METHOD FOR DETECTING ELEMENTS OF INTEREST IN ELECTROPHYSIOLOGICAL SIGNALS AND DETECTOR

Abstract

The invention relates to a method for automatically detecting elements of interest in electrophysiological signals, and to a detector for implementing such a method. The method according to the invention comprises steps in which: electrophysiological signals are delivered; a whitened time-frequency representation of said electrophysiological signals is produced; a threshold is set; this threshold is applied to the whitened time-frequency representation; and, in the whitened time-frequency representation, local maxima that are higher than or equal to the applied threshold are detected.

Claims

1. A method for automatically detecting elements of interest in electrophysiological signals comprising: delivering electrophysiological signals; producing a whitened time-frequency representation of the electrophysiological signals; setting a threshold; applying the threshold to the whitened time-frequency representation; detecting, in the whitened time-frequency representation, local maxima that are higher than or equal to the applied threshold, wherein the producing of the whitened time-frequency representation comprises applying a continuous wavelet transform and calculating a square modulus of the wavelet coefficients after having standardized the real and imaginary parts thereof.

2. The method according to claim 1, wherein the electrophysiological signals are intracranial signals.

3. The method according to claim 2, wherein the intracranial signals are stereo-electroencephalographic signals.

4. The method according to claim 1, wherein the elements of interest are low and high frequency oscillations and points.

5. The method according to claim 4, wherein the continuous wavelet transform is calculated from the following formula: $T_f?\left(b,?\right)=\frac{1}{\sqrt{?}}.Math.{?}_{-?}^{+?}.Math.f?\left(t\right).Math.?.Math.\stackrel{\_}{\left(\frac{t-b}{?}\right)}.Math.\mathrm{dt}$ wherein f is the electrophysiological signal, T is the continuous wavelet transform, ? is the wavelet, ? the dilation factor, b the translation factor and t is the time.

6. The method according to claim 4, wherein the wavelet chosen is a Gaussian derivative wavelet (DoG), analytical and its expression in the frequency domain is as follows:
?(f)=f.sup.nexp(?f.sup.2) for f?0 and f?0 and =0 for f<0 wherein f is the frequency, n is the order of the derivative and ? is the Fourier transform of the wavelet.

7. The method according to claim 4, wherein the normalization factor is calculated for each frequency by adjusting a Gaussian noise model over the central portion of the bar chart of the real coefficients.

8. The method according to claim 1, wherein the threshold is defined by the following formula:
thr?x|lFDR(x)=H.sub.0(x)/H.sub.G(x)<Q wherein thr is the threshold, Q is the acceptable error rate, H.sub.0 is the null hypothesis and H.sub.G is the total distribution.

9. The method according to claim 1, further comprising determining the time and frequency range of the local maxima.

10. The method according to claim 1, further comprising classifying the elements of interest as transient or oscillation.

11. The method according to claim 1, further comprising viewing elements of interest.

12. A detector for the automatic detection of elements of interest in electrophysiological signals, wherein the detector comprises a software in the form of an extension module, wherein the software, when executed, implements a method comprising: delivering electrophysiological signals are delivered; producing a whitened time-frequency representation of said the electrophysiological signals is produced; setting a threshold is set; applying this the threshold is applied to the whitened time-frequency representation; detecting, in the whitened time-frequency representation, local maxima that are higher than or equal to the applied threshold are detected, and according to said method, for wherein the production producing of the whitened time-frequency representation, representation comprises applying a continuous wavelet transform is applied and the calculating a square modulus of the wavelet coefficients is calculated after having standardized the real and imaginary parts thereof.

13. The detector according to claim 12, comprising a classifier.

14. A method of automatic detection of elements of interest in electrophysiological signals of an epileptic patient, comprising applying a detector according to claim 12 to detect the elements of interest in the electrophysiological signals of the epileptic patient.

15. The method according to claim 2, wherein the elements of interest are low and high frequency oscillations and points.

16. The method according to claim 15, wherein the continuous wavelet transform is calculated from the following formula: $T_f?\left(b,?\right)=\frac{1}{\sqrt{?}}.Math.{?}_{-?}^{+?}.Math.f?\left(t\right).Math.?.Math.\stackrel{\_}{\left(\frac{t-b}{?}\right)}.Math.\mathrm{dt}$ wherein f is the electrophysiological signal, T is the continuous wavelet transform, ? is the wavelet, ? the dilation factor, b the translation factor and t is the time.

17. The method according to claim 3, wherein the elements of interest are low and high frequency oscillations and points.

