## 4 Discussion
Hsi has strengths that are not observed in other HRV indices, respiration signal, or ABM. First, Hsi quantifies the spectral shape of HF component independently of its power. This seems advantageous over indices reflecting the power of HRV that is strongly dependent on age [20], respiratory frequency [21], and health states affecting autonomic function [22]. In fact, we observed that the discriminant performance of Hsi was independent of age and AHI. Second, Hsi was developed on the solid physiological basis that respiratory regularity increases with NREM sleep. In contrast, the autonomic indices of HRV and ABM are based on indirect or relative relationships. Although autonomic functions and heart rate dynamics are known to differ with sleep stage [3; 7], the changes of these metrics from wake to sleep are continuous but not discrete, and there is no convincing physiological basis supporting for their ability to distinguish light sleep from awake rest. If Hsi reflects respiratory regularity, it may be speculated that respiration regularity measured directly from respiration signals may indicate better discriminant power of NREM stage than Hsi obtained from ECG. To examine this hypothesis, we calculated Hsi from the power spectrum of respiration. We observed, however, that the discriminant performance of the Hsi of respiration did not exceed that of Hsi of R-R interval. Although the exact mechanisms deserve further studies, a possible mechanism is that the measurements of respiration signal could be affected by noises from sources including body movements and external air flow, while respiratory fluctuation in heart rate is caused by intrinsic central neural mechanisms [23] that may be less affected by such disturbances. This may support for the use of ECG or other heartbeat signals from wearable devices for calculating Hsi. Hsi seems to provide a useful indicator of sleep for both clinical and health promotion fields. Because the cardiac autonomic functions are modulated by sleep and sleep stages [1; 2; 4], the information of sleep period and sleep stage during Holter ECG monitoring are apparently useful for investigating the mechanisms of arrhythmias and other transient phenomena that show heterogeneous temporal distributions during the day. Information on sleep period is also important for ECG screening for sleep-related pathological phenomena such as SDB. SDB can be effectively screened by cyclic variation of heart rate that accompanies the episodes of sleep apnea [5; 6]. Without the information of sleep period, however, it is hard to determine whether a patient does not have SDB or has not slept when the cyclic variation is not observed. In health promotion fields, due to the widespread use of wearable sensors, beat-to-beat heart rate or pulse rate data during daily life are being accumulated as big data. Along with this, the demands for automated algorithms to evaluate health indicators are rising. Hsi seems to provide a powerful and indispensable element for such methods to estimate sleep period and sleep stages from heart rate and pulse rate big data. A limitation of this study is that the dependency of discriminant accuracy on the length of data segment. In this study, consecutive 10 sleep stages were grouped into one 5-min segment for which Hsi was calculated, although sleep stages were determined every 30-s epochs in polysomnography. In a supplementary study in a group of healthy subjects, we have observed the discriminant accuracy of NREM sleep by Hsi is affected by the length of segment; AUCs of discriminant performance of Hsi were 0.88, 0.84, and 0.80 for segment length of 5, 3, and 2 min, respectively (Figure S1). Therefore, we also examined the performance of 5-min segment His to discriminate the sleep stage of 30-s epoch. As expected, the discriminant performance of all indices including Hsi reduced, although Hsi still showed the best performance among them. The temporal resolution and the accuracy of sleep stage are in a trade-off relationship. Another possible limitation is the effects of SDB on Hsi.