Cardiorespiratory coordination: Historical development of analysis methods, current state, and future research prospects

Abstract

Cardiorespiratory coordination (CRC) is defined as a distinct form of cardiorespiratory interaction arising from the reciprocal influence exerted by the cardiac and respiratory cycles on the timing of their respective onsets. In contrast to respiratory sinus arrhythmia and cardiorespiratory phase synchronization, CRC obviates the need for phase estimation, exhibits robustness to irregular cardiac rhythms, and enables the directionality of coupling to be assessed. This narrative review presents the history of the development of CRC analysis methods (1966-2024), from histogram analysis to the automated coordigram method. Notably, no direct investigations of CRC have been conducted to date in major cardiovascular pathologies, including arterial hypertension, myocardial infarction, and chronic ischemic heart disease, nor in prevalent respiratory disorders such as chronic obstructive pulmonary disease and bronchial asthma. Drawing on distinct pathophysiological mechanisms, we advance competing hypotheses regarding the expected direction of CRC alterations in each of these conditions. We conclude that further experiments in patients with these conditions are needed to assess the diagnostic potential of CRC.

Key Words: Cardiovascular system; Respiration; Cardiorespiratory coordination; Coordigram; Hypertension

Core Tip: This review systematizes the development of cardiorespiratory coordination (CRC) analysis methods from 1966 to 2024, highlighting its advantages over respiratory sinus arrhythmia and cardiorespiratory phase synchronization. Unlike these methods, CRC does not require phase detection, is robust to irregular rhythms, and enables directionality assessment. The review identifies a critical gap—no direct CRC studies in arterial hypertension, myocardial infarction, chronic ischemic heart disease, chronic obstructive pulmonary disease, or bronchial asthma—and puts forward competing hypotheses grounded in pathophysiological mechanisms. It ultimately advocates for experimental studies to explore CRC's diagnostic potential in these conditions.

INTRODUCTION

The cardiovascular and respiratory systems are engaged in complex bidirectional interactions[1,2], the characteristics of which serve as sensitive indices of autonomic regulation governing cardiac and respiratory function[3,4]. Among the various manifestations of cardiorespiratory interplay, two phenomena have attracted the most extensive attention: Respiratory sinus arrhythmia (RSA), defined as heart rate acceleration during inhalation and deceleration during exhalation[5], and cardiorespiratory phase synchronization (CRPS), characterized by a propensity for heartbeats to occur at specific phases of the respiratory cycle[6]. The literature abounds with studies employing RSA and CRPS parameters across an exceptionally wide range of applications—from discriminating between wakefulness and anesthesia[7,8] and differentiating sleep stages[9], to assessing emotional self-regulatory capacity[10] and evaluating age-related changes in cardiovascular autonomic control[11], among others.

However, a number of authors have drawn attention to the inherent limitations of applying RSA and CRPS parameters in the analysis of cardiorespiratory interactions[12-18]. For instance, several studies have demonstrated that RSA fluctuations do not consistently reflect changes in tonic vagal cardiac activity; rather, they are closely tied to respiratory activity and depend on a range of additional confounding variables[12]. Consequently, RSA changes are prone to misinterpretation in certain contexts[17]. Moreover, Menuet et al[18] have gone so far as to propose renaming RSA as “respiratory heart rate variability”, a shift that, they argue, would help reconcile disparate interpretations of the phenomenon. Turning to CRPS, a major challenge lies in the accurate determination of signal phase[2,19,20], compounded by its marked sensitivity to respiratory pattern variability—a limitation that substantially curtails its informational value under conditions of pronounced physiological fluctuation[21,22].

In 2014, Riedl et al[23] provided a comprehensive elaboration of the concept of cardiorespiratory coordination (CRC), a distinct form of cardiorespiratory interaction that has since garnered considerable interest in the research community. At its core, CRC arises from the reciprocal influence exerted by the cardiac and respiratory cycles on each other’s onsets, manifesting as a spontaneous tendency toward a stable temporal relationship between the two. In contrast to CRPS analysis, CRC assessment obviates the need for phase calculation or determination. In addition, unlike CRC, the quantitative characteristics of RSA and CRPS do not allow for the establishment of a predominant direction of cardiorespiratory coupling[23]. These methodological advantages have fueled substantial research interest in CRC, particularly in the context of cardiovascular pathology[22,24-26].

Although the core pathogenetic mechanisms underlying the major socially significant cardiovascular diseases (CVD)—notably arterial hypertension (AH), ischemic heart disease (IHD), and chronic heart failure—are well characterized, the subtler autonomic dysregulations that emerge long before overt clinical presentation, along with the methodologies for their early detection, remain incompletely understood and are frequently the subject of conflicting findings[27-31]. It is also important to acknowledge the well-recognized association between CVD and sleep-disordered breathing. At present, however, it remains impossible to differentiate, among patients with sleep apnea, those who will subsequently develop clinically manifest cardiovascular pathology from those who will not[32]. In this context, the investigation of the physiological underpinnings of CRC, the continued refinement of CRC analytical methodologies, and the extension of CRC research to a broader spectrum of pathological conditions may prove instrumental in advancing personalized prediction of CVD onset and progression, with particular relevance to AH.

