Statistics in Biosciences

, Volume 11, Issue 2, pp 288–313 | Cite as

Functional Data Analyses of Gait Data Measured Using In-Shoe Sensors

  • Jihui LeeEmail author
  • Gen Li
  • William F. Christensen
  • Gavin Collins
  • Matthew Seeley
  • Anton E. Bowden
  • David T. Fullwood
  • Jeff Goldsmith


In studies of gait, continuous measurement of force exerted by the ground on a body, or ground reaction force (GRF), provides valuable insights into biomechanics, locomotion, and the possible presence of pathology. However, gold-standard measurement of GRF requires a costly in-lab observation obtained with sophisticated equipment and computer systems. Recently, in-shoe sensors have been pursued as a relatively inexpensive alternative to in-lab measurement. In this study, we explore the properties of continuous in-shoe sensor recordings using a functional data analysis approach. Our case study is based on measurements of three healthy subjects, with more than 300 stances (defined as the period between the foot striking and lifting from the ground) per subject. The sensor data show both phase and amplitude variabilities; we separate these sources via curve registration. We examine the correlation of phase shifts across sensors within a stance to evaluate the pattern of phase variability shared across sensors. Using the registered curves, we explore possible associations between in-shoe sensor recordings and GRF measurements to evaluate the in-shoe sensor recordings as a possible surrogate for in-lab GRF measurements.


Gait analysis Ground reaction force Functional data Curve registration 



This work was supported in part by NSF CMMI Award #1538447. The last author’s research was supported by the Award #R01HL123407 from the National Heart, Lung, and Blood Institute, and by the Award #R01NS097423-01 from the National Institute of Neurological Disorders and Stroke.


