Research of short-term heart rate variability during sleep based on limited penetrable horizontal visibility graph

Heart rate is one of the most easily accessed human physiological data. In recent years, the analysis of sleep function based on heart rate variability has become a new popular feature of wearable devices used for daily health management. Consequently, it is needed to explore various types of short-term characteristic parameters which can be applied to the heartbeat interval time series within the standard sleep staging time window (about 30 s). Utilizing the recently reported limited penetrable horizontal visibility graph (LPHVG) algorithm, together with a weighted limited penetrable horizontal visibility graph (WLPHVG) algorithm proposed in this paper, the short-term heartbeat interval time series in different sleep stages are mapped to networks respectively. Then, 6 characteristic parameters, including the average clustering coefficient C, the characteristic path length L, the clustering coefficient entropy Ec, the distance distribution entropy Ed, the weighted clustering coefficient entropy ECw and the weight distribution entropy Ew are calculated and analyzed. The results show that the values of these characteristic parameters are significantly different in the states of wakefulness, light sleep, deep sleep and rapid eye movement, especially in the case of the limited penetrable distance Lp=1, indicating the effectiveness of LPHVG and WLPHVG algorithm in sleep staging based on short-term heartbeat interval time series. In addition, a preliminary comparison between proposed algorithm and the basic visibility graph (VG) algorithm shows that in this case, the LPHVG and WLPHVG algorithm are superior to the basic VG algorithm both in performance and in calculation speed. Meanwhile, based on the LPHVG and WLPHVG algorithm, the values of network parameters (the clustering coefficient entropy Ec and the weighted clustering coefficient entropy ECw) are calculated from heartbeat interval time series of healthy young and elder subjects in different sleep stages, to further study the aging effect on and sleep regulation over cardiac dynamics. It is found that despite an overall level difference between the values of Ec and ECw in young and elder groups, the stratification patterns across different sleep stages almost do not break down with advanced age, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. In addition, compared with the clustering coefficient entropy Ec based on LPHVG algorithm, the weighted clustering coefficient entropy ECw based on WLPHVG algorithm shows higher sensitivity to discriminating subtle differences in cardiac dynamics among different sleep states. Overall, it is shown that with the simple mapping criteria and low computational complexity, the proposed method could be used as a new auxiliary tool for sleep studies based on heart rate variability, and the corresponding network parameters could be used in wearable device as new auxiliary parameters for sleep staging.