- Email: [email protected]
Chapter 67 Wavelet analysis preceding seizures
Advances in Clinical Neurophy ...ioiogy (Supplements to Clinical Neurophysiology Vol. 54) Editors; R.C. Reisin, M.R. Nuwer, M. Hallett, C. Medina 2002 Elsevier Science B.Y. All rights reserved.
457
Chapter 67
Wavelet analysis preceding seizures Silvia Kochen", Brenda Giagante", Carlos D'Atellis'<", Ricardo Sirne'" and Javier Roitman-" "Epilepsy Center, Hospital 'R. Mejia', Faculty ofMedicine, University ofBuenos Aires, 1428 Buenos Aires (Argentina) "Faculty ofEngineering and Mathematics, University ofBuenos Aires, Buenos Aires (Argentina) 'Faculty ofBio-Engineering, University ofFavaloro (Argentina) 'University National Technological, Buenos Aires (Argentina)
Introduction
Interest in quantification methods and automatic analysis of EEGs has recently increased considerably. These methods offer certain advantages as compared to the more traditional approaches: an objective analysis of the signal, avoiding subjective criteria; the reduction oflongterm EEGs to the significant time intervals during which the epileptic activity is localized; and the detection and classification of epileptic events within these time intervals. Different approaches are used for the performance of signal analysis, including the following methods: parametric (Arakawa et al. 1986); mimetic (Guedes De Oliveira et al. 1983); syntactic (Walters et al. 1989); neural networks (Eberhart et al. 1989); expert systems (Glover et al. 1990); phase-space topography (Iasemidis et al. 1990); mimetic and expert systems (Dingle et al. 1993). Methods based on wavelet transform (Senhadji et al. 1993), Gabor transform (Blanco et al. 1996),
* Correspondence to: Dr. S. Kochen, Epilepsy Center, Hospital 'R. Mejia', Faculty of Medicine, University ofBuenos Aires, 1428 Buenos Aires, Argentina. Fax: 54 11 4863 3086. E-mail: [email protected]
multiresolution entropy (D' Attellis et al. 1997a) , non-linear dynamics (Blanco et al. 1997) and multiresolution analysis (D' Attellis et al. 1997b) have also been used. In spite of these different approaches, signal analysis has not yet been completely resolved. Some ofthe methods are based on the frequency components of the EEG signal. The tools used in these cases have been provided by a specific field within the area of mathematics named as harmonic analysis. The foundations are based on Fourier transform and, more recently, wavelet transform has allowed us to achieve major progress in this field. A glimpse into the history of harmonic analysis will be useful as an introduction to the use of wavelets in signal processing and, specifically, in EEG analysis. The background may be traced back to its origin, the Fourier transform. Around 1820, Joseph Fourier - Napoleon's governor in Egypt - developed the theory currently used in signal analysis, basically, building a bridge between two worlds: the world of time, and the world of frequencies. On this basis, given a signal, i.e. a record of a variable in time - the electrical activity vs. time in the EEG - it is possible to study the frequential components of that signal. This has only been possible thanks to the Fourier transform. Despite its simplie-
458
ity in Fourier analysis it is possible to detect the frequencies that compose the signal. However, there are limitations; as yet it is not possible to determine the time intervals nor the order in which these frequencies appear. Summing up, there is a perfect determination of frequencies, but there is no time localization. Clearly, we can see the different frequencies involved in the signal, but an important problem remains unsolved: the detection in time. This issue implies two aspects: not only the frequency determination, but also the time localization. That is the problem in the case of detection of the characteristic epileptic events in EEGs. In other words, we are facing a problem of localization in the time-frequency plane. During the long evolution from Fourier to the present time, several attempts to solve the problem in the time-frequency domain have been proposed. The first of them was the Gabor transform, and other approaches were also introduced after the mentioned paper was published in 1946, generically known as short-time Fourier transforms. Trying to add a time localization to the properties of the Fourier transform, all of them add a sliding window to the Fourier formula. These transforms represent an improvement to solve the time-frequency localization: a window in the time-frequency relation is defined. Unfortunately, short-time Fourier analysis has another drawback: there is a time-frequency window, but its shape is fixed. In this paper we address a new method based on wavelet transform, which was introduced in 1985 and has led to a dramatic change in the field of signal analysis, specifically in biomedical signals.
