(Stroke. 1998;29:1638-1643.)
© 1998 American Heart Association, Inc.
Preliminary Report of Detecting Microembolic Signals in Transcranial Doppler Time Series With Nonlinear Forecasting
R. W. M. Keunen, MD, PhD;
C. J. Stam, MD, PhD;
D. L. J. Tavy, MD;
W. H. Mess, MD;
B. M. Titulaer, PhD;
R. G. A. Ackerstaff, MD, PhD
From the Department of Clinical Neurology and Neurophysiology, Leyenburg
Hospital, The Hague, and the Department of Clinical Neurology and
Neurophysiology, Antonius Hospital Nieuwegein/Utrecht, The Netherlands.
Correspondence to R.W.M. Keunen, MD, PhD, Department of Neurology and Clinical Neurophysiology, Leyenburg Hospital, Leyweg 275, 2545 CH The Hague, The Netherlands. E-mail cjstam{at}compuserve.com
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Abstract
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Background and Purpose—Most
algorithms used for automatic detection of microembolic
signals (MES) are based on power spectral analysis of the
Doppler shift. However, controversies exist as to whether these
algorithms can replace the human expert. Therefore, a different
algorithm was applied that takes advantage of the periodicity of the
MES. This so-called nonlinear forecasting (NLF) is able to detect
periodicity in a time series, and it is hypothesized that this
technique has the potential to detect MES. Moreover, because of the
lack of prominent periodicity in both the normal Doppler signals
(DS) and movement artifacts (MA), the NLF has a potential to
differentiate MES from normal blood flow variations and MA.
Methods—Twenty single MES and 100 MA were selected by 2 human
experts. NLF was applied to MES and MA and compared with 200 randomly
chosen DS. NLF resulted in a so-called prediction value that ranges
from +1 in signals with prominent periodicity to 0 in signals that lack
periodicity.
Results—NLF revealed that MES are more predictable than the
normal Doppler signals (prediction [MES]=0.829±0.084 versus
prediction [DS]=-0.060±0.228; P<0.0001). Moreover,
MES are more predictable than the MA (prediction [MA]=-0.034±0.223;
P<0.0001). No difference in prediction could be found
between DS and MA.
Conclusions—This preliminary report shows that MES can be
separated from DS and MA by NLF. Research is needed as to whether this
technology can be further developed for automatic detection of MES.
Key Words: emboli • ultrasonics • cerebrovascular diseases • nonlinear analysis
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Introduction
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Since Spencer and
colleagues1 described the on-line detection of
cerebral embolism by transcranial Doppler (TCD) during
carotid surgery, a vast number of reports have been published to
describe the Doppler phenomena of these emboli. Emboli that pass
through a sample volume of the Doppler beam result in a so-called
microembolic signal (MES). MES are characterized by a
unidirectional transient increase of the power in the Doppler
spectrum and a typical musical sound. This musical sound is the result
of the harmonic character of the MES seen in the Doppler signal
(Figure 1
).
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Figure 1. MES observed during carotid surgery. Embolic
signal characterized by a gradual increase in intensity and a more
prominent periodicity compared with background Doppler signal (on
vertical axis an arbitrary scale of the Doppler signal, on
horizontal axis an arbitrary time scale).
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For clinical application, it is vital that MES can be separated from
intensity fluctuations of the Doppler signal that are caused by
normal blood flow and artifacts.2 One of the most
relevant artifacts, which may lead to erroneous embolus classification,
arises from subtle probe movements. These so-called movement artifacts
(MA) normally give bidirectional intensity increases in the lower
frequency range of the velocity spectrum, but they may resemble a MES.
On the other hand, small solid particles that result in only a minor
increase in intensity may erroneously be classified as random
fluctuations. It might be that these low-intensity signals are
forerunners of larger solid emboli that could harm brain
function.3 4 5
Most algorithms used for automatic detection of MES are based on a fast
Fourier transform (FFT) of the Doppler signal. Criteria used in
these algorithms are often based on duration of the signal, intensity
increase, and frequency distribution within the spectrum.
