Dynamic heart rate and power output modeling to predict lactate threshold in recreational cyclists

Objective: This study presents a non-invasive method for estimating the second lactate threshold (LT2) in cyclists by modeling the dynamic heart rate (HR) response to power output (PO) using discrete-time transfer function (TF) techniques.Approach: Eleven trained recreational cyclists completed an incremental step test with simultaneous HR, PO, gas exchange, and blood lactate measurements. Two TF models were developed: a time-invariant (TI) model with constant parameters and a time-variant (TV) model whose parameters adapt over time to reflect physiological changes. LT2 was estimated from deviations in model behavior and validated against laboratory-derived LT2 using the modified Dmax method. Agreement was evaluated using absolute error, Pearson correlation, Spearman rank correlation, and Q-Q plots to assess normality of model residuals.Main results: The TV model provided markedly higher accuracy than the TI model. TV estimates showed a mean absolute error of 4%, with LT2 predicted within 10 W for 9 of 11 participants (Pearson r = 0.947; Spearmanρ = 0.954). TI estimation resulted in an average error of 11%, with only 5 participants within 10 W (Pearson r = 0.759; Spearmanρ = 0.756). Q-Q plots revealed deviations from normality in both models' error distributions, particularly for the TI model, supporting the use of rank-based correlation alongside Pearson's r. The TV model captured characteristic changes in HR-PO dynamics more reliably, especially around the transition to heavy-severe intensity.Significance: The proposed TV modeling approach offers an accurate, practical, and fully non-invasive alternative to blood lactate testing, requiring only HR and PO data typically collected by standard cycling devices. Although the method cannot estimate LT1, it holds promise for regular monitoring of LT2 in both laboratory and field settings and may broaden access to metabolic threshold assessment for athletes and coaches.