1 I n t r o d u c t i o n INVESTIGATION OF heart rate variability (HRV) has been the subject of many different studies (PAGANI et al., 1984; STE- FIKOVA et al., 1986; SCHWARZ et al., 1987; PARATI et al., 1987; SIMPSON and WICKS, 1988). In particular, changes in HRV in patients after acute myocardial infarction or in patients with severe coronary artery disease have been reported by LOMBARDI et al. (1987), AIRAKSINEN et al. (1987) and ZBILUT and LAWSON (1988).

KLEIGER et al. (1987) have recently reported that reduction in HRV, determined from 24 h continuous elec- trocardiographic (ECG) recordings made in the early days after acute myocardial infarction, can be used as a predic- tor of long-term mortality. In their study, recordings were made within the first two weeks after an episode of acute myocardial infarction. The ECG was recorded on tape in analogue form, digitised offline and reanalysed using more or less standard algorithms (BIRMAN et al., 1978) based on the so-called matched-pair sample principle. This analysis resulted in automatic identification of each normal QRS complex (i.e. excitation complexes with a consistent elec- trocardiographic morphology). The resulting sequence of intervals between successive normal complexes (called N-N intervals) was further analysed using the standard

First received 5th October 1988 and in final form 12th January 1989

�9 IFMBE: 1989

Medical & Biological Engineering & Computing

deviation of durations of N-N intervals to express HR variability (HRV) in numerical terms.

However, the methods employed for the analysis of the N-N interval sequence differ in different studies. In addi- tion to the often used standard deviation of N-N intervals (KLEIGER et al., 1987; SCHWARZ et al., 1987; DE NICOLO et al., 1988), these methods include the standard deviation of beat-to-beat (BTB) variability i.e. of the sequence of numbers ( x i - xi+O, where xi is the duration of the ith interval, and x~+~ is the duration of the immediately suc- ceeding interval (BIGGER et al., 1988); percentage of adjac- ent N-N intervals differing by more than a given threshold (EwINt3 et al., 1984); and, in several studies, power spectral analysis (BERGER et al., 1986) was employed (PAGANI et al., 1986; KAMATH et al., 1987; BASELLI et al., 1987; MYERS et al., 1986).

The reported studies also propose a pathophysiological background for the prognostic value of HRV (BIGGER et al., 1988), suggesting that decreased HRV may correlate with decreased vagal nervous activity or increased sympa- thetic activity which may enhance the risk of ventricular fibrillation. Correlation between the sympathetic tone and HRV power spectral components was also reported (LOMBARDI et al., 1987; SAUL et al., 1988).

Therefore, measurement of HRV in postinfarction patients is a promising technique which may prove to be of

November 1989 603

clinical importance, but standardisation of HRV measure- ment poses severe problems at the data-processing level. In many patients, the continuous ECG recording is not perfect and contains noise of both biological and environmental origin. In addition to this, the amplitude and ECG pattern of normal QRS complexes can vary to the extent that even a sophisticated analysis algorithm designed to update the matched sample may not recognise all normal complexes. Similarly, the ECG morphology of ectopic cardiac beats of atrial or atrioventricular nodal origin is not distinguishable from normal sinus rhythm beats and, therefore, such complexes are included into the automatically generated N-N interval sequence.

For all of these reasons, reported studies employ differ- ent methods by which to 'filter' the initial N-N interval sequence. For instance, it has been suggested that analysis should take into ccount only those N-N intervals differing less than 4-20 per cent from the previous interval (KLEI6~R et al., 1987). However, in many situations, such filtering is not effective in removing all artefacts from the original N-N sequence. Therefore, reported studies also employ a visual check of the recorded ECG and manual editing of the N-N sequence prior to establishing the numerical value of HRV.

Unfortunately, the need for visual checking and manual editing is impractical in the clinical setting and discredits the potential clinical value of the whole method because such a time-consuming and specialised operation is beyond the capabilities of a typical clinical cardiology department. Hence, a fully automatic method of HRV measurement in postmyocardial infarction patients would be of value, yet no attempts have been reported until now to determine the optimal method for filtering the N-N sequence and the optimal formula for the numerical expression of HRV.

difference between both groups is obvious: a narrow DDC is frequently obtained in the positive group while the DDCs in the negative group are usually broader. Fig. 2 presents the same DDCs in a quadratic logarithmic scale making the noise and the inaccuracies of the recognition algorithm more visible.

