Spectrotemporal analysis of ventricular late potentials

Spectrotemporal Analysis of Ventricular Late Potentials

Paul Lander, PhD, David E. Albert, MD, and Edward J. Berbari, PhD

Abstract: The authors introduce a new technique for the analysis of ventricular late potentials: spectrotemporal mapping. Spectrotemporal mapping displays a signal in both the time and frequency domains simultaneously, overcoming some of the limitations of single domain analysis. Spectrotemporal analysis of late potentials was developed from a critique of classical spectral analysis methods. Several examples of spectrotemporal analysis of signal-averaged ECG waveforms are presented. These include cases in which spectrotemporal mapping was able to represent late potentials that were not seen after conventional timedomain processing. Spectrotemporal mapping reveals that ventricular late potentials have a time-varying energy spectrum, which theoretically would preclude the use of classical Fourier analysis techniques. Both the vector magnitude and Fourier transformations are a reduced representation of the information available in the signal average. Spectrotemporal mapping combines time and frequency information in a way that is compatible with the basic statistical structure of late potentials. Key words: spectrotemporal mapping, ventricular late potentials.

and possibly variable, the filtering step is undesirable. Attempts have been made to characterize late potentials using classical methods of Fourier analysis.4,5 We discuss this approach and suggest a method for improving the power spectral estimates obtained. We then introduce an extension to a time-varying spectral analysis of the high-resolution ECG. This new approach gives considerable insight into spectral analysis of late potentials and appears more fitted to describing their activity.

Ventricular late potentials are low-amplitude signals occurring after the expected end of the normal QRS complex in the high-resolution ECG. Using the technique of signal averaging, many researcherslm3 have investigated late potentials, primarily for their potential value in predicting future ventricular arrhythmias. Conventionally, three orthogonal XYZ leads are signal-averaged, digitally high-pass filtered, and transformed into a vector magnitude. The filtering is used to separate late potential activity from a relatively large, slow electrocardiographic wave on which it is usually superimposed. Since the frequency characteristics of late potentials are unknown

Basis of Fourier Analysis From the University of Oklahoma Health Sciences Center, Department of Medicine, and Veterans Administration Medical Center, Oklahoma City, Oklahoma. Supported in part by Grant HL36625 from the NIH and grants

The first consideration in planning a spectral analysis is whether the waveform of interest has a realizable Fourier spectrum. In our case, does the class of high-resolution ECG waveforms meet the so-

from the Veterans Administration and the Whitaker Foundation. Reprint requests: Paul Lander, PhD, VA Medical Center ( 15lF). 92 1 Northeast 13th Street, Oklahoma City, OK 73104.

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called “Dirichlet conditions”?” Since the high-resolution ECG has finite energy and frequency content, each waveform, x(t), will have a unique Fourier spectrum, X(f). In this article, the nomenclature x(t) and X(f) refers to continuous-time signals. The discrete equivalents, x(n) and X(k), are used to develop the following analysis so that the practical implementation of the techniques discussed can be more easily envisaged. The Fourier spectrum is found through the Fourier transform, which, for positive frequencies only, is given by: (1)

? 585

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0 679

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X(k) = 2 x(t) exp( -jZnnk/N) n=o

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60

k = O,,(N - 1)/2 The signal-averaged high-resolution ECG is evaluated over the interval of interest (in Fig. 1, eg, periods T1, Tz , or T3 ) . The Fourier spectrum, X(k) , is a complex entity, and the relative power of each frequency component is given by: (2)

Q(k) = lX(k)l*

a(k), usually referred to as the power density spectrum (PDS), is a density spectrum because the power (or energy) of the high-resolution ECG waveform in any particular frequency interval is represented by the area under cP(k).

Theoretical Disadvantages of Fourier Analysis of the High-resolution ECG Using the PDS to characterize late potential activity has some basic theoretical difficulties. These center around two points: the statistical properties of HRECG signals and the problem of how to achieve adequate spectral resolution from measurements of late potential waveforms of short duration.

High-resolution

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Fig. 1.

