Heart rate variability (HRV) is measured as the variability in consecutive R-wave to R-wave intervals (RRI) of the electrocardiogram. It reflects the activity of multiple influences at the sinoatrial (SA) node of the heart, especially those emanating directly from the brain via the sympathetic and parasympathetic efferent pathways of the autonomic nervous system (ANS). Commonly used, standard frequency domain indices of HRV are generated from the RRI power spectrum density (PSD) [11] to reflect the amount of variability within the system calculated as the power of RRI oscillations in various frequency ranges. The overall amount of variability in these ranges of the RRI PSD is an obviously essential dimension of neurocardiac dynamics, but unlikely the only dimension, especially if one considers the possibility that RRI PSD dynamics can change qualitatively and non-linearly in response to perturbation [12]. Reorganization of variability (i.e., redistribution of spectral power) is another key dimension of neurocardiac dynamics, which may be captured in ways other than the standard HRV indices (e.g., change in the ratio of power in the low and high frequency ranges) designated by the Task Force [11].

In this paper, we go beyond the Task Force conceptualization of spectral reorganization by measuring reorganization of variability independently from amount of variability (i.e., disentangling the redistribution of spectral power from the power of RRI oscillations in a given frequency range). We propose that, in and of itself, spectral reorganization may reflect a fundamental mechanism of adaptability that supports changes in response to challenge even when the amount of variability is diminished, for example, by disease states [13], [14] or pharmacological challenges such as alcohol drinking [15]. This implies that adaptive neurocardiac responding might still be accomplished by strategically redistributing power to a given frequency, even when de novo generation of spectral power from the neural inputs at the SA node is impaired (i.e., when the amount of variability is limited or less likely to increase).

This study is the first to apply the Wasserstein distance with exponent 1 (W₁) metric to RRI spectral data in order to quantify redistribution of RRI spectral power as a distinct dimension of real time cardiovascular reactivity. Applying W₁ to RRI data provides a strong approach to characterizing redistributions in the temporal dynamics of the RRI PSD during challenge conditions because it is robust against noise [16], [17] and makes no a priori assumptions about linearity of the data [12]. The utility of W₁ as a measure of dissimilarity between probability distributions [16] and histograms [17] is well-established outside the area of physiology. We computed W₁ from individual RRI PSD in order to measure dissimilarity between power spectra elicited during a resting state compared to a challenge condition, as follows:where the cumulative distribution function (CDF) is defined as

The W₁ metric differs in several important ways from the standard indices of HRV defined by the Task Force [11], which are calculated as the absolute power in predefined spectral frequency bands (e.g., low [LF HRV] and high [HF HRV] frequency bands) or as the ratio between them (LF/HF ratio). First, the W₁ metric integrates the RRI PSD across the entire spectral range (i.e., ~0 to 0.5 Hz); no predefined spectral frequency bands are imposed. Second, the W₁ is a metric on a set of equivalence classes of power spectra. In other words, the RRI PSDs being compared are normalized prior to computing W₁. This implies that two power spectra, which can be obtained from each other by multiplying one of them by a positive constant (i.e., changes only in spectral power), will not be differentiated by W₁. Third, the W₁ metric measures dissimilarity between two PSDs in terms of absolute distance, and thus captures absolute change in the overall shape or structure of the power spectrum in response to perturbation. These features of the W₁ metric make it possible to quantify and visualize the overall extent to which the RRI PSD reorganizes following a perturbation, distinct from increases or decreases in HRV. We suggest that a consideration of spectral power redistribution (W₁), together with changes in power captured by the standard spectral frequency indices (e.g., HF HRV, LF HRV) may be heuristic for further understanding mechanisms that modulate neurocardiac responding.

To refine this approach for assessing change in neurocardiac signaling, it is useful to consider the direction of spectral power redistribution. A redistribution in the RRI spectrum towards lower versus higher frequencies has a different physiological meaning with respect to adaptability. There is consensus that HF HRV, dominated by oscillations around 0.3 Hz, reflects activation of the parasympathetic branch of the ANS mediated by the vagus nerve, and is commonly linked to respiration. HF HRV is thought to be dominant at rest or during restful states. In contrast, LF HRV is influenced by both sympathetic and parasympathetic activity [18] and often includes oscillations at ~0.1 Hz (also called the Mayer wave) that are strongly mediated by the HR baroreflex system [19], [20]. Notably, 0.1 Hz is one of several resonance frequencies in the cardiovascular system [21], [22], [23] that serve to augment variability in the system [22], [24]. To capture the directionality of spectral power redistribution, we derived a new directionality index (D) from W₁. D was computed from individual PSD (using the same CDF definition as W₁) as follows:When D takes on a positive value, it suggests a coordinated reorganization towards lower frequency oscillations. Alternatively, a negative D implies movement towards higher frequency oscillations.

This paper introduces W₁ and D as a new approach to characterizing HRV changes in response to challenge and examines whether it provides non-redundant information to standard indices of RRI spectral power (e.g., LF HRV, HF HRV, LF/HF ratio). We used existing data from a study aimed at understanding physiological mechanisms that modulate alcohol use behaviors in young men and women. The original study collected ECG data at rest and in response to alcohol, placebo, and cognitive-emotional challenges in healthy men and women, and as such provided a rich data source for assessing adaptive reactions to a tiered challenge paradigm. We chose to examine gender differences as a starting point from which to assess the contribution of spectral redistribution (W₁) and directionality of the redistribution (D) to adaptive psychophysiological response because multiple literatures demonstrate inherent differences in adaptive functioning between men and women. For example, women have greater vagal mediation of heart rate [25] and autonomic balance [26] at rest, greater vagal withdrawal in response to stress [27], less suppression of HRV by alcohol [28], and more protection against coronary heart disease [29] compared to men. Moreover, women demonstrate a well-established survival bias which is initiated at conception [30] and evidence longer life expectancies in both developed and developing countries [31].

