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Cardiac Electrophysiology Review 1997;3:329–334 © Kluwer Academic Publishers. Boston. Printed in U.S.A.

Malik

Time-Domain Measurement of HRV

Time-Domain Measurement of Heart Rate Variability Marek Malik Department of Cardiological Sciences, St. George’s Hospital Medical School, London, England

In principle, there are numerous ways of expressing the variability of heart rate and heart periods. The initial methods, predominantly applied to the assessment of foetal rate variability, were oriented to processing of short-term tachograms and periodograms and involved rather simple arithmetic formulae. As the measurement of heart rate variability was being applied to wider groups of laboratory and clinical investigations, the need emerged for developing methods based on a more solid mathematical basis, and the so-called statistical methods appeared. These methods treat the sequence of RR intervals or of pairs of adjacent RR intervals as a set of unordered data and express its variability by conventional statistical approaches. Later, detailed physiological studies required the distinction of different components of heart rate variability that are attributable to individual regulatory mechanisms. This need led to the application of spectral methods to series of RR intervals in which their original order was carefully recorded. Both statistical and spectral methods require a high precision and a reliable quality of RR interval data, which are dif~cult to maintain when analysing longterm electrocardiograms recorded under clinical conditions. This dif~culty led to the introduction of the socalled geometrical methods, which were developed in order to provide approximate assessment of heart rate variability even when applied to RR interval data containing low level of errors and artefacts. Finally, because the physiologic and pathophysiologic mechanisms governing heart rate and its oscillations are not only complex but also substantially irregular in their periodicity, methods of non-linear dynamics are currently under investigation for the analysis of heart rate variability. However, practical experience with these methods is currently limited. Thus, apart from complex non-linear methods, which may play a role in the future, there are in principle two broad categories of methods for heart rate variability measurement: the spectral methods, which treat the RR interval data as a time-ordered series, and the nonspectral methods, which process the sequence of RR intervals or of their pairs without paying any attention to the timing of individual intervals. Substantial numbers of the non-spectral methods report the results of heart rate variability in units or time (e.g., in milliseconds). For this reason, the whole group of non-spectral methods is frequently called the time-domain methods.

Statistical Methods The task of expressing numerically the variability of a series of data is a standard requirement of the descriptive statistics. Thus, having the data on the durations of individual RR intervals or on heart rate in consecutive ECG segments, the application of the formula for calculating standard deviation is an obvious choice. Understandably, a solely mathematical approach does not re_ect any physiological or pathophysiological facets of heart rate variations. Because of this conceptual limitation, some possibilities of how to analyse a continuous series of RR interval durations have been based on simple physiological reasoning. However, the concepts derived in this way resemble to a certain degree the purely mathematical approaches. Therefore, all these possibilities of a numerical manipulation of the RR intervals sequence are frequently grouped together under the term statistical methods.

Data analysed by statistical methods In order to provide meaningful results, reasonable quality and contents of data is required by the statistical methods; namely, coupling intervals and compensatory pauses of atrial and ventricular ectopics have to be excluded. However, the automatic or semi-automatic way of obtaining data from electronically recorded ECGs, and especially long-term ECGs, is not robust and error free. Thus, before applying any statistical method to the data of RR interval durations of consecutive heart rates, visual checks and manual corrections of the automatic ECG analysis have to ensure that all coupling intervals and compensatory pauses of premature cycles have been excluded and that, on the other hand, all sinus rhythm QRS complexes were correctly recognised and included into the data stream. In order to specify this character of intervals included into the analysed data stream and to postulate that extra care has been given to the quality of the data stream, the term “normal-to-normal” intervals (or NN intervals) has been proposed and widely accepted. In principle, the formulae of statistical methods can be applied to sequences of both individual RR interval

Address correspondence to: Marek Malik, M.D., Department of Cardiological Sciences, St. George’s Hospital Medical School London SW17 0PE, U.K. 329

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durations and consecutive heart rate samples. Nevertheless, heart rate samples are also calculated from individual RR interval durations. Thus, application of any statistical method to heart rate samples is merely an application of a slightly modi~ed method to the RR interval series. Moreover, the series of RR interval durations rather than heart rate samples is a more direct result of an automatic ECG analysis. For these reasons, the use of heart rate samples in statistical methods has practically been abandoned in recent studies.

