Section of Anaesthesia, Wellington School of Medicine, PO Box 7343, Wellington, New Zealand*Corresponding author
Accepted for publication: August 14, 2001
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Abstract |
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Br J Anaesth 2001; 87: 82733
Keywords: heart, heart rate; heart, cardioventilatory coupling
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Introduction |
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In addition to cardioventilatory coupling, the timing interaction between breathing and the heart beat is also governed by respiratory sinus arrhythmia (RSA).6 7 The mutually interactive combination of cardioventilatory coupling and RSA forms a complex feedback system; the heart beat affects breathing and breathing affects the heart beat. It is important to appreciate, however, that these processes are distinct; one is not simply the converse of the other. In cardioventilatory coupling, a heart beat triggers inspiratory onset14 and in RSA the breathing cycle modulates the heart rate.6 7
Although coupling primarily influences inspiratory timing, coupling should also influence the pattern of heart rate variability (HRV). This follows because coupling determines the timing of inspiratory onset, which in turn determines the onset of vagal modulation by RSA. Consistent with this, we have identified geometrical features of the heart rate time series that are clearly associated with coupling.8 In contrast, we have been unable to demonstrate any statistical correlation between coupling and standard measures of HRV, such as the distribution of spectral power, approximate entropy or the fractal dimension.9 In the present paper we elaborate on the observation of geometrical patterning in heart rate time series during coupling and we attempt to derive simple quantitative measures of HRV that could be used to suggest the presence of coupling from the heart rate time series.
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Methods |
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Cardioventilatory coupling
To demonstrate cardioventilatory coupling, we determined the time of each R wave peak from the ECG and the start of each inspiration. We then calculated the time interval between each R wave and the following inspiratory onset (RI interval). The RI intervals were then plotted against time of R wave occurrence (RI plot). A fixed relationship between heart beats and inspiration (cardioventilatory coupling) is seen in an RI plot as horizontal banding in which the R wave, in particular that which immediately precedes inspiration, falls in constant temporal relationship with inspiratory onset (Fig. 1).
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Coupling pattern epochs
In order to examine the correlation between a particular coupling pattern and the geometry of the heart rate time series, we selected periods from the RI time series, without any visual reference to the HR time series, in which the pattern of coupling was stable. Epoch patterns were classified, as previously described, as uncoupled or patterns IIV.1 4 5 The minimum coupling pattern epoch length was 50 s and between one and three epochs were extracted from each subject. No two identical patterns were selected from any one subject. These epochs differed from the 256-s coupling pattern epochs used to examine the relationship between spectral measures of HRV and cardioventilatory coupling in the companion paper9 as we were no longer constrained by the requirements of the Fourier transform to use a 2n data set. The use of shorter coupling pattern epochs ensured that these were uncontaminated by other coupling patterns, and a greater number could be obtained from the available data sets.
500-beat RR interval epochs
In any extended HR time series, the pattern of coupling may vary from moment to moment according to a mathematical relationship between the HR and intrinsic breathing frequency.4 5 In order to examine a randomly sampled HR time series for the presence of coupling, we therefore extracted from each subject a single HR epoch, without reference to the RI plot. These epochs were all 500 heart periods in length and were free of rhythm abnormalities, and up to one epoch was extracted from subjects who provided data of suitable length. Where possible, the heart rate time series was chosen to minimize non-stationarity. The relationship between standard non-linear methods of HRV analysis and cardioventilatory coupling in these same epochs is examined in the companion paper [9].
RSA curves
For all epochs, we plotted, for each R wave, the immediately preceding RR interval against the time that the R wave occurred after the preceding inspiratory onset (Figs 1 and 2). These RSA curves reveal the effect of vagal modulation on RR interval and the positioning of R waves relative to inspiratory onset.
