The primary purpose of the present study was to use the Bayesian estimation of correlation to estimate the association between measures of HRV indices, aerobic performance and blood pressure indices using MCMC simulation in an attempt to explain the conflicting results reported in the literature by qualitatively comparing the reported results with the Bayesian estimated results. Hence, to assure the validity of the data presented in this study, a secondary aim was to compare the data produced to the reported norms and to investigate the estimation of the association within the HRV indices in comparison to those reported. The main finding in this study was that the simulation of 20,000 samples to produce the posterior possible association resulted in similar data that were within the reported norms. Furthermore, the association within the HRV indices is in line with what has been reported in the literature. Hence, the Bayesian estimation of correlation using MCMC simulation reproduced and supported the findings reported regarding the norms and within the HRV indices associations. Furthermore, the results of the Bayesian estimation showed that the association between HRV indices and aerobic performance parameters was unclear, indicated by the estimated rho, which has an equal chance to fall within the 95% HDI. Finally, a confirmed probability of association between HRV indices (PNS & SNS) and RPP was observed, and a trivial probability of association between pNN50 (%) and MAP at resting condition were also detected.
4.1. Measures of HRV Indices Compared to Norms
At the time of the task force report, there had been no comprehensive investigation regarding HRV indices, and the reported normal values were based on a few studies reporting both long and short term recordings [
3]. The approximate values reported for the short-term recording (5 min) were for the LF ms
2 = 1170 ± 416, HF ms
2 = 975 ± 203, LF nu = 54 ± 4 and HF nu = 29 ± 3 [
3]. It should be noted that the task force report did not account for age, sex, environment and recording condition (supine (rest), reactivation (during training) and rest (post activation)). Therefore, the normal values from the task force report could be considered incomparable to currently available studies. The most recent comprehensive HRV indices normal values were reported by Nunan et al. [
40]. They investigated 3141 studies for suitability and concluded that from these, 44 studies were suitable (based on the task force guidelines) for further analysis with a total number of 21,438 participants. The study [
40] accounted for age, sex, environment, recording condition and was based on short-term recordings (5 min). Furthermore, another investigation examining the Nunan et al. [
40] study was conducted by Shaffer and Ginsberg [
6]. It indicated that the participants reported on in the Nunan et al. [
40] study had a minimum age of 40 years and were classified based on their sex. Therefore, the author of the present study feels that the Nunan et al. [
40] study would be the most appropriate study for comparison with the results from this study. Based on the most credible value reported in
Table 4, all participants of this study were within the normal range for MeanRR (873 ± 59 ms compared to the normal value range 785–1160 ms), SDNN (29 ± 10 ms compared to the normal value range 32–93 ms), RMSSD (24 ± 8 ms compared to the normal value range 19–75 ms), LF (ms
2) (696 ± 552 ms
2 compared to the normal value range 193–1009 ms
2), LF (nu) (72 ± 18 nu compared to the normal value range 30–65 nu), HF (ms
2) (179 ± 110 ms
2 compared to the normal value range 83–3630 ms
2) and HF (nu) (28 ± 19 nu compared to the normal value range 16–60 nu). Despite the fact that the measured variables in this study fall within the reported norms, the values were lower in this study compared to the norms data. This could be due to the participants in this study being older (53.9 ± 5.7 years) compared to those reported in Nunan et al. [
40] (40 years old) and the different systems used for recording HRV. Research suggests that older people tend to have lower HRV indices values compared to younger people [
2,
6,
7]. However, further research is needed to address the norms of HRV based on age, sex, environment and testing condition. For this reason, the source data are attached to this report (
S1: Source data and all calculations of HRV). No further comparisons were possible because the normal values reported in Nunan et al. [
40] did not report on all the estimated HRV metrics in this study.