Standard deviation-based methods in short-term recordings In NN interval series obtained from short term recordings, the formula of standard deviation can be applied either to durations of individual intervals or to the differences between the neighbouring intervals. The ~rst possibility leads to the so-called SDNN measure of heart rate variability the numerical value which is de~ned as SDNN 5

1 √  )2 S (NN 2m n i n 51

i

where NNI is the duration of the i-th NN interval in the analysed ECG, n is the number of all NN intervals, and m is their mean duration. True standard deviation of all NN intervals is being used rather than its estimate; however, the difference is negligible for large values of n, which are common in all practical applications of SDNN [1,2]. Although the true standard deviation of differences between neighbouring intervals has also been used in some studies, it is much more frequently assumed that the mean of differences between neighbouring intervals is zero. The formula that results from this assumption is the so-called rMSSD measure (root Mean Square of Successive Differences) de~ned as rMSSD 5

1  √ S (NN 12NN ) n 21 n21 i51

i1

i

2

where NNi is again the duration of the i-th NN interval in the analysed ECG and n is the number of all NN intervals [3]. This simple form of the formula assumes that there are not any ectopic beats in the ECG that would lead to the omission of some RR intervals. If there are, the difference between NN intervals that are not immediately successive is omitted from the calculation and the number n is decreased accordingly.

Standard deviation-based methods in long-term recordings When assessing heart rate variability in long-term recordings, there are more possibilities of how to apply the statistical formulae. First of all, both SDNN and rMSSD can be used as such, that is with all the NN

intervals and pairs of NN intervals found in the recording. In addition to that, there are two principal other possibilities of how to apply the methods. Firstly, the methods may be used with shorter segments of the whole recordings (e.g., segments of 1, 5, or 30 minutes, etc.), and the results obtained from such segments averaged in order to characterise the total period of recording. Secondly, the mean NN interval may be found for individual segments and the statistical formulae applied to the resulting series of samples of the mean NN interval. In practice, both these possibilities are being used with the formula of standard deviation of NN interval durations when the long-term recording is divided into segments of 5 minutes. Calculating the SDNN value for each 5-minute segment and averaging the result for the whole recording leads to the so-called SDNN index measure. On the contrary, calculating standard deviation of 5-minute means of NN intervals results in the so-called SDANN measure (Standard Deviation of Averaged NN intervals). The 5-minute duration of individual segments into which the long-term recording is broken has historical rather than physiological or presently valid practical reasons. Indeed, the observations of more recent physiological studies might possibly be interpreted as suggesting that a division of long-term recording into much shorter segments (e.g., segments of 10 to 20 seconds), might perhaps lead to more physiologically related measures of heart rate variability. Thus far, however, no systematic investigation has been performed analysing the effect of different segment durations on the practical value of the SDNN index and the SDANN measures.

Counts and relative counts From a physiological point of view, the fastest changes of heart rate can be attributed to the changes in the parasympathetic tone and to fast-acting neurohumoral regulation. Indeed, release of acetylcholine from the vagal ~bres is associated with marked prolongation of RR intervals that can create large differences between two consecutive cardiac cycles. Similarly, neurohumoral regulation is responsible for immediate increases in heart rate, such as those associated with sudden fright. The degree and frequency of these marked changes of RR intervals contributes naturally to the mathematically de~ned measures of heart rate variability such as SDNN or rMSSD but can be masked by the extent of slower regulatory mechanisms and external stimuli (e.g., by thermoregulation and by psychosomatic responses to the environment). This led to the concept of measuring the immediate changes in heart rate separately from the more gradually acting regulations. The principle of these methods is simple. For a selected threshold t of RR interval prolongation or short-