For each patient, beat-to-beat variability has also been analysed.

3 D a t a - p r o c e s s i n g m e t h o d s The suggested (KLEIGER e t al., 1987) data-processing

involved in elaboration of N-N sequences consists of filter- ing the original sequence and then expressing the numeri- cal value of HRV. In the beat-to-beat analysis both these levels can be combined in one step. Here, we describe our approach to each aspect separately.

o~ u~

Z

._ & o

looo

_A2 I P4 ~ P6 v m

>

P7 ' P9 ~

z

A. O~ O

P l 3 ~ 4 A P,5

durat ion, s

~ 1 N2 N3

N4 ~ I N6

r ~ A

1, N'L ' ,/~ i,

durat ion, s

2 P a t i e n t s and data Between the 1st May 1986 and the 1st May 1988, 230

patients of 70 years of age or less were admitted to the hospital having sustained an acute myocardial infarction.

Among these patients, 177 underwent HRV analysis. In the remaining cases, a long-term ECG recording was either not available or was unsuitable for HRV analysis because of atrial fibrillation. From all these 177 patients who sur- vived until hospital discharge, 15 suffered subsequent death or spontaneous symptomatic sustained ventricular tachycardia. From the remaining patients with an uncom- plicated postinfarction course, a control group of 15 cases was randomly selected. In this way, a positive and a nega- t ivegroup were obtained, each of 15 cases.

To perform the HRV analysis, a continuous 24 h ECG was recorded during the first two weeks after acute myo- cardial infarction. A commercially available ECG digiti- sing, recognition and analysis system (Reynolds Medical Ltd.) was used to analyse the recording made in each patient. The computer analysis (performed on an IBM PC AT computer) resulted in the exact timing (in time scale of units of t2-~a s ~ 8 ms) of each ventricular QRS complex and in the classification of the morphology of each complex as 'physiologic' (including border patterns) or 'aberrant'. For the assessment of HRV, only the physiol- ogic QRS complexes were taken into account: the data produced by the commercial analyser were converted into the exact timing and duration of intervals between adjac- ent physiologic cardiac beats. Fig. 1 presents the distribu- tion density curves (DDC) of N-N interval durations obtained for each patient in the two groups. Visually, the

Fig. 1

o

o~ o m m O >

Z i

Z

if) & $

Fig. 2

The not normalised DDCs of the durations of the original computer recognised N - N intervals in all patients included in this study. The patients of the positive group are identi- fied as P1, P2 . . . . . P15, and the uncomplicated cases as N1, N2 . . . . , N15. The horizontal axes represent the dura- tion of N - N intervals in seconds ,see the scale in the plot o f P1). the vertical axes exhibit the total number of recog- nised N - N intervals with the 9iven length. The durations of N - N intervals were measured in discrete units of ~--~ s

Iooo

~ ~.N4L/~ N5 I~f~. N6

~ P7 O8 P9 .~ ~ N9 ,- ~ . ~ '~JZ~2_,.L_ Z

Z

. . . . ~Cn

durat ion, s dural on, s

The same DDCs as in Fi 9. t plotted in a quadratic logarithmic scale on the vertical axes. Note the noise and artefact in many cases (especially P4, P9, P14. N2. N6 e t c . ,,

604 Medical & Biological Engineering & Computing November 1989

3.1 Filtering o f N - N Sequences

The pre-analysis editing of the N-N sequence which we call ,filtering' is based on the supposition that the physio- logic mechanisms controlling heart rate do not result in a sudden change in rate on a beat-to-beat basis. Therefore, any automatically recognised N-N interval which differs remarkably in duration from the duration of the previous or next interval is unlikely to be a real N-N interval,

In designing such filters, it is debatable whether the duration of each interval should be related to the duration of the previous or next interval and what is the highest acceptable difference between neighbouring intervals. Therefore, we tested different filtering algorithms, each of which depended on a variable parameter for the maximum acceptable beat-to-beat change.