Signal-averaged high-resolution ECG lead, showing the QRS, LP, and ST-segment periods.

the QRS and LP waveforms are statistically nonstationary. For a stationary waveform, the expected value of the mean and variance should be time-independent. This means that there should be no systematic change in mean or variance of the waveform. Such changes are, however, observable in late potentials, and the value of a late potential waveform at any point in time cannot in general be predicted from past samples. The effects of nonstationarity in the QRS and late potential waveforms on their PDS can be seen by considering the auto-covariance function, r(r), of the HRECG waveform, defined as: N-l

(3)

r(7) = 2 x(n) x(n + 7) n=o

7 = O,,N

r(T) describes the correlation between a waveform and itself at a time r previously. For a stationary waveform r(r) is independent of n, the time at which r(T) itself is measured. The Fourier transform of the auto-covariance function is the PDS:

ECG Signal Properties

n-l

(4) Looking at period Tr of Figure 1, the QRS + LP period, it is possible to fit a series of sinusoids to reconstruct this high-resolution ECG waveform. Hence it will indeed have a unique Fourier spectrum. The resulting PDS is not necessarily an accurate estimate of the true signal spectrum. This is because the true signal spectrum varies with time. The PDS has no temporal resolution of the time-varying spectral energy. It therefore represents the time average of these spectral changes. Because of their time-varying or transient nature,

’

a(k)

= nTo r(n) exp t-W*) k = O,,(N - 1)/2

Obviously, if r(r) is time-varying then the PDS, a(k), also varies with time. Figure 2 illustrates this concept, using as an example a sine wave that uniformly varies in frequency from 100 to 8,000 Hz over the observation interval. The PDS is the average of all the theoretical power density spectra that exist over the observation interval. The contribution to the PDS of each ephemeral power density spectrum is directly proportional to the time for which the latter is

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might still have the potential for being a clinically useful measurement. Since the late potential waveform has a relatively short duration, typically several tens of milliseconds, its PDS will suffer from a poor spectral resolution. For a Fourier transform of the period T2, a “nominal” spectral resolution, Af,, exists, given by:

present. Hence the low-frequency components of the waveform dominate the measured PDS (Fig. 2B). This raises a particular diffkulty in computing the PDS of any high-resolution ECG period that includes the ST-segment or QRS. These relatively slow waves could be expected to dominate the PDS similarly, with other high-resolution ECG components substantially underrepresented. To characterize effectively a signal whose energy varies in time and frequency requires a spectrotemporal analysis method. Since the high-resolution ECG waveform is transient or nonstationary in nature, a classical Fourier analysis over any particular time interval will not lead to a complete characterization.

Af, = l/T2

(5)

For example, if T2 = 40 msec, this implies a nominal spectral resolution of 2 5 Hz. This nominal resolution cannot be improved upon by increasing the sampling rate or padding the sampled data with zeros. These approaches only introduce interpolated points in the spectrum between independent spectral values, which are spaced at intervals of Af,. The only way to increase the basic resolution of the spectrum is to increase the observation interval, Tz . In practice, spectral resolution is considerably worse than the nominal value, due to the truncation and windowing of the high-resolution ECG. This truncation is equivalent to applying a rectangular window to the high-resolution ECG. A common practice is to apply a cosinusoidal window to the data (eg, Cain et al.‘). Figure 3 shows a cosinusoidal window, w(t), and its spectrum, W(f). The use of this

Difficulties in Achieving Adequate Spectral Resolution The issue of the nonstationary high-resolution ECG, considered above, extends to the late potential waveform itself (period T2 of Fig. 1). The PDS for the late potential waveform alone, despite being an average of the time-varying late potential spectrum,

t

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A

- fcJ C Fig. 3. (A) Cosinusoidal

f.

D window function.

(B) Its Fourier spectrum.

(C) Cosine wave. (D) Its Fourier spectrum.

