Analysis of multiple waveforms by means of functional principal component analysis: normal versus pathological patterns in sit-to-stand movement

  • Irene Epifanio
  • Carolina Ávila
  • Álvaro Page
  • Carlos Atienza
Original Article


This paper presents an application of functional principal component analysis (FPCA) to describe the inter-subject variability of multiple waveforms. This technique was applied to the study of sit-to-stand movement in two groups of people, osteoarthritic patients and healthy subjects. Although STS movement has not been extensively applied to the study of knee osteoarthritis, it can provide relevant information about the effect of osteoarthritis on knee joint function. Two waveforms, knee flexion angle and flexion moment, were analysed simultaneously. Instead of using the common multivariate approach we used the functional one, which allows working with continuous functions with neither discretization nor time-scale normalization. The results show that time-scale normalization can alter the FPCA solution. Furthermore, FPCA presents better discriminatory power compared with the classical multivariate approach. This technique can, therefore, be applied as a functional assessment tool, allowing the identification of relevant variables to discriminate heterogeneous groups such as healthy and pathological subjects.


Functional assessment Sit-to-stand movement Functional data Principal component analysis 



This study has been partially supported by Spanish Government Grant DPI2006-14722-C02-01 (cofinanced by EU FEDER funds), CICYT MTM2005-08689-C02-02, TIN2006-10134 and Fundació Caixa Castelló P11B2004-15.


