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.

A New Method for Time Normalization Based on the Continuous Phase: Application to Neck Kinematics

“…As a nonlinear registration method, we have chosen the one proposed in [9,17]. Although there are more recent alternatives, such as SRVF-based methods [15,16], we have chosen this nonlinear registration method as it is the most widely used in the context of human movement analysis. Since the state of motion of a dynamic system is defined by position and velocity, we have considered two nonlinear registration methods: (b1) using position curves (angles); and (b2) using velocity curves.…”

“…In the FDA context, other, much more efficient strategies have been developed to reduce phase variability through different nonlinear registration procedures, as reviewed in [10]. Nonlinear time-scale normalization techniques include landmark registration [11], the sequence of states method [12], dynamic time warping [8,13], and curve registration based on correlation criteria [1,9,14] or on the Fisher-Rao Riemannian metric and square-root velocity function (SRVF) [15,16]. Function registration methods could virtually eliminate all phase variability so that the registered curves have the same shape, differing only by the different amplitudes [11,15].…”

“…On the other hand, we have used the nonlinear registration method proposed in [17], as it is the most widely used in the field of Biomechanics. As indicated above, there are other more recent alternatives, such as those based on SRVF [15], whose application in the field of human movement analysis is limited so far [16], but which should provide better results than those based on correlations.…”