Entropy of the RI1 time series
As a quantitative measure of coupling, we determined for each epoch the dispersion of the RI1 interval (the interval between inspiratory onset and the immediately preceding the R wave). These RI1 intervals were then placed in a 10-bin histogram between limits 0 and mean RR1/+1 s, where RR1/+1 is the duration of the RR interval that spans inspiratory onset. The resulting histogram was examined using a measure of entropy (Shannon entropy). In a manner not dissimilar to that of the 2 statistic, Shannon entropy compares the actual bin occupancy against the expected bin occupancy for a series of RI1 intervals that are evenly distributed between histogram bins. Shannon entropy of the RI1 distribution equals 0 if all RI1 intervals fall into a single bin (perfect coupling, in which every breath is cardiac-triggered) and a maximum finite value if they are equally distributed between bins.2 9 Proportional Shannon entropy of the RI1 distribution (HRI1) is the calculated Shannon entropy divided by the maximum value, and it ranges between 0 (perfectly coupled) and 1 (uncoupled). For each data epoch, we passed a 10-point moving window through the RI1 time series, calculating HRI1 for the distribution of RI1 intervals within each window. The median of the HRI1 from these windows was taken as a quantitative measure of coupling for that epoch.
Graphical RR interval plots
From the RR interval time series for each coupling pattern epoch and for each 500-beat epoch we calculated and plotted the following variables: (1) raw RR interval (rr1, rr2,.... rrx) against time; (2) RR interval consecutive differences [(rr2rr1), (rr3rr2),... (rrxrrx 1)] against time (rrn); and (3) RR consecutive difference phase portrait, i.e. RR consecutive difference plotted against the following consecutive difference (rrnrrn1) plotted against (rrn+1rrn), i.e. (
rrn vs
rrn+1).
Qualitative description of structure within the RR interval coupling pattern epochs
Two independent observers examined the three graphical plots derived from the coupling pattern epochs without reference to any other information. For raw RR and consecutive difference RR time series, the observers noted the presence of banding, and in the RR consecutive difference phase portrait they noted the presence of discrete clusters. Banding or clustering was considered present only when the two observers were in agreement.
Quantitative measures derived from the RR interval plots
In a manner similar to that described for calculating the HRI1 for the RI time series (see above), we applied Shannon entropy as a measure of structure to the three forms of RR interval time series plots.
RR interval (rr1, rr2,... rrx) against time
Hrr was calculated as the median proportional Shannon entropy for a moving window of 50 RR intervals with histogram limits set at the minimum and maximum values of the RR interval within that window.
RR consecutive differences (rrn) against time
HCD was calculated as the median proportional Shannon entropy for a 50-rr moving window, with histogram limits set at the minimum and maximum values of
rr within that window.
Consecutive difference phase portrait (rrn vs
rrn+1)
HCDP was calculated from the distribution of points within a square, the boundaries of which encompassed points ranging between the 2.5 and 97.5% of the rrn range. The square was divided into a 10x10 matrix and the distribution of points within the cells of this matrix was treated as a 100-bin histogram and the HCDP calculated as the proportional Shannon entropy of this distribution.
Statistical analysis
All entropy values were treated as non-parametric variables. Statistical analysis included non-parametric analysis of variance (ANOVA) (KruskalWallis), the MannWhitney U-test, the 2 test and the Spearman correlation, as appropriate. P<0.05 was considered significant.
Raw data were extracted with purpose-written software in LabView 5.1 (National Instruments, Austin, TX, USA) and statistical analysis was performed using Statview 4.0 (SAS Institute, Cary, NC, USA).
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Results |
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Figures 1 and 2 show the RI interval plot, RR interval time series, consecutive difference time series, phase portrait, consecutive difference phase portrait and RSA curves for a representative pattern I and uncoupled epoch respectively.
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Despite the apparently clear qualitative relationship between RR interval banding and pattern I coupling, the statistical correlation between our measure of cardioventilatory coupling (HRI1) and entropy measure derived from the RR time series plot (Hrr) approached, but did not achieve, statistical significance for the coupling pattern epochs (P=0.062) and no correlation was found for the 500-heart beat epochs (Table 1). Furthermore, there was no apparent difference in Hrr according to coupling pattern (Table 2).
