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: 81926
Keywords: heart, heart rate; heart, cardioventilatory coupling
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Introduction |
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In addition to frequency domain analysis, there has been considerable interest in the analysis of HRV using non-linear methods, such as the fractal dimension (DF) and approximate entropy (ApEn), both of which attempt to quantify the complexity of heart rate dynamics.
The fractal dimension is a quantification of the space-filling propensity of the heart rate time series. While in Euclidean geometry a line is one-dimensional and a surface is two-dimensional, an irregular curve can be thought of as a line which is attempting to fill a surface. Mathematically, we can therefore describe such a line as having a dimension between one and two. The more the line fills the plane, the higher will be its fractal dimension DF.3
Entropy is a quantification of the repetition of patterns within a given signal.4 Small values of entropy are associated with regularity of patterns within a signal, such that it may be possible to predict the recurrence of a previously identified pattern. Larger values of entropy are associated with greater apparent randomness. Steven Pincus has developed a measure of entropy, approximate entropy (ApEn), as a modification of KolmogorovSinai entropy to allow measurements of entropy from shorter data segments, with simpler mathematics and lower computational demands.5 6 ApEn has been applied to the study of HRV by a number of authors.5 7 8
Cardioventilatory coupling is a temporal coherence of cardiac rhythm and inspiratory timing.9 It is seen in resting subjects, during sleep and spontaneous-breathing general anaesthesia. Experimental and clinical observations are consistent with coupling being a triggering of inspiratory onset by a cardiovascular afferent(s) associated with a preceding heart beat.10 11 During a coupled or cardiac-initiated breath, inspiratory onset will occur a fixed interval (the coupling interval, typically 0.5 s) after an ECG R wave. However, the exact relationship between the timing of the ECG R wave and inspiratory onset is complex and will vary according to whether the breath has been initiated by the intrinsic inspiratory pacemaker or by the cardiac trigger. This variation leads to multiple patterns of coupling, which can be described in terms of variation in coupling interval and entrainment ratio (number of heart beats within each breath).911 These patterns have been classified as I, II, III, IV and uncoupled, although other patterns have been suggested both from clinical observation and from computer modelling.11
The temporal coherence of heart beats and inspiration is a major determinant of breath-to-breath fluctuations in breathing frequency during anaesthesia.10 As breathing influences HRV through respiratory sinus arrhythmia, it is to be expected that cardioventilatory coupling will contribute significantly to the pattern of HRV.9 12 13 By temporally aligning heart beats to the breathing cycle, and given a constant breathing period, heart beats will occur at constant positions within the breathing cycle from breath to breath. Heart beats are therefore subject to repeating patterns of respiratory mediated fluctuations in vagal tone (RSA), giving rise to repeating patterns of HRV. In a previous paper we have demonstrated that, during one particular pattern of coupling (pattern I), the precise positioning of heart beats within each breath results in maximal fluctuations in heart rate due to RSA.13 We have suggested that, on the basis of these repeating patterns of HRV, it may be possible to detect cardioventilatory coupling from heart rate time series. In a preliminary description we have shown that several geometrical features of heart rate time series may occur in association with cardioventilatory coupling12, and in the present work we have examined the relationship between three standard measures of HRV and coupling.
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Methods |
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Anaesthesia was induced in all subjects with propofol and maintained with isoflurane, nitrous oxide and oxygen. Opioids were given according to surgical indications. Subjects breathed through a laryngeal mask airway, with FIO2 adjusted to maintain arterial oxygen saturation (SpO2) at or above 96% at all times.
We monitored SpO2, end-tidal carbon dioxide (Datex Oscar, Datex-Ohmeda, Helsinki, Finland), non-invasive blood pressure (Dinamap) and ECG (lead CM5; Neo-trak 502; Corometrics, Connecticut, USA). Ventilatory timing was measured by an electronically triggered non-return valve within the breathing system. Continuous recordings of ECG and ventilatory timing were made using a Macintosh IIcx computer with a 16-bit ADC board (MIO-16; National Instruments, Austin, TX, USA) and a sampling rate of 500 Hz.