The concept of comparing the durations of neighbour- ing N-N intervals fails when an incorrectly recognised abnormality or recording artefact is repeated during a long-term ECG recording. For example, in a patient in whom ventricular bigeminy appears for a certain time during the recording each normal beat is followed by an ectopic beat with a very different ECG morphology. The projection of these ectopic beats into the chosen ECG lead m a y result in their patterns being skipped by the analysis algorithm, because the aberrant beats do not reach the beat recognition threshold. Thus, a portion of the computer-generated N-N interval sequence could in fact be a sequence of 'normal-ectopic-normal' intervals. Fur- thermore, these incorrectly identified intervals may differ only very slightly in their lengths, so that the beat-to-beat filters will not be able to exclude them.

To overcome this problem, we suggested an alternative filtering method in which the length of each computer- recognised N-N interval was compared with the duration of the last N-N interval accepted by the filter. However, such a filter is very sensitive to its own failures. Once it accepts an artefactual N-N interval, it will omit a large series of real N-N intervals by comparison with the arte- fact. Therefore, we used also a modification of this method in which each N-N interval was compared with the latest accepted interval and with the mean length of all computer-recognised N-N intervals.

In summary, the study reported here involved five differ- ent filtering algorithms. Each of them used a real param- eter r (0 < r < 1) specifying the acceptable difference between the compared intervals. In the following descrip- tion of the filters, I(i) is the ith interval in the computer- recognised succession of N-N intervals (1 < i < n; where n is the number of all analysed intervals); d s is the length of the interval J ; L is the last interval accepted by the given filter; and m is the mean length of all computer-recognised N-N intervals.

N - N f i l ter a for i = 2 to n: I(i) is accepted if [(dl(i)/dt( i_ 1)) - 1 [ < r

N - N f i l ter b f o r i = 2 t o n - 1: I(i) is accepted if [ (d ,o /d m _ 1)) - 1 [ < r

or[(dito/diti+ 1)) - 1[ < r

N - N f i l ter c f o r i = 2 t o n - l " I(i) is accepted i f [ (d i to /d t ,_ 1)) - 11 < r

and [(dm)/dm+l) ) - 1 [ < r

N - N f i l ter d f o r / = 1 t on :

Medical & Biological Engineering & Computing

if L is not defined {no interval has been accepted yet} then l(i) is accepted if l(dm~/m ) - 1 I < r

else I(i) is accepted if l (dm)/dL) - 1 [ < r

N - N f i l t e r e for i = 1 to n: if L is not defined {no interval has been accepted yet} then

1(0 is accepted if l(dm~/m) - 11 < r else

l(i) is accepted i f l (d~ddL) - 11 < r or [(dm)/m ) - 1 < r

3.2 Formulae expressing H R V

When the original N-N interval sequence is filtered, it can be used in the next step, which is the numerical expres- sion of HRV. The usual method of expressing HRV using the standard deviation of the filtered N-N interval sequence (KLEIGER e t al., 1987) is obviously not the only possible way to formulate HRV numerically. Because no method for removing the incorrectly recognised N-N inter- vals can be guaranteed, we devised two other methods for quantifying heart rate variability which are less dependent on the accuracy of the original N-N interval sequence recognition and on the success of the filtering phase.

Hence, we compared three different methods for numeri- cal expression of HRV.

N - N method A Standard deviation of the filtered N -N interval sequence.

N - N method B Baseline width of the main peak of the DDC. It can be

computed as the width of the DDC at a certain threshold derived from its the maximum value. More exactly, i f f is the D D C and M its maximum value, where f ( n ) = M , the baseline width of f can be approximated as X - x, where

X = min {z;(z > n) and ( f ( z ) < eM)}

x = max {z; (z < n) and ( f ( z ) < eM)}

where e(e ~ 1) is a parameter of the method. Similarly to the filtering algorithms, this method

depends on the variable e and should be tested with its different values. However, to keep the computing demands of the study under description at a reasonable level, we used only one value e = 0.05.

N - N method C Because method B may not be able to distinguish such

remarkably different situations as our cases P6 and N10 (Fig. 1), we also used a method expressing the HRV as the reciprocal value (l/M) of the maximum M of the DDC f ; supposing that the D D C f i s normalised so that

Z Z~---1 ct~

In fact, the computerised recognition measures the dura- tions of N-N intervals in a discrete scale (in our case, the unit of the scale of __1_12s s ,-~ 8 ms was used) and, in practice, the 24 h recording is long enough to fill such a discrete scale. Therefore, the equivalent formula for this method is the ratio

N/(max {C(z); 0 < z})

where N is the total number of all recognised N-N inter- vals and C(z) is the number of N-N intervals with the same duration z in the discrete scale.