Unfortunately, these algorithms are often not powerful enough to
discriminate between MES and MA, which restricts the application of
automatic emboli detection in a clinical
setting.6 7 Many positive counts are caused by
false interpretation of artifacts, whereas many small emboli, which do
not reach the critical detection intensity threshold set by the
automatic device, are not detected at all.
Therefore, we sought an alternative approach. First, time-domain data
of the Doppler signal were analyzed instead of the FFT used
in most automatic emboli detection devices. Second, we did not choose
to detect intensity or duration of the time-domain data but took
advantage of the harmonic character of the MES. To classify the
harmonic character, we used an algorithm developed by Sugihara and
May.8 They developed their so-called nonlinear
forecasting (NLF) as a way to detect structure in short time
series.8 NLF is an algorithm similar to the FFT,
but it is not developed to reveal a spectral analysis but it is
used to quantify the presence of periodicity within a time series. The
basic idea is that if periodicity occurs in a signal, it should be easy
to forecast the dynamics of that particular signal if one has a sample
of that signal in which the periodicity occurs. On the contrary, if a
signal lacks any periodicity, the dynamics will be difficult to
forecast. For instance, a pure sine wave is perfectly predictable,
whereas white noise is not predictable at all. Most biological signals
fall somewhat between these two extremes. On visual inspection, MES
have a much more prominent periodicity than the normal fluctuations of
the Doppler signal (Figure 1
). MA lack periodicity on visual
inspection (Figure 2), and, on the basis
of these observations, we thought it should be possible to distinguish
MES and MA in Doppler time series. The purpose of this preliminary
report is to assess whether NLF can be used to distinguish MES from
normal Doppler signals or MA.
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Figure 2. Movement artifact observed during artificial probe
movement during insonation of middle cerebral artery. Movement artifact
is characterized by sudden increase in intensity compared with
background Doppler signal. Signal lacks prominent periodicity (on
vertical axis an arbitrary intensity scale of the Doppler signal,
on horizontal axis an arbitrary time scale).
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Materials and Methods
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Twenty single MES and 100 MA were selected by 2 human experts
(R.G.A.A. and W.H.M.) during carotid surgery. It was uncertain whether
the MES were reflections from gaseous or solid emboli. MES fulfilled
the criteria published by the Consensus Committee of the Ninth
International Cerebral Hemodynamic
Symposium.9 MES were identified on the basis of
their short duration (<300 ms), their typical musical sound, a
unidirectional appearance in the Doppler velocity spectrum, a
random occurrence in the cardiac cycle, and an amplitude exceeding the
background signal by at least 3 dB. The movement artifacts were
recorded during artificial probe movements. They were characterized
by the absence of the high frequency sound, a duration of >300 ms, and
a bidirectional appearance in the Doppler velocity spectrum.
TCD monitoring was performed by means of a PIONEER with a 2-MHz
monitoring transducer. The MCA was insonated just lateral to the
terminal internal carotid artery. The pulse repetition frequency was
adequately chosen to record the maximum blood flow velocity in the
MCA. The time-domain data of the Doppler signal were sampled at the
highest frequency rate and stored in an ASCII file for off-line
analysis.
Software for NLF calculations was developed at the department of
Clinical Neurology and Neurophysiology of the Leyenburg Hospital and
written in Borland Pascal 7.0 for Windows by one of the authors
(C.J.S.). Figures display on their axis intensities and time scales in
arbitrary units. Absolute values are irrelevant for NLF calculations;
the method quantifies changes over time independent of the absolute
value. Statistical analysis was done by the statistical package
Systat (version 5.1 for Windows). Student independent t
tests were applied for discriminating between-group effects.
P values were set at 0.05 for statistical significance.
