SEIZURE SIGNALS SEPARATION USING CONSTRAINED TOPOGRAPHIC BLIND SOURCE SEPARATION

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1 SEIZURE SIGALS SEPARATIO USIG COSTRAIED TOPOGRAPHIC BLID SOURCE SEPARATIO Mi Jig ad Saeid Saei Cetre of Digital Sigal Processig, Cardiff Uiversity Cardiff, CF24 3AA, South Wales, UK {jigm, ABSTRACT Topographic idepedet compoet aalysis (TICA) is a effective tool to group the geometrically earby source sigals. The TICA algorithm further improves the results if the desired sigal sources have particular properties which ca be exploited i the separatio process as costraits. Here the spatial-frequecy iformatio of the seizure sigals is used to desig a costraied TICA (CTICA) for the separatio of epileptic seizure sigal sources from the multichael electroecephalogram (EEG). The results are compared with those from the TICA ad the superiority of the ew CTICA has bee demostrated.. ITRODUCTIO Epilepsy affects more tha fifty millio people i the world. May studies have bee carried out to explore the mechaisms of epileptogeesis ad the possible solutios for aticipatio ad therapia []- [5]. Predictio of seizure has bee ivestigated for decades. The most widely applied approach is based o the oliear aalysis methods for the itracraial EEG recordigs. The oliear aalysis methods cosider the epileptic brai as a dyamical system ad the predictio problems ca be solved by meas of aalysis of the correspodig oliear features. Although the dyamic properties have bee show i the scalp EEGs [6] [7], there are two mai challeges i applyig the traditioal oliear methods to the scalp EEGs: oe is that the scalp sigals are more subject to the evirometal oise ad artifacts; secod, the meaigful sigals are atteuated ad mixed whe passig through the brai, skull, ad scalp. A ovel approach proposed i [8] [9] has already show very promisig results of the predictability from the scalp EEGs by icorporatig the popular blid source separatio (BSS) algorithm. The mai cocept of this approach is to cosider the seizures as the idepedet compoets which are liearly ad istataeously combied together with the oise ad artifacts over the scalp. All idepedet compoets ca be separated by BSS algorithms, ad the seizure sources ca be selected by postprocessig. The traditioal oliear aalysis methods ca be applied to these seizure compoets. This approach ca be improved if the separatio ca achieve better performace. The objective of this work is to develop a method that ca provide more plausible estimatio of the seizure sources ad evetually pave the way for the predictio of epileptic seizure from the scalp EEGs. Idepedet compoet aalysis (ICA) has bee icreasigly applied to brai sigal aalysis for decompositio of A exteded ad detailed versio of this mauscript is to be published i The Joural of Computatioal Itelligece ad eurosciece multivariate EEGs to extract the desired sources. It has foud a fruitful applicatio i the aalysis of multichael EEGs [0] icludig epileptic seizure sigals. The covetioal oise-free ICA model ca be expressed as: x(t) = As(t) () where x(t) = [x (t),x 2 (t),...,x (t)] T, x R is the vector of observed sigals at time t, ( ) T deotes traspose operatio. s(t) = [s (t),s 2 (t),...,s m (t)] T is the ukow idepedet source, s R m, m for the over-determied mixture ad A R m is the mixig matrix. The estimated sources y(t) = [y (t),y 2 (t),...,y m (t)] T ca be obtaied by a separatio matrix W through iversio of the above data model, y(t) = Wx(t) (2) where W = A is the pseudo-iverse of the mixig matrix ad WA = I. There are certai assumptios ad restrictios for this model: ) the source sigals are statistically idepedet; 2) the idepedet compoets must have o- Gaussia distributios; ad 3) the umber of idepedet compoets are less or equal to the umber of iput chaels []. The ICA algorithm has its ow limitatios which are the scale ambiguity ad the permutatio problem. Sometime it caot take all the prior physiological iformatio ito accout ad the results of separatio caot be iterpreted