November 1989 605

3.3 Elaboration o f B T B distribution density curves

One of the possible methods for elaborating the BTB DDC to classify the HRV was reported by EWIN6 et al. (1984). In that study, the relative number of those couples of N-N intervals in which the duration of the second inter- val differed by more than 50 ms was used to measure HRV. In this approach, the lower threshold of 50 ms is in fact the main method of measuring the rate variability. When adding an upper threshold of, for instance, 100 ms, it filters the computer-recognised sequence of N-N inter- vals by excluding those couples of intervals which differ to a larger extent than can be expected from physiologic regulation mechanisms. However, the value of 50 ms (and the additional value of 100 ms) was chosen arbitrarily. Therefore, in this study, we employed a generalised version of this method which was dependent on two variable parameters specifying the lower and upper thresholds.

Another possible elaboration of BTB DDC which expressed the HRV as the standard deviation of the BTB distribution was recently reported by BIGGER et al. (1988). To filter the data and to compare this approach with the previous method, we generalised this approach as well. Two variable parameters corresponding to the lower and upper thresholds restricted the original BTB DDC and specified the part which was taken into account when computing the standard deviation (see the exact formal description of the methods at the end of this section).

Finally, the measurement of the baseline width of BTB DDCs might be an appropriate method for distinguishing between the two groups.

Specifying the methods formally, the following three elaborations of BTB DDCs were employed. In these descriptions, f is the normalised BTB DDC; M is its maximum value; m and n (0 ~< m ~< n) are the parameters of the first two methods, and e (0 < e < 1) is the parameter of the third method.

B T B method A

HRVA(m, n) = f ( z )dz + z)dz

This formula is in fact equivalent to the relative number of those couples of neighbouring N-N intervals, for the dura- tions of which di and d~+ 1 the following holds:

m ~ [d i -- di+l[ ~< n

B T B method B HRVB(m, n)

Z Z - I - Z Z Z A m , n

B T B method C HRVc(e) = X - x

where

X = min {z; (z > O) and ( f ( z ) < eM)}

x = max {z; (z < O) and ( f ( z ) < eM)}

4 R e s u l t s The data-processing methods described in the previous

section were employed to analyse all 30 cases in both groups of patients. Algorithms of these methods were programmed in Turbo Pascal and implemented on a stan- dard configuration of an IBM PS/2 (60) microcomputer which was used in all computations.

4.1 Behaviour o f N - N filters and their 'technical' accuracy

The computer-recognised sequence of N-N intervals for each patient was filtered employing all five N-N filtering algorithms a - e and varying their parameters r = 0.02, 0"04, 0"06 . . . . . 0"78, 0"80. Hence, for each patient, 200 fil- tered sequences of N-N intervals were obtained and com- pared.

Prior to exact comparison of N-N filtering possibilities, each case was examined visually. For that purpose, graphi- cal representation of the DDCs of all 200 was produced which enabled the assessment of how different filters were capable of reproducing the main peak of the DDC and of removing the noise and artefacts. In the case of a smooth DDC, all filters behaved satisfactorily (Fig. 3). In some cases, there was a serious malfunction of filter d (Fig. 4) while the other filtering algorithms performed satisfacto- rily. In other cases, we observed that the filtering algo- rithms a and b and partly the algorithm c were not capable of eliminating the noise and artefacts even when employing very small values of the parameter r (Fig. 5).

Summarising the visual check of different filters in our 30 cases (see the selected cases in Figs. 3-5) we would favour algorithm e employing the parameter r of 0.08-0.1.

Accurate and formally based evaluation of the per- formance of the different filtering methods requires a defi- nition of noise and artefact which is difficult to conceive.

i

durat ion, s

Fig. 3 Performance of 200 different filters of the original N-N interval sequence used to process the N-N DDC of the patient N5. The five parts of the figure (a)- (e) show the filtered DDCs obtained with the filtering methods (a)-(e) described in the text. Each DDC is plotted in the same ratio and scales as in Fig. 2. In each part, the first 40 curves exhibit the DDCs obtained by the corresponding filtering algorithm when increasin9 its parameter r from 0"02 to 0.80 in steps of 0.02. The last DDC in each part (separated by a larger space from the last but one DDC) is the original unfiltered DDC as presented in Fig. 2. Note that in this case all filtering possibilities (with the excep- tion of those employing a very small value of the parameter r) offer a satisfactory result which reproduces the original DDC

606 Medical & Biological Engineering & Computing November 1989

Therefore, we used a heuristic approach to comparing the technical accuracy of the filters.

