The main findings of this study demonstrated that TI and TE had distinct effects on the magnitudes of DC and AC. The newly defined index (HRADC) quantifies the difference between them and showed a close correlation with the conventional HRAGI and HRAPI. Both increasing TI and increasing TE had a positive impact on the magnitudes of the HRA indexes. However, their effects differed in terms of timing. TI had a significant effect when it was ≤ 4 s, whereas TE showed its influence when > 4 s. As a result, the optimal combination for maximizing DC and the HRA indexes was found to be a TI of 4 s and a TE of 6 s. These findings shed light on the specific roles of TI and TE in modulating heart rate variability and asymmetry, providing valuable insights for the optimization of respiratory settings in relation to cardiac autonomic regulation.

In our study, the observed changes in average RRI and respiratory sinus arrhythmia with varying respiratory interval were consistent with previous reports (Brown et al. 1993; Angelone and Coulter 1964). Interestingly, the magnitude of AC was found to be almost unaffected by TI, contrasting with DC that showed significant changes with TI (Fig. 5A). This observation aligns with previous findings when investigating the effects of isolated deep inspirations, where slow and fast inspirations produced identical magnitudes of acceleratory heart rate responses but different deceleration responses, with slow inspirations resulting in larger deceleration responses than fast inspirations (Stern and Anschel 1968). As a result, TI emerged as a major factor contributing to the difference between the magnitudes of DC and AC (Fig. 5B). Conversely, the magnitudes of both DC and AC were enhanced with increased TE. The change in the magnitude of DC was relatively larger than that of AC, particularly at TE of 6 s (Fig. 5A). Hence, TE also played a role in the difference between the magnitudes of DC and AC (Fig. 5B). Notably, the distinct effects of TI and TE on the magnitudes of DC and AC, contributing to the overall asymmetry, were consistent with their effects on HRADC (Fig. 5C).

In our study, we replicated the computation method of HRAGI and introduced a novel index, HRADC, defined as 100 × DC2/ (DC2 + AC2). DC and AC were computed using the formula (RRIn + 1 + RRIn − RRIn-1 − RRIn-2)/4, where RRIn represents the anchor point. In the context of the Poincaré plot, the squared distance of a point (RRIn-1, RRIn) from the line of identity is given by (RRIn − RRIn-1)2/2. Therefore, we squared DC and AC values to calculate HRADC. Interestingly, HRADC exhibited a strong correlation with HRAPI and HRAGI (Fig. 6C). The impacts of TI and TE on HRADC (Fig. 5C) mirrored those observed for HRAGI and HRAPI (Fig. 6B). Consequently, this new index served as a bridge connecting the PRSA technique and Poincaré plot analysis. We used it to show that common autonomic indicators obtained by these methods are closely related in some fixed form.

The effects of respiratory interval on HRA have been previously reported, with HRA increasing as the respiratory interval lengthens (Wang et al. 2013, 2015). The impact of I/E on HRA depends on the specific respiratory interval. For instance, prior research indicates that during 4-s breathing, HRA is greater at 1:1 (TI = 2 s) than at 1:2 (TI = 1.3 s) and 1:3 (TI = 1 s), but no difference is observed among 1:1 (TI = 5 s), 1:2 (TI = 3.3 s) and 1:3 (TI = 2.5 s) during 10-s breathing (Wang et al. 2013). Similarly, HRA significantly increases at 2:1 (TI = 3 s) and 1:1 (TI = 2.25 s) compared to 1:2 (TI = 1.5 s) during 4.5-s breathing (Klintworth et al. 2012). Our current findings align with these prior studies. Interestingly, HRADC at 2:1 (TI = 4 s) is significantly greater than at 1:2 (TI = 2 s) during 6-s breathing, while HRADC remains unaffected by I/E during 8- and 10-s breathing (Fig. 5D). Taken together, these observations emphasize the pivotal role of TI, especially at smaller values. In our investigation, we observed that the effect of TI is maximized at 4 s. Notably, we propose that 2.5 s may represent a critical point since HRA does not exceed 50% even at I2-E6 (8-s breathing; Fig. 5C), yet it becomes significantly greater than 50% at I2.5-E2.5 (5-s breathing) (Wang et al. 2015).

