Phase space methods for non-linear analysis of pedalling forces in cycling

Analysis of Movement Variability in Cycling: An Exploratory Study

The purpose of this study was to determine the test-retest repeatability of Blue Trident inertial measurement units (IMUs) and VICON Nexus kinematic modelling in analysing the Lyapunov Exponent (LyE) during a maximal effort 4000 m cycling bout in different body segments/joints. An additional aim was to determine if changes in the LyE existed across a trial. Twelve novice cyclists completed four sessions of cycling; one was a familiarisation session to determine a bike fit and become better accustomed to the time trial position and pacing of a 4000 m effort. IMUs were attached to the head, thorax, pelvis and left and right shanks to analyse segment accelerations, respectively, and reflective markers were attached to the participant to analyse neck, thorax, pelvis, hip, knee and ankle segment/joint angular kinematics, respectively. Both the IMU and VICON Nexus test-retest repeatability ranged from poor to excellent at the different sites. In each session, the head and thorax IMU acceleration LyE increased across the bout, whilst pelvic and shank acceleration remained consistent. Differences across sessions were evident in VICON Nexus segment/joint angular kinematics, but no consistent trend existed. The improved reliability and the ability to identify a consistent trend in performance, combined with their improved portability and reduced cost, advocate for the use of IMUs in analysing movement variability in cycling. However, additional research is required to determine the applicability of analysing movement variability during cycling.

Quantifying workload using nonlinear dynamical measures of biomechanical parameters during cycling on a roller trainer

The aim of the present study was to determine the effectiveness of nonlinear parameters in distinguishing individual workload in cycling by using bike-integrated sensor data. The investigation focused on two nonlinear parameters: The ML1, which analyzes the geometric median in phase space, and the maximum Lyapunov exponent as nonlinear measure of local system stability. We investigated two hypothesis: 1. ML1α, derived from kinematic crank data, is as good as ML1F, derived from force crank data, at distinguishing between individual load levels. 2. Increasing load during cycling leads to decreasing local system stability evidenced by linearly increasing maximal Lyapunov exponents generated from kinematic data. A maximal incremental cycling step test was conducted on an ergometer, generating complete datasets from 10 participants in a laboratory setting. Pedaling torque and kinematic data of the crank were recorded. ML1F, ML1α, and Lyapunov parameters (λst, λlt, ιst, ιlt) were calculated for each participant at comparable load levels. The results showed a significant linear increase in ML1α across three individual load levels, with a lower but still large effect compared to ML1F. The contrast analysis also confirmed a linearly increasing trend for λst across three load levels, but this was not confirmed for λlt. However, the intercepts ιst and ιlt of the short- and longterm divergence showed a statistically significant linear increase across the load levels. In summary, nonlinear parameters seem fundamentally suitable to distinguish individual load levels in cycling. It is concluded that higher load during cycling is associated with decreasing local system stability. These findings may aid in developing improved e-bike propulsion algorithms. Further research is needed to determine the impact of factors occurring in field application.