18. The method according to claim 17, wherein the continuous wavelet transform is calculated from the following formula: $T_f?\left(b,?\right)=\frac{1}{\sqrt{?}}.Math.{?}_{-?}^{+?}.Math.f?\left(t\right).Math.?.Math.\stackrel{\_}{\left(\frac{t-b}{?}\right)}.Math.\mathrm{dt}$ wherein f is the electrophysiological signal, T is the continuous wavelet transform, ? is the wavelet, ? the dilation factor, b the translation factor and t is the time.

19. The method according to claim 5, wherein the wavelet chosen is a Gaussian derivative wavelet (DoG), analytical and its expression in the frequency domain is as follows:
?(f)=f.sup.nexp(?f.sup.2) for f?0 and f?0 and =0 for f<0 wherein f is the frequency, n is the order of the derivative and ? is the Fourier transform of the wavelet.

20. The method according to claim 5, wherein the normalization factor is calculated for each frequency by adjusting a Gaussian noise model over the central portion of the bar chart of the real coefficients.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0019] The invention shall be better understood when reading the following non-limiting description, written with regard to the accompanying drawings, wherein:

[0020] FIGS. 1A to 1C are bar charts that show the distributions of the real part of the wavelet coefficients at different frequencies, without standardization or with a standardization and in particular with a standardization according to the method according to the invention;

[0021] FIGS. 2A and 2B each show an example of high-frequency oscillations recorded in an epileptic patient by carrying out a whitened time-frequency representation according to the method according to the invention;

[0022] FIG. 3 shows the application of the lFDR for the implementing of the method according to the invention;

[0023] FIGS. 4A and 4B show two examples of detection according to the method according to the invention in the time domain with the signal and the whitened reconstruction thereof (first and second line, respectively) as well as in the whitened time-frequency domain (third line);

[0024] FIGS. 5A and 5B show the detections in the space of parameters and the distribution of the frequencies of the oscillations according to the invention; and

[0025] FIGS. 6A and 6B show an example implementation of the detector and of the simultaneous viewing of the signal in the time domain with the original signal and the whitened reconstruction thereof as well as in the whitened time-frequency domain, in the daily clinical use according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0026] The method of detection according to the invention is a method for representing and automatically detecting elements of interest in electrophysiological signals. These signals are biological/physical plots, regardless of their origin.

[0027] In a first step of the method according to the invention, electrophysiological signals are delivered. These signals are intracranial signals and, in particular, are stereo-electroencephalographic signals (SEEG) noted as f. These are complex signals comprising low and high frequency oscillations and points or transients. These oscillations, points and transients are the elements/events of interest which are detected according to the method according to the invention.

[0028] In light of this detection, a whitened time-frequency representation of said electrophysiological signals is produced. In other words, the signals are rectified while still retaining a good signal-to-noise ratio for the elements of interest.

[0029] The whitening is carried out in the time-frequency domain then applied to the time domain for the viewing.

[0030] For the carrying out of the whitened time-frequency representation, a continuous wavelet transform is applied (CWT) noted as T to said signals. This T transform is calculated using the following formula:

[00002]$T_f?\left(b,?\right)=\frac{1}{\sqrt{?}}.Math.{?}_{-?}^{+?}.Math.f?\left(t\right).Math.?.Math.\stackrel{\_}{\left(\frac{t-b}{?}\right)}.Math.\mathrm{dt}$

[0031] wherein ? is the wavelet, ? the dilation factor, b the translation factor and t is the time. The wavelet chosen is a Gaussian derivative wavelet (DoG), analytical. Its analytical properties make it possible to reconstruct the signal, contrary to Morlet wavelets, and as such obtain the whitened signal in the time domain such as will be specified in the rest of this description according to the invention. Its expression in the frequency domain is as follows:

?(f)=f.sup.nexp(?f.sup.2) for f?0 and f?0 and =0 for f<0

[0032] Once the wavelet coefficients are obtained, they are standardized in order to make it possible to bring out the elements of interest better and, in particular, the high-frequency oscillations. This corresponds to a step according to the invention according to which the time-frequency representation of the signals is standardized, in order to obtain a whitened/standardized representation.