Data analysis
Quantitative and qualitative measures of cardioventilatory coupling
From the ECG and ventilatory timing signals, we determined the time from each R wave to the onset of the following inspiration (RI interval) and plotted successive RI intervals as a time series. Horizontal banding within these RI plots indicates a constant temporal alignment between heart beats and inspiration (i.e. cardioventilatory coupling). The heart beat which immediately precedes inspiratory onset is given a negative subscript (R1) and the interval between that heart beat and the inspiration is designated the RI1 interval. During coupling, RI1 is generally the most constant RI interval.
Patterns of coupling were defined as follows:
Pattern I: constant RI1 alignment and a constant number of heart beats in each ventilatory period (i.e. constant entrainment ratio);
Pattern II: constant RI1 alignment but with a varying entrainment ratio;
Pattern III: RI1 intervals alternate between two values from breath to breath;
Pattern IV: RI1 interval alignment slowly changes (increases or decreases) from breath to breath, but holds transiently at the RI alignment associated with coupling;
Uncoupled: No consistent RI1 interval alignment observed.
The dispersion of RI1 interval values correlates inversely with coupling. During coupling patterns I and II the RI1 interval will be virtually identical from breath to breath, whereas the RI1 interval varies to a greater degree during coupling patterns III and IV, and in uncoupled time series will give the appearance of randomness. Statistical measures of RI1 dispersion therefore correlate with the degree of heart beat to inspiratory alignment. On the basis of computer modelling of the coupling process, the RI1 dispersion is a measure of the proportion of the breaths which have been triggered by a cardiac signal.11 In the present study the RI1 interval dispersion was measured using proportional Shannon entropy of the RI1 interval (HRI1), the details of which have been published previously14 and are given in the Appendix. Values of HRI1 below 0.7 are typically associated with the appearance of cardioventilatory coupling in RI1 time series plots.
Spectral analysis
To determine the effect of cardioventilatory coupling on spectral measures of HRV, we extracted epochs of data, 256 s in length, displaying as near as possible a constant single pattern of coupling throughout.
Spectral analysis was performed using a method based on that of Akselrod and colleagues,1 15 which is given in the Appendix. The spectral power (integrated area under the power spectrum curve) was calculated in each subject for total power and in three frequency bands: high (0.150.45 Hz), low (0.080.15 Hz) and very low (0.020.08 Hz). The proportion of the total power in each frequency band was also calculated.
Data epochs for ApEn and DF
The ApEn and DF of RR interval time series are generally computed from data series of at least 5001000 heart beats.6 8 16 In this study, data epochs of 500 heart beats were used. However, because the pattern and degree of coupling changes over time it was not possible to obtain a sufficient number of 500-heart beat epochs demonstrating a single pattern of coupling throughout for statistical analysis. We therefore extracted a single 500-beat epoch of heart rate time series from as many subjects as possible, without reference to the RI plot. A maximum of one epoch was extracted from each subject and, where possible, the heart rate time series was free of non-stationary trends.
For each epoch of heart rate data, we determined ApEn and DF and calculated HRI1 from the associated RI interval plot. ApEn was calculated using the algorithm of Pincus5 and DF was calculated using the method of Katz;3 both of these methods are given in the Appendix.
Analysis
Data were acquired and variables were calculated using custom-written software in LabVIEW 5 (National Instruments, Austin, TX, USA). Statistical analysis was performed using Statview 5.
We used the KruskalWallis test to examine the relationship between the total spectral power and the proportions of power in the high-, low- and very low-frequency bands, and the different patterns of coupling.
We examined the relationship between HRI1 and total spectral power, proportional band power, DF and each of the ApEn scores (for m=2 as well as m=3, at rEn=0.025, 0.05, 0.075, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5 and 0.6; m is the number of heart periods in a sequence and rEn is the tolerance range within which sequences of m RR intervals are considered to be similar) using the Spearman rank correlation.
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Results |
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Spectral analysis
No significant difference in total spectral power was observed between the different patterns of coupling. However, there was a significant difference in the distribution of power, with a significantly greater proportion of power in the low-frequency band and a corresponding decrease in the proportion of high-frequency power observed in pattern II coupling epochs. This observation was related to the expected10 low breathing frequency in epochs with pattern II coupling (Table 1). As the breathing frequency decreased, movement of the high-frequency respiratory-related spectral peak into the range of the low-frequency band (defined as 0.080.15 Hz) occurred, resulting in an apparent increase in low-frequency power in this group. If we exclude pattern II epochs, there were no significant differences in distribution of power between epochs of different coupling patterns.