Spectrotemporal

window reduces the abrupt truncation by tapering the sequence of data samples to zero at each end of the window. Treating the window as an equivalent low-pass filter of the spectrum, a more realistic spectral resolution can be calculated.‘3*14 Multiplying the data samples in the time domain by a window is equivalent to convolving (or low-pass-filtering) the spectrum with the Fourier transform of the window (W(f) of Fig. 3). As a result, the window’s characteristics largely determine the effective spectral resolution. To illustrate, consider the example of a pure sinusoid, of frequency fO, whose ideal Fourier transform is an impulse at f,,. These waveforms are illustrated in Figs. 3C and 3D. In practice, when the sinusoid is windowed in the time domain, the resulting Fourier transform is W(f), the spectrum of the window, which will be centered at fO. The phenomenon of the smearing of the impulse into the form of W(f) is known as spectral leakage.i5 A reasonable delinition of spectral resolution is the “effective bandwidth” of W(f).‘“,16 This is the frequency interval, A f,, which contains the significant energy of W(f). This is often taken -somewhat conservatively-to be 95% of the total energy. The “effective” spectral resolution could be expressed as: (6)

Af, = K,/Tz

where K, is a constant, unique to each window type, which represents a practical time-bandwidth product. l6 For the class of modem windows, for example, the Blackman-Harris, Hamming, or Kaiser-Bessel types, K, does not vary much and is in the range of 3.6-4.0.16,17 This implies that for a period TZ = 40 msec, the effective spectral resolution is about 90 Hz, as opposed to the nominal value of 25 Hz. In summing the area under W(f) over a bandwidth less than Af,, the error introduced is dependent on the underlying signal spectrum, as well as on the characteristics of the window. If no large signals are spectrally adjacent to the signal of interest, the error will be small. Otherwise, if two adjacent signals exist, spectral leakage will cause their energies to interact by smearing. It has been proposed’ that the ratio of areas under a(f) in the frequency intervals O-20 Hz and 20-50 Hz may be useful for identifying the presence of late potentials. However, measuring the ratio of areas under W(f) between any pair of frequency intervals less than Af, wide will be prone to significant error. Using different windows will result in very different spectral estimates. This is because each window has a unique relationship between mainlobe width and sidelobe levels (Fig. 3). Ideally, W(f) is the impulse of Figure 3D, that is, a narrow mainlobe with maximally suppressed sidelobes. In general, a greater

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sidelobe suppression is accompanied by an increased mainlobe width, which accounts for the uniformity in the values of K,. Hence, an informed choice of window type depends on some a priori knowledge of the true signal spectrum.

Enhancing PDS Estimates of Late Potentials-Spectral Smoothing A major problem of applying a window directly to the late potential waveform is that data samples that lie near the ends of the window are lost. An alternative approach that avoids this arbitrary reduction of information in the late potential waveform and gives much greater flexibility in reducing spectral leakage is the technique of spectral smoothing. The PDS of the late potential waveform is first computed without explicitly windowing the highresolution ECG data samples (ie, using a rectangular window). The PDS is then itself inverse Fouriertransformed to obtain the auto-covariance function, r(r). The auto-covariance function is now multiplied by the window function (w(t) of Fig. 3) to produce r’(r), a tapered or time-limited version of r(r), ie: (7)

r’(r) = r(7).w(t)

The Fourier transform of r’(T) is a’(f), the smoothed PDS estimate of the high-resolution ECG. This approach allows both lighter and heavier smoothing than that obtainable by applying a window to the original late potential waveform. The smoothing window, w(t), can be smoothly truncated to zero at some fraction of the length of r(T) for higher degrees of smoothing or applied only to the tail of r(T) for lesser smoothing. Conventionally in spectral analysis, progressively higher degrees of smoothing are applied in turn until the level is found that most clearly reveals the features of interest in the signal spectrum. I8 For the reasons discussed above, this is of necessity an empirical procedure, since the appropriate window type and degree of smoothing depend on the underlying spectrum of the late potential waveform. The effective spectral resolution, A f,, with this method is still given by equation 6. If a particular window, w(t), is applied to either the original late potential waveform or the autocovariance, r(r), A f, is identical in both cases. A point not considered above is the stability of the PDS estimate. This could loosely be seen as the reproducibility of the PDS, as computed from repeated signal averages of the same subject. In general, the stability of the PDS estimate increases with the heavier smoothing obtainable with the spectral smooth-