4.2. The Association within HRV Indices
The most credible estimate of correlation value found in this study was first between SDNN (ms) (which reflects all factors contributing to HRV including SNS and PNS activities [
7,
8,
10]) and LF ms
2 band (
rho = 0.9; 95% HDI = 0.568–0.982;
Table 5). This relationship is in line with most of the reported studies [
6,
7,
8,
10]. However, HRV can be analyzed using the HF band (0.15–0.4 Hz) and the LF band (0.04–0.15 Hz). The LF band has been shown to reflect mainly the SNS activities in several studies [
2,
3,
6,
7,
10,
16,
40,
55,
56]; however, due to the fact the this study measured HRV in resting condition, the relationship between SDNN (ms) and LF ms
2 could be explained by baroreflex activity affecting the LF band compared to cardiac sympathetic innervation [
2,
3,
6,
7,
10,
16,
40,
55,
56]. Hence, the fact that the PNS affects heart rhythms down to 0.05 Hz compared to the SNS, which has been reported to produce up to 0.1 Hz [
6,
16], explains the oscillations in the heart rhythms that can occur during resting vagal activities which cross over into the LF band [
2,
3,
6,
7,
10,
16,
40,
55,
56], thus explaining the observed association in the present study. This explanation can be further confirmed by the strong association observed between the RMSSD and HF band compared to the LF band (
Table 5) as RMSSD was suggested to be mainly influenced by PNS [
6,
10,
57]. Similar results can be observed between SDNN and SD2 which represent the short- and long-term HRV [
6,
7] with the most credible correlation value of
rho = 0.918 (95% HDI = 0.654–0.987;
Table 5). Since SD2 reflects both SNS and PNS activities contributing to HRV (similar to LF), this association was expected and in line with what has been reported in the literature [
6,
7]. The similarity between SD2 and LF can be further demonstrated by the most credible relationship values found between the two in this study (
rho = 0.893; 95% HDI = 0.575–0.98;
Table 5).
Considering that the LF band does not cross the HF band [
6,
16], researchers concluded that the HF band reflects PSN/vagal activities [
2,
3,
6,
7,
10,
13,
16,
40,
56], which is why it was later named the respiratory band as it relates to HRV indices related to breathing [
6]. Therefore, it was expected that HF ms
2 would have a strong relationship with RMSSD, as the RMSSD was classified as the primary time domain measure that reflects changes related to vagal activities affecting HRV [
7,
16,
57]. This relationship was confirmed in the current study, and the results showed that the most credible correlation value between the two was
rho = 0.9 (95% HDI = 0.567–0.982;
Table 5). Furthermore, since pNN50 and RMSSD were reported to reflect short-term HRV changes and both reflect the PNS activities [
6,
57], it was expected that the pNN50 would add further affirmation to the results in this study when compared to the other studies. Indeed, the relationship found between pNN50 (%) and HF ms
2 in this study confirms the association between RMSSD and HF ms
2 (
Table 5;
rho = 0.896; 95% HDI = 0.574–0.984). Moreover, the SD1, which represents the fast beat to beat variability in IBI [
7], has been reported to be the nonlinear domain metric that is identical to the time domain metric RMSSD [
6]; the similarity between SD1 and HF, which correlates with baroreflex sensitivity [
6,
7], dictated the expectation that SD1 would correlate with RMSSD (
rho = 0.92; 95% HDI = 0.665–0.987) and HF (
rho = 0.895; 95% HDI = 0.582–0.982) which further confirms the relationship between the HF and RMSSD (
Table 5).
It should be noted that no further confirmed probable associations were observed between time, frequency and nonlinear-domain variables in comparison to those reported by the task force [
3] (
Table 5). However, this might be due to the short-term measurement (5 min) used in this study compared to the 24 h measurements reported in the task force report, where the lack of association was caused by “both mathematical and physiological relationships [
3]”. Furthermore, the used statistical analysis in this study, which is based on the Bayesian estimation of correlation [
49], indicates that the highest probability (95% HDI) of the correlation values overlapped zero or near zero; therefore, those relationships were regarded as unclear. Finally, the reported short-term estimated relationships between time, frequency and nonlinear-domain variables reported in the literature [
2,
3,
6,
7,
10,
13,
16,
56] are comparable to the associations observed in this study.
