Nonlinear analysis of the alcoholic's EEG

PROGRESS IN NATURAL SCIENCEVol. 12 ,No. 12 , December 2002Nonlinear analysis of the alcoholic' s EEG”SHAO Chenxil** , SHEN Linfeng' , WANG Xufa' and YIN Shijie2(1. Department of Computer Science & Technology , University of Science & Technology of China , Hefei 230027 , China ;2. Depart-ment of Neurology , University of Medical Science of Anhui , Hefei 230022 ,China )Received June 5 , 2002 ; revised July 3 , 2002AbstractThe nonlinear analysis is used to study the EEGs of the alcoholic and the control. Three kinds of expansions are dis-cussed in order to get a more proper delay and then Liangyue Cao algorithm is implemented fficiently. Totally , there are 40 subjects in-volved in this study and the average values and the sample variances of D2s are computed. The results show that the average value of D2sof the aloholie is larger than that of the control when the same electrode was used , which means that the brain dynamics of the alcoholieis more complex than that of the control. On the other hand , for most of the eletrodes , the sarmple variance of D2s of the alcobolie is larg-er than that of the control , suggesting that the brain dynamics of the alcoholic is less steady.Keywords: EEG , alcoholice , nonlinear dynamics , complexity , sabilit.The research on human brain is more and moregeneral，the delay is obtained when the slope first de-active due to its potential in many fields such as phi-creases to less than 40% of the initial value5]. Butlosophy and medicine. In recent years nonlinear anal-from the result of our experiments this procedure mayysis has been an efficient new technique for studyingnot get the most proper delay. Since the selection ofEEG. Some researches show that EEG of the epilep-the delay affects the result obviously , sometimes moretic is chaotic and low dimensionat1l. On the con-than the embedding dimensiortl , it is necessary totrary , the dimension of normal EEG changes in adiscuss these cases. The expansion- delay curves couldlarger range. The correlation dimension of EEG is af-be classified into the following three cases.fected by some parameters such as data number ,samplingtime , time delay , and changes berween 2 and C21.The first is shown in Fig. 1. This is the normalcase called normal- expansion. We sample the X -com-A two-step process composes nonlinear analysis.ponent values of the Lorent 7lattractor with the usualThe first step is state-space reconstruction , i.e. reparameters. After discarding the first 5000 points we .constructing the state space from the observed timeget 1000 data. When M changes from 2 to 10 , theseries. The most important method is time. delay em-expansion-delay plot( Fig.1 )is obtained. F rom curvebedding 3]. The second step is characterizing numeri-1 tocurve9 ,M=2 ,L=6;M=3 ,L=16 ; M=cally the geometry properties of the attractor. The4 ,L=11 ;M=5,L=9;M=6,L=7 ;M=7 ,most often used parameter is the correlation dimen-L=6 ;M=8,L=5 ;M=9 ,L=5 ;M=10 ,L=sion( D2 ) that is the relative measure of the complex-4. In Fig.1 we can find that the greater M is , theity of a system. The Grassberger and Procaccia algo-smaller L is , when M is larger than 2.rithm is commonly used to calculate D24]. The accu-rate estimation of D2 is affected by time-delay L ( fora discrete time series ) , embedding dimension M anddata number N ,so it is necessary to select these pa-rameters accurately.1 Methods .中国煤化工sot +011.1 Discussions on the proper time- delayPHCNMHG-_.DelayThe proper delay is always larger than 1. InFig. 1. The expansion delay curves of Lorenz attractor.* Supported by the National Natural Science Foundation of China( Grant No. 69974038 ) and National High Performance Computing Foundation(Grant No.門为数据，** To whom correspondence should be addressed. E-mail : cxshao@ ustc. edu. cn916Progress in Natural Science Vol. 12 No. 122002The second case is shown in Fig.2( curve1). Inpansions ( Mexp ), and then compare Mexp with thethis case , the expansion increases too fast. We call itexpansion when L is 1( lexp). If lexp is between(( 1excess- expansion. The data( 1000 points ) are gener--ExpFac )X Mexp )and(( 1 + ExpFac )X Mexp),aated from torus7I. The parameter t begins at 0 anduniform-expansion is detected. Here ExpFac is a con-the sampling time is0. 