[0033] The standardization chosen is a standardization referred to as Z.sub.HO or H.sub.0 Z-score. This standardization allows for an optimum representation of the high-frequency oscillations, without reducing the signal-to-noise ratios or losing the content of the low frequencies. Contrary to conventional methods, the power of the background activity at each frequency is estimated directly over the data of interest and does not require the difficult defining of a baseline. Concretely, a Gaussian noise model is adjusted over the central portion of the bar chart of the real coefficients at each frequency. Then the coefficients are transformed into z by the following formula:

[00003]$T_{f,z_{n_o}}^i?\left[n,m\right]=\frac{T_f^i?\left[n,m\right]-??\left[m\right]}{??\left[m\right]}.$

where n and m are respectively the time and frequency indexes,
T.sub.f.sup.i,Z.sub.H.sub.O and T.sub.f.sup.i[n,m] are the coefficient i (real or imaginary) for the indexes n and m after and before standardization, ?[m] and ?[m] correspond to the means and the standard deviation of the estimated Gaussian at the frequency of index m. The standardization transforms the background activity into a white noise in order to balance the power of the activities through the frequencies. The spectrum is therefore whitened. In addition, it makes possible the optimum representation of the whitened signal both in the time-frequency domain and in the time domain. This standardization places on the same scale all of the distributions of the real and imaginary coefficients by frequency.

[0034] FIGS. 1A to 1C show bar charts that show, for different frequencies, the distributions of the real part of the wavelet coefficients at different scales, without standardization or with a standardization and, in particular, with the standardization Z.sub.H0. In FIG. 1A, the distributions of the real part of the wavelet coefficients are not standardized. Note a large difference in width between the distributions. In FIG. 1B, the distributions are standardized with the mean and the standard deviation?[?] and ?[?]estimated over all of the distributions. A difference between the widths of the distributions is still noted. In FIG. 1C, the distributions are standardized by means of the aforementioned standardization Z.sub.H0. This time, all of the distributions have the same range through the frequencies.

[0035] In order to obtain the whitened time-frequency representation, according to the invention, the square modulus of the wavelet coefficients is calculated after having standardized the real and imaginary parts thereof.

[0036] FIGS. 2A and 2B each show an example of high-frequency oscillations recorded in an epileptic patient. For each example, the top line shows a signal comprising elements of interest in the time domain, the intermediate line shows the associated raw time-frequency representation, and the bottom line shows the whitened time-frequency representation by means of the standardization referred to as Z.sub.H0. In FIG. 2A, the oscillations are FR oscillations. In FIG. 2B, the oscillations are HG oscillations. On the top line of FIG. 2A, the insert corresponds to a zoom on the high-frequency FR oscillations. It appears that the high-frequency oscillations are difficult to identify on the lines at the top and the intermediate lines. However, they appear clearly on the bottom line, thanks to the standardization Z.sub.H0.

[0037] As the distribution of the real part of the coefficients is identical through the frequencies, it is possible to study them at the same time and to apply a single threshold based on the local false discovery rate (lFDR Efron 2005). According to another step according to the invention, a threshold is therefore set.

[0038] The lFDR is an empirical Bayes approach that assumes that the noise H.sub.0 composes most of the center of the distribution H.sub.G and that the rest of the distribution H.sub.1 is produced by the signal of interest. The threshold is defined in the following formula:

thr?x|lFDR(x)=H.sub.0(x)/H.sub.G(x)<Q

[0039] wherein thr is the threshold, Q is the acceptable error rate, H.sub.0 is the null hypothesis and H.sub.G is the total distribution.

[0040] In practice, two thresholds are obtained. This entails a first threshold thr.sup.? for the negative portion and a second threshold thr.sup.+ for the positive portion. The threshold of the lFDR is:

[00004]${\mathrm{thr}}_{\mathrm{lFDR}}=\frac{{\mathrm{thr}}^{+}-{\mathrm{thr}}^{-}}{2}$

[0041] By studying the bar charts of the real coefficients of the human background activity (Real Human Background, BKG), it is noted that these distributions are described by a Gaussian. The central portion of the bar chart of the T.sub.f.sup.i,Z.sub.H.sub.O taken as a whole can then be modeled by a reduced centered Gaussian and the error rate Q is left to the appreciation of the user.

[0042] An illustration of the application of the lFDR is shown in FIG. 3. In this figure, the total distribution HG, the null hypothesis H.sub.0 as well as the lFDR are represented as dashed, solid black and dotted strokes, respectively. The threshold on the error rate Q is represented by a solid horizontal line. The thresholds thr+ and thr? are obtained at the intersection of the lFDR and of Q.

[0043] According to another step of the method according to the invention, the threshold is applied to the standardized time-frequency representation. To this effect, the threshold obtained thanks to the lFDR is squared:

thr.sub.Z.sub.HO=thr.sub.I.sup.2.sub.FDR

[0044] It is then possible to detect, in the standardized time-frequency representation, the local maxima which are higher or equal to the applied threshold, and which correspond to elements of interest that come out of the noise. Thanks to the whitening of the data and to the study of the events in time-frequency, the points and the oscillations are detected, whether or not they occurred at the same time.