The aim of this narrative review is to systematize the historical development of CRC analysis methods, compare methodological approaches, and substantiate the prospects for studying CRC in AH, myocardial infarction (MI), chronic IHD, chronic obstructive pulmonary disease (COPD), and bronchial asthma (BA), based on existing pathophysiological data.

METHODS

This work constitutes a narrative review dedicated to the phenomenon of CRC. The narrative format was adopted as a methodological framework owing to the breadth and inherently heterogeneous nature of the subject matter, which encompasses historical aspects, diverse methodological approaches, physiological interpretation, and clinical implications. A formal systematic review was not performed, given the considerable variability in study designs, experimental protocols, and patient populations across the original investigations.

The literature search was conducted across the following electronic databases: PubMed (including MEDLINE), the Russian Science Citation Index (RSCI), SpringerLink, and ScienceDirect. The search encompassed the period from 1966 to 2024 inclusive. The lower temporal boundary was selected to coincide with the publication of the first documented study to analyze the temporal relationship between cardiac contraction and the onset of inhalation. The search strategy employed the following keywords and their combinations, using the Boolean operators AND and OR: “cardiorespiratory coordination OR cardioventilatory coupling OR non-synchronous coupling”, “respiratory sinus arrhythmia”, “cardiorespiratory phase synchronization”, “coordigram”, “R-peak AND respiration”, “hypertension AND cardiorespiratory coordination”, “myocardial infarction AND cardiorespiratory coordination”.

The retrieved articles were evaluated according to several predefined criteria, including the conceptualization of CRC, the analytical methods employed, the physiological underpinnings of the phenomenon, the distinction between CRC and other forms of cardiorespiratory interaction, and the clinical applicability of the findings.

A BRIEF DIGEST OF THE HISTORY OF CRC ASSESSMENT METHODS

The trajectory of CRC research and the evolution of analytical methods can be divided into several time periods (Figure 1).

Figure 1 Timeline of key methodological advances in cardiorespiratory coordination analysis (1966-2024). CRC: Cardiorespiratory coordination; tRSE: Transformed relative Shannon entropy; CRPS: Cardiorespiratory phase synchronization; FWHM: Full width at half maximum.

Scholarly interest in this type of cardiorespiratory interaction first emerged in the 1960s[33]. Although the term “cardiorespiratory coordination” was not formally introduced until considerably later, the pioneering work of Stutte and Hildebrandt[33] constituted a cornerstone of CRC analysis and exerted a decisive influence on the subsequent direction of the field. The principal analytical approach employed in this study involved the computation of time intervals between the onset of inhalation and the preceding R-peaks. Notably, the authors departed from the prevailing practice of earlier investigations, which had focused on calculating the average frequency ratio (pulse-respiratory ratio); instead, they examined the distribution of the obtained time intervals through histogram analysis. The non-uniform distribution pattern they observed led the investigators to infer that inspiration is bound to specific, discrete positions within the cardiac cycle. This finding marked a pivotal moment in the conceptualization of CRC, effectively laying the groundwork for all subsequent research in the area.

However, there was no further rapid development in this area, and the 1970s can be called a “quiet period” in CRC research, presumably because the physiological interpretation of the findings was limited[34]. The late 1980s witnessed the publication of several studies addressing the phenomenon of CRC and its analytical approaches[35-37]. The definitive resurgence of CRC research, however, did not occur until 1995, when Moser et al[38] published a seminal study that, building upon the methodological framework established by Stutte and Hildebrandt[33] and extending it to a larger experimental cohort, proposed the first physiological model to account for the previously documented temporal “binding” of inhalation to the cardiac cycle. In their analysis, histograms of the distribution of time intervals between the onset of inhalation and the preceding heartbeat revealed three distinct peaks: P1 (50-150 ms), P2 (200-350 ms), and P3 (450-650 ms). The authors attributed the first peak (P1) to the systolic phase of cardiac contraction. The third peak (P3), which emerged during diastole, was interpreted as potentially arising either from afferent pathways activated by endosystolic myocardial relaxation or from stretch-sensitive volume receptors in the right atrium stimulated by venous return. The remaining peak (P2) was associated with the impulse wave passing by the baroreceptors in the carotid sinus. In this manner, the authors succeeded in correlating the observed non-uniform distribution of time intervals with specific physiological processes and the anatomical structures involved in their generation.

Two years later, Galletly and Larsen[39] published a study that extended the accumulated body of knowledge on CRC to an investigation of healthy volunteers under midazolam-induced sedation. The authors demonstrated the significance of CRC not only as a fundamental physiological phenomenon, but also as a promising diagnostic marker of changes in the coordinated functioning of the respiratory and cardiovascular systems. Their analytical approach involved constructing a time-expanded graph plotting the intervals between the R wave of the ECG and the subsequent ventilatory peak, designated as R-wave-to-ventilation intervals (RV-intervals). The interpretation of this graph hinged on the identification of horizontal bands, signifying regions where RV-interval values either remained constant or deviated only marginally. The authors termed this observed phenomenon “nonsynchronous coupling” and further showed that it manifests during sedation and is virtually abolished following the administration of an anti-sedative agent.