Nonlinear Forecasting
Nonlinear forecasting explores the functional relation between
future and previous data in a time series. After visual inspection of
the Doppler signal, a time window was placed across the MES or MA
(Figure 3). NLF was performed on the time
series within the window. The time window always included a part of the
MES in which the periodicity was most prominent on visual inspection.
Each MES and MA was compared with 10 randomly chosen normal TCD signals
of similar length (Figure 3).
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Figure 3. Two time windows (A and B) are placed across MES
in channels 10 and 12 during off-line analysis. Tables on right
list prediction values of all signals within time windows A and B. MES
in channels 10 and 12 have high predictability (0.91) compared with
signals in other channels because of prominent periodicity. Note that
prediction values of both MES are similar, although their intensities
are quite different.
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The time series within the window was split in 2 equal parts: the first
part of the time series (t1) and the following or
second part (t2). The goal was to analyze
t1 to predict the time series
t2. Once the time series t2
is predicted, one can compare the actual t2 with
the predicted t2 and calculate the difference
between these two time series. If both time series completely match,
the prediction is 100%, but if both time series completely mismatched,
the signal is in fact unpredictable. For periodic signals the
prediction (p)1.0, which means that the signal is
100% predictable. For uncorrelated white noise, the prediction will be
0; if the prediction is exactly the opposite of the original
curve (a hypothetical situation) then P=-1.0. The
prediction therefore varies between +1 and -1.
To perform this "prediction" calculus, one has to know the dynamics
of t1. To study the dynamics of a signal,
mathematicians have developed a 2-step procedure. The first step is
called "reconstruction of trajectories in phase space"; the second
step involves characterization of the reconstructed dynamics. The
reconstruction of trajectories in phase space is a mathematical
procedure by which the time domain data are reconstructed in at least a
2-dimensional figure (the phase space) to study the coherence of all
data points over time of the signal in a visually instructive manner,
which in addition facilitates the calculation of the dynamics of such a
signal. The reconstruction is done by a procedure of "time-delay
embedding," a procedure explained in the Appendix. Calculus behind
the NLF is also explained.
To make the reader familiar with trajectories in phase space, we show
in Figure 4 an example of trajectories of
a sine wave with some additive noise in phase space. Notice that the
trajectories form a closed loop and the noise component results in a
relative broad banding of the trajectories. Figure 5 shows the phase space of the MES signal
given in Figure 1. It shows a cluster of trajectories in the
center of the phase space with a number of trajectories at the
periphery of the phase space. The center trajectories relate to the
background TCD signal, whereas the trajectories at the periphery relate
to the MES. The trajectories at the periphery appear to have less
complex dynamics than the trajectories in the center of the phase
space, which suggests that MES have a more prominent periodicity than
background TCD.
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Figure 4. Phase space of sine wave with some additive noise.
x-axis shows value of signal at a certain moment X(t);
y-axis shows value of signal at fixed interval ahead in
time [X(t+ t)]. Trajectories form closed circles and because of
additive noise trajectories show relatively broad banding.
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Figure 5. Phase space of MES and background Doppler
signal of time series shown in Figure 1. Trajectories in center of
phase are related to background Doppler signal; trajectories at
periphery are related to MES.
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Results
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Figure 6 shows the
predictability for MES, MA, and background Doppler signals. MES
show the highest prediction values, which range from 0.97 to 0.67. The
prediction of the MA and background Doppler signals are similar and
ranged between 0.45 and -0.80 for MA and from 0.44 to -0.69 for
Doppler signals. Statistical analysis reveals that MES
(n=20) are significantly better predictable than the background
Doppler signals (n=200) (prediction [MES]=0.829±0.084 versus
prediction [Doppler signals]=-0.060±0.228;
P<0.0001). Moreover, MES are also significantly better
predictable than the MA (n=100) (prediction [MES]=0.829±0.084 versus
prediction [MA]=-0.034±0.223; P<0.0001). No significant
difference in prediction is found between background Doppler
signals and MA.
