1/4 FRACTAL DIMENSION AS A FEATURE FOR ADAPTIVE ELECTROENCEPHALOGRAM SEGMENTATION IN EPILEPSY M.E. Kirlngic, D. Pérez, S. Kudryvtsev, G. Griessbch, G. Henning, G. Ivnov Institute o Biomedicl Engineering nd Inormtics, Ilmenu Technicl University, Ilmenu, Germny e-mil: Eylem.Kirlngic@inormtik.tu-ilmenu.de Abstrct-In previous studies the rctl dimension (FD) hs been shown to be useul tool to detect non-sttionrities nd trnsients in biomedicl signls like electroencephlogrm (EEG) nd electrocrdiogrm (ECG). The chnges in FD re shown to chrcterise ltertions in EEG due to chnges in physiologicl sttes o brin, not only in norml but lso in pthologicl unctioning like epilepsy. The importnce o long-term EEG monitoring or clinicl evlution in epilepsy hs been lso emphsised. Adptive EEG segmenttion nd clssiiction o the obtined segments hve been ddressed to be convenient solution to the problem o visul inspection o huge EEG dt sets. The perormnce o dptive segmenttion plys n essentil role in correct evlution o the recordings. Thus, our im in this study is to nlyse the FD s eture or dptive EEG segmenttion nd compre its perormnce with those o previously used etures on epileptic EEG dt. Keywords EEG, dptive segmenttion, rctl dimension, epilepsy I. INTRODUCTION The importnce o long-term EEG monitoring or dierentil dignosis nd therpy evlution in epilepsy is described in severl studies. Logr [1] mentions long-term EEG monitoring s tool improving the dignostic vlue o stndrd EEG recordings nd providing dditionl necessry dignostic inormtion. Lopes d Silv [2] stresses the essentility o pttern recognition nd quntiiction o EEG or determintion o dierent physiologicl sttes in nesthesi, sleep nd other long durtion recordings. The long-term EEG recordings yield, however, the problem o nlysing nd quntiying huge dt sets. Adptive segmenttion nd clustering o the obtined segments o EEG hve been ddressed to be convenient solution to the problem o visul inspection o the huge EEG dt sets [3-5]. The perormnce o dptive segmenttion, which depends highly on the eture(s) used, is key issue in correct evlution o the dt with this pproch. FD is commonly pplied in both system nd signl nlysis. In non-liner system nlysis it is used or representing ttrctors which hve rctionl dimensions. The most commonly used lgorithm or this purpose is the Grssberger nd Proccci method [6]. In signl processing, FD is ddressed or detecting non-sttionrities in time series. It hs been shown to be useul tool to detect trnsients lso in EEG [7, 8]. Thus, in this study we exmine the FD s eture or dptive EEG segmenttion in epilepsy. II. METHODOLOGY A. Adptive Segmenttion Algorithm The dptive segmenttion lgorithm used hs been proposed by Silin nd Skrylev [9]. The lgorithm uses two successive windows moving on the time series in which the selected eture(s) is/re clculted. A mesure dierence unction is obtined through the dierence o eture(s) in the two successive windows. The dptive segment boundries re then ssigned to be the locl mxim o this mesure dierence unction. In the originl orm o the lgorithm spectrl chnge mesure clculted by st Fourier trnsorm (FFT) is used s the eture to detect non-sttionrities. Becuse the computtion o the spectrl chnge mesure by FFT is ineicient, the method hs been modiied by Värri [], who introduced dierence mesure composed o requency mesure,, estimted by the sum o the F di dierence o conutive signl smples, nd n mplitude mesure,, the sum o the bsolute vlues o the signl A di in the relevnt windows [3, ]. F di = wl i= 1 wl i= 1 x x (1) i i 1 A di = x i (2) where wl = window length, is the i th dt point. The mesure dierence unction,g, is then deined s, G j = k A A x i + k F F di j+ 1 di j di j+ 1 di j where k nd k re coeicients or mplitude nd th requency mesures respectively, j is the j window nlysed. In order to void excessive segmenttion due to redundnt smll segments, Krjc [3] introduced threshold or the mesure dierence to the lgorithm. The locl mxim o the unction G, which re over the ssigned threshold re ccepted to be positioning the segment boundries. Krjc [3] suggested lso vlues or k nd k (k = 1, k = 7 ) which were determined ccording to results o experiments with simulted signls. B. Frctl Dimension In signl processing, there re severl methods to pproximte the FD in time vrint signls. In the study by Esteller [11] the most prominent methods or FD computing used in EEG nlysis re compred. It is concluded tht the Ktz s lgorithm is the most consistent (3)