In 1999, Larsen et al[40] reported findings from a study conducted in patients with atrial fibrillation under general anesthesia. In contrast to earlier investigations, the authors derived time intervals between the onset of inhalation and the preceding R-peak (RI plot), as well as between the onset of inhalation and the following R-peak (IR plot). The study additionally examined phase relations between the cardiac and respiratory cycles, although this aspect, pertaining to CRPS, lies beyond the scope of the present review. The phase relationships are mentioned only to highlight the authors' conclusions: Among the five graphical methods for assessing cardiorespiratory interactions evaluated in their study, the variability in the interval between the onset of inhalation and the preceding heartbeat proved to be smaller than that of any other phase or temporal relationship examined. This finding lent support to a model of cardioventilatory coupling, wherein cardiac contraction serves as the trigger for the onset of inhalation. While not discounting the existence of CRPS, the authors contended that, in the setting of arrhythmic cardiac activity associated with atrial fibrillation, CRC analysis affords greater informational yield. These conclusions have since been corroborated by subsequent investigations.

Subsequently, CRC analysis was extended to longer experimental recordings, encompassing a six-hour period of nocturnal sleep[34]. Two principal observations emerged from this line of investigation. First, the findings revealed a marked inconsistency in CRC throughout the sleep period, thereby providing a rationale for subsequent examinations of the relationship between CRC and sleep stage architecture. Second, among the six quantitative methods for assessing CRC that were evaluated, the phase recurrence method was identified as the most informative, and subsequently served as the foundation for the development of other CRC analytical approaches.

Friedman et al[41] were the first to analyze four distinct time intervals within a single sample: From inhalation onset to the preceding R-wave, from inhalation onset to the following R-wave, from exhalation onset to the preceding R-wave, and from exhalation onset to the following R-wave. Their findings highlighted the particular significance of the interval from inhalation onset to the preceding R-wave compared to the other intervals. Furthermore, to test whether the observed CRC might be a random phenomenon, the authors performed repeated measurements on the same cohort and established that, under reproducible conditions, CRC represents a stable individual characteristic.

Finally, the aforementioned work by Riedl et al[23] constituted a pivotal contribution to the evolution of CRC research, formalizing the phenomenon and explicitly defining it as “the mutual influence of cardiac and respiratory oscillations on their occurrence”. The authors further drew a clear conceptual distinction between CRC, RSA, and CRPS, thereby establishing ‘cardiorespiratory coordination’ as a separate and independent term, distinct from the various designations (such as ‘cardioventilatory coupling’ or ‘non-synchronous coupling’) that had been employed in prior studies. Of particular note is the fact that this study introduced an analytical method that has since become the standard in the field: The construction of a coordigram. Unlike previously used methods (IR-graph, RI-graph, traditional synchrogram), the coordigram takes into account both directions of cardiorespiratory interaction—from heart rate to respiration and vice versa—simultaneously, and also allows researchers to overcome the limitations of earlier methods. Applying this method to a cohort of volunteers with obstructive sleep apnea syndrome, the authors obtained findings of considerable significance: CRC was observed substantially more frequently during and immediately after respiratory sleep disturbances than during undisturbed breathing. This observation ran counter to the prevailing assumption that spontaneous CRC occurs exclusively during periods of relaxed sleep or quiet wakefulness[35,37]. Notwithstanding these insights, the authors noted that the mechanism underlying the development of CRC remains unknown and put forward a hypothesis that the heart's influence on respiration is associated with the activity of the parafacial respiratory group, and that the reverse influence is associated with the activity of the pre-Bötzinger complex, which provided a basis for future researchers of the CRC phenomenon.

Balagué et al[42] pursued further research into CRC and its analytical methodologies. In a departure from the prevailing approach of earlier studies, the investigators adopted the premise that the human body, as a complex system, operates as an indivisible, integrated whole—one that cannot be reduced to a quantitative summation of the functions of its constituent subsystems—and that CRC should be conceptualized as a global coherence among a range of physiological variables, a perspective that principal component analysis is particularly well suited to address. This method was applied to time series of six cardiorespiratory variables recorded during an exercise test. A key innovative finding of this study was that CRC, when examined as a composite variable, was augmented following six weeks of training and diminished after three weeks of detraining. Moreover, alterations in CRC were found to precede changes in established markers of cardiorespiratory reserve and maximal performance, such as maximum heart rate, peak exercise power, and maximal minute ventilation, among others.

The year 2017 witnessed a surge of noteworthy studies investigating CRC and the methodologies for its assessment. Berg et al[24] were the first to examine CRC in pregnant women with preeclampsia, demonstrating significant differences relative to healthy pregnant controls and thereby corroborating the hypothesis advanced in[23] concerning the association between sympathicotonia and augmented CRC. Particular mention should be made of the work by Krause et al[25], in which the authors sought to establish the fundamental distinction between CRC and CRPS, as well as the independence of CRC from RSA. Furthermore, it was proposed to evaluate the coordigram not only qualitatively, but also quantitatively, specifically by approximating the distribution of time shifts Δt by a normal distribution and calculating the full width at half maximum.