  1. 1.
    Arborelius UP, Wretenberg P, Lindberg F (1992) The effects of armrests and high seat heights on lower-limb joint load and muscular activity during sitting and rising. Ergonomics 35(11):1377–1391CrossRefGoogle Scholar
  2. 2.
    Astephen JL, Deluzio KJ (2005) Changes in frontal plane dynamics and the loading response phase of the gait cycle are characteristic of severe knee osteoarthritis application of a multidimensional analysis technique. Clin Biomech 20(2):209–217. doi: 10.1016/j.clinbiomech.2004.09.007 CrossRefGoogle Scholar
  3. 3.
    Conover WJ (1998) Some methods based on ranks. Practical nonparametric statistics, 3rd edn. Wiley, New York, pp 269–467Google Scholar
  4. 4.
    Daffertshofer A, Lamoth CJ, Meijer OG, Beek PJ (2004) PCA in studying coordination and variability: a tutorial. Clin Biomech 19(4):415–428. doi: 10.1016/j.clinbiomech.2004.01.005 CrossRefGoogle Scholar
  5. 5.
    Deluzio KJ, Wyss UP, Costigan PA, Sorbie C, Zee B (1999) Gait assessment in unicompartmental knee arthroplasty patients: principal component modelling of gait waveforms and clinical status. Hum Mov Sci 18(5):701–711. doi: 10.1016/S0167-9457(99)00030-5 CrossRefGoogle Scholar
  6. 6.
    Deluzio KJ, Wyss UP, Zee B, Costigan PA, Serbie C (1997) Principal component models of knee kinematics and kinetics: normal vs. pathological gait patterns. Hum Mov Sci 16:201–217. doi: 10.1016/S0167-9457(96)00051-6 CrossRefGoogle Scholar
  7. 7.
    el Nahass B, Madson MM, Walker PS (1991) Motion of the knee after condylar resurfacing—an in vivo study. J Biomech 24(12):1107–1117CrossRefGoogle Scholar
  8. 8.
    Hughes MA, Myers BS, Schenkman ML (1996) The role of strength in rising from a chair in the functionally impaired elderly. J Biomech 29(12):1509–1513Google Scholar
  9. 9.
    Ikeda ER, Schenkman ML, Riley PO, Hodge WA (1991) Influence of age on dynamics of rising from a chair. Phys Ther 71(6):473–481Google Scholar
  10. 10.
    Ivanenko YP, Poppele RE, Lacquaniti F (2004) Five basic muscle activation patterns account for muscle activity during human locomotion. J Physiol 556(1):267–282. doi: 10.1113/jphysiol.2003.057174 CrossRefGoogle Scholar
  11. 11.
    Jevsevar DS, Riley PO, Hodge WA, Krebs DE (1993) Knee kinematics and kinetics during locomotor activities of daily living in subjects with knee arthroplasty and in healthy control subjects. Phys Ther 73(4):229–242Google Scholar
  12. 12.
    Lamoth CJ, Daffertshofer A, Meijer OG, Lorimer Moseley G, Wuisman PI, Beek PJ (2004) Effects of experimentally induced pain and fear of pain on trunk coordination and back muscle activity during walking. Clin Biomech 19(6):551–563. doi: 10.1016/j.clinbiomech.2003.10.006 CrossRefGoogle Scholar
  13. 13.
    Leardini A, Chiari L, Della Croce U, Cappozzo A (2005) Human movement analysis using stereophotogrammetry. Part 3. Soft tissue artifact assessment and compensation. Gait Posture 21(2):212–225. doi: 10.1016/j.gaitpost.2004.05.002 CrossRefGoogle Scholar
  14. 14.
    Li ZM, Tang J (2007) Coordination of thumb joints during opposition. J Biomech 40(3):502–510. doi: 10.1016/j.jbiomech.2006.02.019 CrossRefGoogle Scholar
  15. 15.
    Mizner RL, Snyder-Mackler L (2005) Altered loading during walking and sit-to-stand is affected by quadriceps weakness after total knee arthroplasty. J Orthop Res 23(5):1083–1090. doi: 10.1016/j.orthres.2005.01.021 CrossRefGoogle Scholar
  16. 16.
    Mouchnino L, Mille ML, Martin N, Baroni G, Cincera M, Bardot A et al (2006) Behavioral outcomes following below-knee amputation in the coordination between balance and leg movement. Gait Posture 24(1):4–13. doi: 10.1016/j.gaitpost.2005.07.007 CrossRefGoogle Scholar
  17. 17.
    Page A, Ayala G, Leon MT, Peydro MF, Prat JM (2006) Normalizing temporal patterns to analyze sit-to-stand movements by using registration of functional data. J Biomech 39(13):2526–2534. doi: 10.1016/j.jbiomech.2005.07.032 CrossRefGoogle Scholar
  18. 18.
    Page A, Epifanio I (2007) A simple model to analyze the effectiveness of linear time normalization to reduce variability in human movement analysis. Gait Posture 25(1):153–156. doi: 10.1016/j.gaitpost.2006.01.006 CrossRefGoogle Scholar
  19. 19.
    Ramsay J, Dalzell C (1991) Some tools for functional data analysis. J R Stat Soc Ser B Methodol 3(3):539–572MathSciNetGoogle Scholar
  20. 20.
    Ramsay JO, Silverman BW (2002) Applied functional data analysis: methods and case studies. Springer, New YorkMATHGoogle Scholar
  21. 21.
    Ramsay JO, Silverman BW (2005) Functional data analysis. Springer, New YorkGoogle Scholar
  22. 22.
    Raptopoulos LSC, Dutra MS, Pinto FANC, de Pina Filho AC (2006) Alternative approach to modal gait analysis through the Karhunen–Loève decomposition: an application in the sagittal plane. J Biomech 39(15):2898–2906. doi: 10.1016/j.jbiomech.2005.09.017 CrossRefGoogle Scholar
  23. 23.
    Rodosky MW, Andriacchi TP, Andersson GB (1989) The influence of chair height on lower limb mechanics during rising. J Orthop Res 7(2):266–271CrossRefGoogle Scholar
  24. 24.
    Saari T, Tranberg R, Zugner R, Uvehammer J, Karrholm J (2004) The effect of tibial insert design on rising from a chair; motion analysis after total knee replacement. Clin Biomech 19(9):951–956. doi: 10.1016/j.clinbiomech.2004.06.010 CrossRefGoogle Scholar
  25. 25.
    Sadeghi H, Sadeghi S, Prince F, Allard P, Labelle H, Vaughan CL (2001) Functional roles of ankle and hip sagittal muscle moments in able-bodied gait. Clin Biomech 16(8):688–695. doi: 10.1016/S0268-0033(01)00058-4 CrossRefGoogle Scholar
  26. 26.
    Schultz AB, Alexander NB, Ashton-Miller JA (1992) Biomechanical analyses of rising from a chair. J Biomech 25(12):1383–1391CrossRefGoogle Scholar
  27. 27.
    Su FC, Lai KA, Hong WH (1998) Rising from chair after total knee arthroplasty. Clin Biomech 13(3):176–181. doi: 10.1016/S0268-0033(97)00039-9 CrossRefGoogle Scholar
  28. 28.
    Troje NF (2002) Decomposing biological motion: a framework for analysis and synthesis of human gait patterns. J Vis 2(5):371–387CrossRefGoogle Scholar
  29. 29.
    Wrigley AT, Albert WJ, Deluzio KJ, Stevenson JM (2005) Differentiating lifting technique between those who develop low back pain and those who do not. Clin Biomech 20(3):254–263. doi: 10.1016/j.clinbiomech.2004.11.008 CrossRefGoogle Scholar
  30. 30.
    Wrigley AT, Albert WJ, Deluzio KJ, Stevenson JM (2006) Principal component analysis of lifting waveforms. Clin Biomech 21(6):567–578. doi: 10.1016/j.clinbiomech.2006.01.004 CrossRefGoogle Scholar

Copyright information

© International Federation for Medical and Biological Engineering 2008

Authors and Affiliations

  • Irene Epifanio
    • 1
  • Carolina Ávila
    • 2
  • Álvaro Page
    • 2
  • Carlos Atienza
    • 2
  1. 1.Departament de MatemàtiquesUniversitat Jaume ICastellónSpain
  2. 2.Instituto de Biomecánica de ValenciaUniversidad Politécnica de ValenciaValenciaSpain

Personalised recommendations