Wavelet transform method Intuitively,we would like an adaptive window, long in time for the detection of low frequencies, short in time to detect and simultaneously localize high frequencies. This is achieved by using wavelets. Wavelet transforms are based on a basic short oscillating function known as wavelet. From this basic wavelet, using translations and dilations, it is possible to build a frame in which the frequential characteristics 0 f the signal, and, simultaneously,
its localization in time, are determined. Thus, wavelet transform is a powerful tool for localizing events in time and in frequency. In mathematical terms, wavelet transform is based on a basic wavelet psi(t) of a signal fit) is given by:
WTlj/f(a, b) =
~
J
vi a I _~
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,,1l t: b )dt 't"
When the dilations are dyadic, i.e. the changes in the scale of the basic wavelet are a power of two, wavelet analysis becomes multiresolution analysis (i.e. a = 2)). Fig. 1 shows the deconstruction of the signal in each band of frequency. The different levels of the multiresolution correspond to bands of frequencies. The corresponding algorithm is implemented by a bank of digital filters qhit decimation (Fig. 2). Coming back to our specific problem, the EEG signal, the bank of digital filters allow us to separate epileptiform and background activities, analysing the behavior of the energy of the signal in each level of the multiresolution, eight levels corresponding to a sampling rate of 256 Hz. The spikes and waves detection is made using levels 3-7, comparing the signal energy with background energy. The seizure detection is made using the euclidean distance between the eight dimensional vectors Ps and Ph, where:
P = (El, £2, ... , E8)/Et, Et = £1 + E2 + ... + £8 Ej = energy in the scale), and Ph and Ps = the vector P for the segment of background and nonoverlapping intervals. In our experience, visual analysis of epileptic activity was performed in patients who were candidates for epilepsy surgery, from record EEG scalp and depth electrodes. The seizure activity, its start and the spread, and also its spatial and temporal organization, were identified.
Results Some results obtained using multiresolution analysis on EEGs of epileptic patients are shown below. By using the wavelet transform method, we
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can detect and classify different types of epileptiform activities, and we are also able to analyze seizure onset and its propagation. This information is useful, especially in epileptic patients who are considered to be candidates for surgery. Within this population it is essential to achieve the topographic diagnosis ofthe epileptogenic zone through to the signal EEG in order to decide upon the strategy of surgical treatment. In our experience, the visual analysis of epileptic activity was performed from scalp and depth
electrode EEG recordings for those epileptic patients considered to be candidates for surgery, allowing us to identify the interictal activity (Fig. 3A), seizure activity, its onset and propagation as well as its spatial and temporal organization (Fig. 3B). The multiresolution representation obtained from this wavelet transform and the digital filters derived therefrom have not only allowed us to separate epileptiform and background activities, but have also provided detection of epileptic events.
460
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A Fig. 3. Different examples of detector output of interictal EEG activity (A) and ictal EEG activity (B).
461
Conclusions The good localization of the information in the time-frequency domain, and the real-time implementation ofthe algorithm proposed offers an interesting contribution to the diagnosis of the area epileptogenic. We can detect and classify different types of epileptiform activities, and also analyze the onset and the spread of seizure. This information is useful, especially in patients who are candidates for epilepsy surgery; in this population it is essential to obtain the topographic diagnostic of the epileptogenic zone through to the signal EEG in order to decide the strategy of surgical treatment
Reference Aldroubi, A. and Unser, M. Wavelets in Medicine and Biology. CRC Press, Boca Raton, FL, 1996. Arakawa, K., Fender, D., Harashima, H., Miyakawa, H. and Saitoh, Y Separation of a non-stationary component from the EEG by a nonlinear digital filter. IEEE Trans. Biomed. Eng., 1986,33: 724-726. Blanco, S., D' Attellis, CE., Isaacson, S.L, Rosso, O. and Sirne, R.O. Time-frequency analysis of EEG series (II): comparison between methods based on Gabor and wavelet transforms. Physical ee«, 1996,54. Blanco, S., Kochen, S... Quian Quiroga, R., Riquelme, L., Rosso, O.A. and Salgado, P. Characterization of epileptic EEG time series (I): Wavelet transform and information theory. In: CE. D' Attellis and E.M. Fernandez-Berdaguer (Eds.), Wavelet Theory and Harmonic Analysis in Applied Sciences. Birkhauser, Boston, MA, 1997: 18()'-226. Casdagli, M.C Characterizing non-linearity in weather and epilepsy data. In: CD. Cutler and D.T. Kaplan (Eds.), Nun-Linear Dynamics and Time Series. American Mathematical Society, Providence, 1997: 20 [-222.
