Non-linear methods for the quantification of cyclic motion

Abstract

Traditional methods of human motion analysis assume that fluctuations in cycles (e.g. gait motion) and repetitions (e.g. tennis shots) arise solely from noise. However, the fluctuations may have enough information to describe the properties of motion. Recently, the fluctuations in motion have been analysed based on the concepts of variability and stability, but they are not used uniformly. On the one hand, these concepts are often mixed in the existing literature, while on the other hand, these concepts have been related to different methods for non-linear and chaotic time series analysis. After the clarification of these concepts, this dissertation presents the analysis of the evidence for chaos in cycling motion. Further, new algorithms are described for the analysis of the variability of the observed variables from the gait motion by means of a novel curve registration method. Finally, a novel approach for the estimation of torque variation from pedal motion during cycling ergometry is introduced and validated. This thesis includes three main parts. In the first part, a case study of knee motion during cycling ergometry is presented using the state-of-the-art tools. Non-linear methods and hypothesis testing based on surrogate data were used to analyse whether the aperiodic behaviour of noisy data captured from knee motion data originating from a low-dimensional deterministic (possibly chaotic) process or whether it was governed by stochastic ones. The critical sensitivity of chaotic systems to both the initial conditions and perturbations may explain the irregular behaviour of pedalling motion. However, the time series recorded from knee motion did not show a clear scaling region typical in chaotic time series. Further, evidence of chaos based on surrogate data could not be found for all time series. In addition, an improvement of the statistical criterion for hypothesis testing based on surrogate data is discussed. In the second part, a novel tool for curve registration that facilitates the analysis of cycles in cyclic motion is presented and validated using gait acceleration data. The equalized DBA (eDBA) method calculates the average of a set of cycles based on dynamic time warping (DTW) and a modification of DTW barycentric averaging (DBA). The eDBA algorithm allows the study of the kinematic variables in cyclic motion depending on the phase using the eDBA average cycle as the reference for phase registration. A novel quality definition is given which provides a criterion for the selection of the best phase angle for further analysis. Further, the effects of phase registration using the eDBA method on Self-Organizing Maps (SOMs) are described. The quality of the SOMs and the classification rate improved when the registration was applied in the preprocessing step. In the third part, a novel approach for the estimation of torque variation from pedal motion in cycling ergometry is presented and validated. For an ergometer with almost constant brake torque, we may assume that variations in the net torque can be extracted from the pedal motion alone. The key problem is to reliably estimate the angular pedal acceleration from measurements of pedal motion, which can be made in the laboratory using motion-capturing with two light-emitting diodes (LEDs) or a plain commercial video camera with two light-emitting diodes (LEDs). The results from video were close to motion capturing data (MoCap) results when a novel method for the correction of the marker position was applied.