Author(s): NACHER-CASTELLET, V., RABOST-GARCIA, G., GARCIA, D.M., GONZALEZ, J.R., Institution: ISGLOBAL, Country: SPAIN, Abstract-ID: 1723

INTRODUCTION:
Accurate detection of the second lactate threshold (LT2) is central to endurance training prescription and performance optimization. Existing mathematical approaches (e.g., Dmax-type, OBLA, log-log) may yield substantially different intensities and often require curve inspection or specific assumptions. A fully automated and computationally efficient method would facilitate large-scale analysis and integration into wearable devices. This study developed and validated a derivative-based method (Der2) to estimate LT2 from step incremental cycling tests.
METHODS:
Twenty-four graded cycling graded exercise tests (Sendra-Perez, C. et. al., 2023) with capillary blood lactate were analyzed. LT2 was calculated using the lactater R package: Log-log, OBLA-4, Dmax, ModDmax, Exp-Dmax, Log-Poly-ModDmax, Log-Exp-ModDmax, and LTP2 (Mattioni Maturana, 2021).

Der2 fits a third-degree polynomial to the lactate-intensity curve and defines LT2 as the intensity where the first and second analytical derivatives are equal.

LT2 intensities were compared using linear mixed models with method as fixed effect and subject as random effect. Type III ANOVA and Bonferroni-adjusted pairwise comparisons were performed. Agreement between Der2 and each method was assessed using mean absolute error (MAE), mean absolute percentage error (MAPE), Bland-Altman analysis, correlation coefficients, and Lin concordance correlation coefficient.
RESULTS:
Method significantly affected LT2 intensity (F(17,422)=53.1, p<0.001). Compared with Der2, Log-log and OBLA-4 produced lower intensities (p<0.001), whereas LTP2 did not differ (p>0.05).

Classical Dmax showed moderate deviation from Der2 (MAE about 0.45 W kg-1; MAPE about 16 percent). ModDmax and Exp-Dmax showed smaller errors (MAE 0.26-0.33 W kg-1; MAPE 7-11 percent) and narrow limits of agreement. Log-Poly-ModDmax and Log-Exp-ModDmax were statistically indistinguishable from Der2 (p>0.05), with low error (MAE 0.26-0.37 W kg-1), small bias, and moderate-to-large correlations.

Overall, Der2 closely matched advanced Dmax-type methods and LTP2, while differing from simpler OBLA and Log-log thresholds. The algorithm requires only a single low-order polynomial fit with closed-form derivatives.
CONCLUSION:
The derivative-based Der2 method reproduces LT2 intensities from established Dmax-type and LTP2 approaches with small bias and acceptable error, while eliminating manual curve inspection. Its low computational cost and deterministic structure make it suitable for large-scale processing and real-time implementation inresource‑constrained wearable devices (e.g. muscle oxygenation or inferring lactate dynamics devices), supporting automated endurance training prescription.

References
Sendra-Perez, C., Priego-Quesada, J. I., & Encarnacion-Martinez, A. (2023). A comparative analysis of mathematical methods for detecting lactate thresholds during a graded cycling test (V1). Mendeley Data.
Mattioni Maturana, F. (2021). lactater: Tools for Analyzing Lactate Thresholds. CRAN.