physiologically. Topographic ICA (TICA) proposed by Hyvärie et al. [2] is a modified ICA model, which relaxes the assumptio of statistical idepedecy of the compoets, cosiderig the compoets topographically closed to each other are ot completely idepedet but have certai depedecies. The depedecies are used to defie a topographic order betwee these compoets. This provides a efficiet approach for separatio of the multichael EEG source sigals, because the depedecies betwee such sources caot be simply cacelled out by some statistical assumptios. I this work, we show how TICA ca be used for separatio of the seizure sigals from EEGs, ad how the performace ca be improved by itroducig the ovel spatial ad frequecy costraits. (The costraied TICA is deoted as CTICA). The paper is orgaized as follows. Sectio 2 describes the algorithm developmet. The basic TICA model ad priciples are explaied ad the CTICA model is developed. Sectio 3 gives the experimetal results obtaied by applyig the proposed methods to the epileptic seizure EEGs, the performace of CTICA ad TICA is compared ad the superiority of CTICA is demostrated. The fial sectio cocludes the paper EURASIP 236

2 2. ALGORITHM DEVELOPMET 2. Topographic ICA I the covetioal ICA, the sources are assumed to be completely statistically idepedet ad the estimated sigals have o particular order. But i most real applicatios, some sources maybe more or less depedet o each other, such as the EEG sources which are fired from close locatios withi the cortex. I order to estimate the depedecy of the idepedet compoets, Hyvärie et al. proposed the TICA [2]. I TICA, the idepedecy of the compoets has bee relaxed, which meas that the sources geometrically far from each other i topography are cosidered approximately idepedet ad the sources close to each other are assumed to have certai depedecies. The depedecy is defied as the higher-order correlatio betwee the estimated sources, such as the correlatio of the eergies. I the TICA model, the variaces of estimated compoets are ot costat, istead, they are geerated by some high-order idepedet variables. These variables are mixed liearly i the topographic eighborhood, which are defied by a eighborhood fuctio h(i, j). Based o this model, the estimated compoets i the same eighborhood are eergy correlated. The approximatio of the desity of source s i is give as: p(s) = k exp(g( h(i,k)s 2 i )), (3) i where k is the idex of the compoets withi the same eighborhood. G( ) is the scalar fuctio defied by icorporatig certai oliearity as those defied i [2]. The approximatio of the log-likelihood of this model is give as: log L(W) = t= j= G( i= h(i, j)(w T i x(t)) 2 ) + log( detw ) (4) where, w i is the colum vector of the umixig matrix, is the legth of the data, ad h(i, j) is the eighborhood fuctio, which ca be defied as a mootoically decreasig fuctio of some distace. The secod term of the above equatio ca be igored because the umixig matrix is costraied to be orthogoal ad the determiat of a orthogoal matrix is oe. Therefore, the estimatio of the TICA model chages to choosig the optimal matrix W opt that maximizes the above log likelihood fuctio. The estimatio of maximizatio of the log-likelihood ca be foud by: W log L(W) W=Wopt = 0 (5) The computatio of the gradiet ca be foud i [2]: Wk = 2 t=x(t)(w T k x(t)) h(k, j)g( j= i= h(i, j)(w T i x(t)) 2 ) where g( ) is the derivative of the scalar fuctio G( ). 2.2 Costraied Topographic ICA The estimated compoets from the TICA maybe depedet if they fall ito the same eighborhood, i.e, the sources comig from the earby locatio will be grouped together. However, the performace of TICA algorithm has certai limits. (6) It maybe ot easy to obtai the sources grouped together uless the earby sources are active at the same time. I [2], i order to obtai better visualizatio results, the experimet was set to geerate some typical high eergy sources such as bitig teeth for 20 secods. But i the most cases of real applicatios, the source sigals may ot be so sigificat, or there maybe oly