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diminishes, how-

Methods Spectrotemporal

Analysis

Considering the theoretical results presented above, a time-varying spectral analysis of the highresolution ECG waveform may be useful for analyzing late potentials. This can be seen intuitively by considering what is the equivalent time domain operation of computing the PDS . Measuring the energy of the PDS in any particular frequency interval is equivalent to applying a bandpass filter in the time domain and summing the energy of the filtered waveform. When seen from this perspective, the time interval over which the PDS is measured obviously influences the relative spectral energies, in particular frequency intervals. The characteristics of this equivalent bandpass filter are determined by the type of time window used to compute the PDS. Having selected the “effective” bandwidth of the futer ( Afe) (i.e., the frequency interval of interest), its “effective” impulse response duration (Tz) is given by equation 6.13 Classical methods of time-varying spectral analysis have to contend with the same basic problems presented by short-time, nonstationary signals. Conceptually, when the energy of a waveform is measured over finite time and frequency intervals, its representation becomes probabilistic.22*23 In engineering terms, this energy representation becomes a complex entity that may assume physically unrealizable (ie, negative) values.23,24 In constraining timevarying spectral energy to a range of physically meaningful values, only an approximation to the true spectrotemporal energy distribution is achievable. This issue is beyond the scope of this article but has been discussed extensively.22-25

Running Fourier Transform Approach One method of obtaining a meaningful time-varying spectrum is the running Fourier transform approach, originated by Page.25 With this method, a sequence of spectra are computed using a moving time window. Figure 4 illustrates this approach, showing a spectrotemporal analysis of the variablefrequency sine wave shown in Figure 2. The resulting time-varying spectrum, l(t,f), is displayed as a three-

dimensional plot of energy versus time and frequency. Comparing Figure 4B to Figure 2B, the timevarying spectral analysis is able to characterize the sine wave energy far more effectively than the PDS. Ideally, c(t,f) is a sequence of impulses. As discussed above, each impulse is represented by the spectrum of the window applied in the time domain. l(t,f) consists of a sequence of spectral slices. The spectral slice computed at time to (Fig. 4A) is given by N-l

e(to,k) =

c

x (n + t,-, - T/2)-w(n)

Il=O

(8) exp( - j2=nk/N)

k = O,,(N - 1)/2

The next spectral slice, l(to + 7,f) , is found by shifting the time window, w(t), by an amount 7.

Spectrotemporal Resolution The main issue in time-varying spectral analysis is that of spectrotemporal resolution. As the observation interval in time is increased, the resolution of changes in the temporal energy of signals is decreased in l(t,f) , but the spectral resolution, Af,, of each spectral slice is increased. For each spectral slice, the spectrotemporal resolution is given by (9)

Afs = K,/T

which is a “short-time” PDS measurement. A perennial problem in spectral analysis is how to select the parameters of the anaIysis, in this case T and 7. This is almost always performed empirically.‘8~‘9~26 The choice of T primarily determines the spectrotemporal resohttion of each spectral sIice of c(t,f). The greater the length of each time window, T, the better the spectral resolution. However, as T is increased, temporal resolution, or the ability to represent transient signals, is worsened. If T is set to be equal to the observation interval, the resulting spectrotemporal distribution is a single spectral slice, which is the PDS. The value of T should reflect the time-frequency structure of the high-resolution ECG. The choice of r affects only the temporal resolution of c(t,f). As a general rule, 7 should be small compared with T. In this study, the values of T = 16 msec and 7 = 2 msec seemed consistently to reveal the timefrequency structure of the high-resolution ECG. These parameters offer little spectral detail (Af, = 60 Hz, Af, = 226 Hz), but the compromise between spectral and temporal resolution consistently represented time-varying changes in the high-resolution ECG spectrum. The exact value of T is not critical.

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A

Fig. 4. Time-varying

spectrum of a variable-frequency sine wave. (A) The sine wave, x(t), which is windowed by w(t). (B) Its spectrotemporal energy distribution. Each spectral slice of e(t,f) is computed over a time interval of T. Spectral slices are spaced at intervals of 7.

