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

Figures

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  Fig 1. Method for calculating ML1 using the example ML1F. A sliding window considering 50 full z-standardized and time-normalized pedaling cycles to calculate ML1F (see bottom of Fig 1; 30 instead of 50 pedaling-cycles are considered). The geometric median in 2-dimensional phase-space with a 25% delay was determined (see right side of Fig 1) for these cycles.

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  Fig 2. Method for calculating Lyapunov-exponent. A: Average Mutual Information (AMI) for all time series to determine overall delay. B: Distribution of considered delays as first AMI minimum. Overall delay was set to τ = 29. C: Calculation of False Nearest Neighbors to define overall embedding dimension, which was stated as ed = 4. D: Logarithmic divergence for calculating the short-term Lyapunov exponent as the slope for the first 100 points (λst) and long-term Lyapunov exponent as slope for 400 to 1000 points (λlt). Short-term and long-term intercepts were also considered.

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  Fig 3. Results of the ML1 calculation. Individual participants are displayed as dashed lines. A: ML1F across relative power intervals using crank force data. B: ML1α across relative power intervals using crank acceleration data.

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  Fig 4. Results of the Lyapunov calculation. A: Short-term Lyapunov exponents as slope λst across relative power intervals show a slight increasing trend. B: Long-term Lyapunov exponents as slope λlt across relative power intervals show no trend. C: Short-term Lyapunov intercepts ιst show an increasing trend across relative power intervals. D: Long-term Lyapunov intercepts ιlt also show an increasing trend across relative power intervals.

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  Fig 5. Results of the calculation of the standard deviation. An increase of the standard deviation across relative power intervals was present for 5 out of 10 participants.

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  Fig 6. Spectral analysis. Exemplary time series with labeled characteristic frequencies.