Report Documenttion Pge Report Dte 25OCT2001 Report Type N/A Dtes Covered (rom... to) - Title nd Subtitle Frctl Dimension s Feture or Adptive Electroencephlogrm Segmenttion in Epilepsy Contrct Number Grnt Number Progrm Element Number Author(s) Project Number Tsk Number Work Unit Number Perorming Orgniztion Nme(s) nd Address(es) Institute o Biomedicl Engineering nd Inormtics, Ilmenu Technicl University, Ilmenu, Germny Sponsoring/Monitoring Agency Nme(s) nd Address(es) US Army Reserch, Development & Stndrdiztion Group (UK) PSC 802 Box 15 FPO AE 09499-1500 Perorming Orgniztion Report Number Sponsor/Monitor s Acronym(s) Sponsor/Monitor s Report Number(s) Distribution/Avilbility Sttement Approved or public relese, distribution unlimited Supplementry Notes Ppers rom the 23rd Annul Interntionl Conerence o the IEEE ENgineering in Medicine nd Biology Society, October 25-28, 2001, held in Istnbul, Turkey. See lso ADM001351 or entire conerence on cd-rom. Abstrct Subject Terms Report Clssiiction unclssiied Clssiiction o Abstrct unclssiied Clssiiction o this pge unclssiied Limittion o Abstrct UU Number o Pges 4
2/4 method or discrimintion o epileptic sttes rom intercrnil EEG. Thereore, we selected Ktz s lgorithm or rctl dimension clcultion in our ppliction. According to Ktz, D, the FD o curve is deined s: log ( L) D = (4) log ( d) where L is the totl length o the curve, nd d is the dimeter estimted s the distnce between the irst dt point nd the dt point tht gives the lrgest distnce. Normlising the distnces with y, the verge distnce between successive dt points, we get: Deining n log( L / y) D = (5) log ( d / y) = L / y, the number o steps in the curve, log( n) D = (6) log ( d / L) + log ( n) For FD clcultion Ktz s lgorithm is implemented nd tested on simulted dt which is produced using the deterministic Weierstrss cosine unction [12]: W ( nh n t i ) = cos( ω ti n= 0 ω ) (7) where ω >1 nd 0 < H < 1, nd the rctl dimension o the generted signl is given by D = 2 - H. For the dptive segmenttion ppliction, we ssigned the FD s the only mesure or the unction G. Thus the corresponding G unction is, G = D + D, j = 1,..., N 1 (8) j j 1 j where N is the totl number o windows in nlysis. The mesure dierence unction G is normlised by / mx( G) within the intervl o nlysis in order to be G j ble to hve stndrd vlues or the thresholds. C. EEG Dt In order to compre the perormnces o the etures, 30 dierent epileptic ptterns re chosen rndomly rom clinicl EEG dt. The signls re cquired ccording to interntionl /20 system with smpling rte o 128 Hz. III. RESULTS AND DISCUSSION The irst observtion ws tht the FD decresed in epileptic pttern intervls (ig. 1, 3, 5, 7). Secondly, we observed tht in 14 epileptic ptterns out o 30, the FD ws more sensitive to the end points o the ptterns wheres the etures proposed by Värri detected some redundnt boundries within the pttern beore the end points were detected, tht is, in order to detect the end points o the pttern, the threshold hs to be decresed mening tht the redundnt segment boundries re needed to be included (eg. Pttern1 (ig. 1 nd 2), Pttern 2 (ig. 3 nd 4), Pttern 4 (ig. 7 nd 8)). Additionlly, there observed to be 3 ptterns or which the Värri mesures iled to detect the end points correctly such s the exmple pttern 3 (ig. 5 nd 6). The results or the rest 13 ptterns were similr. 0.4 Fig. 1. Segmenttion result o FD, pttern 1. Window width=1.1, overlpping=60%, threshold=0.4. 0.45 Fig. 2. Segmenttion result o Värri mesures, pttern 1. Window width=1.1, overlpping=60%, threshold=0.4 (*) nd 0.45 (o). 0.5 Fig. 3. Segmenttion result o FD, pttern 2. Window width=1.1, overlpping=60%, threshold=0.5.