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Approximate entropy
We observed no correlation between HRI1 and ApEn for any combination of m or r values selected in this study (Table 2). ApEn correlated negatively with RR interval at r=0.025 for both m=2 and m=3 and positively with RR interval at 0.075, 0.1, 0.15 and 0.2 for both m=2 and m=3. We also observed a negative correlation between respiratory frequency and ApEn at all values of m and rEn with the exception of r= 0.025 for both m=2 and m=3, where no significant relationship was observed. The high-frequency spectral power correlated with all ApEn values except for that at rEn=0.05 with m=2 or 3; for low rEn values the correlation was negative and for values above 0.05 it was positive.
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Discussion |
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RSA is determined by ventilatory phase-related vagal modulation. The degree of modulation is influenced by a variety of factors, including age, position, underlying vagal tone and respiratory frequency.17 Vagal tone is reduced soon after inspiratory onset, causing a brief acceleration in heart rate. Vagal tone then returns and heart rate decreases before the onset of the next inspiration. The vagal modulation, and hence heart rate variation, is therefore cyclic, with a maximum and minimum heart rate at specific phases of the breathing cycle. This cyclic RSA response can be demonstrated in the form of an RSA curve, where the duration of the RR interval between two consecutive R waves (Rn and Rn+1) is plotted against the time that Rn+1 occurs after inspiratory onset (or against the phase of the ventilatory cycle). Coupling relates to this curve in at least two ways.
First, in the majority of individuals with pattern I coupling, the two consecutive R waves which immediately follow inspiratory onset (R+1 and R+2) tend to fall at the extremes of the RSA curve.13 R+1 is therefore preceded by the longest RR interval and R+2 is preceded by the shortest RR interval that can occur for the particular RSA curve. This leads to an apparent maximization of RSA; that is, for most breaths the difference between the maximum and minimum RR intervals within the breath is as great as is possible for the given RSA curve. It would be expected that this would lead to an increase in power in the high (respiratory) frequency band. That we did not observe this in our pattern I data epochs may relate to at least two factors: (1) we know that the effect does not occur in all subjects;13 and (2) high-frequency power is already high and there is a wide inter-individual difference in spectral power; because the numbers of epochs with pattern I of sufficient length were small, it is therefore difficult statistically to detect significant variation in high-frequency power.
The absence of a relationship between coupling and distribution of spectral power suggests that the coupling pattern is independent of cardiac autonomic tone. This observation is consistent with our demonstration that the coupling pattern is determined by the ratio of heart rate to intrinsic breathing frequency as well as the magnitude of the cardiac-related afferent trigger.11
The HRV power spectrum will be influenced by factors other than autonomic tone. For example, the position and character of the high-frequency peak will be influenced by ventilatory frequency fluctuations. As coupling, specifically the coupling pattern, determines much of the ventilatory variability of spontaneously breathing anaesthetized subjects, the coupling pattern should affect the characteristics of the respiratory spectral peak. These minor effects are, however, beyond the scope of this paper.
The second relationship between the RSA curve and coupling arises because coupling is a triggering of inspiratory onset by cardiac activity and therefore inspiration is temporally aligned to the preceding, triggering heart beat (usually RI1). It follows that each of the subsequent heart beats (R+1, R+2, etc.) will also align themselves to the preceding inspiratory onset. Thus each heart beat will become aligned to constant phases of the ventilatory cycle. Each heart beat within a ventilatory cycle will therefore be modulated differently according to its position on the RSA curve. In pattern I coupling, where the entrainment ratio remains constant (i.e. there is a constant number of heart beats within each ventilatory period), identically repeating sequences of HRV will occur with each breath. One observes this repetition as discrete banding of the RR interval time series.12 Coupling should therefore be associated with regularity of the heart rate time series. To a degree, this regularity may be disrupted if the entrainment ratio is varying from breath to breath, as it does in coupling patterns II, III and IV. Thus, although regularity should be a feature of HRV during pattern I coupling, this may be less likely for patterns II, III and IV and uncoupled epochs.