For every patient, the main peak of the N-N DDC was approximated by a DDC of a normal distribution. To obtain such an approximation, the following algorithm was used: Let f be the normalised original N-N DD C and m its mean value; and let N[m, s] be the probability density function of the normal distribution with the mean m and standard deviation s. Then, for a real parameter u, we define a real value G(u) given by a formula:

G(u) = fo + + ( f - NEM(u), S(u)])2(z)dz

where M(u) and S(u) are the mean and standard deviation of the subset of the original N-N sequence which includes those intervals the durations d of which satisfy the condi- tion:

I d - m l < u

By varying the parameter u along the discrete scale of the D D Cf , the value u o can be established, for which

G(Uo) = rain {G(u); 0 < u < m}

Then, the normally distributed density function NEM(uo), S(uo)] was used as the normal approximation of the DDC

f These normal approximations of N-N DDCs were

employed to compare all 200 filter possibilities. Exactly, each filtered N-N sequence was used to construct its DDC f* , and its square difference from the normal approx-

Fig. 4

imation N of the original DDC f was computed according to the formula

~0 I-Q~ ( f * N)2(z)dz

Thus for each patient, that filtering algorithm (including the value of its parameter) was established for which the square difference from the normal approximation of the original DDC was minimum. Fig. 6 presents the per- formance of the 'best' filters established in this way and shows that the main peak of the original DDC was repro- duced satisfactorily in all cases. Obviously, the 'best' filters were different from case to case.

To establish a general power for each filtering method, each of the 200 filtered N-N interval sequences for each patient was compared with the 'optimum' filter for that particular case. As an evaluation criterion, again the square differences between DDCs were used, and for each filtering method, the sum of such differences over all 30 patients was computed. In a more exact way, the general accuracy of a filter 9 with the parameter r was established as the value:

where f~o,,) is the DDC obtained when filtering the N-N sequence of the patient p by the filter g with the parameter r; and bp is the DDC obtained when filtering the N-N sequence of the patient p by its optimum filter. Here, the numbering of the patients 1 . . . . . 30 included both positive and negative groups.

The results of this 'technical' comparison of all 200 filter-

I

dura t i on , s

Fig. 5

Performance of 200 different filters of the original N-N interval sequence used to process the N-N DDC of the P l l patient. For explanation of the symbols of the figure, see the legend of Fig. 3. In this case, filter (b) is not capable of removing the high-frequency noise, which is only restricted by the filters (a) and (c). For the values of r = 0.06, 0"08 . . . . . 0.18, thefilter (e) reproduces the main peak of the original DDC. The filter (d) behaves chaoti- cally; for the values of r = 0.14, 0.16 . . . . . 0"22 it repro- duces only the high-frequency noise and does not accept the main peak of the original DDC

P14 I

d u r a t i o n , s

Performance of 200 different filters of the original N-N interval sequence used to process the N-N DDC of the patient P14. For explanation of the symbols of the figure, see the legend of Fig. 3. Only the filter (e) behaves satis- factorily. With small values of its parameter it reproduces the main peak of the original DDC only; however, as the value of its parameter increases, the filter starts to accept both noise and artefact

Medical & Biological Engineering & Computing November 1989 607

ing methods are presented in Fig. 7. It can be seen that maximum accuracy was achieved for the filter e with its parameters r --- 0.08 and r = 0.10. This is in good accord with visual judgement. However, when excluding the filter d, which behaves very unsatisfactorily in many cases, there is little difference between different methods, suggesting that the optimum filter and optimum parameters are highly individual and that a filter which operates ade- quately in some cases may fail in others.