Values of T = 12 msec and T = 20 msec produced broadly similar results. Note that the prior objection to using a time window, the arbitrary suppression of

end data samples, is removed, since all parts of the high-resolution ECG waveform will appear in the center of the window at some time.

Removal of the ST-Segment Slope The problems of signal nonstationarity and pooramplitude resolution in the spectrum can be partially accommodated by using a trend removal technique on the ST-segment slope. Figure 2 illustrated how a

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large, unwanted signal can mask and suppress other, time-varying spectral information. By choosing a short-time window, the high-resolution ECG waveform will appear less nonstationary in the windowed interval. The slope of the ST-segment can be seen as a trend in the window. It can be modelled using a polynomial function,” which implies that this component of the high-resolution ECG is nonstationl9 Attenuating the ST slope by simple differencary. ing or mean value subtraction can lessen this nonstationarity. It also improves the dynamic range and resolution of the spectral estimate. The procedure of trend removal alters the signal spectrum by acting as a high-pass filter. Differencing produces a high-resolution ECG waveform, y(t), from the original signal average, x(t), such that: (IO)

y(t) = x(t) - x(t - I)

This is a very simple finite impulse response-type filter. It can be expected to reduce the effects of the ST-segment slope on e(t,f) but will alter the spectrum of the late potentials. Mean removal, however, only affects the dc or 0 Hz component.

Computational

Procedures

For this study spectrotemporal mapping (STM) data were computed using an IBM-AT compatible, 80386-based personal computer. Signal-averaged waveforms were acquired at a sampling rate of 2,000 Hz. A 200-msec period of interest was visually selected to include the QRS, late potential (if present) and ST-segment waveforms. No filtering or trend removal techniques were performed. A Hamring window was used to segment the time domain waveform. Each segment had the mean removed before windowing and was padded with zeros. A 5 12 point FFT was then applied. The window length, T, and time shift, 7, selected were 16 msec and 2 msec, respectively.

Results We studied a total of 26 subjects in this initial study. Of these, 6 were normal, healthy volunteers, 10 were patients presenting with syncope, and 10 were patients presenting with clinical sustained monomorphic ventricular tachycardia. The syncope patients had no evidence of heart disease, with a negative electrophysiologic study, no prior MI, and an ejection fraction greater than 50%. The VT group was inducible for sustained monomorphic VT during

EPS, had either an acute or old MI, and had an ejection fraction less than 40%. These two groups permit a clear-cut comparison between STM and high-resolution ECG results for patients with and without VT. Figures 5 and 6 show spectrotemporal maps of an individual signal-averaged lead for a normal healthy subject and a VT patient, respectively. Figure 5A is the unfiltered signal-averaged Z lead from a normal healthy subject. Figure 5B shows the STM, computed over the 140-msec period Z0 to Zz. The QRS offset, Zi, is automatically measured from the high-pass-filtered signal-averaged lead and is noted on the STM. The STM is plotted on a logarithmic scale over a frequency interval of 0- 1,000 Hz. Figure 6A shows the three unfiltered signal-averaged XYZ leads from a VT subject. Figure 6B is their vector magnitude after high-pass filtering at 25 Hz. The measured filtered QRS duration is 112 msec and the root mean square amplitude of the terminal 40 msec of the QRS (RMS40) is 32 I.LV.By previously published criteria this is a normal signal-averaged ECG result. Figure 6C shows the STM of lead X, computed over a 164-msec period X0 to X2. The QRS offset is marked at time Xi. The STM is plotted on a logarithmic scale over a frequency interval of O-1,000 Hz. The principle feature of interest of this STM is the low-level tail at the end of the QRS. This lowlevel signal has a time-varying spectrum that is consistent with decaying, transient signals in the time domain signal average. This activity is absent in the normal STM of Figure 5. In theory, the STM contains the same information as the unfiltered signal average. To test this, RMS40 measurements from the vector magnitude function and the three-lead summed STM were compared. The summed STM was formed by adding the STMs of leads X, Y, and Z. The RMS40 value was found by integrating the STM over a 40-msec time interval, corresponding to the last 40 msec of the vector magnitude QRS, and over the frequency interval 40-250 Hz. Figure 7 is a scatter-plot of the RMS40 values due to the vector magnitude and summed STM, for the 10 syncope and 10 clinical VT patients. There is a strong correlation between the two sets of RMS40 measurements (r = 0.92, p = 0.0001). The differences between individual values found by the two methods is due to the differences in filtering. The vector magnitude explicitly uses a fourth-order Butter-worth filter. The STM is filtered implicitly, in the sense that the spectral energies at different frequencies are determined by the window type and length, T. The summed STMs of the 10 syncope and 10 clinical VT patients were investigated to determine whether differences in spectral energy were discernible between the two groups. Figures 8A and 8B il-

