Length of Time-Series Gait Data on Lyapunov Exponent for Fall Risk Detection
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Published
Aug 24, 2021
Victoria Smith Hussain
Christopher W. Frames
Thurmon E. Lockhart
Abstract
Falls are the leading cause of disability in older adults with a third of adults over the age of 65 falling every year. Quantitative fall risk assessments using inertial measurement units and local dynamics stability (LDS) have shown that it is possible to identify at-risk persons. However, there are inconsistencies in the literature on how to calculate LDS and how much data is required for a reliable result. This study investigates the reliability and minimum required strides for 6 algorithm-normalization method combinations when computing LDS using young healthy and community dwelling elderly individuals. Participants wore an accelerometer at the lower lumbar while they walked for three minutes up and down a long hallway. This study concluded that the Rosenstein et al. algorithm was successfully and reliably able to differentiate between both populations using only 50 strides. It was also found normalizing the gait time series data by either truncating the data using a fixed number of strides or using a fixed number of strides and normalizing the entire time series to a fixed number of data points performed better when using the Rosenstein et al. algorithm.
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Keywords
Gait, Lyapunov exponents, Fall risk
References
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Bergen, G., Stevens, M. R., & Burns, E. R. (2016). Falls and Fall Injuries Among Adults Aged ≥65 Years — United States, 2014. MMWR. Morbidity and Mortality Weekly Report, 65(37), 993–998. https://doi.org/10.15585/mmwr.mm6537a2
Bizovska, L., Svoboda, Z., Kubonova, E., Vuillerme, N., Hirjakova, Z., & Janura, M. (2018). The differences between overground and treadmill walking in nonlinear, entropy-based and frequency variables derived from accelerometers in young and older women – preliminary report. Acta of Bioengineering and Biomechanics, 20(1), 93–100. https://doi.org/10.5277/ABB-00987-2017-02
Broomhead, D. S., & King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena, 20(2–3), 217–236. https://doi.org/10.1016/0167-2789(86)90031-X
Bruijn, S. M., Meijer, O. G., Beek, P. J., & Van Dieën, J. H. (2013). Assessing the stability of human locomotion: a review of current measures. Journal of the Royal Society, Interface / the Royal Society, 10(83), 20120999. https://doi.org/10.1098/rsif.2012.0999
Bruijn, S. M., van Dieën, J. H., Meijer, O. G., & Beek, P. J. (2009). Statistical precision and sensitivity of measures of dynamic gait stability. Journal of Neuroscience Methods, 178(2), 327–333. https://doi.org/10.1016/j.jneumeth.2008.12.015
Burns, E. R., Stevens, J. A., & Lee, R. (2016). The direct costs of fatal and non-fatal falls among older adults — United States. Journal of Safety Research, 58, 99–103. https://doi.org/10.1016/j.jsr.2016.05.001
Cignetti, F., Decker, L. M., & Stergiou, N. (2012). Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets. Annals of Biomedical Engineering, 40(5), 1122–1130. https://doi.org/10.1007/s10439-011-0474-3
Dingwell, J. B., & Cusumano, J. P. (2000). Nonlinear time series analysis of normal and pathological human walking. Chaos: An Interdisciplinary Journal of Nonlinear Science, 10(4), 848. https://doi.org/10.1063/1.1324008
Dingwell, J. B., Cusumano, J. P., Cavanagh, P. R., & Sternad, D. (2001). Local Dynamic Stability Versus Kinematic Variability of Continuous Overground and Treadmill Walking. Journal of Biomechanical Engineering, 123(1), 27. https://doi.org/10.1115/1.1336798
Dingwell, J. B., & 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. https://doi.org/10.1016/j.jbiomech.2004.12.014
Fino, P. C. (2016). A preliminary study of longitudinal differences in local dynamic stability between recently concussed and healthy athletes during single and dual-task gait. Journal of Biomechanics, 49(9), 1983–1988. https://doi.org/10.1016/j.jbiomech.2016.05.004
Hamacher, Daniel, Singh, N. B., Van Dieën, J. H., Heller, M. O., & Taylor, W. R. (2011). Kinematic measures for assessing gait stability in elderly individuals: a systematic review. Journal of the Royal Society, Interface / the Royal Society, 8(65), 1682–1698. https://doi.org/10.1098/rsif.2011.0416
Hamacher, Dennis, Hamacher, D., Singh, N. B., Taylor, W. R., & Schega, L. (2015). Towards the assessment of local dynamic stability of level-grounded walking in an older population. Medical Engineering and Physics, 37(12), 1152–1155. https://doi.org/10.1016/j.medengphy.2015.09.007