~176176 a : '~"~ ) 1 ~ : P1 ] A P2 3 '~..~ ~ l~i--~N2 1 ~ N3

.c_ P8 .E 9

P I 5 ~ N 1 5

d u r o l i o n d u r o l i o n s

Fig. 6 The same original DDCs as in Fig. 2 (in the same scale as in that Figure) are compared with the 'technically optimum' filter of each case (see the text for details. The black areas show the parts of the original DDCs which were accepted by the 'optimum' filter in each case. Note that, only with a few debatable exceptions (P6, N7, N15), the filter found as the 'technical optimum' reproduces accu- rately the main part of the DDC and removes both noise and artefact

filters a, b and c employing the parameter r from the inter val of approximately < 0-3, 0-5 > corresponds to the sligh increase of the technical accuracy of these filters which can be observed in Fig. 7 within the same interval of the parameter r.

iil,, li! il

V

1

o ' 0'.2 ' o'.4 ' o'-6 ' 0'.6 r

Fig. 7 Comparison of the technical accuracy of all filters (see the text for details). The horizontal axis r represents the values of parameters of filtering algorithms, the vertical axis t exhibits the achieved technical accuracy in arbitrary units corresponding to the formula which is described in the t e x t ( t h e lower the value, the higher the accuracy achieved)

filter (a) . . . . filter (b) . . . . filter (c) - . - f i l ter ( d ) - - - f i l t e r ( e )

4.2 Practical value o f f i l ters and H R V formulae

The different methods for filtering the N-N sequences can also be compared from the practical point of view in terms of how capable they are of distinguishing statistically between the negative and positive groups of patients. Each filtering method must then be combined with each of the different methods for expressing the HRV numerically.

To perform such a comparison, each of the 200 filtering possibilities was combined with the HRV expression N-N methods A-C. Each of such combinations resulted in a set of numerical values expressing the HRV for all patients. For each set of values, the two sample t-test was then employed to distinguish between the positive and negative groups of patients. Results of these statistical comparisons are presented in Fig. 8.

Excluding the chaotically behaving filter d, each filter operates nearly independently of its parameter r. This is in a good accord with our theoretical evaluation (Fig. 7) where, with the exception of very small values of the parameter r, the technical accuracy was also almost inde- pendent of it.

When comparing the filtering algorithms a, b, c and e, the only important difference between them was observed when combining them with method A (standard deviation of the filtered DDC), which is, as we pointed out earlier, highly sensitive to noise and artefact. In this case (Fig. 8A), the filter e offers a more significant distinction between the two groups of patients than the filters a, b and c (again with the exception of the extreme values of the parameter r). Note also, that the slightly increased probabilistic power of distinguishing between the two groups with the

0"01 0"02 0"05 %10

P

%01 0.02

~ ~ ~- 040 v p

J

0.Of 0"02 0'05 0")0

P

Fig. 8

B

0 0"4 0.8 0 0-4 0'8

r r

--~-" ' ~ ~ 0"02 ~\ 0-05

~ 0 " I 0

p

C D

. . . . , ~ i , , i h i . . . .

o 0.4 o'.~ o 0-4 o o r r

Statistical evaluation of the different combinations of N-N sequence filters with N-N methods of numerical H R V expression. Cases (A), (B) and (C) correspond to the combinations of different filters with N-N H R V expression methods (A), (B) and (C), respectively; the case (D) is a combination of the H R V established by the method (C) with the mean HR (see the text for details). In each part of the figure, each curve corresponds to a combination of one filtering algorithm with the particular HRV expression method and shows the probabilistic level (vertical axes p), at which the positive and negative groups of patients can be distinguished dependent upon the parameter of the filter (horizontal axes r ). - - filter (a) . . . . filter (b) - - filter (c) - . - f i l ter (d) - - - f i l t e r (e)

608 Medical & Biological Engineering & Computing November 1989

The difference between the filters a, b, c and e disappears when combining them with the other methods of numeri- cal HRV expression. In general, the method B offers a more marked distinction between the positive and negative groups than method A, and, similarly, method C is more efficient than method B. An even more significant differ- ence between the two groups was established when com- bining the HRV with the mean HR. Fig. 8D presents the same comparison of the five filters when assigning to each patient the product of the HRV derived from method C and the mean of the filtered DDC.

4.3 Practical value o f B T B analysis

As with the practical evaluation of the combinations of N-N filters and HRV expression methods, the three sug- gested methods of BTB analysis were computed with dif- ferent combinations of their parameters. The two sample t-test was again employed to distinguish between the posi- tive and negative groups of patients.