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Spectrotemporal analysis of a normal subject. (A) Unfiltered Z lead. (B) The STM of lead Z from time ZOto time Zz. The end of the QRS, as selected from the STM, is at time Z1.

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A rvu,rs

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0.181 0.141 0.111

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o.oao 0.040 O.ORo

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Fig. 6. Spectrotemporal

analysis of a subject with VT. Note the low-level LP energy with spectrotemporal energy variations. (A) Unfiltered XYZ leads. (B) Their vector magnitude filtered at 25 Hz. (C) STM of lead X from time X0 to time X2. Time X1 denotes the end of the QRS as measured from the STM.

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Scatterplot of RMS40 values found from the three-lead summed STM and the vector magnitude function, for the clinical VT and syncope populations. Trend lines for the two sets of measurements are also shown.

typical summed STMs for a syncope and a clinical VT subject, respectively. The STMs are plotted on a linear scale over a frequency interval of O300 Hz. STMs from the clinical VT group have a longer QRS duration (VT, 131 ? 12.6 vs. syncope, 102 + 10.5) and a characteristic low-amplitude tail, representing the terminal QRS.

lustrate

Discussion Spectrotemporal mapping illustrates the difficulties that are encountered when spectral analysis is applied to the signal-averaged ECG. These difficulties center around the characteristics of the signal-averaged QRS waveform and the available spectral resoIution. The spectra1 resolution of the QRS or late potential waveform is ultimately limited by the waveform’s duration and is not improved by including other areas of the ECG, such as the ST-segmenf, in the period for analysis. STM reveals that late potentials and the QRS have a time-varying spectrum, while the ST-segment waveform does not. Hence late potentials can be distinguished from the ST-segment by their spectral characteristics. Our re-

sults suggest that the normal QRS and late potential waveforms cannot be consistently differentiated by their time-varying spectral characteristics. These spectra are “featureless,” that is, they do not have distinct peaks or other consistent features. A qualitative (ie, visual) analysis of the STMs for the syncope and clinical VT groups does not show a unique spectrotemporal signature for late potentials, other than the presence of a low-amplitude tail following the QRS. There do not appear to be spectral features from within the QRS that separate the two groups. Hence it is not possible to identify visually spectrotemporal patterns of normal and abnormal ventricular conduction within the main body of the QRS. Quantitative analysis of STMs, that is, integrating energy over particular intervals of time and frequency, can lead to significant errors. This is due to the fact that the spectra are estimates, dependent upon the window type and length. Energy at a particular frequency is spread across a range of frequencies due to the constraints of spectral resolution. This lack of differentiation between electrocardiographic patterns due to normal and abnormal ventricular conduction is a principal difficulty for highresolution ECG spectral analysis. A normal QRS complex is the product of a uniform activation pat-

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iPECTRAL MAI 1632. STS 6115189 ;TMBASIC.CF(

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summed STMs for (A) a syncope patient and (B) a clinical VT patient.

