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

Abstract

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.

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Acknowledgements

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.

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Correspondence to Jihui Lee.

Appendix

Appendix

In Sect. 4.4, we apply functional analysis methods to examine the association between VGRF measurement and in-shoe sensor curves for Subject 2; here, we present the results of functional regression models for Subjects 1 and 3.

Analogous to Fig. 7, Fig. 11 shows the correlations between VGRF and in-shoe sensor curves for Subjects 1 and 3. Similar to Subject 2, these two subjects show neither a clear off-diagonal band nor an obvious peak along the diagonal.

The results in Fig. 12 of cross-validation study for Subjects 2 and 3 are similar to those in Fig. 8 from the main manuscript. For both Subjects 1 and 3, the heel seems most useful, but the model with all four predictors performs the best.

Figures 13 and 14 are analogous to Figs. 9, and 10 in the main manuscript, respectively. Rows in Fig. 13 show the estimated coefficients of function-on-function regression models with all four in-shoe sensors as predictors for Subjects 2 and 3. The estimated coefficients are distinctively different across subjects, implying the unique relationship between VGRF and in-shoe sensors for each subject.

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Lee, J., Li, G., Christensen, W.F. et al. Functional Data Analyses of Gait Data Measured Using In-Shoe Sensors. Stat Biosci 11, 288–313 (2019). https://doi.org/10.1007/s12561-018-9226-3

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Keywords

  • Gait analysis
  • Ground reaction force
  • Functional data
  • Curve registration