Chui, CK. An Introduction to Wavelets. Academic Press, San Diego, CA, 1992. D' Attellis, CE., Gamero, L.G., Isaacson, S.L, Sirne, R.O. and Torres, M.E. Characterization of epileptic EEG time series (II): wavelet transform and information theory. In: CE. D' Attellis and E.M. Fernandez-Berdaguer (Eds.), Wavelet Theory and Harmonic Analysis in Applied Sciences. Birkhauser, Boston, MA, 1997: 227-262. D' Attellis, C, Isaacson, S. and Sirne, R. Detection of epileptic events in electroencephalograms using wavelet analysis. Ann. Biomed. Eng., 1997,25: 286-293. Dingle, A.A., Jones, R.D., Carroll, GJ. and Fright, W.K A multistage system to detect epileptiform activity in the EEG. IEEE Trans. Biomed. Eng., 1993,40: 1260--1268. Eberhart, R.C, Dobbins, R.W. and Webber, W.R. EEG waveform analysis using Case-Net. Proc. Con]. IEEE Eng. Med. Biol. Soc., 1989,2046-2047. Glover, J.R., Varmazis, D.N. and Ktonas, P.Y Continued development ofa knowledge-based system to detect epileptogenic sharp transients in the EEG. Proc. Can! IEEE Eng. Med. Biol. Soc., 1990,1374-1375. Guedes de Oliveira, P., Queiroz, C and Lopes da Silva, EH. Spike detection based on a pattern recognition approach using a microcomputer Electroencephalogr: Clin. Neurophysiol., 1983,56: 97-103. Iasemidis, L.D., Sackellares, re., Zaveri, H.P. and Williams, WJ. Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures. Brain Topogr., 1990,2,3: 187201. Senhadji, L., Carrault, G. and Bellanger, J.J. Detection et cartographie multiechelles en EEG. In: Y. Meyer and S. Roques (Eds.), Progress in Wavelet Theory and Applications. Editiones Frontieres, Paris, 1993. Sirne, R.O., Isaacson, S.L and D' Attellis, CE. A data-reduction process for long-term EEGs. IEEE Eng. Med. Biol., 1999, 56-{i1. Strang, G. and Nguyen, T. Wavelets and Filter Banks. WellesleyCambridge Press, Wellesley, MA, 1996. Unser, M., Aldroubi, A. and Eden, M. A family ofpolinomial spline wavelet transforms. Signal Proc., 1993,30: 141-162. Walters, R., Principe, J. and Park, S. Spike detection using a syntactic pattern recognition approach. Proc. Con! IEEE Eng. Med. Biol. Soc., 1989, [810--[811.
457
Chapter 67
Wavelet analysis preceding seizures Silvia Kochen", Brenda Giagante", Carlos D'Atellis'<", Ricardo Sirne'" and Javier Roitman-" "Epilepsy Center, Hospital 'R. Mejia', Faculty ofMedicine, University ofBuenos Aires, 1428 Buenos Aires (Argentina) "Faculty ofEngineering and Mathematics, University ofBuenos Aires, Buenos Aires (Argentina) 'Faculty ofBio-Engineering, University ofFavaloro (Argentina) 'University National Technological, Buenos Aires (Argentina)
Introduction
Interest in quantification methods and automatic analysis of EEGs has recently increased considerably. These methods offer certain advantages as compared to the more traditional approaches: an objective analysis of the signal, avoiding subjective criteria; the reduction oflongterm EEGs to the significant time intervals during which the epileptic activity is localized; and the detection and classification of epileptic events within these time intervals. Different approaches are used for the performance of signal analysis, including the following methods: parametric (Arakawa et al. 1986); mimetic (Guedes De Oliveira et al. 1983); syntactic (Walters et al. 1989); neural networks (Eberhart et al. 1989); expert systems (Glover et al. 1990); phase-space topography (Iasemidis et al. 1990); mimetic and expert systems (Dingle et al. 1993). Methods based on wavelet transform (Senhadji et al. 1993), Gabor transform (Blanco et al. 1996),
* Correspondence to: Dr. S. Kochen, Epilepsy Center, Hospital 'R. Mejia', Faculty of Medicine, University ofBuenos Aires, 1428 Buenos Aires, Argentina. Fax: 54 11 4863 3086. E-mail: [email protected]
multiresolution entropy (D' Attellis et al. 1997a) , non-linear dynamics (Blanco et al. 1997) and multiresolution analysis (D' Attellis et al. 1997b) have also been used. In spite of these different approaches, signal analysis has not yet been completely resolved. Some ofthe methods are based on the frequency components of the EEG signal. The tools used in these cases have been provided by a specific field within the area of mathematics named as harmonic analysis. The foundations are based on Fourier transform and, more recently, wavelet transform has allowed us to achieve major progress in this field. A glimpse into the history of harmonic analysis will be useful as an introduction to the use of wavelets in signal processing and, specifically, in EEG analysis. The background may be traced back to its origin, the Fourier transform. Around 1820, Joseph Fourier - Napoleon's governor in Egypt - developed the theory currently used in signal analysis, basically, building a bridge between two worlds: the world of time, and the world of frequencies. On this basis, given a signal, i.e. a record of a variable in time - the electrical activity vs. time in the EEG - it is possible to study the frequential components of that signal. This has only been possible thanks to the Fourier transform. Despite its simplie-
