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(Stroke. 1995;26:2044-2047.)
© 1995 American Heart Association, Inc.

Articles

Importance of Time-Window Overlap in the Detection and Analysis of Embolic Signals

Hugh Markus, MRCP, DM

From the Department of Neurology, King's College Hospital School of Medicine and Dentistry, and the Institute of Psychiatry, London, UK.

Correspondence to Dr Hugh Markus, Department of Neurology, Institute of Psychiatry, De Crespigny Park, London, SE5 8AF, UK.

	Abstract

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Background and Purpose The detection of asymptomatic embolic signals by Doppler ultrasound may offer a powerful investigational tool in the management of cerebrovascular disease. However, early studies, particularly in patients with carotid artery disease, have reported very different frequencies of embolic signals. While this may reflect differences in patient groups and the criteria used for embolic signal identification, the degree of time-window overlap may be important. If this is insufficient, some embolic signals may fall between two time windows and not appear on the spectral display. Furthermore, the use of nonrectangular time windows, such as the Hanning window, may result in variation of the intensity of an embolic signal depending on where it is detected within the time window.

Methods To test the importance of this potential problem, the same 25 embolic signals recorded as the audio signal on digital audiotape were each played repeatedly through a transcranial Doppler ultrasound (TCD) system using fast Fourier transform analysis. An older system with no time-window overlap was used, and a more modern system was also used in which three different degrees of overlap were used: -9%, 27%, and 57%. The number of signals audible but not appearing on the spectral display was recorded. The variability in the relative intensity increase for the same embolic signal played repeatedly was estimated by calculating the coefficient of variation of the relative intensity increase.

Results With the older system, 39/500 (7.8%) of embolic signals were missed. With the newer system, the number of embolic signals missed was fewer and decreased with increasing degrees of overlap (10/500 for -9% overlap, 1/500 for 27% overlap, and 0/500 for 57% overlap). For those setups in which embolic signals were missed, there was a highly significant relationship between duration of embolic signal and number of signals missed. In parallel with these results, the coefficient of variation of the relative intensity increase became progressively less with increasing degrees of time-window overlap. For all processing setups, the coefficient of variation was greater for the less intense and shorter duration signals, but this dependence, as estimated by the slope of the regression line, became less strong with higher degrees of overlap.

Conclusions Inadequate degrees of fast Fourier transform time-window overlap will result in the failure of current TCD machines to detect embolic signals. Furthermore, this and the time windowing currently usually used may result in variability in the relative intensity increase of identical embolic signals. These factors need to be taken into account when comparing data on the frequencies of embolic signals recorded by different researchers and in the design of future TCD equipment.

Key Words: cerebral embolism • ultrasonics

	Introduction

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The detection of circulating cerebral emboli with Doppler ultrasound may have a number of applications in the prevention and treatment of cerebrovascular disease. Both gaseous and solid emboli reflect and scatter more of the incident ultrasound than the surrounding blood and appear as short-duration high-intensity signals, or "embolic signals," within the flow spectrum.¹ Embolic signals in the cerebral arteries have been detected in patients with potential embolic sources including carotid artery disease,^{2 3 4} prosthetic cardiac valves,^{4 5 6} and atrial fibrillation⁷ and during invasive procedures including cardiopulmonary bypass⁸ and carotid endarterectomy.⁹ Early studies in patients with carotid artery disease have reported a marked variation in the number of embolic signals detected.^{2 3 4 10 11} This may reflect differences in the patient populations being studied, such as different treatment regimens, differences in the monitoring protocols, or differing interpretation of what is an embolic signal. However, it may also reflect the use of different equipment and different machine settings.

