From diagnostics to prediction: development and validation of a multi-domain power-duration model

Current models of the power-duration relationship often focus on limited time domains. This study aims to develop and validate a Multi-Domain Power-Duration model (MuDo-PD) to predict power outputs across a wide range of exercise duration (up to 60 min) in cycling, using peak power output (PPO), maximal aerobic power (MAP), and power at lactate threshold 2 (PLT2). Thirty-three well-trained male cyclists (29.2 ± 9.7 yrs; V̇O₂max: 67.2 ± 5.1 mL·min⁻¹·kg⁻¹) performed lab tests to determine PPO (15-s sprint), MAP (ramp test), and PLT2, and completed time trials from 30 to 3600 s. Based on the resulting power-duration profiles and three anchor points (PPO, MAP, PLT2), individual exponential time decay constants (k) were calculated for short (1–300 s; Anaerobic Power Reserve, kAnPR) and long durations (300–3600 s; Aerobic Power Reserve, kAePR), forming the basis of the MuDo-PD model. Internal validation was performed within the modeling cohort by comparing the MuDo-PD to an established critical power approach (OmPD). External validation involved predicting the target power output during a time-to-exhaustion trial in an independent sample of 75 well-trained athletes. Decay constants were kAnPR = -0.023 ± 0.003 s− 1 and kAePR = -0.0023 ± 0.0008 s− 1. The MuDo-PD model showed moderate to excellent agreement with actual power (ICC = 0.63–0.95; RSE = 29 ± 9 W), comparable to OmPD (ICC = 0.80–0.98, RSE = 19 ± 7 W). External validation confirmed excellent accuracy of MuDo-PD (ICC = 0.988; bias = 0.01 ± 17.8 W). The MuDo-PD model enables performance prediction across intensity domains up to 60 min using laboratory diagnostic parameters, offering a practical tool for performance assessment and training control.