Conversely, TE seems to play a more significant role at larger values. For instance, HRA at I2.5-E2.5 is smaller than at I5-E5 (Wang et al. 2015), whereas HRA at I2.5-E7.5 is comparable to that at I5-E5 (Wang et al. 2013). Our data also indicate that the magnitude of HRA is maximized with a TE of 6 s. Collectively, these results suggest that an optimal approach to maximize the effect of slow respiration would involve a TI of 3–4 s paired with a TE of 7–6 s. Previous studies have applied paced breathing with a TI of 3 s and a TE of 7 s (Raupach et al. 2008; Tsai et al. 2015), which is in line with our proposed optimal combination.

The underlying mechanism of HRA appeared to be closely linked to cardiac vagal activity, given that both DC and AC have been demonstrated to rely solely on vagal activity in a model study (Pan et al. 2016). Further support can be drawn from physiological findings. Respiration is known to mechanically induce fluctuations in intrathoracic pressure, cardiac filling, and arterial pressure, which subsequently triggers baroreceptor reflex responses leading to variations of RRI in accordance with the respiratory cycle (Zhang et al. 2002). The cardiac baroreflex response is characterized by asymmetry; the slopes of RRI lengthening during arterial pressure increase are steeper than the slopes of RRI shortening during arterial pressure decrease. Interestingly, changes in muscle sympathetic nerve activity exhibit comparable patterns during both falling and rising arterial pressure (Rudas et al. 1999). Similar RRI responses are observed with the application of the neck chamber technique, which triggers baroreceptor activity (Eckberg 1980). Notably, atropine abolishes RRI responses to both neck suction and neck pressure, while propranolol only augments RRI prolongation, leaving RRI shortening unaffected (Eckberg 1980).

It is important to note that mean cardiac vagal activity might remain relatively unchanged during varying respiratory phase durations. Mean cardiac vagal tone, as estimated from the mean RRI under β-adrenergic blockade, has been found to be unaffected by changes in respiratory rate or tidal volume (Grossman et al. 1991; Hayano et al. 1994). In line with this, the mean RRI in our study, although not under β-adrenergic blockade, remained comparable across the different respiratory settings. However, the heightened HRA magnitude observed during slow respiration implies a periodic short-term and high-intensity activation of vagal activity coupled with a gradual vagal withdrawal. The alterations in vagal activity align with clinical observations that carry significant implication. The reduction in DC that corresponds to the decreases in vagal activity has been identified as a marker associated with increased mortality in patients who have experienced an acute myocardial infarction. Moreover, DC, compared to AC, is a more accurate and sensitive parameter for risk prediction (Bauer et al. 2006a).

In this study, we investigated young healthy volunteers in the sitting position. The results may be different in subjects with different posture or with an altered baroreflex function such as elderly, diabetic, or hypertensive individuals. Inspiratory and expiratory durations were controlled at 2, 4, and 6 s to cover the physiological ranges in breathing frequency and respiratory time ratio. The reverse ratio was also tested here. Whether the results would be the same at shorter or longer respiratory durations was not evaluated. The speed of inhalation and exhalation was not controlled in this study. We asked the participants to adjust tidal volume by themselves in order to maintain constant alveolar ventilation and normal arterial CO2 levels. Therefore, our results should be considered as the combined effects of respiratory duration and tidal volume. There were no training sessions before the 7-min formal recordings, but 2-min data were allowed to be excluded if visually unstable. We further examined the stationary nature of selected RRI time series using reverse arrangement test. Participants were excluded if necessary.

In conclusion, our study delved into the intricate interplay between respiratory phase durations and heart rate variations. The findings underscore the distinct impacts of TI and TE on both DC and HRA. Notably, while a TI exceeding 4 s did not yield significant benefit, a TE surpassing 4 s exhibited a positive effect in maximizing the influence of slow respiration on these autonomic indexes. Based on our results, we propose that a targeted TI of 3 to 4 s coupled with a TE of 7 to 6 s constitutes an optimal standard for achieving the desired outcomes of slow respiration. This recommendation is intended to guide the practice of controlled breathing techniques for individuals seeking to modulate heart rate variability and enhance autonomic balance.