oe or two of active sources. This could be the factor that affects the performace of TICA. Aother factor is the umber of iput chaels. It is obvious that the more iput chaels, the more iformatio oe ca have ad the better results ca be achieved. This ca be aother limitatio for the practical applicatios. However, the performace ca be improved by itroducig certai costraits i the algorithm. Applicatio of the costraied ICA for EEG aalysis has bee previously reported [8] [3]- [7]. The classic ICA dose ot exploit the depedecy of the sources therefore ot always provides the desired outputs. For EEGs, there are valuable prior kowledge which ca help to separate the desired sources. I this study, we cosider two costraits which are based o spatial ad frequecy iformatio. Firstly, i the focal epileptic seizures, the locatio of the seizure sources, epileptogeic zoe, is ofte kow as the prior iformatio. Secodly, seizure sigals maifest themselves withi certai frequecy bad. Based o the research fidigs from the cliicias ad the eurologists, although the domiat frequecy may vary for differet types of seizures, the frequecy bad of the epileptic seizure oset is ormally from 2.5 to 5.5 Hz. (Frequecies below 2.5 Hz are cosidered to be maily due to eye-blikig artifacts) [8] [9] [20]. Therefore, the costrait ca be determied based o both spatial ad frequecy domai iformatio. The model of the costraied TICA problem ca be preseted as: maxj m (W) s.t. mij c (W) (7) where J m (W) is the mai cost fuctio, here the mai cost fuctio is give i Eq. (4). J c (W) is the costraied cost fuctio, which ca be defied as miimizig the distace betwee the output ad a referece sigal: J c (W) = argmi w t= w T i x(t) y r (t) 2 2 (8) where y r is the referece sigal defied based o the spatial ad frequecy costraits. 2 is the Euclidea distace. The CTICA is the chaged to a ucostraied fuctio by usig a Lagrage multiplier. Therefore, the overall cost fuctio is writte as: J(W,Λ) = J m (W) ΛJ c (W) (9) where Λ = diag{λ ii },i =,...,m, is a diagoal weight matrix formed by Λ = p diag(cor(y r,y i )) (0) where p is a adjust costat, cor( ) is the correlatio measuremet, ad y i is the ith estimated source. The the update equatio is obtaied as: W(k + ) = W(k) + µ(k){ J m(w) W + Λ(X(WX Y r) T )} () where µ is the step size which is updated iteratively. Y r is 2007 EURASIP 237

3 the matrix with the referece sigal y r i each row. 3. EXPERIMET 3. Data acquisitio ad the experimet setup The multichael EEGs with the frotal focal epileptic seizure were recorded from the stadard silver cup electrodes applied accordig to the Maudsley electrode placemet system, which is a modificatio of the exteded 0-20 system [2]. The 6 chaels EEGs were sampled at 200 Hz ad badpass filtered i the frequecy rage of Hz. The system iput rage was 2 mv ad data were digitized with a 2-bit aalog-to-digital coverter [8]. The EEGs were filtered by a 0th order Butterworth digital filter with a cut frequecy of 45Hz i order to elimiate the 50Hz frequecy compoet. The data used i the followig experimets were trucated from the origial recordigs to iclude the duratio of 0 secods with seizure oset as show i Fig.. Fp Fp2 F3 F4 C3 C4 P3 P4 O O2 F7 F8 T3 T4 T5 T6 Scalp EEG 25.6 simple detectio rule based o the domiat frequecy ad respective estimated spectrum is applied to select the sources which have the sigificat ictal activities. The source with a maximum spectrum amplitude higher tha a threshold ad also with the domiat frequecy i the seizure bad, is take as a seizure source. These sources are, IC7, IC8, IC9 ad IC0 i Fig. 2, IC5, IC6, IC7 ad IC8 i Fig. 3. Oe ca see that the high amplitude spike sigal are separated from the other sources. Aother distict source related to the eye blik ca be see from both of the outputs, which is IC2 i Fig. 2 ad IC4 i Fig. 3. IC IC2 IC3 IC4 IC5 IC6 IC7 IC8 IC9 IC0 IC IC2 IC3 IC4 IC5 IC6 Estimated idepedet sources Time ( secod ) Figure 2: EEG source sigals estimated by the TICA..24 Time ( secod ) Figure : Multichael EEGs from a epileptic