and Aaron, R. K. (2011). Synchronizing to a "noisy" metronome induces corresponding shifts in fractal gait dynamics. Paper presented at the North American Society for Psychology in Sport and Physical Activity, Burlington, VT.
89. Rhea, C. K., Silver, T. A., Hong, S. L., Ryu, J. H., Studenka, B. E., Hughes, C. M. L., and Haddad, J. M. (2011). Noise and complexity in human postural control: Interpreting the different estimations of entropy. PLoS ONE, 6(3), e17696.
90. Richman, J. S. and Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol., 278(6), H2039-H2049.
91. Riley, M. A., Balasubramaniam, R. and Turvey, M. T. (1999). Recurrence quantification analysis of postural fluctuations. Gait and Posture 9(1), 65-78.
92. Riley, M. A. and Clark, S. (2003). Recurrence analysis of human postural sway during the sensory organization test. Neuroscience Letters, 342(1-2), 45-48.
93. Roerdink, M., Haart, M. D., Daffertshofer, A., Donker, S. F., Geurts, A. C. H., and Beek, P. J. (2006). Dynamical structure of center-of-pressure trajectroies in patients recovering from stroke. Experimental Brain Research, 174, 256-269.
94. Rosenstein, M. T., Collins, J. and Luca, C. D. (1994). Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D, 73, 82-98.
95. Rosenstein, M. T., Collins, J. J. and DeLuca, C. J. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Physica D, 65, 117-134.
96. Rudolph, K., Axe, M., Buchanan, T., Scholz, J., and Snyder-Mackler, L. (2001). Dynamic stability in the anterior cruciate ligament deficient knee. Knee Surgery, Sports Traumatology, Arthroscopy, 9(2), 62-71.
97. Scafetta, N., Marchi, D. and West, B. J. (2009). Understanding the complexity of human gait dynamics. Chaos, 19, 026108.
98. Schmidt, R. A. (1975). A schema theory of discrete motor skill learning. Psychological Review, 82(4), 225-260.
99. Schmit, J. M., Regis, D. I. and Riley, M. A. (2005). Dynamic patterns of postural sway in ballet dancers and track athletes. Experimental Brain Research, 163(3), 370-378.
100. Schmit, J. M., Riley, M. A., Dalvi, A., Sahay, A., Schear, P. K., Schockley, K. D., and Pun, R. Y. K. (2006). Deterministic center of pressure patterns characterize postural instability in Parkinson's disease. Experimental Brain Research, 168(3), 357-367.
101. Seigle, B., Ramdani, S. and Bernard, P. L. (2009). Dynamical structure of center of pressure fluctuations in elderly people. Gait and Posture, 30(2), 223-226.
102. Shumway-Cook, A. and Woollacott, M. H. (1995). Motor Control: Theory and Practical Applications. Baltimore: Lippincott Williams and Williams.
103. Stanley, H. E., Amaral, L. A. N., Goldberger, A. L., Havlin, S., Ivanov, P. C., and Peng, C.-K. (1999). Statistical physics and physiology: Monofractal and multifractal approaches. Physica A, 270, 309-324.
104. Stergiou, N. and Decker, L. M. (2011). Human movement variability, nonlinear dynamics, and pathology: Is there a connection. Human Movement Science, 30(5), 869-888.
105. Stergiou, N., Harbourne, R. T. and Cavanaugh, J. T. (2006). Optimal movement variability: A new theoretical perspective for neurologic physical therapy. Journal of Neurologic Physical Therapy, 30, 120-129.
106. Stolze, H., Kuhtz-Buschbeck, J. P., Mondwurf, C., Boczeck-Funcke, A., Johnk, K., Deuschl, G., and Illert, M. (1997). Gait analysis during treadmill and overground locomotion in children and adults. Electroencephalography and Clinical Neurophysiology, 105, 490-497.
107. Takens, F. (1981). Detecting strange attractors in turbulence Vol. 898. D. Rand and L. S. Young (Eds.), Dynamical Systems and Turbulence.
108. Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Physics Letters A, 223, 255-260.
109. Vaillancourt, D. E. and Newell, K. M. (2000). The dynamics of resting and postural tremor in Parkinson's disease. Clinical Neurophysiology 111(11), 2046-2056.
110. Vaillancourt, D. E. and Newell, K. M. (2002). Changing complexity in human behavior and physiology through aging and disease. Neurobiology of Aging 23(1), 1-11.
111. Van Orden, G. C., Holden, J. G. and Turvey, M. T. (2003). Self-organization of cognitive performance. Journal of experimental psychology: general, 132(3), 331-350.
112. Van Orden, G. C., Kloos, H. and Wallot, S. (2011). Living in the pink: Intentionality, wellbeing, and complexity. In: C. A. Hooker (Ed.), Philosophy of Complex Systems. Handbook of the Philosophy of Science (pp. 639-684). Amsterdam: Elsevier.
113. Vierordt, K. V. (1881). Ueber das Gehen des Menschen in Gesunden und Kranken Zustaenden nach Selb-stregistrireden Methoden. Tubingen: Laupp.
114. Von Porat, A., Henriksson, M., Holmstrom, E., Thorstensson, C. A., Mattsson, L., and Roos, E. M. (2006). Knee kinematics and kinetics during gait, step and hop in males with a 16 years old ACL injury compared with matched controls. Knee Surgery, Sports Traumatology, Arthroscopy, 14, 546-554.
115. Webber, C. L. and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. Journal of Applied Physiology, 76(2), 965-973.
116. Webber, C. L. and Zbilut, J. P. (2005). Recurrence quantification analysis of nonlinear dynamical systems M. A. Riley and G. C. V. Orden (Eds.), Tutorials in contemporary nonlinear methods for the behavioral sciences Retrieved from http://www.nsf.gov/sbe/bcs/pac/nmbs/nmbs.jsp.
117. West, B. J. and Goldberger, A. L. (1987). Physiology in fractal dimensions. American Scientist, 75, 354-365.
118. West, B. J. and Griffin, L. (1999). Allometric control, inverse power laws and human gait. Chaos, Solitions and Fractals, 10(9), 1519-1527.
119. West, B. J. and Scafetta, N. (2003). A nonlinear dynamical model of human gait. Physical Review E, 67, 051917.
120. Williams, G. P. (1997). Chaos theory tamed. Washington DC: John Henry Press.
121. Wrisley, D. M., Marchetti, G. F., Kurharsky, D. K., and Whitney, S. L. (2004). Reliability, internal consistency, and validity of data obtained with the Functional Gait Assessment, Physical Therapy, 84(10), 906-918.
122. Yakhdani, H. R. F., H. A. Bafghi, Meijer, O. G., Bruijn, S. M., Dikkenberg, N. v. d., Stibbe, A. B., ... Dieen, J. H. v. (2012). Stability and variability of knee kinematics during gait in knee osteoarthritis before and after replacement surgery. Clinical Biomechanics, 25, 230-236.
123. Zbilut, J. P. and Webber, C. L. (2008). Laminar recurrences, maxline, unstable singularities and biological dynamics. The European Physical Journal-Special Topics 164(1), 55-65.