458
ity in Fourier analysis it is possible to detect the frequencies that compose the signal. However, there are limitations; as yet it is not possible to determine the time intervals nor the order in which these frequencies appear. Summing up, there is a perfect determination of frequencies, but there is no time localization. Clearly, we can see the different frequencies involved in the signal, but an important problem remains unsolved: the detection in time. This issue implies two aspects: not only the frequency determination, but also the time localization. That is the problem in the case of detection of the characteristic epileptic events in EEGs. In other words, we are facing a problem of localization in the time-frequency plane. During the long evolution from Fourier to the present time, several attempts to solve the problem in the time-frequency domain have been proposed. The first of them was the Gabor transform, and other approaches were also introduced after the mentioned paper was published in 1946, generically known as short-time Fourier transforms. Trying to add a time localization to the properties of the Fourier transform, all of them add a sliding window to the Fourier formula. These transforms represent an improvement to solve the time-frequency localization: a window in the time-frequency relation is defined. Unfortunately, short-time Fourier analysis has another drawback: there is a time-frequency window, but its shape is fixed. In this paper we address a new method based on wavelet transform, which was introduced in 1985 and has led to a dramatic change in the field of signal analysis, specifically in biomedical signals.
Wavelet transform method Intuitively,we would like an adaptive window, long in time for the detection of low frequencies, short in time to detect and simultaneously localize high frequencies. This is achieved by using wavelets. Wavelet transforms are based on a basic short oscillating function known as wavelet. From this basic wavelet, using translations and dilations, it is possible to build a frame in which the frequential characteristics 0 f the signal, and, simultaneously,
its localization in time, are determined. Thus, wavelet transform is a powerful tool for localizing events in time and in frequency. In mathematical terms, wavelet transform is based on a basic wavelet psi(t) of a signal fit) is given by:
WTlj/f(a, b) =
~
J
vi a I _~
f(t)
,,1l t: b )dt 't"
When the dilations are dyadic, i.e. the changes in the scale of the basic wavelet are a power of two, wavelet analysis becomes multiresolution analysis (i.e. a = 2)). Fig. 1 shows the deconstruction of the signal in each band of frequency. The different levels of the multiresolution correspond to bands of frequencies. The corresponding algorithm is implemented by a bank of digital filters qhit decimation (Fig. 2). Coming back to our specific problem, the EEG signal, the bank of digital filters allow us to separate epileptiform and background activities, analysing the behavior of the energy of the signal in each level of the multiresolution, eight levels corresponding to a sampling rate of 256 Hz. The spikes and waves detection is made using levels 3-7, comparing the signal energy with background energy. The seizure detection is made using the euclidean distance between the eight dimensional vectors Ps and Ph, where:
P = (El, £2, ... , E8)/Et, Et = £1 + E2 + ... + £8 Ej = energy in the scale), and Ph and Ps = the vector P for the segment of background and nonoverlapping intervals. In our experience, visual analysis of epileptic activity was performed in patients who were candidates for epilepsy surgery, from record EEG scalp and depth electrodes. The seizure activity, its start and the spread, and also its spatial and temporal organization, were identified.
Results Some results obtained using multiresolution analysis on EEGs of epileptic patients are shown below. By using the wavelet transform method, we
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can detect and classify different types of epileptiform activities, and we are also able to analyze seizure onset and its propagation. This information is useful, especially in epileptic patients who are considered to be candidates for surgery. Within this population it is essential to achieve the topographic diagnosis ofthe epileptogenic zone through to the signal EEG in order to decide upon the strategy of surgical treatment. In our experience, the visual analysis of epileptic activity was performed from scalp and depth
electrode EEG recordings for those epileptic patients considered to be candidates for surgery, allowing us to identify the interictal activity (Fig. 3A), seizure activity, its onset and propagation as well as its spatial and temporal organization (Fig. 3B). The multiresolution representation obtained from this wavelet transform and the digital filters derived therefrom have not only allowed us to separate epileptiform and background activities, but have also provided detection of epileptic events.