[0045] In practice, this detection consists in selecting all of the local maxima which are higher than the threshold set by the lFDR. The local maxima are relative to events located both in time and in frequency as are the oscillations sought. It is then possible to have the time of occurrence as well as the oscillation frequency. The epileptic points are also located in time-frequency, but are more spread out in frequency and less spread out in time than the oscillations and their local maximum is lower than the frequency band of the high-frequency oscillations. Inversely, artifacts of the Dirac type do not produce local maxima and therefore are not detected. In reality, an artifact mixed with noise or a very brief transient with an oscillation can sometimes create erroneous local maxima at high frequency. However, as the detections are made in the theoretical framework of wavelets, the width of the blob relative to the local maximum can be compared with the theoretical width of the blob which would have been generated by a Dirac peak. This makes it possible to differentiate a brief element (i.e. an epileptic point or a brief transient) in relation to an oscillation regardless of its frequency. In addition, as the frequency width of the wavelets is constant on a logarithmic scale, it is also possible to distinguish the oscillations that still have a limited frequency width regardless of their frequency, transients that have a frequency width that is more extended.

[0046] Two examples of detection are shown in FIGS. 4A and 4B. In this figure, the crosses correspond to the local maxima higher than the threshold, the white circles to the measured width at mid-height (Full Width at Half Maximum, FWHM), the asterisks to the theoretical width at mid-height, the large circle to an epileptic point (spike) and the triangle to a high-frequency oscillation. It appears that the theoretical time width is very close to the measured time width for one point.

[0047] The method according to the invention therefore makes it possible to view and to identify several types of physiological activities such as high-frequency oscillations, the epileptic points and the oscillations of lower frequency. The parameters used to classify the events do not depend on frequencies. Thanks to this method, the identification of the cerebral zones producing high-frequency oscillations is facilitated, as it is automatic.

[0048] Note that the combined steps of standardization and of the lFDR make it possible to differentiate the background activity of the elements of interest and ensure their authenticity. The combination of these two steps also makes it possible to detect the high-frequency oscillations that would have been rejected because they are not visible in the original signal. In addition, each oscillation will be labeled by a frequency. It is as such possible to determine the physiological and pathological frequency bands for the patients which was not possible with the other detectors. Note that the method does not presuppose a cutting into frequency bands.

[0049] In FIG. 5A, all of the detections are represented by a point of coordinates, their frequency range and their time ratio. A threshold on the limit of duration, equivalent to the number of oscillations, and on the spectral range makes it possible to separate the oscillations of the epileptic points and non-oscillating events, i.e. comprising less than 3 or 4 oscillations. The oscillations, the epileptic points and the non-oscillating events are illustrated by points. The detections selected as points and as oscillations are respectively represented by circles and triangles.

[0050] The bar charts of the frequencies of the points and of the oscillations detected are shown in FIG. 5B. A non-parametric adjustment is carried out in a dashed line for the points and in a solid black line for the oscillations. Note that the zone studied produces substantially more high-frequency oscillations than low-frequency oscillations. Thanks to this representation, it can be realized that it would be more interesting to place the cut-off of the oscillations R/FR at 170 Hz rather than to take as a mark the conventionally defined bands R and FR.

[0051] The detector according to the invention can be implemented in a software such as the AnyWavem software in the form of an extension module (plugin) for regular clinical use. This software platform is described for example in the document entitles AnyWave: a cross-platform and modular software for visualizing and processing electrophysiological signals, Colombet et al., Journal Neurosciences Methods, March 2015, 242, 118-26. The plugin is comprised of two elements, an interface (FIG. 6A) that makes it possible to select several channels of the various electrodes and to run the detector as well as to show the results in the form of a diagram of the detection rates of the epileptic points and of the oscillations by frequency bands chosen by the user, and a second interface (FIG. 6B) that makes it possible to view the signal of a channel synchronously in the time domain and in the standardized time-frequency domain and to display the signal in the detection time obtained previously: simultaneous viewing of the signal in the time domain with the original signal and the whitened reconstruction thereof as well as in the whitened time-frequency domain. Each plugin communicates with the software in order to acquire the signals and their information. The software comprising the plugin is intended to be implemented by a workstation, possibly in liaison with a server, in a conventional IT environment of the Windows? type. The workstation comprises at least one memory wherein the software will be recorded, a processor for the execution thereof, and a screen for displaying the results. The detection is automatic. The implementation of the method does not require the presence of a qualified person from a medical standpoint.