4.3. The Relationship between Measures of HRV Indices and Both Measures of Blood Pressure Indices and Aerobic Capacity Parameters
The Bayesian estimation of correlation relocates credibility across possibilities [
49,
50,
51]. Thus, the possibilities are reflected by the 95% HDI, and the probability of the estimated Bayesian correlation falling at any point within the 95% HDI is equal. Based on the Bayes’ rule, an estimated coefficient (
rho = median) would not be enough evidence of association if the 95% HDI overlapped zero [
48,
49]. Therefore, the findings from this study did not provide enough evidence of the association between the measures of HRV indices and the parameters from the aerobic capacity test (i.e., VO2
Peak, BPM, HR
max and Time to exhaustion;
Table 6). Nevertheless, the results (
Table 6 and
Figure 2) indicate a possible association (regardless of the strength) between pNN50% and MAP, MeanRR (ms) and RPP, SDNN (ms) and RPP, LF (ms
2) and RPP and SD2 and RPP (
Figure 2).
Several studies have investigated changes in HRV indices as a result of performance adaptations in response to different exercise protocols. The results of these studies indeed confirm that changes in VO2
max are accompanied by changes in HRV indices [
21,
23,
26,
27,
28,
31]. The changes observed differed based on age and measuring condition (i.e., supine, standing) [
28], duration of intervention [
27,
28,
38], participants’ background [
23,
26] and measurement of time of day [
39]. Nevertheless, the fact that research shows that the measures of resting HRV were not affected by exercise in the middle-aged group (50–59 years old) compared to the young group [
26,
28], that changes in HRV indices appear to flatten after 12 weeks of exercise [
27] and that the maintenance of those changes could be achieved by exercising regularly [
26], could in part explain
i) the lack of evidence of association between measures of HRV indices and variables from the aerobic capacity test in this study and ii) the conflicting results reported in the literature. Another possible explanation is the newly reported results by Phoemsapthawee et al. [
38], showing that changes in vagal-related HRV are related to individual ability to adapt to exercise. This was further confirmed by the multiple stepwise regression, which did not show a meaningful relationship between measures of HRV indices and changes in VO2
peak [
38].
Studies investigated the relationship between measures of HRV indices and aerobic capacity directly and/or indirectly through establishing a prediction model to estimate aerobic capacity using the frequentist approach to data analysis [
21,
27,
29,
30,
32,
33,
36,
37,
58]. Interestingly and regardless of whether the association was observed [
30,
33,
36,
37] or not [
27,
32], all the correlations reported in these studies falls within the 95% HDI reported in this study (
Table 6). Several authors proposed explanations for the disparity in the results across those studies, which can be summarized by 3 major reasons: The first reason is the differences in the participants’ background, type of sport and age [
26,
29,
32,
33,
35,
58]. The results from these reports confirm that associations were detected in soccer players, distance runners, patients with chronic obstructive pulmonary disease and young people [
26,
29,
32,
33,
58], but were not confirmed in middle-aged participants, untrained subjects, sprinters and throwers [
26,
29,
32,
36]. The variation related to the participants’ background was explained by the fact that the participants with already high values of vagal-related HRV indices in resting conditions tend to reach their anaerobic threshold at a higher exercise intensity compared to those who have lower values of vagal-related HRV indices [
33]. The second reason is measurement position (i.e., supine, standing etc.). Studies have reported notably higher PNS activities in the seated rest compared to the standing position [
21]. It was further investigated and reported that out of 30 possible correlations between HRV indices and aerobic capacity, only two from the supine position were associated with aerobic capacity compared to 15 from a standing position [
32]. The third reason was the measuring time of day and condition (i.e., sleeping, early morning, evening); reported results showed that HRV indices measured in a resting supine position early in the morning (at wake up) did not differ between young and older participants. Nevertheless, the results indicate that there were differences in vagal-related HRV between age groups when measured during sleep, with the young group having higher values [
28]. Furthermore, a review conducted by Vitale et al. [
39] concluded that higher vagal-related HRV indices in the morning, compared to the evening, were observed and that they differed between individuals, which the authors used further to advise coaches and trainers to consider when planning the timing of exercise. Among all the studies above, no association was reported in a similar age group to the one in this study.