460
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A Fig. 3. Different examples of detector output of interictal EEG activity (A) and ictal EEG activity (B).
461
Conclusions The good localization of the information in the time-frequency domain, and the real-time implementation ofthe algorithm proposed offers an interesting contribution to the diagnosis of the area epileptogenic. We can detect and classify different types of epileptiform activities, and also analyze the onset and the spread of seizure. This information is useful, especially in patients who are candidates for epilepsy surgery; in this population it is essential to obtain the topographic diagnostic of the epileptogenic zone through to the signal EEG in order to decide the strategy of surgical treatment
Reference Aldroubi, A. and Unser, M. Wavelets in Medicine and Biology. CRC Press, Boca Raton, FL, 1996. Arakawa, K., Fender, D., Harashima, H., Miyakawa, H. and Saitoh, Y Separation of a non-stationary component from the EEG by a nonlinear digital filter. IEEE Trans. Biomed. Eng., 1986,33: 724-726. Blanco, S., D' Attellis, CE., Isaacson, S.L, Rosso, O. and Sirne, R.O. Time-frequency analysis of EEG series (II): comparison between methods based on Gabor and wavelet transforms. Physical ee«, 1996,54. Blanco, S., Kochen, S... Quian Quiroga, R., Riquelme, L., Rosso, O.A. and Salgado, P. Characterization of epileptic EEG time series (I): Wavelet transform and information theory. In: CE. D' Attellis and E.M. Fernandez-Berdaguer (Eds.), Wavelet Theory and Harmonic Analysis in Applied Sciences. Birkhauser, Boston, MA, 1997: 18()'-226. Casdagli, M.C Characterizing non-linearity in weather and epilepsy data. In: CD. Cutler and D.T. Kaplan (Eds.), Nun-Linear Dynamics and Time Series. American Mathematical Society, Providence, 1997: 20 [-222.
Chui, CK. An Introduction to Wavelets. Academic Press, San Diego, CA, 1992. D' Attellis, CE., Gamero, L.G., Isaacson, S.L, Sirne, R.O. and Torres, M.E. Characterization of epileptic EEG time series (II): wavelet transform and information theory. In: CE. D' Attellis and E.M. Fernandez-Berdaguer (Eds.), Wavelet Theory and Harmonic Analysis in Applied Sciences. Birkhauser, Boston, MA, 1997: 227-262. D' Attellis, C, Isaacson, S. and Sirne, R. Detection of epileptic events in electroencephalograms using wavelet analysis. Ann. Biomed. Eng., 1997,25: 286-293. Dingle, A.A., Jones, R.D., Carroll, GJ. and Fright, W.K A multistage system to detect epileptiform activity in the EEG. IEEE Trans. Biomed. Eng., 1993,40: 1260--1268. Eberhart, R.C, Dobbins, R.W. and Webber, W.R. EEG waveform analysis using Case-Net. Proc. Con]. IEEE Eng. Med. Biol. Soc., 1989,2046-2047. Glover, J.R., Varmazis, D.N. and Ktonas, P.Y Continued development ofa knowledge-based system to detect epileptogenic sharp transients in the EEG. Proc. Can! IEEE Eng. Med. Biol. Soc., 1990,1374-1375. Guedes de Oliveira, P., Queiroz, C and Lopes da Silva, EH. Spike detection based on a pattern recognition approach using a microcomputer Electroencephalogr: Clin. Neurophysiol., 1983,56: 97-103. Iasemidis, L.D., Sackellares, re., Zaveri, H.P. and Williams, WJ. Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures. Brain Topogr., 1990,2,3: 187201. Senhadji, L., Carrault, G. and Bellanger, J.J. Detection et cartographie multiechelles en EEG. In: Y. Meyer and S. Roques (Eds.), Progress in Wavelet Theory and Applications. Editiones Frontieres, Paris, 1993. Sirne, R.O., Isaacson, S.L and D' Attellis, CE. A data-reduction process for long-term EEGs. IEEE Eng. Med. Biol., 1999, 56-{i1. Strang, G. and Nguyen, T. Wavelets and Filter Banks. WellesleyCambridge Press, Wellesley, MA, 1996. Unser, M., Aldroubi, A. and Eden, M. A family ofpolinomial spline wavelet transforms. Signal Proc., 1993,30: 141-162. Walters, R., Principe, J. and Park, S. Spike detection using a syntactic pattern recognition approach. Proc. Con! IEEE Eng. Med. Biol. Soc., 1989, [810--[811.