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Identification of energy‑system–specific impulse–response parameters

Identify the energy-system–specific impulse–response parameters—namely the fitness and fatigue weighting factors (k1, k2) and time constants (T1, T2)—for the oxidative system (critical power, CP), glycolytic work capacity (W′), and maximal sprint power (Pmax) to enable separate performance management charts and predictions for each system.

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Background

The authors argue that adaptation kinetics differ across energy systems and that separate impulse–response parameters are needed for CP, W′, and Pmax. Existing literature reports parameters derived from one-dimensional models that amalgamate responses and may not reflect system-specific kinetics.

They explicitly note that published data establishing such energy-system–specific parameters are lacking, underscoring the need for empirical determination to operationalize the three-dimensional model in practice.

References

While no published data exist to support the energy-system specific model parameters, the assumption of their independence is suggested by data demonstrating that anaerobic performance can be enhanced in shorter time frames (different t) and with much smaller doses (different k) than aerobic performance (Gibala et al., 2006; Mølmen et al., 2025; Roberts et al., 1982; Ross & Leveritt, 2001).

— The three-dimensional impulse-response model: Modeling the training process in accordance with energy system-specific adaptation (2503.14841 - Kontro et al., 19 Mar 2025) in Section IV. The three-dimensional impulse-response model, subsection “What are the model parameters for each energy system?”