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ening, the number of cases may be counted in which a NN interval is prolonged or shortened by more than t within one cardiac cycle, that is the number of NN intervals that are longer than NN9 2 t or longer than NN9 1 t, where NN9 is the duration of the immediately preceding NN interval. Alternatively, both such counts can be merged together by counting all NN intervals that differ from the immediately preceding NN interval by more than t. The performance of such a method naturally depends on the value of the threshold t. Originally, the method has been proposed with the threshold t of 50 ms. The heart rate variability measures NN 1 50 (count of prolongation of NN intervals), NN 2 50 (count of shortening of NN intervals) and NN50 (both counts together) are de~ned in this way [4]. Whether such a value is the optimum has never been systematically investigated, but it seems that the optimum threshold depends also on the goal of the study in which the method of counts is used to measure heart rate variability. The numerical values of NN 1 50, NN 2 50, and NN50 crucially depend on the length of the recording. This is a serious disadvantage because, to standardise the length of recording absolutely is not practical, especially with long-term recordings performed in clinical setting (nominal 24-hour recording frequently varies between, say, 22 and 25 hours and such a variation may on its own lead to differences in counts of more than 10%). For this reason, the concept of relative counts has been proposed. The value of heart rate variability measures pNN50 (and similarly pNN 1 50 and pNN 2 50) is de~ned as the relative numbers of NN intervals differing by more than 50 ms from the immediately preceding NN interval; in other words pNN50 equals to NN50 divided by the number of NN intervals in the whole analysed ECG. Although it may seem to be smart, the concept of relative counts (that is, of the pNN9 threshold method) is to a certain degree illogical and contradicts the original idea which was behind the introduction of the methods of counts. If the goal is to measure the frequency of occurrences of strong vagal and neurohumoral discharges, the counts should be normalised by the duration of the whole recording rather than by a number of all NN intervals, which makes the method dependent on the underlying heart rate. Unfortunately, the measurement of the duration of recording is also not straightforward because it should exclude intervals surrounding ectopic beats, episodes of invalid data, etc. Perhaps this is the reason why normalisation of counts by the recording duration has never been seriously attempted. It is also possible that the manifestation of the suddenly acting regulatory mechanisms depends on the underlying heart rate. Should this be the case, the absolute threshold of 50 ms would create a bias between episodes of slow and fast heart rate, which can both be present during a longer recording. Having this in mind, a proportional threshold has also been proposed. Such a proportional count enumerates the in-

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stances in which a NN interval differs from the immediately previous NN interval by more than q percent. Speci~cally, a threshold q of 6.25% has been proposed (this corresponds to a 50 ms difference at a heart rate of 75 beats per minute). However, there is very little experience in comparison of such counts of proportional differences with the more common counts of absolute differences, and the argument for counting the proportional differences is presently only theoretical. Unfortunately, independently of whether the absolute or the proportional threshold is used, the method of counts is bound to suffer from peculiar statistical properties of its results. From a point of view of statistical robustness, this is not really surprising since the statistical properties of the results are related to the discrete nature of the method of counts (in spite of the huge difference, NN interval prolongations by 1 and 49 ms are treated equally, whilst in spite of the negligible difference NN interval prolongations of 49 and 51 ms are treated differently). This makes the method rather sensitive to the precision with which the sequence of RR intervals is obtained. The discrete nature of the method is also bound to contribute to poor reproducibility of the counts and to hugely abnormal distributions of their values in clinical populations.

Geometrical Methods The major practical limitation of the statistical methods is their dependency on the quality of data of RR interval series. This dependency was fully appreciated when the conventional statistical methods were applied to RR data obtained by an automatic analysis of long-term electrocardiograms. Although a high quality of long-term (e.g., 24-hour electrocardiograms) is in principle achievable, it requires not only careful maintenance of the recording equipment and appropriate subject-speci~c positioning of the electrodes but also a high degree of cooperation from the patient who is the subject of the recording in respect of the electrode contact, lead stability, etc. This makes high-quality long-term electrocardiograms dif~cult to sustain in clinical settings. In principle, there are two practical methods for assessing heart rate variability from imperfect longterm records. Firstly, the RR interval sequence obtained from such records can be “~ltered” using different physiologically based requirements of the data. For instance, it has been proposed that the durations of neighbouring RR intervals of sinus rhythm should never differ by more than 20% [2]. Only the subset of RR intervals, which satisfy the logical “~lter,” are then used in the statistical formulae. Unfortunately, this logical ~ltering is not always successful and in some cases makes the sequence RR intervals even less valid [5]. This leads to a second possibility for processing imperfect records using completely different methods, which are substantially less affected by the quality of

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the data. In searching for such techniques, the socalled geometrical methods were invented.