1. When M changes from2 tostant that should be determined through experiments.10 , we get the expansion-delay plot( Fig.2 ). FromWe recommend that ExpF ac take a value between 0.1curve 1 tocurve9 , M=2 ,L=1 ;M=3, L= 13 ;and 0.2.M=4 ,L=9 ;M=5 ,L=7 ;M=6 ,L=6; M=7 ,L=5; M=8,L=4 ;M=9,L=4; M= 10 ,These discussions may help to select a moreL =4. When implementing the algorithm, L is ini-proper delay.tialized with the value 1. Only when the proper delay1.2 The efficiency of Liangyue Cao algorithmcomesout is the initial L replaced. Since the properdelay is always larger than 1 , if the delay is 1 , itAfter analyzing Liangyue Cao algorithnf7], wemeans that the expansion increases too fast and thefind out that for dimension d the time complexity uproper delay cannot be obtained. In this case , we(Nd)ismorethanBXdXN2andthetimecom-could select a middle value according to our require-plexity of the whole algorithm u( N ,D ) is more thanment to avoid a too large or too small value.AXD2x N2. Here A and B are all constants. Pa-rameter d is between 1 and D ,and N is data num-ber. It is obvious that the computation of M will bevery slow when N is large( Fig.4 ).D=202709 s-2The curve before optimization30s 421s201The curve afterDelay20 soptimization 1Fig.2. The expansion-delay curves of torus attractor.0中301s'The third case is shown in Fig. 3. The expan-2s 10s 26s 44ssions on the same curve are almost the same. We call0200040006000800010000this case uniform-expansion. The data( 1000 points )Data numberig. 4. The time-N curves before and after optimizing the algo-rithm. .In fact ，when choosing the neighbor , the dis-tance between the two neighbors and the index of theneighbor are important information. Recording theinformation would be useful for computing a( i ,d ).It is space consuming to record all the distances a-10- 2站mong the vectors. In fact ，the efficiency can begreatly improved by only recording the index ofFig. 3. The expansion-delay curvesofEq. (1 ).Yn(ia{ d )( the neighbor of y;( d )) and the distanceare generated from a four- -dimension systent7I :between the two vectors. Fig. 5 shows this point.X+4 =sir( X, + 5)+ sir(2Xn+1 + 5)Whe中国煤化工!( d ) becomes steady.+ sir( 3Xn+2 + 5)+ sir(4Xn+3 + 5)(1)But) changes acutely. ThismeaJMYH. CNMH Gale neighbor dereaseswith the sampling time 0.1. When M changes from2 to 10 , the corresponding delays are all 2. In Fig.3rapidly with the increaseof d and is very small whenwe can see that the expansion is almost saturated , sod is larger than M.the proper delay could be 1. To detect such a case ,Assume that when the dimension is d，thefor each历方数据uld compute the mean value of ex-neighbor of vector i is Nei( d ,i ), and the distanceProgress in Natural Science Vol. 12 No.12 200291740rN=4000The curve beforeoptimization直20Dimension0Fig. 5. The E1-d curves of Lorenz atractor when L changesfrom1 to 13.Fig.6. The time-durves before and after optimizing the algo-between the two vectors is Dis( d ,i ,Nei( d ,i )),rithm when N is a constant.and the distance between the axes n of vector i andthat of j is DistIJ(d i j m ). Now the dimension isnia!. There were 122 subjects and each subject com-d+1.IfNei(di)isnotmorethanN-(d+1)xpleted 120 trials where different stimuli were shown.L ,compute DistIJ(d +1 ,i ,Nei(d ,i),d+1). IfThe electrode positions were located at standard sitesDistIJ( d+ 1 ;i ,Nei( d i),d+ 1 )is not more than( Standard Elctrode Position Nomenclature , Ameri-Dis(d ,i ,Nei(d ,i )), we get the following two e-can Electroencephalographic Association 1990 ). .Zhang et al. described in details the data collectionquations :process-). There are three versions of the EEG dataNei(d+1i)=Nei(di)(2)set : the small data set , the large data set and the fulldata set. They all contain measurements from 64andDis(d + 1 i ,Nei(d+1 i ))= Dis(d i ,Nei(d ,i )).(3)electrodes placed on the scalp sampled at 256 Hz. TheIn this case , the efficiency would be greatly im-full data set has all of the data and the other two haveproved. We call this case the successive- case.only a part. These data have been applied in some re-searche58]. The data of 20 alcoholic subjects and 20Since the probability of false neighbor becomescontrol subjects are selected from the full data setvery small and steady after an acute change in the( Table 1 ), and then the data of the 105th trial areE1-d plot , the probability of the successive-caseused.changes from a small value to a greater one acutelyand becomes steady. The great improvement on the2.2 Analysis of resultsefficiency is