In a recent study of a sample of 226 people with varying degrees of sleep apnea severity, an automated coordigram method was introduced[22]. The premise for creating the method was the fact that, despite existing research into the CRC phenomenon and growing interest in this field, as of 2024, there were no automated algorithms for detecting CRC, which are necessary for analyzing large sets of experimental data. The implementation of automation facilitated the elimination of manual processing of experimental records, the standardization of parameters and threshold values optimized through surrogate data analysis, and the formalization of CRC detection criteria. Table 1 presents the main papers published since 1995 describing various methods of CRC analysis[41-43].

Table 1 Characteristics of cardiorespiratory coordination assessment methods based on published studies.

Ref.	Experimental sample	Method	Description of the method
[38]	160 healthy volunteers	Construction of a histogram of the distribution of time intervals between the R-peak and the onset of inhalation	To construct a histogram for each respiratory cycle (out of 18000 recorded), the time from the onset of inhalation to the preceding R-peak is measured. A histogram of these intervals is constructed. Three peaks are observed: P1 (50-150 ms), P2 (200-350 ms), and P3 (450-650 ms). As a result, the authors conclude that inhalations begin with fixed delays after the last preceding heartbeat, since otherwise the histogram of the distribution of these time intervals would be uniform. This is a direct measurement of cardiorespiratory coordination
[39]	8 male volunteers (aged 20-27) under sedation with midazolam	Search for discrete bands in R-peak-inhalation intervals	Monitoring of cardiorespiratory coordination is based on the method described in[32]. The authors determine the time of occurrence of each R wave. From the ventilation signal, the peak time of each inhalation is determined. For each R-wave, the time interval (R-wave-to-ventilation intervals) to the next ventilation peak is calculated and its value is plotted on the graph. The relationship between heart rate and ventilation, which the authors termed non-synchronous coupling, manifests itself in the form of dense horizontal bands of the R-wave-to-ventilation intervals, indicating a constant temporal coupling between the heartbeat and subsequent ventilation. The number of bands indicates the degree of this coupling
[40]	8 elderly patients (aged 72–92) with atrial fibrillation under general anesthesia	Two graphical methods: RI-graph and IR-graph	The following temporal relationships are analyzed: (1) The temporal relationship between respiration and the preceding heartbeat (cardiorespiratory coupling is demonstrated by showing a constant interval between the onset of inhalation and the preceding heartbeat); and (2) The temporal relationship between respiration and the subsequent heartbeat (cardiorespiratory coupling is demonstrated by showing a constant interval between inhalation and the subsequent heartbeat
[34]	20 healthy participants (7 women, mean age: 34.9) during a period of night-time sleep	Qualitative analysis of cardiorespiratory coordination: “coordination diagram”. Quantitative analysis of cardiorespiratory coordination: (1) “Synchronization-λ”; (2) “Phase recurrences” of relative distances φi; (3) “Phase recurrences” of absolute distances ti; (4) “Quantitative assessment of histograms” of relative distances φi; (5) “Quantitative assessment of histograms” of absolute distances ti; and (6) “Quantitative assessment of the distribution of relative distances βj”	(1) Detection of cardiorespiratory coordination using “Synchronization-λ”. For ECG and respiration signals, phases φ1 and φ2 are introduced. φ1 increases linearly over the interval (0, 2π) between two consecutive R-peaks, and φ2 increases linearly between two consecutive inhalation onsets. Then the phase threshold value θ is selected. Each time φ1 reaches the value θ, φ2 is determined at the same moment. Next, to obtain a more reliable result for different values of θ, the circular variance λ is calculated and averaged. Coordination is present if λ exceeds a predefined threshold; (2) and (3) Detection of cardiorespiratory coordination using the method of “phase recurrences” (separately for absolute ti and relative φi values of the distances between the onset of inhalation and successive R-peaks). The phases φi of all R-peaks are determined. These phases are then compared between successive R-peaks. To establish m:n coordination, the phase values must not differ from each other by more than the permissible value ε during at least k successive R-peaks, where k has to be equal to or greater than the value of m; (4) and (5) Detection of cardiorespiratory coordination using “quantitative assessment of histograms” (separately for absolute ti and relative φi values of the distances between the onset of inhalation and successive R-peaks). A sliding window of nF successive phases φi is used, which moves over the entire series of phases. For each window, the phase distribution φi is calculated. If cardiorespiratory coordination is present, the phase distribution φi shows distinct, equally spaced local maxima (e.g., four local maxima in the case of 4:1 coordination). In the absence of coordination, local maxima do not appear. Then each distribution is quantified using a Fourier transform. The appearance of pronounced local maxima in the power spectrum is used to identify cardiorespiratory coordination; and (6) Detection of cardiorespiratory coordination using “Quantitative assessment of the distribution of the onset of inhalation in RR intervals”. The relative values of the time distances between the onset of inhalation and the preceding R-peak—the βj values—are analyzed. The values of βj, which lie in the interval (0, 1), are plotted on the interval (0, 2π). Then the distribution of βj over a data window of length nF is quantified by calculating the circular variance γ (0 ≤ γ ≤ 1). If γ = 0, βj is uniformly distributed, indicating a completely decoordinated case. If γ = 1, βj is constant throughout the data window, indicating a coordinated case. Subsequently, R-peaks in the respiratory cycle following a coordinated inhalation onset are labeled as coordinated. For each method, the percentage of coordinated R-peaks was encoded as a grayscale plot, resulting in a coordination diagram”
[41]	19 healthy young adults (aged 17-43) at rest	Statistical analysis of time interval histograms using χ2 test and tRSE	Four types of time intervals are assessed: (1) R-to-I: The time from the onset of inhalation to the preceding R-wave; (2) I-to-R: The time from the onset of inhalation to the next R-wave; (3) R-to-E: The time from the onset of exhalation to the preceding R-wave; and (4) E-to-R: The time from the onset of exhalation to the next R-wave. For each of the four interval types, histograms of their duration distributions are constructed. Then these empirical distributions are compared with a random distribution. The degree of cardiorespiratory coordination is assessed using tRSE and the negative logarithm of the P value obtained from the χ2 test