Principles of geometrical methods As the name suggests, the geometrical methods use the sequence of RR intervals to construct a geometrical form and extract a heart rate variability measure from this form. The geometrical forms used in different methods vary; in most cases, the methods are based on the sample density histogram of NN interval durations, on the sample density histogram of differences between successive NN intervals, and on the so-called Lorenz plots or Poincarè maps, which plot the duration of each NN or RR interval against the duration of the immediately preceding NN or RR interval. The way in which the heart rate variability measure is extracted from the geometrical form varies from method to method. In general, three approaches are used. Firstly, some measurements of the geometrical form are taken (e.g., the baseline width or the height of a sample density histogram), and the measure is derived from these values. Secondly, the geometrical pattern is approximated by a mathematically de~ned shape, and heart rate variability measures are derived from the parameters of this shape. Finally, the general pattern of the geometrical form can be classi~ed into one of several pre-de~ned categories, and heart rate variability measure or characteristic is derived from the selected category. Methods based on the RR interval histogram The most studied geometrical methods include the sample density histogram of NN interval durations. The incorrect NN intervals are usually either substantially shorter or substantially longer than the population of correct NN intervals. The short incorrect intervals are frequently obtained when the computerised analysis of a long-term electrocardiogram recognises a tall T wave or recording noise as a QRS complex; the long incorrect intervals are most frequently acquired when the analysis fails to identify one or several QRS complexes and measures an RR interval that is in reality composed of two or even more interbeat intervals. Such incorrect measurements of RR interval fall outside the major peak of the distribution histogram and can frequently be clearly identi~ed. The geometrical methods processing the histogram reduce the effect of the incorrect NN intervals by concentrating on the major (e.g., the highest) peak of the sample density curve. The simplest method is the socalled HRV triangular index, which is based on the idea that, if the major peak of the histogram were a triangle, its base-line width would be equal to its area divided by one half of its height [6]. The height H of the histogram can easily be obtained as the number of RR intervals with modal duration, whilst the area A of the histogram equals the number of all RR intervals used

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to construct it. Thus, the HRV triangular index approximates the baseline width of the histogram by a simple fraction A/H. The numerical value of the index depends on the sampling applied to construct the histogram, that is, on the discrete scale used to measure the NN intervals. Most experience with the method has been obtained with sampling of 128 Hz (i.e., when measuring the NN intervals on a scale with steps of approximately 8 ms, precisely 7.8125 ms) [7]. However, slight departures from this sampling frequency do not affect the results of the method greatly. The method is particularly suited when the NN interval histogram contains only one dominant peak. This is frequent in recordings obtained from subject exposed to a stable environment without physical and mental excesses. Such an environment is often present during in-hospital recordings, which makes these geometrical methods easily applicable to many clinical studies. On the contrary, 24-hour recordings of normally active healthy individuals frequently register two distinct populations of RR intervals corresponding to active day and resting night periods. In such situations, the geometrical algorithms concentrate on the most dominant peak of the histogram and lead to underestimation of global value of heart rate variability

Methods based on the histogram of successive differences Approaches similar to those used to process the histograms of NN interval durations can be applied to the histograms of differences between successive intervals. However, the differential histograms are much narrower than the interval histograms, and their approximation by triangles is not as appropriate as in the case of interval histograms. Thus, those geometrical methods that are proposed for the processing of differential histograms concentrate on the sharpness of the peak of the differential histogram. Unfortunately, very little experience exists with these methods. Lorenz plots Simple visual judgement of heart rate variability in a long-term ECG is perhaps best facilitated by the Lorenz plot, which is a map of dots in Cartesian coordinates. Each pair of successive RR or NN intervals is plotted as a dot with coordinates [duration RiRi11, duration Ri11Ri12]. The incorrectly measured RR intervals or the coupling intervals and the compensatory pauses of atrial and ventricular premature beats lead to easily visible outliers in the map of the plot. Thus, compared to the histograms of RR durations, the Lorenz plots are even more appropriate to judge the quality which the RR intervals that were identi~ed in a long-term electrocardiogram although such a possibility is not frequently exploited in commercial Holter systems. Preserved physiologic RR interval variations lead to a wide-spreading Lorenz plot, while a record with

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markedly reduced heart rate variability produces a compact pattern of the plot. Based on such a visual judgement, some studies have led to proposals for classi~cation of patterns of Lorenz plots and distinguished, for instance, “comet” and “torpedo” shapes [8]. While such approaches are valid for initial visual judgement, they lack a precise de~nition of each category and, as different plots create a continuous spectrum between the “comet” and “torpedo” shapes, are subject to a signi~cant operator bias. Thus, these simple classi~cations of the shape of the plots are not very well suited for systematic studies of large clinical populations, and therefore the practical experience with them is limited.