In this study, a possible inverse relationship was detected between MeanRR and RPP (
Table 6,
Figure 2). This was expected and was confirmed in the majority of published studies: simply stated, when the human body is exposed to a stressful demand (such as standing, performing daily activities and exercise), the SNS activities trigger the heart, and an increase in HR can be observed to meet the demands imposed on the body. This increase in HR is coupled with a decrease in time between the beat to beat interval [
22]. This process is a good example of the combined actions of PNS and SNS in opposite directions, where the HR speeds up in response to a stimulus from the SNS and slows down in response to a stimulus from the PNS [
59]. This can be further extended to explain the possible positive association observed between HRV indices reflecting mainly SNS activities (LF ms2 and SD2) and RPP (
Table 6), indicating that an increase in SNS activities would cause higher RPP [
10,
16,
59]. It is important to be reminded, as described earlier in this article, that the relationship between PNS and SNS is dynamic and that PNS activity could be associated with low, high or no SNS activities [
6]. Therefore, the trivial (lower band of the 95% HDI at zero but not overlapping;
Table 6) possible association between SDNN and RPP could be explained by the fact that measurements were carried out at resting condition, causing the PNS to be the dominant system. However, since RPP is the product of HR and systolic arterial pressure, and the systolic arterial pressure is only affected by the SNS [
59], which has been reported to produce up to 0.1 Hz and crosses over to the LF band, it is expected that this trivial possibility will vanish with increased activity (see
Section 4.2.). Finally, the relationship between HRV indices and MAP showed a potential but trivial (since the 95% HDI was almost at zero but not overlapping) possibility for association between pNN50 (a parameter primarily reflecting PNS activity) and MAP (
Table 6). Nevertheless, while it was not expected to find a relationship at rest, it was expected that measures of PNS correlate positively with MAP [
18]. This association could also be explained by the dynamic relationship between PNS and SNS explained earlier [
6]. Furthermore, MAP involves both systolic and diastolic blood pressure [
19,
24], and the possible association could further be explained by the fact that the autonomic nervous system’s role in regulating MAP is to maintain it at the homeostasis level [
18]. Hence, an elevation in MAP has been reported to cause a decrease in SNS activities and an increase in PSN activities [
6,
18,
59].
In line with other studies, this study is not without limitations. Due to the difficulties involved in conducting such studies, the sample size was small, but still in line with the recommendation from the task force [
3] to be able to establish norms through meta-analysis studies. The small sample size was compensated for by using the within-subjects experimental design as advised [
4,
5,
9], the simulation of data using MCMC producing a simulated sample [
49], the retrospective power analysis based on PPC and the assessment of representativeness and accuracy by examining the convergence of the MCMC algorithm. Furthermore, the number of participants in this study is in line with the majority of studies examining HRV in the field [
12,
15,
28,
31,
35,
60]. Participants’ in this study were tested during resting supine position only, which can also be viewed as a limitation; however, due to the measurement equipment used in this study, the measurements under other conditions (reactivation (during training) and rest (post-activation)) would have produced unreliable results. For those reasons, and due to the fact that this is the first study within sport sciences that uses the Bayesian estimation of correlation on MCMC simulated data using the 95% HDI, the author has attached all the necessary information for replicability (
supplementary materials) in order to contribute to future advancements in the field.