Non-invasive lactate threshold estimation using deep learning: practical applications across endurance sports

Abstract

Purpose: To develop a non-invasive deep learning

Method: for estimating heart rate at the 2 mmol·L⁻¹ lactate threshold (HR₂ₘₘₒₗ) and evaluate its cross-sport generalisation across endurance disciplines.

Methods: We analysed 823 incremental exercise tests from 537 male and 286 female athletes across running, cycling, rowing, and kayak. A deep learning model predicted HR₂ₘₘₒₗ from heart rate and power/pace data and was compared with D-max, modified D-max, OBLA-4, and machine learning baselines using 5-fold cross-validation. Generalisation was assessed through leave-one-sport-out experiments.

Results: The model achieved a mean absolute error of 5.56 bpm, comparable to laboratory test-retest variability, and outperformed modified D-max by 35.8% (3.10 bpm). Cross-sport application increased error by 37–103%, with kayak showing the poorest performance (11.27 bpm). Bootstrap analysis suggested physiological differences limited running generalisation, whereas cycling failure was related to sample size, although not significantly (p = 0.65).

Conclusion: Deep learning accurately estimated HR₂ₘₘₒₗ within trained sports, supporting its use as a screening tool. However, sport-specific validation remains essential, and individual uncertainty prevents replacing direct blood sampling for precise training prescription.