It has been suggested that ApEn has value in distinguishing between regularity in HRV under pathophysiological conditions and greater irregularity in HRV in normal individuals.18 19 ApEn is, however, a family of statistics, and its correlation to any physiological process will depend upon the selection of values for N (number of RR intervals), m and r.6 In the present study the correlation between ApEn and DF or high-frequency spectral power (i.e. RSA) was critically dependent upon the selection of rEn in the range 0.0250.075. It is possible that this dependence on the control variables may lead to entirely different conclusions. Thus, Palazzolo and colleagues16 observed a good correlation between ApEn (N=2048, m=2, r=0.07) and the high-frequency spectral component of HRV in resting dogs and found that sympathetic blockade did not alter ApEn, whereas parasympathetic blockade produced significant decreases in ApEn. It was therefore concluded that ApEn was positively related to RSA. In contrast, Mansier and colleagues4 computed ApEn (N=1000, m=2, r=0.05) in the mouse and found that the administration of atropine was associated with a significant increase in ApEn. The authors noted that there was a decrease in the total variability associated with atropine treatment, as measured by spectral analysis, but that the complexity of the series increased according to ApEn and other non-linear measures. These authors therefore concluded that ApEn was inversely related to RSA. It seems probable that the divergent opinions of Mansier and Palazzolo can be explained by their choice of control variables.
ApEn did not correlate with the dispersion of the RI1 interval (i.e. cardioventilatory coupling) at either m=2 or m=3 for any of the rEn values used in the present study. As coupling is associated with repeating geometrical patterns of HRV12 and ApEn is said to be a measure of regularity, this observation was surprising. Several explanations will now be considered.
(1)Coupling during anaesthesia is characterized by rapid transitions between coupling patterns, which are in turn determined by the heart rate/breathing frequency ratio.10 11 Each coupling pattern is associated with a different entrainment ratio variation from breath to breath. As the entrainment ratio variation will alter the position of heart beats on the RSA curve, transitions in coupling pattern will therefore disrupt the regularity of HRV and could thereby alter ApEn.
(2)In clinical time series, non-stationarity (an overall trend) in the heart rate time series is difficult to avoid. Thus, although repetitive patterns may occur throughout the time series, in the presence of trend they will fall outside the tolerance rEn. In order to reduce this effect, we also examined the correlation between ApEn and HRI1 where ApEn was measured (for all 20 combinations of m and rEn) from the RR interval consecutive time series [i.e. (rr2rr1), (rr3rr2), (rr4rr3)... (rrnrrn-1)]. As with the ApEn derived from the raw RR time series, however, no significant correlation was found.
(3)In some subjects the magnitude of RSA is small and, as in paragraph (2) above, any small variation in HRV due to noise will mask the pattern repetition and cause repeating patterns to fall outside the tolerance rEn.
(4)It is possible that dispersion of the RI1 interval, as measured by its Shannon entropy, is itself limited as a measure of coupling. In a previous paper we have demonstrated that HRI1 correlates well with the appearance of coupling in the RI interval plot, in particular during patterns I and II. During coupling patterns III and IV, however, where RI1 dispersion is greater, the difference in HRI1 with uncoupled epochs is measurable but small. However, it should noted that ApEn and DF did not differ between pattern I and uncoupled epochs. In addition, having observed the lack of correlation between ApEn and HRI1, we also examined the correlation between the set of 20 ApEn values and other measures of RI1 dispersion, although none correlated significantly with any value from the ApEn set (these measures included the proportional Shannon entropy derived from all RI1 intervals in each epoch rather than the median of the 10-breath moving window; RI1 standard deviation; mean RI1 consecutive difference; and standard deviation RI1 consecutive difference).
(5) ApEn measures the log likelihood that short epochs of data with a similar pattern will remain similar as the epoch length is increased. As coupling is associated with repetition of a specific pattern, a statistic which examines the likelihood that a pattern is similar might be a better correlate with coupling. ApEn may therefore be measuring a quality of RR variability different from that resulting from coupling.