[23]	27 men with obstructive sleep apnea syndrome	Qualitative analysis of the presence of cardiorespiratory coordination using a coordigram. Quantitative analysis of visual patterns of cardiorespiratory coordination based on the estimation of the distribution of time delays using the Gaussian kernel. The χ2 test and Bonferroni correction were used to statistically evaluate differences in the frequency of occurrence of cardiorespiratory coordination	The coordigram is formed by columns of data points representing the time interval between the onset of respiration and the onset of cardiac activity in the preceding and subsequent respiratory cycles. The coordigram combines standard RI and IR graphs. Cardiorespiratory coordination is recorded if parallel horizontal lines appear on the coordigram. Then, in a sliding window (3 respiratory cycles long), the distribution of time delays between events is estimated using a Gaussian kernel. Cardiorespiratory coordination is assumed if the power of the spectral component of the main oscillation of this assessment exceeds the threshold value ε = 0.0828 in the positive and/or negative range of the coordigram
[42]	32 healthy physically active men (age 21.2 ± 2.4)	Principal component analysis of cardiorespiratory variables	To examine cardiorespiratory coordination, principal component analysis was performed on time series of cardiorespiratory variables for each participant: The fraction of exhaled O2, the fraction of exhaled CO2, lung ventilation, systolic blood pressure, diastolic blood pressure, and heart rate. The number of principal components to be summarized was determined using the Kaiser–Guttman criterion. The optimal solution for the extracted principal components was obtained using the Varimax orthogonal rotation criterion. The Tucker congruence coefficient was used to compare the structures of the extracted principal components
[24]	69 pregnant women (age 28.45 ± 4.94) with preeclampsia, and 69 pregnant women (age 27.93 ± 4.80) who formed the control group	Qualitative analysis of the presence of cardiorespiratory coordination: Construction of a coordigram with the Gaussian kernel estimation. Quantitative analysis of visual patterns of cardiorespiratory coordination: The ε-method	For each R-peak, the time differences Δt to the previous and next inhalation onsets are calculated. The distribution of these Δt values is smoothed using a Gaussian kernel estimate with a window width b equal to twice the sampling frequency. The resulting curve is normalized to a maximum value of 1. In the colour-coded display, coordination is visualized as bright yellow horizontal lines. Negative Δt values reflect the influence of the heart on respiration, while positive values reflect the influence of respiration on the heart. Two parameters of the ε-method are used: The width of the epsilon of the ε-neighborhood (time duration) and its length l (the number of respiratory cycles). A heartbeat is considered coordinated if there are l-1 other heartbeats within the ε-neighborhood relative to the onset of inhalation. Then the proportion of coordinated heartbeats is calculated for each recording
[25]	This paper presents the results of an analysis of two time series: The first series is from a participant in a preeclampsia study[24], and the second series is a part of a dataset[23] from men with sleep apnea	Qualitative analysis of the presence of cardiorespiratory coordination: Construction of a coordigram with the Gaussian kernel estimation Quantitative analysis of visual patterns of cardiorespiratory coordination: Approximation of the distribution of time intervals Δt by a normal distribution and calculation of the FWHM of the Gaussian curve	The construction of the coordigram is carried out as in the work[24]. For each set of Δt values (corresponding to horizontal lines in the coordigram), a smoothed density distribution estimate is constructed. This allows the position of peaks and their spread to be determined. Then a Gaussian curve fit is performed for each peak. After that, the FWHM of this curve is calculated. The smaller the FWHM, the more closely the Δt values are grouped, the more accurate the timing, and the higher the degree of coordination
[26]	15 healthy adults (6 males, 9 females; age 22.5 ± 3.1)	Principal component analysis. Estimation of information entropy. Eigenvalues of the first PC1	Principal component analysis was conducted as described in[42]. The number of principal components was determined by the Kaiser–Guttmann criterion, similarly to[42]. The information entropy and the eigenvalues of the first PC1 were used as quantitative measures of coordination. The rise of entropy and diminishment of the eigenvalues were interpreted as an indication of lower coordination
[43]	41 healthy adults (38 males, 3 females; age 26 ± 49)	Qualitative analysis of cardiorespiratory coordination: Distribution of the time intervals between inspiration and the preceding and following R-spikes plotted as histogram; analysis of the coordigrams. Quantitative analysis of cardiorespiratory coordination: Estimation of Shannon entropy	The time intervals between the start of inhalation and the preceding (RI-1) and the following (RI1) R-peaks were calculated, and the distribution of the intervals was plotted as a histogram. The authors noted the asymmetry of the RI-1 и RI¹ distributions: RI-1 distribution was narrow, while RI¹ distribution was wide and spread. It was concluded that inhalation is strongly linked to the preceding cardiac contraction. Coordigrams were plotted as shown in[23]. The presence of pronounced horizontal lines indicates cardiorespiratory coordination. Shannon entropy was estimated as shown in[44]. The threshold value SHT = 0.85 was based on the entropy of white noise
[26]	20 healthy adults (16 males, 4 females; age 27 ± 6)	Principle component analysis	Principal component analysis was based on the following cardiovascular indices: End-exhalation oxygen partial pressure, end-exhalation carbon dioxide partial pressure, lung ventilation, and heart rate. The number of principal components was derived using the Kaiser–Guttmann criterion, similarly to[42]. Similarly to[45], the authors also calculated the eigenvalues of the first principal component
[22]	226 patients with varying degrees of sleep apnea (117 men and 109 women; age 48.6 ± 13.9)	Automated coordigram method	The R-peak time difference between all adjacent heartbeats in the selected time interval is taken into account. As a first step, the start time of the respiratory cycle is obtained when the respiratory phase is equal to π. For all heartbeats within 4 s before and 0.5 s after the onset of breathing, the difference between the onset time of breathing and the time of heartbeats is plotted along the vertical axis, forming a cardiorespiratory coordigram. The coordigram is divided into overlapping time windows of 25 s length with a 20 s overlap, and the points on the coordigram are compared to study the time shifts. That is, within each window, all pairs of adjacent R-peaks that belong to the same horizontal line are identified. For each such pair, the difference in their appearance times relative to the onset of inspiration is calculated. Coordination in the current window is determined if: (1) The distribution of the obtained time shifts does not differ significantly from the zero mean (t-test, P < 0.05), meaning that the horizontal lines do not drift; and (2) The distribution width does not exceed the threshold of 0.25 s (obtained from the analysis of surrogate data)