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Figure 6. Prediction data of movement artifacts (n=100),
background Doppler signals (n=200), and
microembolic signals (n=20).
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Discussion
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This study shows that MES can be separated from both the
background TCD signal and MA by NLF. This opens the possibility to
design algorithms that are based on the NLF principles for automatic
embolus detection in a clinical setting. Emboli detection is often a
time-consuming and mentally strenuous procedure. The large number of
patients that are candidates for this examination will rapidly grow,
and automatic software devices are required to replace the human
expert. However, Van Zuilen and coworkers10
showed that current automatic software devices for embolus detection
are not yet capable of being used as a "stand-alone system." The
interobserver agreement of human experts is still much higher than the
agreement that can be reached by the use of automatic software devices.
Early automatic detection devices relied on a sudden increase in
intensity of the returned signal. More sophisticated devices recognize
the bell-shaped increase in the relative power occurring with an
embolus.11 Some include a so-called artifact
rejection algorithm, which looks for the occurrence of a bidirectional
power increase. The most promising approach seems to be embolus
detection by neural networks, but one still must realize that a neural
network can only classify embolic events with a high accuracy when the
training of the network allows such an
identification.12 Therefore it is of the utmost
importance that the input of the neural networks is based on
information that characterizes the embolic events. We think that NLF as
used in this study will be very useful as an input variable for
future neural networks designed for emboli detection.
The reason that nonlinear analysis is so powerful in detection
of emboli lies in the fact that it quantifies an essential character of
emboli: the prominent periodicity of the MES. This periodicity of MES
is related to the fact that the Doppler signal contains information
of a relatively constant velocity: the velocity at which the embolus
travels. However, the velocity of the embolus is not completely stable.
During the travel through the sample volume it may accelerate,
decelerate, or change its direction. All these possibilities result in
a frequency modulation.13 The MES shown in Figure 1 shows such a characteristic frequency modulation. Initially the
periodicity has a low intensity and a relatively high frequency when
the embolus enters the sample volume. When the embolus is in the middle
of the sample volume the intensity reaches its maximum value, and when
the embolus leaves the sample volume both the frequency and intensity
of the signal decreases. Especially air emboli appear to produce this
frequency modulation compared with the relative stable frequency
modulations observed in particulate emboli.13
Nevertheless, although the frequency of the MES modulates when the
embolus travels through the sample volume, the periodicity is strong
enough to result in a marked NLF of the actual signal compared with the
background Doppler signal. Therefore we strongly support the idea
that the prominent periodicity of the embolic signal should be included
in the definition of embolic events.
Another important remark is that this technique has a potential to
detect low intensity emboli. Although we did not analyze the
relation between signal intensity and prediction in this particular
study, we noticed, for example, in Figure 3 that both MES (A and B) did
have the same prediction values although both MES differ in their
intensities by visual inspection. In future studies we will focus on
this important relation between intensity and prediction of MES in a
more systematic way.
One remark must be made about NLF and MA. MA can have a typical low
frequency sound that theoretically could lead to some degree of
predictability beyond the level of the background Doppler signal.
The reason that NLF did not reveal an increased predictability in MA is
because these Doppler signals were examined on a relatively short
time scale. During these short observations the MES show, in contrast
to MA, prominent periodicity. Thus MA may exhibit a certain periodicity
albeit on a much longer time scale than applied in this study.