In conscious subjects, Yeragani and colleagues20 observed that DF was positively correlated to both ApEn and high-frequency spectral power, suggesting that both measures reflected parasympathetic modulation of heart rate, and on this basis it was suggested that the two measures (ApEn and DF) could be used interchangeably. Similar results were reported by Jartti and colleagues.8 In the present study we found high correlations between DF and ApEn, as suggested by Yeragani and colleagues, at values of rEn0.05, although, as noted above, at lower values of r an inverse relationship is seen. Both DF and ApEn strongly correlated with high-frequency power and therefore it is probable that the dominant influence on each of these measures is RSA. As with ApEn, we observed no relationship between DF and cardioventilatory coupling.
In conclusion, using standard spectral and non-linear measures of HRV we were unable to demonstrate an effect of cardioventilatory coupling on heart rate time series. However, graphical displays of clinical time series plainly show that, during periods of coupling, the heart rate time series may take on a qualitative appearance which is different from that observed in uncoupled time series. Alternative analytical techniques are therefore desirable for the detection of coupling in heart rate time series, and these are explored in the accompanying paper.21
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Appendix |
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N
Shannon entropy=H= Pb*log(Pb)
b=1
Maximum Shannon entropy=Hmax=log(1/N)
HRI1=H/Hmax
where P is the actual histogram bin probability, b is the bin number and N is the number of histogram bins.
The median value from successive moving windows over the entire RI1 time series was used as a measure of RI1 dispersion. Values below 0.7 are typically associated with the appearance of cardioventilatory coupling in RI1 time series plots.14
Spectral analysis
To determine the effect of cardioventilatory coupling on spectral measures of HRV, we extracted epochs of data, 256 s in length, displaying as nearly as possible a constant single pattern of coupling throughout.
Spectral analysis was performed using a method based on that of Akselrod and colleagues.1 15 The 256-s RR interval time series, free of ectopy, was sampled at the rate of 4 Hz to produce a series of 1024 discrete RR interval values. This series was then high-pass filtered to remove fluctuations less than 0.015 Hz and low-pass filtered at 2 Hz to remove components at greater than Nyquist frequency. A fast Fourier analysis was performed using a Hanning window. The spectral power (integrated area under the power spectrum curve) was calculated in each subject for total power and in three frequency bands: high (0.150.45 Hz), low (0.080.15 Hz) and very low (0.020.08 Hz). The proportion of the total power in each frequency band was also calculated.
Approximate entropy (ApEn)
ApEn was calculated using the algorithm of Pincus.5 Starting from the first RR interval, a segment or window of m heart periods is taken, these forming a short sequence of RR interval variation. The entire RR time series is then examined for sequences with similar values (within a tolerance of rEn) and the number of similar sequences is counted. The window is then moved to the next consecutive RR interval and the number of similar sequences to this is then computed. This procedure is repeated as the window moves across the time series. The resulting count is then compared with a similar count for the sequence value (m+1). In this manner, ApEn measures the log likelihood that runs of data with a particular pattern will retain the same pattern for the next incremental observation. To compute ApEn, three input values must be decided according to the variables: (1) the number of data points (N) to be analysed, in this study N=500 heart beats, as discussed above; (2) the embedding dimension (sequence length m) for comparison (for heart rate time series, m=2 and m=3 are the most commonly used embedding dimensions)6 7 16 and in the present study ApEn values were computed for both m=2 and m=3; (3) the tolerance range (rEn) within which sequences of m RR intervals are considered to be similar. Values of rEn are typically expressed as a fraction of the standard deviation of the RR interval time series and values in the range 0.050.25 are generally used.57 16 However, to prevent missing a correlation with coupling resulting from selecting inappropriate rEn values, we chose to use a range of r values wider than is normally used, selecting rEn=0.025, 0.05, 0.075, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5 and 0.6 of the standard deviation of the RR interval time series. Thus, for our 500-beat time series, ApEn was calculated for 20 combinations of m and rEn.
Fractal dimension (DF)
DF was calculated using the method of Katz:3
DF=log(n)/[log(n) + log(d/L)]
where n is the number of data points, d is the planar extent of the curve (the distance in time from the starting point to the nth point) and L is the total length of the curve. This algorithm generates a value for DF between 1 (representing a signal with low space-filling capacity) and 2 (representing a signal with high space-filling capacity).
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