Huisinga, J. M., Mancini, M., George, R. St., & Horak, F. B. (2013). Accelerometry reveals differences in gait variability between patients with multiple sclerosis and healthy controls. Ann Biomed Eng, 41(8), 1670–1679. https://doi.org/10.1007/s10439-012-0697-y.Accelerometry
Huisinga, J. M., Mancini, M., St. George, R. J., & Horak, F. B. (2013). Accelerometry Reveals Differences in Gait Variability Between Patients with Multiple Sclerosis and Healthy Controls. Annals of Biomedical Engineering, 41(8), 1670–1679. https://doi.org/10.1007/s10439-012-0697-y
IJmker, T., & Lamoth, C. J. C. (2012). Gait and cognition: The relationship between gait stability and variability with executive function in persons with and without dementia. Gait and Posture, 35(1), 126–130. https://doi.org/10.1016/j.gaitpost.2011.08.022
Liu, J., Zhang, X., & Lockhart, T. E. (2012). Fall Risk Assessments Based on Postural and Dynamic Stability Using Inertial Measurement Unit. Safety and Health at Work, 3, 192. https://doi.org/10.5491/SHAW.2012.3.3.192
Lockhart, T. E., & Liu, J. (2008). Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics, 51(12), 1860–1872. https://doi.org/10.1080/00140130802567079
Mehdizadeh, S. (2018). The largest Lyapunov exponent of gait in young and elderly individuals: A systematic review. Gait and Posture, 60, 241–250. https://doi.org/10.1016/j.gaitpost.2017.12.016
Raffalt, P. C., Kent, J. A., Wurdeman, S. R., & Stergiou, N. (2019). Selection Procedures for the Largest Lyapunov Exponent in Gait Biomechanics. Annals of Biomedical Engineering, 47(4), 913–923. https://doi.org/10.1007/s10439-019-02216-1
Raffalt, P. C., Vallabhajosula, S., Renz, J. J., Mukherjee, M., & Stergiou, N. (2018). Lower limb joint angle variability and dimensionality are different in stairmill climbing and treadmill walking. Royal Society Open Science, 5(12), 180996. https://doi.org/10.1098/rsos.180996
Reynard, F., & Terrier, P. (2014). Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. Journal of Biomechanics, 47(1), 74–80. https://doi.org/10.1016/j.jbiomech.2013.10.011
Riva, F., Bisi, M. C., & Stagni, R. (2014). Gait variability and stability measures: Minimum number of strides and within-session reliability. Computers in Biology and Medicine, 50, 9–13. https://doi.org/10.1016/j.compbiomed.2014.04.001
Riva, Federico, Grimpampi, E., Mazzà, C., & Stagni, R. (2014). Are gait variability and stability measures influenced by directional changes? BioMedical Engineering Online, 13(1), 1–11. https://doi.org/10.1186/1475-925X-13-56
Rosenstein, M. T., Collins, J. J., & De Luca, C. J. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 65(1–2), 117–134. https://doi.org/10.1016/0167-2789(93)90009-P
Smith, V. A. (2019). Standardizing the Calculation of the Lyapunov Exponent for Human Giat using Inertial Measurement Units. Arizona State University. Retrieved from https://repository.asu.edu/items/55626
Stenum, J., Bruijn, S. M., & Jensen, B. R. (2014). The effect of walking speed on local dynamic stability is sensitive to calculation methods. Journal of Biomechanics, 47(15), 3776–3779. https://doi.org/10.1016/j.jbiomech.2014.09.020
Takens, F. (1981). Detecting strange attractors in turbulence. In D. Rand & L. Young (Eds.), Dynamical Systems and Turbulence, Warwick 1980 (pp. 366–381). Berlin, Heidelberg: Springer. https://doi.org/10.1007/BFb0091924
Tao, W., Liu, T., Zheng, R., & Feng, H. (2012). Gait analysis using wearable sensors. Sensors (Basel, Switzerland), 12(2), 2255–2283. https://doi.org/10.3390/s120202255
Terrier, P., & Reynard, F. (2014). To What Extent Does Not Wearing Shoes Affect the Local Dynamic Stability of Walking?: Effect Size and Intrasession Repeatability. Journal of Applied Biomechanics, 30(2), 305–309. https://doi.org/10.1123/jab.2013-0142
Terrier, P., & Reynard, F. (2015). 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(1), 170–174. https://doi.org/10.1016/j.gaitpost.2014.09.024
Toebes, M. J. P., Hoozemans, M. J. M., Furrer, R., Dekker, J., & Van Dieën, J. H. (2012). Local dynamic stability and variability of gait are associated with fall history in elderly subjects. Gait and Posture, 36(3), 527–531. https://doi.org/10.1016/j.gaitpost.2012.05.016
Weisenfluh, Morrison, A., Fan, T., & Sen. (2012). Epidemiology of falls and osteoporotic fractures: a systematic review. ClinicoEconomics and Outcomes Research, 5, 9. https://doi.org/10.2147/CEOR.S38721
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285–317. https://doi.org/10.1016/0167-2789(85)90011-9
Wurdeman, S. R. (2016). Lyapunov Exponents. In N. Stergiou (Ed.), Nonlinear Analysis for Human Movement Variability (pp. 83–110). Boca Raton, FL: CRC Press.
