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

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.

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

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.