Spectrotemporal tern in the ventricles. High-frequency components appear in the spectrum due to the effects of windowing and in proportion to the width of the QRS (typically 80- 100 msec) . An abnormal QRS complex is the product of some uniform activation and some nonuniform activation, that is, slow and disordered conduction due to abrupt changes in the magnitude and direction of the activation wavefront in ischemic regions. High-frequency components are also present with abnormal conduction, due to these effects and the use of a window function. The abnormal QRS complex is typically longer than the normal (ie, > 120 msec). This factor lowers high-frequency content in proportion to the QRS width. Conduction disorders occur on macroscopic and microscopic scales. Examples of large-scale conduction disorders are bundle branch block and big infarctions, which produce major changes in the ECG waveform. Conduction disorders that may form a reentry substrate in ischemic zones are responsible for late potentials in the high-resolution ECG. This is a microscopic since it usually involves small phenomenon, amounts of myocardium. Microscopic phenomena are not normally seen in the normal ECG. In this simple approach to determining the origins of highfrequency content of the high-resolution ECG there are thus four factors: (1) width of the QRS complex, (2) the properties of the window function used, (3) macroscopic patterns of ventricular activation, and (4) microscopic patterns. The first three factors are almost certain to predominate in the high-resolution ECG spectrum. This is due to the relatively small contribution overall of ischemic border zone activity and the effects on the spectral estimate of the window function. Poor spectral resolution will tend to mask the small contribution of abnormal activation patterns to the spectrum. Unfortunately, it is not possible to distinguish these different contributions to the high-frequency content of the high-resolution ECG. The advantage of STM is that it allows the spectrum throughout the QRS to be localized in time. However, a unique pattern of late potential (or abnormal) activity within the QRS is not evident in our results, primarily because of the limited spectral resolution available. Since inadequate spectral resolution is the principal problem with ECG spectral analysis, it is worth considering whether methods other than the Fourier transform may give improved results. Autoregressive (AR) modelling approaches can be usefully applied to signals with strong sinusoidal components to enhance peaks to the spectrum. Fitting an AR model to a waveform without some prior knowledge of its true spectrum is problematic. The observation from this work, that the QRS has a featureless spectrum,

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indicates that AR models will not give better spectral resolution in practice than the Fourier ‘transform. The results of this study showed that spectrotemporal mapping can display the time-frequency structure of the signal-averaged ECG with limited resolution. The STM contains information comparable to that of the signal-averaged XYZ leads and supports the idea that there may be late potential information present in the individual leads that is obscured by the vector magnitude transformation. There are some patient groups, such as those who have long QRS durations without necessarily having a reentry substrate or patients with bundle branch block, in whom conventional time domain analysis methods cannot identify patients with VT. In these patients STM may reveal more consistent spectrotemporal characteristics associated with VT. In this study, STM did not reveal either qualitative or quantitative differences in spectral characteristics between VT-inducible and noninducible patients. These results have to be interpreted with the limited spectral resolution of the method in mind. STM and other methods of spectral analysis have a limited spectral resolution, which is principally due to the nature of ECG signals, and not the techniques used.

References 1. Berbari EJ, Scherlag BJ, Hope RR, Lazzara R: Recording from the body surface of arrhythmogenic activity during the ST segment. Am J Cardiol 41:697, 1978 2. Simson MB: Use of signals in the terminal QRS complex to identify patients with ventricular tachycardia after myocardial infarction. Circulation 64:235, 1981 3. Breithardt G, Schwarzmaier J, Borggrefe M et al: Prognostic significance of late ventricular potentials after acute myocardial infarction. Eur Heart J 4:487, 1983 4. Denes P, Santarelli P, Hauser RG, Uretz E: Quantitative analysis of the high frequency components of the terminal portion of the body surface QRS in normal subjects and in patients with ventricular tachycardia. Circulation 67: 1129, 1983 5. Kuchar DL, Thorbum CW, Sammel NL: The role of signal averaged electrocardiography in the investigation of unselected patients with syncope. Aust NZ J Med 15:697, 1985 6. Gomes JA, Winters SL, Stewart D et al: A new noninvasive index to predict sustained ventricular tachycardia and sudden death in the first year after myocardial infarction: based on signal-averaged electrocardiogram, radionuclide injection fraction, and Holter monitoring. J Am Co11Cardiol 10:349, 1987

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Journal of Electrocardiology

Vol. 23 No. 2 April 1990

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