RR interval consecutive difference time series
As with the raw RR time series, consecutive difference RR interval banding was significantly related to the presence of coupling and varied with specific coupling pattern. Banding was observed in 54% of pattern I epochs, diminished with other coupling patterns and occurred least (11%) in uncoupled epochs (Table 2). Referring to the pattern I example in Fig 1E, the RR interval consecutive difference time series shows two distinct bands, one (possibly two bands) ranging between 0 and 0.08 s and a second, narrower band at 0.1 s. In contrast, in Fig. 2E the RR interval consecutive difference time series for the uncoupled epoch shows an apparently random distribution of values between 0.05 and 0.05 s. As with the RR banding, the banding of the RR interval consecutive time series was found to correspond with repeating sequences of RR intervals (and hence RR interval consecutive differences) consequent upon the RR alignment to inspiratory onset.
We observed a significant correlation between HCD and HRI1 for both the coupling pattern and 500 heart beat epochs (Table 1). The HCD values were lower during epochs of pattern I and II coupling than during patterns III and IV and uncoupled epochs (Table 2).
Consecutive difference phase portrait
Multiple complex patterns were observed in the consecutive difference phase portrait [(rrnrrn 1) vs (rrn+1rrn)]. The most commonly observed pattern was three discrete clusters of points (Fig. 1F) in various degrees of rotation. The observed clustering was significantly related to the presence of coupling and the specific coupling pattern. Clustering was observed in 62% of pattern I epochs, diminished with other coupling patterns and occurred least (11%) in uncoupled epochs. As with the other graphical plots, clustering was consistent with the stepwise RR interval and consecutive difference fluctuations. The number and distribution of clusters varied according to the pattern of RR interval variation during each ventilatory cycle and the point distribution expanded or contracted according to the degree of RSA. Where RSA was very low, little discrete clustering was observed within the small point distribution. Uncoupled epochs were associated with a central globular cluster or ring distribution; an example is shown in Fig. 2F.
HCDP significantly correlated with HRI1 (Table 1) and varied significantly with coupling pattern, being lowest during pattern I and III epochs (Table 2).
Modifying influences
A number of subjects, despite showing good evidence of coupling on the basis of the RI interval plot, failed to show any evidence of structure in the graphical RR time series plots. Conversely, banding or clustering was occasionally observed despite the absence of coupling. Epochs that were not consistent with the overall trend were therefore examined further. We were able to identify the following three factors that clearly altered the relationship between coupling and the qualitative appearance of structure and the associated quantitative measures.
Low RSA
Some subjects showed minimal heart rate variation due to RSA. RR and consecutive difference time series were therefore confined to a single narrow band and the consecutive difference phase portrait was confined to a small point distribution. Combined with the small degree of noise in these time series, this destroyed any definable structure within these plots despite the presence of coupling. Furthermore, at very low RR interval variation, the quantizing error of our 500 Hz sampling frequency became significant and an artefactual time series banding or clustering erroneously gave the appearance of structure when none existed. Although the low RSA and the quantizing effect were readily apparent from the graphical plots, in isolation the quantitative measures derived from these plots gave no clue as to their artefactual origin.
Heart rate/breathing frequency=2:1
For time series in which the heart rate/breathing frequency ratio approached 2:1, RR acceleration was followed by deceleration, and deceleration by acceleration. Despite the absence of coupling, this alternating pattern of HRV gave rise to a symmetrically double-banded appearance of the consecutive difference time series and a double cluster of points in its associated phase portrait. As with RSA, this error was readily apparent from the graphical plots.
Coupling pattern
The positioning of heart beats relative to inspiratory onset (and hence RSA) is different for different coupling patterns. Because the alignment of heart beats to the RSA is determined by the cardiac triggering, coupling patterns in which cardiac triggering occurs most commonly (patterns I, II and III) are associated with the most structured plots.