A specific theoretical problem is the speed of processing and time windowing of current commercially available transcranial Doppler (TCD) machines.¹² This problem is suggested by the observation that a typical clicking or chirping sound characteristic of an embolic signal may be heard in the audio Doppler signal, without a high-intensity signal appearing on the spectral display, and that this is particularly common for low-intensity and short-duration signals, such as those detected in patients with carotid artery disease. Most TCD machines use a fast Fourier transform (FFT) during signal processing; each FFT is then displayed as one column on the time/velocity (or frequency) display. The execution of each FFT requires a specific amount of time, and depending on the speed of the processor, a variable amount of the FFT time window can be overlapped with the next FFT. If no overlap occurs, there is the possibility that an embolic signal may pass through the sample volume but arrive between the sampling periods of the two time windows and not be displayed on the screen (Fig 1, top). Many currently used TCD machines were designed for flow-velocity measurement, not with embolus detection specifically in mind, and are equipped with computers unable to process the Doppler signal rapidly enough to ensure a high degree of FFT overlap; this could theoretically account for embolic signals being missed. A related problem that may arise from an inadequate degree of FFT overlap is variability in the measurement of the relative intensity of an embolic signal. To improve the spectral appearance, a time window (such as a Hanning time window) is usually used during signal analysis.¹³ This increases the relative amplitude of signals occurring during the center of the time window, but signals occurring at the temporal edges of the time window will have their relative amplitude reduced (Fig 1). If there is sufficient overlap of the time windows, this will not create a problem, but if the overlap is insufficient, an embolic signal being sampled in the center of an FFT sampling time is likely to result in a more intense embolic signal than one that is sampled at the temporal edges of a sampling period (Fig 1, bottom). Embolic signal intensity depends on both embolus size and material^{1 14} and may allow limited characterization of embolus type and size¹⁵ ; however, estimates of intensity increase for short-duration embolic signals could be inaccurate if such processing difficulties occur.

View larger version (52K): [in this window] [in a new window]   Figure 1. Schematic diagram of a Doppler signal illustrating the effect of time-window overlap and the shape of the time window on the detection and intensity of embolic signals. In each diagram, the upper tracing (1) illustrates the ultrasound signal before signal processing. The middle tracing (2) illustrates the time window, and the lower tracing (3) represents the ultrasound signal after time windowing. Top, In the absence of overlap, embolic signals may not be displayed on the spectral processor. An embolic signal (A) (an increase in amplitude on the upper tracing) that is sampled during the middle of a time window (tracing 2) is displayed as signal A1. However, a similar signal (B) arriving between two time windows is not detected. Bottom, With higher degrees of overlap no signals will be missed, but the position of the signal during the time window may affect the intensity of the spectral signal. An embolic signal sampled during the middle of the time window (A) is detected as a higher intensity signal (A1) than a similar signal (B) sampled midway between the centers of two time windows (B1).

In this study, the importance of processing speed and FFT time-window overlap was examined using embolic signals recorded from patients, which were subsequently analyzed in standard TCD systems.

	Materials and Methods

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Embolic signals recorded from the middle cerebral arteries of patients by a transcranial Doppler machine with a 2-MHz probe (TC2000 TCD machine, EME) were studied. The analogue Doppler audio signal was recorded onto digital audiotape; this allowed subsequent playback in real time through the processor, at which point the FFT transform was performed and the time velocity spectra displayed on a computer screen. The same pulse repetition frequency (PRF) of 8 kHz was used for both recording and playback. A modified Hanning time window was used for processing.

Twenty-five embolic signals were analyzed. Each embolic signal was played back 20 times using each of four different processing setups. (1) The first was a TC2000 equipped with a 286 processor. This is an older system with no time-window overlap, although determination of the exact degree of overlap is not possible. For the other setups, the same TC2000 was used equipped with a 386 processor in place of the 286 processor. By altering the sweep speed, three degrees of FFT overlap were used: (2) 57% (sweep time, 3.5 seconds); (3) 27% (sweep time, 6.0 seconds); and (4) -9% (sweep time, 8.9 seconds). Overlap was calculated as overlap(%)=PRF/FFT points ([FFT points/PRF]-[sweep time/columns]), where FFT points is the number of points in the FFT (128 in this study), sweep time is time(s) taken for the signal to sweep the screen once, and columns is the number of columns in the spectral display (512 in this study).