tRSE: Transformed relative Shannon entropy; FWHM: Full width at half maximum; PC1: Principle component.

CRC IN CVD

A literature search specifically addressing CRC characteristics in AH proved unrevealing, yielding no pertinent studies. There are studies regarding the analysis of changes in CRPS and RSA in acute and chronic cardiovascular pathologies. For instance, it has been demonstrated that normotensive offspring of parents with AH exhibit lower levels of CRPS at rest, indicative of early disruption of cardiorespiratory coupling[43-46]. Moreover, CRPS levels were also observed to decline during psychological stress in participants without a family history of AH; conversely, among those with a positive family history, this stress-induced CRPS reactivity was conspicuously absent, a finding that may plausibly be interpreted as reflecting exhaustion of adaptive regulatory mechanisms[46]. RSA has likewise been extensively investigated in the context of AH[47-50]. Nevertheless, as noted above, no studies analogous to these, employing CRC analysis, have been identified in the available literature to date. Consequently, in the absence of direct experimental evidence, we can only advance hypotheses, grounded in the well-characterized pathophysiological mechanisms underlying the onset and progression of AH, regarding the anticipated direction of CRC alterations in this condition. These hypotheses, however, await empirical verification through dedicated experimental investigations.

Autonomic dysfunction, and hypersympathicotonia in particular, is widely recognized as a key factor underpinning the development and progression of AH[28,51-53]. One of the earliest and best-known markers of autonomic dysfunction in AH is a reduction in baroreflex sensitivity[54,55], leading to a weakening of the key afferent signal that normally participates in the fine-tuning of the respiratory rhythm in response to the cardiac cycle, as activation of baroreceptors can modulate respiratory activity, influencing the onset of the next inhalation[54]. Such perturbations would be anticipated to diminish the propensity for a stable temporal relationship between the onsets of cardiac contraction and inspiration, the very foundation of CRC. It is therefore plausible to hypothesize that CRC levels in patients with AH are lower than those observed in healthy individuals.

