Validation of the Area1 of Approximate Entropy (a1ApEn) in Empirical Data of Heart Rate

Aims: To validate the use of the non-linear estimator a1ApEn in empirical data.

Study Design: Comparison of heart rate variability/complexity (HRV/C) between rest and low intensity exercise.

Methodology: R-R intervals were obtained from electrocardiogram recordings in 15 healthy volunteers during 30 minutes of rest followed by 30 minutes of treadmill walking (≅ 4 km/h). The R-R series were linearly detrended, checked for stationarity, and windows of 150 non-overlapping intervals were sequentially extracted. HRV/C estimators were obtained: standard deviation (SDNN), root mean square (RMSSD), power of frequency bands (LF, HF and VHF, i.e., above 0.40 Hz) by STFT, normalized power (nu), a1ApEn. Correlations were studied intra-individual between conditions and intra-population. Additionally, in the Fourier Transform data, phases were randomly shuffled, an inverse transform applied (reconstituted rR-R), and RMSSD and a1ApEn were computed. Finally, the scaling profile of a1ApEn between conditions was addressed.

Results: All the HRC/V estimators, except nuLF and nuVHF, showed a decrease in low intensity exercise. For intra-population, all the estimators, except VHF, demonstrated highly significant negative correlations with heart rate. In the reconstituted rR-R series, both RMSSD and a1ApEn increased due to the phase shuffling, while the effect being more intense in a1ApEn. The scaling profile of a1ApEn was compatible with normally distributed random noise in both rest and walk.

Conclusion: As is currently known, HRV/C estimators are intrinsically correlated to heart rate, and a1ApEn follows this rule. Differently from what is usually obtained for plain ApEn, here we show a decrease in complexity values with physical effort. Also, the rR-R analysis indicates that a1ApEn is more sensitive to temporal organization than RMSSD. At the same time, the scaling profile indicates that the complexity of heart rate control keeps the same features from rest to walk. Therefore, we show that a1ApEn is a valid tool in time-series analysis of empirical data.