patiet with the seizure oset. The referece was obtaied by first averagig the special chaels closed to the epileptogeic zoe. I the experimet, F3, F4, F7, F8, C3 ad C4 were selected. The 3-5Hz badpass filterig was udertake to extract the iformatio withi the seizure frequecy bad. The fial referece is a vector bouded withi the desiged spatial ad frequecy iformatio of the seizure. The eighborhood fuctio idicates how the estimated sources are eergy correlated with each other, which ca be defied as a fuctio of the width of the eighborhood. I this study, because of the limited umber of iput chaels, the fuctio was chose as the simple oe-dimesioal form, such as h(i, j) =, if i j m, otherwise, h(i, j) = 0. m is the width of the eighborhood. It ca be oticed that the eighborhood fuctio is symmetric as h(i, j) = h( j,i). 3.2 Results The separatio results of TICA ad CTICA are give i Fig. 2 ad Fig. 3, both with the width of eighborhood m =. A The differeces betwee the source cadidates may ot be easily oticed by visual ispectio of the time course of the sources, hece the topography is applied for this purpose. Fig.4 ad Fig.5 show the topography of the sources estimated by TICA ad CTICA respectively. Topography ca be achieved by backprojectig the estimated source oto the origial sigal space, i.e. multiplyig each colum vector of the iverse of umixig matrix by the correspodig estimated source. Topography reveals how each source sigal cotributes to the electrode sigals. For example, oe ca otice that i both sets of results, the distributio of eye blik (IC2 i Fig. 4 ad IC4 i Fig. 5) appears o the area ear the electrodes Fp ad Fp2. It ca be foud that, the four selected ICs are grouped together. The differece is, i Fig. 5, the selected ICs (IC5, IC6, IC7 ad IC8) from the CTICA are localized i the frotal regio, but i Fig. 4, the distributio of the correspodig sources (IC7, IC8, IC9 ad IC0) by the TICA are rather dispersed. For istace, for IC0, the spatial distributio is highlighted i both frotal ad temporal areas. A similar result ca be oticed for IC. The differeces ca also be evaluated by comparig the performace i terms of the sigal-to-iterferece ratio (SIR). Here, we defie SIR to be the averaged sigal eergy for the estimated source y(t) from the direct source divided 2007 EURASIP 238

4 Estimated idepedet sources IC IC2 IC3 IC4 IC5 IC6 IC7 IC8 IC9 IC0 IC IC2 IC3 IC4 IC5 IC Time ( secod ) Figure 3: EEG source sigals estimated by the CTICA. Figure 5: Topography of the estimated EEG sources from CTICA. by the eergy stemmig from the other sources as: SIR = m m i W ii 2 < y i 2 > m(m ) m i j m j W i j 2 < y j 2 > (2) where W ii icludes the diagoal elemets i the iverse of umixig matrix, i.e. the weights from source y i to sesor x i. The off-diagoal elemets W i j provide the weights from the source y j to the sesor x i. It shows how the source y j iterferes the source y i, sice each colum of the iverse of umixig matrix idicates the distributio of each source i the mixture, ad a higher value idicates a better performace. The performace of the algorithm is evaluated by the average of five trials for both the TICA ad the CTICA. Fig. 6 shows the separatio performace via the chages of the width of the eighborhood. It ca be oticed that, the SIR of TICA decreases with icreasig the eighborhood width. This is because the wider the eighborhood is, the more the sources will be separated based o the eergy correlatio. However, for the CTICA, because of the spatial ad frequecy costraits, the SIR slightly decreases at the begiig, the stays approximately at certai level. It shows that geerally, the CTICA has a better performace tha the TICA. It also works better tha the TICA whe the width of the eighborhood icreases. Figure 4: Topography of the estimated EEG sources from TICA. 4. COCLUSIO A ew costraied topographic BSS algorithm has bee developed to separate the epileptic seizure sources from the EEG sigals. The icorporated costraits are based o the prior iformatio about spatial ad frequecy of the focal epileptic seizures. The experimetal results show that seizure 2007 EURASIP 239