The methods A and B were examined varying their

Fig. 9 Systematic evaluation of the BTB method (A) for the H R V expression. The axes m and n correspond to the parameters m and n of the method, The axis n drawn in the front of the figure has, in fact, the same origin as the axis m (the left upper corner of the basal plane corresponds to the values [0, O] of the parameters, and the right lower corner to the values [0.5, 0.5]). As in Fig. 8, the resulting three-dimensional surface shows the probabilistic level (vertical axis p), at which the positive and negative groups of patients can be distinguished dependent upon the param- eters of the filter

Fig. I0 Systematic evaluation of the BTB method (B) for the HRV expression. For technical explanation of the organ- isation of the figure, see the legend of Fig. 9

Medical & Biological Engineering& Computing

parameters m and n along the discrete sampling scale so that 0 ~< m ~< n ~< 0.5s.

The results evaluating the method A are presented in Fig. 9. Note that the portion of the resulting surface corre- sponding to m = 0 is very different from that of m = 8 ms, 16ms etc. The high significance level reached for the small values of m ~ 8ms, 16ms etc. and n near to 0.5 is caused by the omission of the values of DDCs for 0.0 s. In fact, the combination of parameters m _--- 8 ms and n = 0.5 s charac- terises (with a certain error due to noise and artefact) the HRV by numbers l-q, where q is the HRV established with the same method A and parameters m = n = 0. Hence, the high significance level reached for the values of parameters m = n = 0 suggest that the relative number of those pairs of neighbouring N-N intervals which have the same length in the discrete sampling scale can also be used to distinguish between the positive and negative cases. Otherwise, the smooth form of the surface in Fig. 9 shows that this method is nearly independent of the values of its parameters.

The smooth pattern shown in Fig. 9 is very different from that presented in Fig. 10, which displays the results obtained in the same way for the method B. Naturally, for a small difference of parameters m and n, the formula for computing the standard deviation is meaningless and the results of the method B are strongly affected by the results of the method A, which is included in the formula of the method B. Otherwise, the chaotic pattern of the results suggests that this method is not stable and, in our case, it is highly sensitive to the parameter values. Such an obser- vation offers serious evidence against the utility of this method.

The method C has been evaluated with variation of its parameter e = 0.01, 0.02, 0.03 . . . . . 0.98, 0.99. The results of the performed statistical test are presented in Fig. 11. We can see that for the parameter e within the interval of approximately <0.2, 0.5 > , the method is able to signifi- cantly distinguish between the two groups of patients. However, in general, this method appears to be less power- ful than the N-N method C (see Fig. 8C).

Fig. 11

.01

02

.05

.1

0 0.5 '1.'0 r

Systematic evaluation of the BTB method (C) for the H R V expression. The plot shows the probabilistic level (vertical axis p) at which the positive and negative groups of patients can be distinguished dependent upon the parameter of the filter (horizontal axis r)

5 Discussion 5.1 Limitation of the study

The practical value of the different data-processing methods and their combinations were assessed for their ability to distinguish between two groups of patients using

November 1989 609

a statistical test, the two-group t-test. We cannot be certain that the same results would be obtained wth other groups of positive and negative cases. The control group was also selected without regard to antiarrhythmia treatment, but KLEIGER et al. (1987) and our other investigations proved that while mean heart rate, the use of fl-blockers and HRV are inter-related, the HRV provides independent prognos- tic information over the other two variables, Nevertheless, useful conclusions can be drawn especially regarding the sensitivity of the different methods to their parameters and to the effect of noise and artefact in the original computer- recognised N-N interval sequence.

Secondly, our present study does not concentrate on the importance of analysing the long-term ECG recordings. HRV is certainly a result of several physiological mecha- nisms including respiration and blood pressure regulation, which can be easily assessed from recordings taken over several minutes during which the quality of the recording can be assured and manual editing of the recording to exclude ectopics and artefacts is acceptable. This problem has been addressed in our other study (MALIK e t al., 1989), which proved that diurnal rhythm and other long-term components of HRV enable a more significant distinction between the positive and negative postmyocardial infarc- tion patients than the short-term components of HRV which can be estimated in short ECG recordings.

Thirdly, the filtering algorithms and HRV expression methods tested represent only a selection of the many dif- ferent data-processing possibilities. For instance, PARER et al. (1985) examined 22 mathematical formulae proposed to quantify foetal HRV. However, in their study, artificially generated sequences of numbers with known variability were used to test the formulae. The use of natural data in our study necessitated use of only a selection of evaluation methods to keep the computational demands of the inves- tigation at an acceptable level. For the same reason, power spectral analysis was not included in our present study.

