Entropy Analysis of Heart Rate Variability in Different Sleep Stages

Abstract

How the complexity or irregularity of heart rate variability (HRV) changes across different sleep stages and the importance of these features in sleep staging are not fully understood. This study aimed to investigate the complexity or irregularity of the RR interval time series in different sleep stages and explore their values in sleep staging. We performed approximate entropy (ApEn), sample entropy (SampEn), fuzzy entropy (FuzzyEn), distribution entropy (DistEn), conditional entropy (CE), and permutation entropy (PermEn) analyses on RR interval time series extracted from epochs that were constructed based on two methods: (1) 270-s epoch length and (2) 300-s epoch length. To test whether adding the entropy measures can improve the accuracy of sleep staging using linear HRV indices, XGBoost was used to examine the abilities to differentiate among: (i) 5 classes [Wake (W), non-rapid-eye-movement (NREM), which can be divide into 3 sub-stages: stage N1, stage N2, and stage N3, and rapid-eye-movement (REM)]; (ii) 4 classes [W, light sleep (combined N1 and N2), deep sleep (N3), and REM]; and (iii) 3 classes: (W, NREM, and REM). SampEn, FuzzyEn, and CE significantly increased from W to N3 and decreased in REM. DistEn increased from W to N1, decreased in N2, and further decreased in N3; it increased in REM. The average accuracy of the three tasks using linear and entropy features were 42.1%, 59.1%, and 60.8%, respectively, based on 270-s epoch length; all were significantly lower than the performance based on 300-s epoch length (i.e., 54.3%, 63.1%, and 67.5%, respectively). Adding entropy measures to the XGBoost model of linear parameters did not significantly improve the classification performance. However, entropy measures, especially PermEn, DistEn, and FuzzyEn, demonstrated greater importance than most of the linear parameters in the XGBoost model.300-s270-s.

Keywords: complexity; entropy; heart rate variability (HRV); sleep stage.

Figure 1

The schematic of 270-s and 300-s epoch construction. Each small square represents a 30-s epoch, and the content in the square represents the sleep stage annotation. The sub-epochs painted in orange constitute the currently constructed epoch. (a) A window of 270-s in length slides forward with 30-s as the step length. The red box represents the middle 30-s sub-epoch, which represents the annotation of the current 270-s epoch. (b) A window of 300-s in length slides forward with 30-s as the step length. The red boxes indicate the current 300-s epoch was reserved, while purple boxes indicate that it has been excluded. The RR interval series corresponding to the current 270-s or 300-s epoch is the time series to be analyzed.

Figure 2

Entropy results of the RR intervals computed based on 270-s epochs. (a) ApEn. (b) SampEn. (c) FuzzyEn. (d) DistEn. (e) CE. (f) PermEn. The error bars indicate the standard error in each stage. *: W vs. N1, N2, N3, and REM; ^†: N1 vs. N2, N3, and REM; ^§: N2 vs. N3 and REM; ^¶: N3 vs. REM. The number of symbols indicates the degree of significant difference, e.g., *, ^†: p < 0.05; **, ^††, ^§§, ^¶¶: p < 0.01; ***, ^†††, ^§§§, ^¶¶¶: p < 0.0001.

Figure 3

Entropy results of the RR intervals computed based on 300-s epochs. (a) ApEn. (b) SampEn. (c) FuzzyEn. (d) DistEn. (e) CE. (f) PermEn. The error bars indicate the standard error in each stage. *: W vs. N1, N2, N3, and REM; ^†: N1 vs. N2, N3, and REM; ^§: N2 vs. N3 and REM; ^¶: N3 vs. REM. The number of symbols indicates the degree of significant difference, e.g., *, ^†: p < 0.05; **, ^††, ^§§, ^¶¶: p < 0.01; ***, ^†††, ^§§§, ^¶¶¶: p < 0.0001.

Figure 4

Importance of input features on sleep stage classification. Upper panels: results using 270-s epochs. Lower panels: results using 300-s epochs. Left panels (a1,a2) five-class classification. Middle panels (b1,b2) four-class classification. Right panels (c1,c2) three-class classification. The abscissa value corresponding to each feature is the weight that the feature plays in the classification.