As mentioned by Markus and Harrison,14 it is
vital that a consensus on the optimal definition of emboli is developed
and validated in subsequent studies. We think that neither the duration
nor the maximum intensity itself are the essentials of MES. It is the
periodicity that describes the core characteristics of the MES. A
number of nonlinear algorithms are available for signal
analysis. Originally, these algorithms were designed to detect
the underlying dynamics of the systems that generate the signal. Most
of them are very complex and time-consuming calculations. For detailed
information of these algorithms, the reader is referred to Kaplan and
Glass,15 who clearly explain the background of
nonlinear analysis. The reason to choose the NLF is the fact
that this method is a relatively simple and fast procedure (capable for
both off-line and on-line analysis) with a strong capacity to
distinguish signals with different underlying dynamics. If we were
unaware of the system that generates the signal (eg, the interaction of
the embolus and the ultrasound beam), we should conclude from this
analysis that the underlying system of the MES has a high
predictability, which means that the degrees of freedom of such a
system probably will have only 1 variable. Obviously, the
relatively constant frequency of the Doppler signal, being a result
of the actual embolus velocity, is the most important variable that
leads to a prominent periodicity.
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Appendix 1
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Time Delay Embedding
The recorded TCD is a discrete time series Vt,
t=1,2,3,...N. From this discrete time series, vectors
Xt in a m-dimensional embedding dimension were obtained
with the time-delay procedure16 :
 | (1) |
where L is the time delay and m is the embedding dimension. We
used a combination of the procedure of Rosenstein to choose L and the
procedure of Kennel to choose m.17 18 Briefly, this method
works as follows: We started with an embedding dimension of 1 and a lag
of 1. We then calculated the expansion ("unfolding") of the
attractor from the main diagonal in state space. Subsequently, the lag
was increased in steps of 1 until the expansion of the attractor no
longer increased. The percentage of false nearest neighbors was then
calculated. False nearest neighbors are vectors that lie close together
in the reconstructed state space because of insufficient unfolding of
the attractor and not because of dynamic correlations. Following Kennel
et al (1992), 2 vectors Xi and Xj were
considered false nearest neighbors when
 | (2) |
where the vertical bars denote the absolute value and
Rm(i,j) is the euclidian distance between the two vectors
Xi and Xj.
Next, the embedding dimension m was increased with 1, and the whole
procedure (determining the optimum lag and then the percentage false
nearest neighbors) was repeated.
This procedure was continued until either (1) The percentage of
false nearest neighbors dropped under 0.05 or (2) The percentage false
nearest neighbors no longer decreased with further increments of the
embedding dimension. In the last case, we used the value of m, which
gives the lowest percentage of false nearest neighbors.
Nonlinear Forecasting
We used the algorithm described by Sugihara and May for
nonlinear forecasting. Given a starting point in the time series
Vt, we would like to predict Vt+1,
Vt+2, Vt+3, and so on, a number of steps ahead,
and compare the predictions, which we will designate Pt+n,
with the actual time series. First we used the time-delay procedure
described above to obtain m-dimensional vectors Xi from the
time series Vt. However, for ease of reference, the time
index of the vector Xi will now correspond with the last
coordinate (i=t+(m-1)xL). Now for each vector Xi we
located the m+1 nearest neighbors in the m-dimensional state space. We
will designate the k nearest neighbor vectors of Xi as
NNk,j. The k index indicates the number (from 1 to m+1) of
the nearest neighbor (the k,j index its time index in the original time
series). We excluded nearest neighbors with time indexes k,j when
|i-k.j|<3x
( is the time after which the autocorrelation
function drops to 1/e of its original value). This procedure is called
"within-sample" prediction. Sugihara and May used
"out-of-sample" prediction. For a time series of length N, out of
sample prediction requires i>0.5xN and j<0.5xN+constant. There are
no fundamental differences between both procedures, only within-sample
prediction may be more suitable for short data sets. Now the predicted
value for n steps ahead prediction was given by
 | (3) |
where wk is the weight assigned to the
kth nearest neighbor according to
 | (4) |
Predictions for n ranging from 1 to 20 were made for a
number of 100 different Vt evenly distributed along the
time series. Next, the correlation coefficients r between
the actual time series Vt+n and the predicted values
Pt+n were calculated and plotted as a function of n.
Received December 5, 1997;
revision received March 27, 1998;
accepted April 24, 1998.
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Abstract
Introduction