In practice, because the processor performs both FFT analysis and other functions simultaneously, the above calculations are an approximation; the actual degree of overlap is likely to be less than stated, but the relative differences between the different settings will be similar.

For each embolic signal and processing setup, the number of embolic signals missed (heard as a typical sound but not displayed) was recorded. Where a visible embolic signal was present, the maximum relative intensity increase of each embolic signal during each of the 20 playbacks was measured. To calculate the variability of the relative intensity increase associated with a single embolic signal, the coefficient of variation (%) of relative intensity increase across the 20 playbacks was then calculated for each embolic signal and setup combination.

The embolic signals were selected to represent a range of durations and relative intensity increases. Relative intensity increase (decibels) was calculated from the equation 10 log (maximum intensity of embolic signal/mean background intensity), and duration was calculated from the duration (number of time columns) of the high-intensity (>4 dB) embolic signal. Fourteen signals were from patients with symptomatic carotid artery disease, and 11 were from patients with mechanical heart valves. Mean±SD relative intensity increase was 8.3±1.42 dB (range, 5.0 to 9.9 dB), and mean±SD duration was 32.4±18.6 milliseconds (range, 5 to 80 milliseconds); values were higher for valve than carotid emboli (intensity increase: 9.2 versus 7.9 dB, t test P=.0028; duration: 47.7 versus 20.4 milliseconds, t test P=.0001). When calculating correlations, the values of relative intensity increase and duration of embolic signal for each embolic signal were taken from the replay (of the 20 replays) in which the embolic signal had the maximum relative intensity increase; it was assumed that during this replay the embolic signal was processed nearest to the center of the time window.

	Results

Top Abstract Introduction Materials and Methods Results Discussion References

 
286 Processor
Thirty-nine of a total of 500 (7.8%) embolic signals were not displayed or "missed." The number missed varied from 0/20 to 6/20 for the 25 different embolic signals and was negatively correlated with duration of embolic signals as shown in Fig 2 (Spearman's corrected for ties=-0.815, P=.0001). No embolic signals with a duration of more than 40 milliseconds were missed. More carotid emboli than valve embolic signals were missed (mean±SD, 2.64±2.06 versus 0.18±0.41; t test P=.0007), which was consistent with the carotid embolic signals being of shorter duration and lower intensity.

View larger version (9K): [in this window] [in a new window]   Figure 2. Graph shows relationship between duration of high-intensity signal and number of embolic signals not displayed or missed by the 286 processor. Each embolic signal has been processed 20 times.

386 Processor
The number of embolic signals missed was fewer and decreased with increasing degrees of FFT overlap (10/500 for -9% overlap, 1/500 for 27% overlap, and 0/500 for 57% overlap). For analysis using the -9% overlap, there was a highly significant relationship between duration and number missed (Spearman's corrected for ties=-0.567, P=.01); no embolic signals with a duration greater than 15 milliseconds were missed.

Paralleling these results, the coefficient of variation of the relative intensity increase became progressively less with increasing degrees of FFT overlap (Fig 3). For all processing setups, the coefficient of variation was greater for the shorter duration signals, but this dependency, as estimated by the regression coefficient and the slope of the regression line between duration of embolic signal and coefficient of variation in relative intensity increase, became less strong with higher degrees of FFT overlap and was no longer significant for the highest degree of overlap. Values for Pearson correlation coefficient (r) and the slope of the regression line were r=-.566, P=.0032, and slope=- 0.125 dB/ms for -9% overlap; r=-.404, P=.045, and slope=-0.09 dB/ms for 27% overlap; and r=.239, P=.25, and slope=-0.034 dB/ms for 57% overlap.