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Discussion |
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A conspicuous feature of raw heart rate time series is the fast, respiratory phase-related modulation by RSA. With the onset of inspiration, vagal tone decreases to the sino-atrial pacemaker and a brief acceleration in heart rate ensues. During the expiratory phase, vagal tone returns and heart rate decreases.6 7 The specific pattern of heart rate acceleration and deceleration which occurs with breathing is determined by the pattern of vagal modulation and the positioning of heart beats within the ventilatory phases. Because cardioventilatory coupling determines the timing of inspiratory onset it also determines the timing of vagal heart rate modulation by RSA. Furthermore, because the coupling interval (that between the initiating cardiac trigger and inspiratory onset) is fixed for a cardiac triggered breath at approximately 0.5 s,1 4 heart beats tend to fall in fixed relationship with the waxing and waning pattern of vagal tone.1 8 11 Because of this, the pattern of heart rate vagal modulation for the heart beats occurring during one breath will be similar to that in the following and each subsequent breath. In particular for pattern I coupling (constant entrainment and constant coupling interval), this HRV pattern repetition generally, although not invariably, causes a banded appearance in the RR interval time series and the RR interval consecutive difference time series, and the formation of discrete clusters within the RR consecutive difference phase portrait (Fig. 1).8
Because different coupling patterns vary in the degree to which they are cardiac-triggered, the best alignment between heart beats and the RSA curve (and hence the best correlation between coupling and geometric structure) is found for those coupling patterns associated with the greatest proportion of cardiac-triggered breaths. Thus phase portrait structure is seen best for pattern I, then patterns II and III, and least well for patterns IV and uncoupled.
Although we observed a statistical correlation between coupling and the entropy of the RR interval consecutive difference time series and its associated phase portrait, we could find no correlation with the entropy of the RR interval time series plot. There are at least two explanations for the improved correlation with the consecutive difference measures.
First, trends or non-stationarity in the heart rate time series are less apparent with consecutive difference measures. Thus, a trend in raw heart rate will tend to scatter RR intervals into varying histogram bins during the process of entropy measurement for Hrr. Consecutive difference measures ignore the absolute values of heart rate and measure only the beat-to-beat difference. Non-stationarity is therefore less of a problem in the calculation of HCD and HCDP.
Secondly the consecutive difference time series corresponds to a series of values that define the relationship between consecutive pairs of RR intervals, i.e. the relationship between two RR intervals or three heart beats. Each point on the phase portrait of the consecutive difference time series defines the relationship between three RR intervals or four heart beats. In contrast, RR interval time series plots display a series of single RR intervals or the relationship between two heart beats. In clinical epochs, heart rate/ventilation rate ratios of 3:1 and 4:1 are seen most commonly, and hence during coupling the repeating RR interval patterns are occurring over three or four RR intervals. Unlike the RR measures, therefore, the consecutive difference measures will tend to display the full structure of the pattern repetition.
In this paper we have demonstrated the presence of coupling without the need for a ventilatory signal. This is of potential value in many experimental protocols because, in contrast to the determination of the RR time series from the ECG, the determination of an inspiratory time series is technically difficult; inspiratory timing is prone to error and, unless care is taken, cardiac contamination of a ventilatory flow signal may lead to artefactual coupling. The methods described for the demonstration of coupling in HR time series are understandably limited in the absence of RSA, as it is RSA that provides the displacement necessary to reveal the heart rate repetition, which in turn is the marker of coupling. If RSA is taken into account, cardioventilatory coupling may be added to the range of physiological processes that are revealed by beat-to-beat HRV analysis. Although generally applied to the influences of cardiac autonomic tone and the effect of respiration on heart rate, we have demonstrated that the heart rate time series is also capable of revealing the complex bidirectional interaction that exists between cardiac and respiratory frequency control.
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References |
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