Advantages and Disadvantages of Individual Methods Statistical methods Statistical methods, especially those based on the standard deviation formula, can be applied to any recording ranging from the very short ones to 24- or 48hour or possibly even longer ECGs. The results provided are stable and have suitable statistical properties. For processing of short-term recordings, the statistical measures are the method of choice in cases that are not suitable for processing by spectral methods. Thus, SDNN and/or rMSSD are valuable also for physiological studies (which are otherwise best served by spectral methods) when the tachogram of the recorded ECG is not stationary (e.g., during dynamic phases of provocative manoeuvres). Similarly, statistical methods are preferential for the analysis of shortterm recordings that contain too many premature beats, the interpolation around which would invalidate the more detailed spectral analysis. High quality of data extracted from short-term recordings can easily be maintained because it is not impractical to review the record of each cardiac cycle visually and to localise ectopic beats manually. If the frequency methods are excluded for the above-mentioned or other reasons, the statistical methods are the only possibility for heart rate variability measurement. In cases of long-term ECGs, statistical methods should be used when the quality of the NN interval data is guaranteed. In such recordings, the SDNN measure characterises the overall variability of heart rate while the rMSSD measure assesses the fast components. The SDANN measure using 5-minute averages is believed to be a measure of the very slow components of heart rate variability, although physiological understanding of such components is lacking. (It is not even obvious whether an exactly de~ned physiological correlate of such very slow components exists.) The SDNN index measure integrates the fast and intermediate components of heart rate variability. However, evident practical advantages of SDANN and SDNN index over

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SDNN and rMSSD have never been clearly demonstrated. The major disadvantage of the statistical methods, especially when they are used for processing of longterm ECGs, is their sensitivity to the quality of NN interval data. This is a signi~cant obstacle to the use of statistical methods in a number of clinical studies (e.g., assessment of heart rate variability in patients with frequent ventricular arrythmias). The need for having high-~delity NN data applies to all statistical methods.

Geometrical methods The geometrical methods are capable of providing a reasonable assessment of heart rate variability even when the quality of data does not permit the use of conventional statistical and spectral methods. This does not mean that the geometrical methods can replace the other methods entirely; their results are only approximate and they are not as precise at the more exact statistical and spectral analyses. The approximate nature of the results of geometrical methods is, of course, their limitation. Another important limitation of the methods lies in the fact that, in general, a substantial number of RR or NN intervals is needed to construct a representative geometrical pattern. Experience shows that at least 20-minute recordings are needed to create a valid histogram of RR interval durations and an even longer record is needed to obtain a satisfactory shape of the Lorenz plot. Naturally, the longer the recording, the better is the de~nition of the derived geometrical pattern. Thus, it is optimal to apply geometrical methods to 24-hour or even longer recordings. The need to record a suf~cient number of cardiac cycles excludes the geometrical methods from being used in physiological studies that investigate shortterm recordings made under speci~c conditions. However, the accuracy and quality of recordings obtained during such studies, in usually high and careful manual editing of short records, can easily be performed. In principle, this removes the need to use geometrical methods in physiological studies and makes the statistical and spectral methods more appropriate. Thus, the application of geometrical methods should be restricted to clinical investigations and to cases in which obtaining an error-free sequence of RR intervals is impractical. Those geometrical methods that analyse the histogram of RR durations provide assessment of overall heart rate variability and error-free sequences of RR intervals without clear bi-modal distribution provide results comparable with the SDNN results.

References 1. Wolf MM, Varigos GA, Hunt D, Sloman JG. Sinus arrhythmia in acute myocardial infarction. Med J Australia 1978;2: 52–53. 2. Kleiger RE, Miller JP, Bigger JT, Moss AJ, and the Mul-

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ticenter Post-Infarction Research Group. Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. Am J Cardiol 1987;59: 256–262. 3. Bigger JT, Kleiger RE, Fleiss JL, Rolnitzky LM, Steinman RC, Miller JP, and the Multicenter Post-Infarction Research Group. Components of heart rate variability measured during healing of acute myocardial infarction. Am J Cardiol 1988;61:208–215. 4. Ewing DJ, Neilson JMM, Traus P. New method for assessing cardiac parasympathetic activity using 24-hour electrocardiograms. Br Heart J 1984;52:396–402. 5. Malik M, Cripps T, Farrell T, Camm AJ. Prognostic value of heart rate variability after myocardial infarction—A com-

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parison of different data processing methods. Med Biol Eng Comput 1989;27:603–611. 6. Malik M, Farrell T, Cripps T, Camm AJ. Heart rate variability in relation to prognosis after myocardial infarction—Selection of optimal processing techniques. Eur Heart J 1989; 10:1060–1074. 7. Cripps TR, Malik M, Farrell TG, Camm AJ. Prognostic value of reduced heart rate variability after myocardial infarction: Clinical evaluation of a new analysis method. Br Heart J 1991;65:14–19. 8. Woo MA, Stevenson WG, Moser DK, Middlekauff HR. Complex heart rate variability and serum norepinephrine levels in patients with advanced heart failure. J Am Coll Cardiol 1994;23:565–569.