View larger version (16K): [in this window] [in a new window]   Figure 3. Bar graph shows relationship between degree of fast Fourier transform (FFT) overlap and coefficient of variation measured from each embolic signal played 20 times for the 386 processor.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

 
Current TCD machines were designed for the measurement of flow velocity rather than the detection of embolic signals. In such systems, the ideal output is a clear Doppler spectral display; a high temporal resolution for the detection of short-duration intensity increases is not required. Time-window filters are introduced to improve the quality of the spectral display; these result in less spectral power leakage compared with a rectangular time window. Embolus detection makes quite different demands on a Doppler system: an important requirement is a high temporal resolution to ensure the detection of short-duration changes in signal amplitude. These data demonstrate that the temporal resolution of some currently used systems results in a failure to detect short-duration embolic signals. With an older machine equipped with a 286 processor (although manufactured only 5 years ago and still in widespread use), 8% of embolic signals were missed, and this figure was over 13% when only carotid embolic signals were considered. Using more recent machines based on a 386 processor, few emboli were missed, and with an overlap of approximately 57% no embolic signals were missed. Nevertheless, even when all signals were detected using the 57% overlap, the resulting signals displayed as spectra were variable, as demonstrated by the variation in the relative intensity increase of the same embolic signal played repeatedly.

The number of "missed" signals is greater for short-duration low-intensity signals. Therefore, it is unlikely that a significant number of embolic signals recorded from patients with mechanical heart valves will be missed, as these signals have a higher intensity compared with those in patients with carotid artery disease.¹⁵ However, this is likely to be a problem in studies in carotid stenosis, and there has been a particularly wide variation in the frequency of embolic signals in patients with carotid artery stenosis, in whom the embolic signals are often of low intensity and short duration. Furthermore, many current studies use a threshold relative intensity increase as one of the criteria for identifying an embolic signal; the variation in relative intensity increase for smaller signals may result in only a proportion of identical embolic signals being detected in the middle of the time frame, therefore exceeding the threshold intensity used in identifying embolic signals. This may account for variation in the number of embolic signals reported in different studies even when embolic signals are not completely "missed" on the spectral display.

The variability in the intensity of the same embolic signals will also be important if information on embolus size and material is to be derived from analysis of the spectral display. Experimental studies have demonstrated a relationship between embolus size and both relative intensity increase and duration of high-intensity signal.^{14 16} These studies were performed using larger experimental emboli, for which the effect of inadequate FFT overlap is likely to be unimportant. The situation may be different for the much lower amplitude and shorter duration signals recorded in conditions such as carotid artery disease and atrial fibrillation.

A number of alternative strategies will reduce this problem. A higher degree of overlap is possible with the newest TCD machines, which use more powerful processors, but this will be reduced in these machines if recordings are made from multiple channels simultaneously. Alternative time windows that are not so heavily weighted toward the signal in the center of the time frame may reduce the variability of the relative intensity increase. Different methods of signal analysis, such as Wigner analysis with its higher temporal resolution, offer an alternative approach.¹⁷

The detection of embolic signals may offer a useful tool in the investigation and management of patients with or at risk for cerebrovascular disease. However, before it can be used in routine clinical practice and before multicenter prospective outcome studies can be performed, the reason for the differences in the frequency of embolic signals in different centers needs to be determined. While this may represent differences in patient groups, this study demonstrates that machine characteristics are important and that the degree of overlap can have dramatic effects on the number of embolic signals visualized on the spectral display. Future studies should take the degree of time frame overlap into account; a simple assessment of its importance for different systems can be performed by recording the Doppler audio signal before it has undergone its FFT analysis and repeatedly replaying the portion containing an embolic signal. The degrees of overlap will vary within individual machines according to recording parameters such as pulse repetition frequency and sweep speed, and these need to be accounted for in any such analysis.

	Acknowledgments

 
Some of this work was carried out at St George's Hospital Medical School, and I am very grateful to Dr Martin Brown for his support. Dr Sid Leeman provided technical advice.

Received July 25, 1995; revision received July 25, 1995; accepted July 27, 1995.

	References

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