Bergen, G., Stevens, M. R., & Burns, E. R. (2016). Falls and Fall Injuries Among Adults Aged ≥65 Years — United States, 2014. MMWR. Morbidity and Mortality Weekly Report, 65(37), 993–998. https://doi.org/10.15585/mmwr.mm6537a2
Bizovska, L., Svoboda, Z., Kubonova, E., Vuillerme, N., Hirjakova, Z., & Janura, M. (2018). The differences between overground and treadmill walking in nonlinear, entropy-based and frequency variables derived from accelerometers in young and older women – preliminary report. Acta of Bioengineering and Biomechanics, 20(1), 93–100. https://doi.org/10.5277/ABB-00987-2017-02
Broomhead, D. S., & King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena, 20(2–3), 217–236. https://doi.org/10.1016/0167-2789(86)90031-X
Bruijn, S. M., Meijer, O. G., Beek, P. J., & Van Dieën, J. H. (2013). Assessing the stability of human locomotion: a review of current measures. Journal of the Royal Society, Interface / the Royal Society, 10(83), 20120999. https://doi.org/10.1098/rsif.2012.0999
Bruijn, S. M., van Dieën, J. H., Meijer, O. G., & Beek, P. J. (2009). Statistical precision and sensitivity of measures of dynamic gait stability. Journal of Neuroscience Methods, 178(2), 327–333. https://doi.org/10.1016/j.jneumeth.2008.12.015
Burns, E. R., Stevens, J. A., & Lee, R. (2016). The direct costs of fatal and non-fatal falls among older adults — United States. Journal of Safety Research, 58, 99–103. https://doi.org/10.1016/j.jsr.2016.05.001
Cignetti, F., Decker, L. M., & Stergiou, N. (2012). Sensitivity of the Wolf’s and Rosenstein’s Algorithms to Evaluate Local Dynamic Stability from Small Gait Data Sets. Annals of Biomedical Engineering, 40(5), 1122–1130. https://doi.org/10.1007/s10439-011-0474-3
Dingwell, J. B., & Cusumano, J. P. (2000). Nonlinear time series analysis of normal and pathological human walking. Chaos: An Interdisciplinary Journal of Nonlinear Science, 10(4), 848. https://doi.org/10.1063/1.1324008
Dingwell, J. B., Cusumano, J. P., Cavanagh, P. R., & Sternad, D. (2001). Local Dynamic Stability Versus Kinematic Variability of Continuous Overground and Treadmill Walking. Journal of Biomechanical Engineering, 123(1), 27. https://doi.org/10.1115/1.1336798
Dingwell, J. B., & 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. https://doi.org/10.1016/j.jbiomech.2004.12.014
Fino, P. C. (2016). A preliminary study of longitudinal differences in local dynamic stability between recently concussed and healthy athletes during single and dual-task gait. Journal of Biomechanics, 49(9), 1983–1988. https://doi.org/10.1016/j.jbiomech.2016.05.004
Hamacher, Daniel, Singh, N. B., Van Dieën, J. H., Heller, M. O., & Taylor, W. R. (2011). Kinematic measures for assessing gait stability in elderly individuals: a systematic review. Journal of the Royal Society, Interface / the Royal Society, 8(65), 1682–1698. https://doi.org/10.1098/rsif.2011.0416
Hamacher, Dennis, Hamacher, D., Singh, N. B., Taylor, W. R., & Schega, L. (2015). Towards the assessment of local dynamic stability of level-grounded walking in an older population. Medical Engineering and Physics, 37(12), 1152–1155. https://doi.org/10.1016/j.medengphy.2015.09.007
Huisinga, J. M., Mancini, M., George, R. St., & Horak, F. B. (2013). Accelerometry reveals differences in gait variability between patients with multiple sclerosis and healthy controls. Ann Biomed Eng, 41(8), 1670–1679. https://doi.org/10.1007/s10439-012-0697-y.Accelerometry
Huisinga, J. M., Mancini, M., St. George, R. J., & Horak, F. B. (2013). Accelerometry Reveals Differences in Gait Variability Between Patients with Multiple Sclerosis and Healthy Controls. Annals of Biomedical Engineering, 41(8), 1670–1679. https://doi.org/10.1007/s10439-012-0697-y
IJmker, T., & Lamoth, C. J. C. (2012). Gait and cognition: The relationship between gait stability and variability with executive function in persons with and without dementia. Gait and Posture, 35(1), 126–130. https://doi.org/10.1016/j.gaitpost.2011.08.022