However, the studies discussed above[23,24] present a seeming paradox: They demonstrate increased CRC levels in preeclampsia, a condition characterized by elevated blood pressure, as well as during episodes of sleep apnea, which are defined by periods of heightened autonomic stress. These observations would appear, at first glance, to run counter to the hypothesis we have advanced. Yet a closer examination of the causes of sympathetic nervous system hyperactivation in these conditions reveals important distinctions from those operating in AH. One of the key mechanisms in the development of preeclampsia is chronic inflammation, characterized by oxidative stress, the production of pro-inflammatory cytokines and autoantibodies, as well as endothelial dysfunction[56]. It is conceivable that this inflammatory component contributes to the modulation of CRC. With respect to sleep apnea episodes, hypersympathicotonia has been observed during and immediately following apneic events, and has been interpreted by researchers as a response to acute stress, most likely serving to mobilize the respiratory center urgently and restore normal ventilation. AH, by contrast, is not characterized by such episodes of acute respiratory center stimulation; rather, it is distinguished by the gradual, insidious development of autonomic imbalance. This may also be the cause of the opposing changes in CRC in these two conditions. Hypotheses about CRC changes in AH are summarized in Table 2.

Table 2 Pathophysiological substantiation of hypotheses about cardiorespiratory coordination changes in arterial hypertension.

Pathway	Expected direction of cardiorespiratory coordination change	Substantiation
Reduced baroreflex sensitivity	Decrease (fewer coordinated heart beats)	Weakening of the afferent signal modulating respiration
Hypersympathicotonia	Increase (similar to sleep apnea and preeclampsia)	Increased central respiratory activity
Endothelial dysfunction	Indeterminate	Lack of direct data

It is plausible that the net effect on CRC in AH is contingent upon the stage of the disease and the presence of associated factors, including comorbid sleep apnea, systemic inflammation, and the duration of hypertensive disease. Cross-sectional studies using the ε-method or automated coordigram are recommended in patients with stage 1-2 of AH without concomitant respiratory pathology.

MI, representing both the most severe and the most common complication of AH, is also characterized by pronounced autonomic imbalance and attenuated baroreflex sensitivity[57-59]. Notwithstanding their interrelationship, however, MI and AH are fundamentally distinct entities, differing in the temporal course of the pathological process (acute vs chronic), in reversibility (irreversible vs partially reversible), in the underlying pathophysiological mechanisms (ischemia vs elevated arterial pressure), and in the clinical presentation (intense chest pain, dyspnea, diaphoresis, and fear of impending death vs recurrent headaches, tinnitus, visual disturbances, and nausea), among other features. In AH, autonomic dysfunction develops gradually and persists for a long time, while MI is an acute event, after which other compensatory mechanisms may be activated, which in the long term are capable of restoring cardiorespiratory parameters[60,61]. To date, we have identified no studies in the literature examining changes in CRC indices following acute MI. It thus remains a matter of conjecture whether CRC values in patients who have sustained an acute MI are likely to be reduced in the immediate post-infarction period, as a consequence of acute myocardial damage, neurohumoral activation, and evolving autonomic imbalance, yet may, in the later post-infarction phase, not only recover but potentially exceed the values characteristic of healthy individuals. Clearly, this biphasic hypothesis awaits empirical validation through longitudinal studies of post-MI patients assessed at successive time points following the acute event.

CIHD, defined by a persistent mismatch between myocardial oxygen supply and demand, is associated with a cascade of pathological alterations that affect cardiorespiratory interactions[62]. These include mitochondrial dysfunction, oxidative stress, chronic inflammation, and remodeling of both myocardial tissue and autonomic regulatory centers[63,64]. Although these conditions share certain pathogenetic mechanisms, each is distinguished by specific pathophysiological features that must be taken into account when analyzing CRC. Table 3 summarizes the principal distinctions between AH, MI, and CIHD—distinctions that are critical for formulating hypotheses regarding CRC changes in these conditions[65-71].

Table 3 Principal distinctions between arterial hypertension, myocardial infarction, and chronic ischemic heart disease relevant to cardiorespiratory coordination hypothesis formulation.

Characteristic	AH	MI	CIHD
Clinical course	Chronic, relatively stable (with adequate therapy)[28]	Acute, followed by a recovery phase[65]	Chronic, progressive, with episodes of exacerbation[66]
Primary pathophysiological process	Functional and structural vascular remodeling; elevated blood pressure[67]	Acute coronary occlusion resulting in myocardial necrosis[65]	Atherosclerosis with recurrent ischemia-reperfusion episodes in the absence of necrosis[63]
Mechanism of ischemia	May arise from coronary microvascular dysfunction even in the absence of atherosclerotic lesions in the epicardial arteries[68]	Acute mismatch between myocardial oxygen delivery and demand, precipitated by complete and abrupt coronary artery occlusion[69]	Chronic mismatch between myocardial oxygen supply and demand, most often attributable to long-standing atherosclerotic obstruction of the coronary arteries[70]
Autonomic regulation dynamics	Sustained imbalance with no tendency toward recovery[51-53]	Sympathetic activation with potential for compensatory recovery[61]	Gradual parasympathetic withdrawal with progressive sympathetic activation[71]

The distinctions outlined above correspond to the classical, uncomplicated presentations of these conditions. However, in the presence of comorbidities or at advanced disease stages, these boundaries may become less distinct. AH: Arterial hypertension; MI: Myocardial infarction; CIHD: Chronic ischemic heart disease.