Fourthly, the technical accuracy of compared N-N filter- ing methods was established using an arbitrarily chosen method. In reality, we know of no reason why the main part of the N-N DDC should be approximated by a single normally distributed peak. On the contrary, in many of our cases, N-N DDC appeared to be composed of a small number of normally distributed populations of N-N inter- vals (for instance, note this phenomenon in Fig. 1 in cases P6, P10, N2, N7, N9 etc). Such an observation is an important argument against our approximation of the DDC by a single normal peak and suggests one of the future areas for investigation of HRV analysis. Neverthe- less, Fig. 6 shows that when using the normal approx- imation of original DDCs only for establishing the 'techni- cally optimum' filter in each case, our approach was acceptable.

Finally, application of the two-sample t-test requires that the statistically compared samples are normally dis- tributed and that their standard deviations are equal; these assumptions were not verified in this study. It is known (BLAND, 1987) however, that departures from these condi- tions do not greatly influence the results of the test.

5.2 Conclusions

First, we can conclude that appropriate filtering of the computer recognised N-N interval sequences is highly individual. On average, after excluding the N-N filter d which behaved chaotically according to its parameter value, none of the filtering methods (whatever the value of the parameter) was significantly more powerful than the others. This was found when considering both the techni-

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cal accuracy of the filters and their practical value in com bination with the different methods for HR'~ quantification.

Secondly, evaluation of different combinations of the N-N sequence filters and the HRV expression method~ suggest that the methods B and C which are not very sensitive to noise and artefact within the original N-N interval sequence, can distinguish between the positive and negative cases better than sophisticated and complex filter- ing combined with the previously published method A.

We have also observed that in larger groups of patients, the N-N method C applied to unfiltered data is fully suffi- cient and indeed rather powerful in identifying those postmyocardial infarction patients who later suffer sudden death or sustained ventricular tachycardia.

Finally, the evaluation of the BTB data-processin~ methods presented discredits the BTB method B and suggest that a future investigation should be performed to assess the utility of the BTB method A with its parameters m = n = 0 .

In conclusion, our results suggest that clinically useful information may be obtained from HRV analysis of long- term ECG recordings in recent myocardial infarction patients employing a fully automated method which is independent of a low level of recording noise and beat misrecognition artefact. Skilled visual editing is rendered unnecessary and the analysis process becomes rapid, reproducible, operator independent and therefore, acces- sible to any clinical unit equipped by a simple personal computer and conventional facilities for 24h ECG analysis.

Acknowledgment--Professor Malik of Charles University, Prague, is currently supported by the British Heart Foundation.

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Authors" biographies Dr Marek Malik graduated from Charles Uni- versity in Prague, in both Mathematics and Medicine. He is Professor of Computer Science at Charles University and Consultant of Biomedical Computing at University Hos- pital in Prague. Currently, he is Visiting Pro- fessor at St George's Hospital, London, supported by the British Heart Foundation. His interests include computer simulation of

biomedical systems, especially in the cardiological area.

Dr Tim Cripps graduated from Cambridge University in Natural Sciences in 1977 and from Oxford University in Medicine in 1980. Following posts in cardiology at Ham- mersmith and Brompton Hospitals, he is cur- rently Research Registrar in the Department of Cardiological Sciences, St George's Hospi- tal, London. His interests include assessment of the post-infarction patient and clinical

applications of high-gain signal-averaged electrocardiography.

Dr Thomas G. Farrell was educated at St Augustines Grammar School in Manchester and graduated from Leicester University Medical School. Previously, he was a Regis- trar in General Medicine and Cardiology at St George's Hospital, London. Currently, he is Research Fellow in the Department of Cardio- logical Sciences, St George's Hospital Medical School. His interests include autonomic

nervous system function and its relationship to cardiac disease.

Dr John Camm is Professor of Cardiovascular Medicine at St George's Hospital, London; and heads the Department of Cardiological Sciences. Prior to this, he practised cardiology at both St Bartholomew's Hospital and Guy's Hospital in London. He works in the field of clinical electrophysiology, arrhythmias and cardiac pacing, and has authored several hundred papers and several books.

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