Liu, J., Zhang, X., & Lockhart, T. E. (2012). Fall Risk Assessments Based on Postural and Dynamic Stability Using Inertial Measurement Unit. Safety and Health at Work, 3, 192. https://doi.org/10.5491/SHAW.2012.3.3.192
Lockhart, T. E., & Liu, J. (2008). Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics, 51(12), 1860–1872. https://doi.org/10.1080/00140130802567079
Mehdizadeh, S. (2018). The largest Lyapunov exponent of gait in young and elderly individuals: A systematic review. Gait and Posture, 60, 241–250. https://doi.org/10.1016/j.gaitpost.2017.12.016
Raffalt, P. C., Kent, J. A., Wurdeman, S. R., & Stergiou, N. (2019). Selection Procedures for the Largest Lyapunov Exponent in Gait Biomechanics. Annals of Biomedical Engineering, 47(4), 913–923. https://doi.org/10.1007/s10439-019-02216-1
Raffalt, P. C., Vallabhajosula, S., Renz, J. J., Mukherjee, M., & Stergiou, N. (2018). Lower limb joint angle variability and dimensionality are different in stairmill climbing and treadmill walking. Royal Society Open Science, 5(12), 180996. https://doi.org/10.1098/rsos.180996
Reynard, F., & Terrier, P. (2014). Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. Journal of Biomechanics, 47(1), 74–80. https://doi.org/10.1016/j.jbiomech.2013.10.011
Riva, F., Bisi, M. C., & Stagni, R. (2014). Gait variability and stability measures: Minimum number of strides and within-session reliability. Computers in Biology and Medicine, 50, 9–13. https://doi.org/10.1016/j.compbiomed.2014.04.001
Riva, Federico, Grimpampi, E., Mazzà, C., & Stagni, R. (2014). Are gait variability and stability measures influenced by directional changes? BioMedical Engineering Online, 13(1), 1–11. https://doi.org/10.1186/1475-925X-13-56
Rosenstein, M. T., Collins, J. J., & De Luca, C. J. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 65(1–2), 117–134. https://doi.org/10.1016/0167-2789(93)90009-P
Smith, V. A. (2019). Standardizing the Calculation of the Lyapunov Exponent for Human Giat using Inertial Measurement Units. Arizona State University. Retrieved from https://repository.asu.edu/items/55626
Stenum, J., Bruijn, S. M., & Jensen, B. R. (2014). The effect of walking speed on local dynamic stability is sensitive to calculation methods. Journal of Biomechanics, 47(15), 3776–3779. https://doi.org/10.1016/j.jbiomech.2014.09.020
Takens, F. (1981). Detecting strange attractors in turbulence. In D. Rand & L. Young (Eds.), Dynamical Systems and Turbulence, Warwick 1980 (pp. 366–381). Berlin, Heidelberg: Springer. https://doi.org/10.1007/BFb0091924
Tao, W., Liu, T., Zheng, R., & Feng, H. (2012). Gait analysis using wearable sensors. Sensors (Basel, Switzerland), 12(2), 2255–2283. https://doi.org/10.3390/s120202255
Terrier, P., & Reynard, F. (2014). To What Extent Does Not Wearing Shoes Affect the Local Dynamic Stability of Walking?: Effect Size and Intrasession Repeatability. Journal of Applied Biomechanics, 30(2), 305–309. https://doi.org/10.1123/jab.2013-0142
Terrier, P., & Reynard, F. (2015). 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(1), 170–174. https://doi.org/10.1016/j.gaitpost.2014.09.024
Toebes, M. J. P., Hoozemans, M. J. M., Furrer, R., Dekker, J., & Van Dieën, J. H. (2012). Local dynamic stability and variability of gait are associated with fall history in elderly subjects. Gait and Posture, 36(3), 527–531. https://doi.org/10.1016/j.gaitpost.2012.05.016
Weisenfluh, Morrison, A., Fan, T., & Sen. (2012). Epidemiology of falls and osteoporotic fractures: a systematic review. ClinicoEconomics and Outcomes Research, 5, 9. https://doi.org/10.2147/CEOR.S38721
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985). Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285–317. https://doi.org/10.1016/0167-2789(85)90011-9
Wurdeman, S. R. (2016). Lyapunov Exponents. In N. Stergiou (Ed.), Nonlinear Analysis for Human Movement Variability (pp. 83–110). Boca Raton, FL: CRC Press.
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