Examination of gender differences in the D index showed that during alcohol and placebo challenges, women's RRI PSD shifted more towards lower frequencies in response to the visual cues than did men's (Figure 3). These gender differences were statistically significant for the most emotionally valenced (positive and negative) cues, but not in response to B2, nor to the emotionally-neutral cues (Nt). It is interesting to note that in the second baseline (B2) of the control condition, the averaged D values were negative (i.e., redistribution was towards higher frequencies), potentially indicating greater vagal mediation in cases where there is an absence of challenge and participants have had the opportunity to acclimate to the testing environment.

Men and women also demonstrated distinct patterns of change in standard HRV indices in response to the tiered challenge paradigm. Notable changes (from baseline) in spectral power were observed in both the LF band (LF HRV) and the HF band (HF HRV) of the RRI PSD. Measured as a change from baseline, women showed greater increases in LF HRV in response to negative and neutral cue stimulation (p<.05) in the control condition (with a trend towards greater LF HRV to positive cues, p<.09). They also showed greater increases in LF HRV to all cue types in alcohol conditions (p's<.05), and to all cue types but neutral in the placebo condition (p's<.05; neutral cues p<.06, Figure 4). Gender differences in HF HRV were limited to the alcohol challenge condition, wherein women's HRV was generally less dampened by the alcohol challenge compared to men (Figure 5). These gender differences were statistically significant (p<.05) during the B2 baseline task as well as during the neutral and negative cue stimulation tasks. Changes in power in the overall RRI PSD (total HRV) also differed by gender (Figure 6). Women showed a greater increase in total HRV in response to negative emotional cues during the control condition (p<.05) and during B2 and to the neutral and negative emotional cues (p<.05) during the alcohol condition. Finally, computation of the LF/HF ratio (Figure 7) revealed a pattern of results that was distinct from the LF HRV and HF HRV indices as well as from the W₁ and D analyses. Women had greater LF/HF ratios in response to emotion cue tasks in the control condition (p's<.05) and to the B2 and negative emotional cue task in the placebo condition (p<.05); gender differences to neutral and positive cue tasks in the placebo condition were at the level of a trend (p's<.10). No gender differences were noted in LF/HF ratio during the alcohol condition.

Clearly, further research and discussion are needed to understand the implications of this new dimension of spectral change; however, using gender differences as a starting point, we offer some initial speculations as to the significance of the W₁ metric and D index that build on our ongoing research into the arterial baroreflex system and the role of resonance in adaptive responding. As a first example, in the control condition, there were no significant gender differences in spectral power redistribution (W₁) in response to cognitive emotional visual cues, but women did show greater increases in LF HRV and a greater LF/HF ratio compared to men. We interpret these findings as showing that when the cardiovascular system, and its bidirectional communication with the brain, is performing optimally (participants were all young healthy adults), the “primary” adaptive response to the visual cue challenge was to provoke greater neural activation at the SA node to generate more low frequency oscillations; this was accomplished more robustly by women than men.

As a second example, following alcohol consumption, the power of the total RRI spectrum (total HRV index) was decreased, but both the LF HRV and HF HRV suppression was significantly less prominent in women than in men [28]. The W₁ metric and D index further showed that the relative contribution of RRI oscillations with different frequencies to the power spectrum changed considerably, and that the extent of this redistribution was greater, and towards lower frequencies, in women than in men. One interpretation of this finding is that when neural input at the SA node is dampened by alcohol, the system attempts to compensate for this reduction by redistributing remaining power towards lower frequencies. If spectral reorganization is serving as a mechanism by which the cardiovascular system compensates for reduced neural input at the SA node and helps to offset or override the effects of alcohol, then the fact that women are both less suppressed by alcohol and more able to redistribute power towards lower frequencies is consistent with an adaptive advantage.

There is an abundance of research demonstrating that greater HF HRV at rest (i.e., unchallenged) is associated with health and well-being. Here we assert that the story is different in the face of challenge; namely, that oscillations in the low frequency range also serve important adaptogenic functions that support health and well-being. During a mild challenge, such as viewing visual cues with emotional content, an increase in power in the LF band of the RRI PSD may be adaptive because it signals activation of neural inputs to promote alertness and vigilance. When neural communication with the heart is compromised by alcohol or other adverse conditions, maintaining low frequency oscillations, even at the expense of high frequency oscillations, may be adaptive because oscillations at lower frequencies can generate a resonance response. Resonance amplifies cardiovascular oscillations and thus may compensate for reduced “efferent-induced” oscillations. We propose that through resonance, the heart-brain biofeedback loop can be maintained. It is noteworthy that both vagal stimulation [33] and resonance breathing biofeedback [34], which induces high oscillations at 0.1 Hz, show promise in the treatment of various physical and mental health problems [35], [36], [37].

As a final point, we note that our results clearly demonstrate that W₁ does not capture the same spectral movement as the LF/HF ratio. In the control condition, a change in the shape (or structure) of the RRI PSD was detected by the standard LF/HF ratio index but not the W₁ metric. In the alcohol condition, on the other hand, a change in the structure of the RRI PSD was detected by the W₁ metric, but not the LF/HF ratio index. A major difference between the LF/HF ratio index and W₁ metric is that the latter compares normalized spectra and thus can differentiate amount of variability (i.e., RRI spectral power) from organization of variability (i.e., shape of RRI PSD). Another key difference is that the ratio compares two portions of a single RRI PSD using predefined frequency bands, whereas the metric captures shifts across the entire spectral range between two independent RRI PSDs. The conceptual significance of these differences is open to debate.