5 Sigal to Iterferece Ratio (db) TICA CTICA Width of the eighborhood Figure 6: Performace compariso of the TICA ad the CTICA. sources comig from the epileptogeic zoe are grouped together. The CTICA algorithm achieves better performace i terms of seizure source separatio, ad also works better whe the width of the eighborhood icreases. REFERECES [] L. D. Iasemidis, Epileptic seizure predictio ad cotrol, IEEE Tras. o Biomedical Egieerig, vol.50, pp , [2] F. H. L da Silva, W. Blaes, S.. Kalitzi, J. Parra, P. Suffczyski, ad D.. Velis, Dyamical diseases of brai systems: differet routes to epileptic seizures, IEEE Tras. o Biomedical Egieerig, vol. 50, pp , [3] M. L. V. Quye, J. Martierie, V. avarro, M. Baulac ad F. J. Varela, Characterizig eurodyamic chages before seizures, J. Cli. europhysiol., vol. 8, o. 3, pp, 9-208, 200. [4] L. D. Iasemidis, D. S. Shiau, W. Chaovalitwogse ad J. C. Sackellares, Adaptive epileptic seizure predictio system, IEEE Tras. o Biomedical Egieerig, vol. 50, pp , [5] L. D. Iasemidis, J. C. Priciple, ad J. C. Sackellares, Measuremet ad quatificatio of spatio-temporal dyamics of huma eplptic seizures, oliear Sigal Processig i Medicie, IEEE Press, 999. [6] D. S. Shiau ad L. D. Iasemidis Detectio of the preictal period by dyamical aalysis of scalp EEG, Epilepsia, vol.44(s.9), pp , [7] J. C. Sackellares, L. D. Iasemidis, D. S. Shiau, R. L. Gilmore ad S.. Roper, Detectio of the preictal trasitio from scalp EEG recordigs, Epilepsia, vol.40(s7), pp.76, 999. [8] J. Corsii, L. Shoker, S. Saei, ad G. Alarco, Epileptic seizure predictability from scalp EEG icorporatig BSS, IEEE Tras. o Biomedical Egieerig, vol. 53, o. 5, pp , [9] M. Jig, S. Saei, J. Corsii, ad G. Alarco, Icorporatig BSS to Epileptic Seizure Predictability Measure from Scalp EEG, 27th Aual Iteratioal Coferece of Egieerig i Medicie ad Biology Society (IEEE- EMBS 2005), pp , [0] S. Saei ad J. Chambers, EEG Sigal Processig, Joh Wiley - Sos, [] A. Hyvärie, J. Karhue ad E. Oja, Idepedet Compoet Aalysis, Wiley-Iterscice Publicatio, 200. [2] A. Hyvärie, P. O. Hoyer ad M. Iki, Topographic Idepedet Compoet Aalysis, eural Computatio, vol. 3, pp , 200. [3] W. Wag, M. G. Jafari, S. Saei ad J. Chambers, Blid sepratio of covolutive mixtures of cyclostatioary sigals, It. J. Adapt. Cotrol Sigal process, vol. 8, pp , [4] M. A. Latif, S. Saei, J. Chambers, ad L. Shoker, Localizatio of Abormal EEG Sources Usig Blid Source Separatio Partially Costraied by the Locatios of Kow Sources IEEE Sigal Processig Letters, vol. 3, o. 3, pp. 7-20, [5] L. Spyrou, M. Jig, S. Saei, ad A. Sumich Separatio ad Localisatio of P300 Sources ad Their Subcompoets Usig Costraied Blid Source Separatio, EURASIP J. o Advaces i Sigal Processig, vol. 2007, pp. -0, [6] W. Wag, S. Saei ad J. Chambers, Pealty Fuctio- Based Joit Diagoalizatio Approach for Covolutive Blid Separatio of ostatioary Sources IEEE Tra o sigal processig, vol. 53, o. 5, pp , [7]. Ille, R. Beucker, ad M. Scherg, Spatially costraied idepedet compoet aalysis for artifact correctio i EEG ad MEG, euroimage, vol. 3, S59, 200. [8] G. Latz, C. M. Michel, M. Seeck, O. Blake, T. Ladis, ad I. Rose, Frequecy domai EEG source localizatio of ictal epileptiform activity i patiets with partial complex epilepsy of temporal lobe origi, Cli. europhysiol., vol. 0, pp , 999. [9] O. Blake G. Latz, M. Seeck, L. Spielli, R. Grave de Peralta, G. Thut, T. Ladis, ad C. M. Michel, Temporal ad Spatial Determiatio of EEG-Seizure Oset i the Frequecy Domai, Cli. europhysiol., vol., pp , [20] P. Wahlberg ad G. Latz, Approximate time-variable coherece aalysis of multichael sigals, Multidimesioal Systems ad Sigal Processig, vol. 3, pp , [2] J. L. Ferdez, G. Alarc, C. D. Biie, ad C. E. Polkey, Compariso of spheoidal, forame ovale ad aterior temporal placemets for detectig iterictal epileptiform discharges i presurgical assessmet for temporal lobe epilepsy, Cli. europhysiol., vol. 0, pp , EURASIP 240