In light of these distinctions, it is reasonable to posit that CRC indices in CIHD are likely to exhibit a sustained and progressive decline. However, whereas the anticipated reduction in CRC values in AH would most likely be attributable to a primary neurogenic defect, detectable even prior to the onset of elevated blood pressure, the decrement in CRC observed in CIHD would be expected to be secondary in nature, serving as a marker of the severity of underlying myocardial structural and functional impairment, and intensifying as coronary perfusion deteriorates. In contrast to MI, CIHD lacks an acute precipitating event that would activate compensatory mechanisms; consequently, any subsequent recovery of CRC indices is improbable. To the best of our knowledge, no studies examining CRC alterations in CIHD have been identified in the literature to date. Accordingly, all of the foregoing hypotheses necessarily await rigorous experimental validation.

CRC IN RESPIRATORY DISEASES

An equally important group of conditions with the potential to influence CRC comprises pathologies of the respiratory system. Foremost among these, in this context, is COPD, a disorder that in most cases also entails cardiovascular complications[72,73], which in turn affect cardiorespiratory interactions. Persistent inflammation in COPD can lead to the systemic release of inflammatory mediators, oxidative stress, and endothelial dysfunction, culminating in thromboinflammatory cross-talk and myocardial injury[74]. Dynamic pulmonary hyperinflation contributes to reduced filling of both the right and left ventricles, impaired myocardial contractility, and diminished cardiac output[75]. The resultant pulmonary hypertension may progress to cor pulmonale[76]. An investigation of cardiorespiratory interaction in patients with COPD demonstrated that lower synchronogram indices were associated with reduced 6-Minute Walk Distance and Distance-Saturation Product, both established predictors of mortality in this population[77]. To the best of our knowledge, no direct studies examining CRC alterations in COPD have been reported in the literature to date. It may therefore be hypothesized that CRC in patients with COPD is lower than in healthy individuals, reflecting the combined impact of chronic sympathetic activation, altered respiratory mechanics, systemic inflammation, and endothelial dysfunction, all of which are sustained by the chronic, progressive nature of the disease.

BA constitutes another prevalent and clinically challenging respiratory disease that warrants consideration in the context of CRC. A pivotal distinction between BA and both COPD and the cardiovascular pathologies discussed earlier lies in the pattern of autonomic dysregulation, namely, parasympathetic overactivity coupled with sympathetic suppression[78], a profile that is further exacerbated by suboptimal disease control[79]. It is also noteworthy that BA is characterized by a phasic clinical course, manifested in the alternation of exacerbation episodes with periods of remission, during which partial restoration of respiratory function may occur[80]. Like COPD, BA can also give rise to cardiovascular complications. Cardiorespiratory interactions in BA may be modulated by chronic systemic inflammation, oxidative stress, recurrent hypoxic episodes, and autonomic imbalance[81]. Transient hypoxemia can precipitate an imbalance between oxygen delivery and tissue demand, including that of the myocardium. Bronchial obstruction—which, in contrast to the obstruction observed in COPD, is reversible—can lead to vascular bed constriction, elevated pulmonary vascular resistance, and the development of pulmonary hypertension. As pulmonary hypertension advances, the hemodynamic burden on the right heart increases, thereby limiting the coronary fraction of cardiac output and compromising conduction processes[82]. Finally, in the absence of direct studies examining CRC alterations in BA, it may only be hypothesized that CRC exhibits a dynamic pattern, in contrast to COPD, where, as noted above, a sustained progressive decline is more probable. Specifically, CRC values are likely to decrease during acute exacerbations and to partially recover during remission phases.

LIMITATIONS OF THE REVIEW

Several limitations of the present review warrant acknowledgment. First, the heterogeneity in experimental protocols and sample sizes across the studies examined limited our ability to directly compare methods and to standardize metrics for the quantitative assessment of CRC. Second, the literature search was confined to four scientific databases, namely, PubMed (including MEDLINE), the RSCI, SpringerLink, and ScienceDirect. Third, to the best of our knowledge, no direct studies of CRC alterations have been conducted in the cardiovascular and respiratory conditions examined in this review. Consequently, the hypotheses advanced herein regarding the probable direction of CRC changes in these pathologies must be considered provisional and require further experimental corroboration. Notwithstanding these limitations, the systematic account presented here offers a valuable framework for future investigations in this area.

CONCLUSION

The study of CRC has progressed from isolated empirical observations to the establishment of a formalized concept, one that is methodologically and conceptually distinct from both CRPS and RSA. The principal advance of recent years has been the development and refinement of quantitative and qualitative approaches to CRC analysis. In contrast to conventional CRPS, which is susceptible to variability in respiratory pattern and hinges critically upon accurate phase determination, CRC entails direct analysis of the intervals between R-peaks and respiratory cycles, an approach that confers upon it greater resilience to non-stationary conditions, such as those encountered in atrial fibrillation.

At the same time, changes in CRC in CVD, including AH, MI, and CIHD, and in respiratory diseases, such as COPD and BA, remain unexplored. We propose the phase recurrences method[34] and the automated coordigram method[22] as potentially successful approaches that could allow for the quantitative assessment of these CRC changes in future practical studies. This choice is based on the fact that these methods are robust to the non-stationarity of experimental signals and allow for the assessment of CRC on longer recordings.