  1. 1.
    Benedetti M, Merlo A, Leardini A (2013) Inter-laboratory consistency of Gait analysis measurements. Gait Posture 38(4):934–939CrossRefGoogle Scholar
  2. 2.
    Bilodeau RA, Fullwood DT, Colton JS, Yeager JD, Bowden AE, Park T (2015) Evolution of nano-junctions in piezoresistive nanostrand composites. Compos Part B Eng 72:45–52CrossRefGoogle Scholar
  3. 3.
    Crane EA, Cassidy RB, Rothman ED, Gerstner GE (2010) Effect of registration on cyclical kinematic data. J Biomech 43(12):2444–2447CrossRefGoogle Scholar
  4. 4.
    Daoud AI, Geissler GJ, Wang F, Saretsky J, Daoud YA, Lieberman DE (2012) Foot strike and injury rates in endurance runners: a retrospective study. Med Sci Sports Exerc 44(7):1325–1334CrossRefGoogle Scholar
  5. 5.
    Earls C, Hooker G (2017) Combining functional data registration and factor analysis. J Comput Graph Stat 26(2):296–305MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Earls C, Hooker G (2017) Variational bayes for functional data registration, smoothing, and prediction. Bayesian Anal 12(2):557–582MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gasser T, Kneip A (1995) Searching for structure in curve samples. J Am Stat Assoc 90(432):1179–1188zbMATHGoogle Scholar
  8. 8.
    Goldsmith J, Greven S, Crainiceanu C (2013) Corrected confidence bands for functional data using principal components. Biometrics 69(1):41–51MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Goldsmith J, Scheipl F, Huang L, Wrobel J, Gellar J, Harezlak J, McLean MW, Swihart B, Xiao L, Crainiceanu C, Reiss PT (2016) Refund: regression with functional data. R package version 0.1-16.
  10. 10.
    Hausdorff JM, Cudkowicz ME, Firtion R, Wei JY, Goldberger AL (1998) Gait variability and basal Ganglia disorders: stride-to-stride variations of Gait cycle timing in Parkinson’s disease and Huntington’s disease. Mov Disord 13(3):428–437CrossRefGoogle Scholar
  11. 11.
    Hausdorff JM, Peng CK, Goldberger AL, Stoll AL (2004) Gait unsteadiness and fall risk in two affective disorders: a preliminary study. BMC Psychiatry 4(1):39CrossRefGoogle Scholar
  12. 12.
    Helwig NE, Hong S, Hsiao-Wecksler ET, Polk JD (2011) Methods to temporally align Gait cycle data. J Biomech 44(3):561–566CrossRefGoogle Scholar
  13. 13.
    Hyldahl RD, Evans A, Kwon S, Ridge ST, Robinson E, Hopkins JT, Seeley MK (2016) Running decreases knee intra-articular cytokine and cartilage oligomeric matrix concentrations: a pilot study. Eur J Appl Physiol 116(11–12):2305–2314CrossRefGoogle Scholar
  14. 14.
    Johnson OK, Kaschner GC, Mason TA, Fullwood DT, Hansen G (2011) Optimization of nickel nanocomposite for large strain sensing applications. Sens Actuators A Phys 166(1):40–47CrossRefGoogle Scholar
  15. 15.
    Karamanidis K, Arampatzis A, Brüggemann GP (2004) Reproducibility of electromyography and ground reaction force during various running techniques. Gait Posture 19(2):115–123CrossRefGoogle Scholar
  16. 16.
    Kneip A, Gasser T (1992) Statistical tools to analyze data representing a sample of curves. Ann Stat 20:1266–1305MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Kneip A, Ramsay JO (2008) Combining registration and fitting for functional models. J Am Stat Assoc 103(483):1155–1165MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Kneip A, Li X, MacGibbon K, Ramsay J (2000) Curve registration by local regression. Can J Stat 28(1):19–29MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Marron J, Ramsay JO, Sangalli LM, Srivastava A (2014) Statistics of time warpings and phase variations. Electr J Stat 8(2):1697–1702MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Marron JS, Ramsay JO, Sangalli LM, Srivastava A (2015) Functional data analysis of amplitude and phase variation. Stat Sci 30(4):468–484MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Merrell AJ, Fullwood DT, Bowden AE, Remington TD, Stolworthy DK, Bilodeau A (2013) Applications of nano-composite piezoelectric foam sensors. In: ASME 2013 conf on smart materials, adaptive structures and intelligent systemsGoogle Scholar
  22. 22.
    Owings TM, Grabiner MD (2004) Variability of step kinematics in young and older adults. Gait Posture 20(1):26–29CrossRefGoogle Scholar
  23. 23.
    Peter A, Rangarajan A (2006) Shape analysis using the Fisher-Rao Riemannian metric: unifying shape representation and deformation. In: 3rd IEEE international symposium on biomedical imaging: nano to macro, 2006. IEEE, pp 1164–1167Google Scholar
  24. 24.
    Pietrosimone B, Loeser RF, Blackburn JT, Padua DA, Harkey MS, Stanley LE, Luc-Harkey BA, Ulici V, Marshall SW, Jordan JM (2017) Biochemical markers of cartilage metabolism are associated with walking biomechanics 6-months following anterior cruciate ligament reconstruction. J Orthop Res 35:2288–2297CrossRefGoogle Scholar
  25. 25.
    Ramsay J, Li X (1998) Curve registration. J R Stat Soc Ser B 60(2):351–363MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Ramsay JO (1998) Estimating smooth monotone functions. J R Stat Soc Ser B 60(2):365–375MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Rice H, Jamison S, Davis I (2016) Footwear matters: influence of footwear and foot strike on load rates during running. Med Sci Sports Exerc 48(12):2462–2468CrossRefGoogle Scholar
  28. 28.
    Rosquist PG, Collins G, Merrell AJ, Tuttle NJ, Tracy JB, Bird ET, Seeley MK, Fullwood DT, Christensen WF, Bowden AE (2017) Estimation of 3d ground reaction force using nanocomposite piezo-responsive foam sensors during walking. Ann Biomed Eng 45:2122–2134CrossRefGoogle Scholar
  29. 29.
    Sadeghi H, Allard P, Shafie K, Mathieu PA, Sadeghi S, Prince F, Ramsay J (2000) Reduction of gait data variability using curve registration. Gait Posture 12(3):257–264CrossRefGoogle Scholar
  30. 30.
    Sadeghi H, Mathieu PA, Sadeghi S, Labelle H (2003) Continuous curve registration as an intertrial gait variability reduction technique. IEEE Trans Neural Syst Rehabil Eng 11(1):24–30CrossRefGoogle Scholar
  31. 31.
    Scheipl F, Staicu AM, Greven S (2015) Functional additive mixed models. J Comput Graph Stat 24(2):477–501MathSciNetCrossRefGoogle Scholar
  32. 32.
    Seeley MK, Son SJ, Kim H, Hopkins JT (2017) Walking mechanics for patellofemoral pain subjects with similar self-reported pain levels can differ based upon neuromuscular activation. Gait Posture 53:48–54CrossRefGoogle Scholar
  33. 33.
    Seliktar R, Yekutiel M, Bar A (1979) Gait consistency test based on the impulse-momentum theorem. Prosthet Orthot Int 3(2):91–98Google Scholar
  34. 34.
    Silverman BW (1995) Incorporating parametric effects into functional principal components analysis. J R Stat Soc Ser B 57:673–689MathSciNetzbMATHGoogle Scholar
  35. 35.
    Srivastava A, Klassen E, Joshi SH, Jermyn IH (2011a) Shape analysis of elastic curves in Euclidean spaces. IEEE Trans Pattern Anal Mach Intell 33(7):1415–1428CrossRefGoogle Scholar
  36. 36.
    Srivastava A, Wu W, Kurtek S, Klassen E, Marron J (2011b) Registration of functional data using Fisher-Rao metric. arXiv:1103.3817
  37. 37.
    Teng HL, Wu D, Su F, Pedoia V, Souza RB, Ma CB, Li X (2017) Gait characteristics associated with a greater increase in medial knee cartilage t1\(\rho \) and t2 relaxation times in patients undergoing anterior cruciate ligament reconstruction. Am J Sports Med 45:3262–3271CrossRefGoogle Scholar
  38. 38.
    Thies SB, Tresadern PA, Kenney LP, Smith J, Howard D, Goulermas JY, Smith C, Rigby J (2009) Movement variability in stroke patients and controls performing two upper limb functional tasks: a new assessment methodology. J Neuroeng Rehab 6(1):2CrossRefGoogle Scholar
  39. 39.
    Tucker JD, Wu W, Srivastava A (2013) Generative models for functional data using phase and amplitude separation. Comput Stat Data Anal 61:50–66MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Tucker JD, Wu W, Srivastava A (2014) Analysis of proteomics data: phase amplitude separation using an extended Fisher-Rao metric. Electron J Stat 8(2):1724–1733MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Wu W, Srivastava A (2014) Analysis of spike train data: alignment and comparisons using the extended Fisher–Rao metric. Electron J Stat 8(2):1776–1785MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Yao F, Müller HG, Wang JL (2005) Functional data analysis for sparse longitudinal data. J Am Stat Assoc 100(470):577–590MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© International Chinese Statistical Association 2018

Authors and Affiliations

  1. 1.Department of Healthcare Policy and ResearchWeill Cornell MedicineNew YorkUSA
  2. 2.Department of BiostatisticsColumbia UniversityNew YorkUSA
  3. 3.Department of StatisticsBrigham Young UniversityProvoUSA
  4. 4.Department of Exercise SciencesBrigham Young UniversityProvoUSA
  5. 5.Department of Mechanical EngineeringBrigham Young UniversityProvoUSA

Personalised recommendations