3/4 0.75 0.38 Fig. 4. Segmenttion result o Värri mesures, pttern 2. Window width=1.1, overlpping=60%, threshold=0.6 (*) nd 0.75 (o). Fig. 7. Segmenttion result o FD, pttern 4. Window width=1.1, overlpping=60%, threshold=0.38. 0.35 Fig. 5. Segmenttion result o FD, pttern 3. Window width=1.1, overlpping=60%, threshold=0.35. 0.4 Fig. 6. Segmenttion result o Värri mesures, pttern 3. Window width=1.1, overlpping=60%, threshold=0.3 (*) nd 0.4 (o). The window width should not be selected very lrge in order to be ble to detect non-sttionrities iner. It should lso conorm to the number o dt points required to clculte the selected eture suiciently. Additionlly, the smller the window width is, the higher the computtionl lod is.
4/4 ound re. This mens longer computtion time nd increse in the number o redundnt segments. However, i the overlpping is too smll the necessry segment boundries to be detected cn be missed. The threshold plys n importnt role in sensitivity o the lgorithm. The higher the threshold is, the less sensitive the lgorithm to the non-sttionrities is. I the threshold is too low then there is gin the problem o redundnt segmenttion. In our sotwre reliztion these prmeters cn be input s desired so tht their inluences on the perormnce o the lgorithm cn be observed. The sotwre lso llows the utomtion o the nlysis where we ssign the window width nd the overlpping priori ccording to experimentl results o the lgorithm. For utomted nlysis, the threshold or FD is determined dptively ccording to the distribution o the vlues o FD through the dt intervl nlyzed. The medin vlue in the distribution is ssigned to be the threshold. V. CONCLUSION The use o FD s eture in dptive segmenttion o epileptic EEG hs dvntges over the previously used prmeters. First one is tht FD cn be used s single eture without the need o ny coeicients to combine dierent mesures. Secondly, its higher sensitivity to end points o the epileptic ptterns yields better reduction o redundnt segmenttion, which cn be lso interpreted s FD being more stble within the epileptic pttern intervl. These results need to be veriied on lrger set o dierent epileptic ptterns. REFERENCES [1] C. Logr, B. Wlzl, nd H. Lechner, Role o long-term EEG monitoring in dignosis nd tretment o epilepsy, Eur. Neurol., vol. 34 (supp. 1), pp. 29-32, 1994. [2] F. Lopes d Silv, Computer-ssisted EEG dignosis: Pttern recognition nd brin mpping, in Electroencephlogrphy, E. Niedermeyer nd F. Lopes d Silv, Eds., 4 th ed., pp.1164-1189, Willims&Wilkins, Bltimore, 1999. [3] V. Krjc, S. Petrnek, I. Ptkov, nd A. Värri Automtic identiiction o signiicnt grphoelements in multichnnel EEG recordings by dptive segmenttion nd uzzy clustering, Int. J. Biomed. Comput., vol. 28, pp. 71-89, 1991. [4] G. Bodenstein nd H.M. Pretorius, Feture extrction rom electroencephlogrm by dptive segmenttion, Proc. IEEE, vol. 65 (5), pp. 642-652, 1977. [5] G. Bodenstein, W. Schneider, nd C. Von der Mlsburg, Computerized EEG pttern clssiiction by dptive segmenttion nd probbility density unction clssiiction. Description o the method, Comp. Biol. Med., vol 15 (5), pp. 297-313, 1985. [6] P. Grssberger nd I. Proccci, Chrcteriztion o strnge ttrctors, Physicl Review Letters, vol. 50, no. 5, pp. 346-349, 1983. [7] A. Accrdo, M. Ainito, M. Crrozzi, nd F. Bouquet, Use o rctl dimension or the nlysis o electroencephlogrphic time series,, Biol. Cybern., vol. 77, pp 339-350, 1997. [8] R. Esteller et l., Frctl dimension chrcterizes seizure onset in epileptic ptients, Proceedings o 1999 IEEE Int. Con. On Acoust. Speech nd Sign. Process., vol. 4, pp. 2343-2346, Arizon, 1999. [9] D.Y. Silin nd K.M. Skrylev, Avtomticeskj segmentcij EEG, Zurnl vyssej nervnoj dejtelnosti, vol. 36, pp. 1152-1155, 1986. [] A. Värri, Digitl Processing o the EEG in Epilepsy, Licentite Thesis, Tmpere University o Technology, Tmpere, Finlnd, 1988. [11] R. Esteller, G. Vchtsevnos, J. Echuz, nd B. Litt, "A comprison o rctl dimension lgorithms using synthetic nd experimentl dt," Proc. IEEE Interntionl Symposium on Circuits nd Systems (ISCAS'99), Orlndo, FL, My 30-Jun. 2, 1999, vol. III Adptive Digitl Signl Processing, pp. 199-202. [12] C. Tricot, Curves nd Frctl Dimension, pp. 154-157, Springer-Verlg, New York, 1995.