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. ML1(α), derived from kinematic crank data, is as good as ML1(F), 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. ML1(F), ML1(α), and Lyapunov parameters (λ(st), λ(lt), ι(st), ι(lt)) were calculated for each participant at comparable load levels. The results showed a significant linear increase in ML1(α) across three individual load levels, with a lower but still large effect compared to ML1(F). The contrast analysis also confirmed a linearly increasing trend for λ(st) across three load levels, but this was not confirmed for λ(lt). However, the intercepts ι(st) and ι(lt) 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.