Threshold estimation in running using dynamical correlations of RR intervals

Abstract

We study the estimation of aerobic threshold (AeT) and anaerobic threshold (AnT) using dynamical detrended fluctuation analysis (DDFA). Conventionally, the thresholds are estimated in laboratory settings, where the subject performs an incremental exercise test on a cycloergometer or treadmill. We compared DDFA-based thresholds (DDFAT₁ and DDFAT₂) with lactate thresholds (LT₁ and LT₂) and examined thresholds derived from theoretical and measured maximal heart rates (HR). The analysis was conducted on 58 subjects undergoing an incremental treadmill running test. Our findings indicate significant discrepancies between thresholds derived from theoretical and measured maximal HRs compared to lactate thresholds. Specifically, theoretical maximal HR thresholds consistently underestimated lactate thresholds, exhibiting systematic bias. Measured maximal HR thresholds also showed a consistent underestimation, though with improved alignment to lactate thresholds. In contrast, the DDFA-based method demonstrated reasonable agreement with lactate thresholds and lacked systematic bias. The DDFA-based approach offers a simple and accurate alternative for estimating AeT and AnT. Its potential for continuous monitoring makes it suitable for integration into wearable devices such as smartwatches and heart rate monitors.

Keywords: aerobic threshold; anaerobic threshold; exercise physiology; heart rate variability.

FIGURE 1

Illustration of the DDFA thresholds (cyan vertical lines) compared to the lactate thresholds (black vertical lines) as a function of binned heart rate (HR). The integrated scaling exponent $\tilde{\alpha }\left({\mathrm{HR}}_{\mathrm{bin}}\right)$ and the lactate concentration as a function of binned HR are represented with the black line and pink line, respectively.

FIGURE 2

Illustration of the behavior of integrated scaling exponent $\tilde{\alpha }\left(t\right)$ (black line) and the lactate concentration (cyan line) during the exercise as a function of time. The lactate thresholds are plotted with cyan vertical lines, and the gray line corresponds to heart rate during the exercise.

FIGURE 3

Aggregate plot of the DDFA scaling exponents for all studied subjects as a function of normalized lactate concentration. The black line corresponds to the integrated scaling exponent α(La_norm).

FIGURE 4

Bland–Altman plots of the differences between (a) ${\mathrm{HR}}_{\max }^{\text{theor}}$ T₁ and LT₁, (b) ${\mathrm{HR}}_{\max }^{\text{theor}}$ T₂ and LT₂, (c) ${\mathrm{HR}}_{\max }^{\text{meas}}$ T₁ and LT₁, (d) ${\mathrm{HR}}_{\max }^{\text{meas}}$ T₂, and LT₂, (e) DDFAT₁ and LT₁, and (f) DDFAT₂ and LT₂. The black solid lines correspond to the difference of 0 BPM, blue solid lines correspond to the mean differences and the blue dashed lines correspond to the 95% limits of agreement (= ± 1.96× standard deviation (SD)) of the studied set of data.

FIGURE 5

The error of the estimation for each of the compared method for (a) first lactate threshold, and (b) second lactate threshold. The boxenplots correspond to the mean differences of the estimates, and the red lines correspond to the 95% confidence intervals (CI) after bias‐corrected and accelerated (BCa) bootstrapping (10⁴ times).