obvious( Figs.4 and 6).We applied the nonlinear analysis to the selecteddata and computed the D2 at each electrode. In order2 Results and discussionsto find out the differences between the alcoholic and2.1 Source of datathe control ,for all of the D2s at the same electrode ofthe same kind of subject we calculated the averageThe EEG data of the alcoholic and the controlvalue( ACD ) and the sample variance( SV ). The re-used in our study are all from University of C alifor-sult is shown in Table 2.Table 1. Indexes of the data selected from the full data setAloholicControlco2000364c∞20000365co2a0000369co20000337c∞20000338co20000339co20000370co2a0000371co20000372co2d0000340co20000341co20000342co2a0000375co2a0000377co20000378co2c0000344co20000345co0000346co2a0000380co20000381co20000382中国煤化工co20000357 .ca20000384ca200003880∞20000390MYHCNMHG020000392co20000394co20000395co2a0000398c∞2a0000402.Co20000382co200003831 )The UCI KDD Archive , Information and Computer Science , University of California , Irvine , CA 92697-3425 , Last modified : October 14 ,1999..2) The descrnption of the data from University of California , 1995.918Progress in Natural Science Vol. 12 No. 122002Table2. The ACD and the SV at each electrode of the alcoholic and the controlAlcoholicControlAlcoholieElectrodeACDSVFP14. 6179602. 2923934. 0615811. 126831AF75. 4044961. 6072894. 4671581. 350189FP24. 7767941. 8450634. 4935811. 454388AF84. 3292801. 3961063. 890683 0. 265500F74.540845 0. 7130373. 9987560.587859254. 4570741. 5927294. 0192381. 0025964. 488082 1. 349586 .3. 9574690. 481768F65.1392251. 7896224. 2913711. 497083AF14.107309 0. 7557283. 8564020. 776238FT74.2899121.7245074. 0449430. 5826074. 4199800.7581553. 8301710.870130FT84. 5357871. 5785744. 0569250. 730470FZ4.315405 1. 7428023. 7507281.120534FPZ4. 5266482.3508904.148214 1. 053298F4. 0461111. 0086904.0228911. 4433784. 4507561.2957853. 851890 0. 500898F34.047376 0. 715897.3. 7464010.977235FC34. 5350562. 0725283. 6559031 .026159FC64.0641400. 6773883. 8050630.944855C64.2162801.8563354.151446 1. 034514FC54.158427 1. 5089063. 8813730. 841957C54. 1908161. 3148233.8314790. 748772FC24.1185171.6795593.8181710.65432324.3613882.6389894. 0545621.723101FC14. 160868 0. 9904513. 7508180.776749F13. 9719841. 1747173. 3936260. 264367T84.537607 2. 3439813. 7994820. 419079TP84. 2696291.7661173. 4714570. 5314194. 7956253. 7741794. 2527180.849297TP74.5455961. 6819243. 6417610. 338949CZ4. 6463301. 8283393. 7182350.413223AFZ4.0722560. 8498754. 0407011. 8859844.254170 1. 5841473. 8135510.596667CP34. 1936661.138605.4. 148797 1. 294937C44. 504207 1. 5260323. 8976060.867706CP44. 6780052.3806673. 4524740. 356062CPS3. 9983580. 739459.3. 7804310.63748353.9388200. 7638333. 633749 0. 560512CP64. 346815 1. 1549433. 6778850.456504P64. 3697091. 3480053. 5188180. 496270CP14.013410 0. 4822033. 7688721.173755 .C13.9327950.7916693.2383430. 536677CP24. 5682371. 0876923. 5383151. 764929C23. 909320.0.8840283. 646806 0. 8235194. 166596 0. 9572333.3842440.711229PO74. 115880.8230404.0835291. 146358P.4. 3233241. 4475323. 334030. 521687PO8 .4.2001750. 8378814. 115010 1. 080271PZ4. 3988081. 2832483.2142970.312628FCZ3. 9397640.8973113. 6356720. 6693334. 0843251.4482133. 3053800.485471POZ4.0434760. 6614153.282422 0. 415148P74.362125 1. 8839033. 6652420.535328OZ3. 9544580.6528043. 6423930. 680631PO24. 0098111. 4861763. 2485310.3889334.2159660.9814163. 416997 0. 676805PO14.189838 1. 1839913. 5827510.939424P13. 9550171.0686123. 6761021. 328803O24.2887581. 1322453. 5640130.734193CPZ3.8636620.5615603. 3806180. 539808O3. 873509 0. 7529623. 4879000. 778420nd4. 5723072.1652593.793405 0. 650009X4. 7362692. 6935463. 89570.832383Y4. 3328031. 9301434.000644 0. 961535Let the electrode be the abscissa , and the ACDbe the vertical coordinate. We plot the ACD- electrodeAlcoholic、curves of the alcoholic and the control( Fig. 7 ). Inthe following figures , the abscissa is electrode. F romleft to right , the electrodes are FP1 ,FP2 ,F7 ,F8 ,AF1,AF2,FZ,F4,F3,FC6,FC5,FC2,FC1，T8 ,T7 ,CZ,C3 ,C4 ,CP5 ,CP6 ,CP1 ,CP2 ,P3 ,NP4,PZ,P8,P7,PO2,PO1,O2,01,X,AF7,AF8,F5 , F6,FT7 ,FT8, FPZ, FC4 , FC3 , C6，ElecrodeC5 ,F2 ,F1 ,TP8 ,TP7 ,AFZ ,CP3 ,CP4 ,P5 ,P6，C1,C2,PO7,PO8，FCZ,POZ,OZ,P2，P1，Fig.7.The ACD eletrode curves of the alooholic and the con-CPZ,ndandY.InFig.7,wecanfindthatthe中国煤化工ACDs of the alcoholic are mostly between 4 and 5 andresulTHCNMH Gnamics of the alcoholiethose of the control are mostly between 3 and4. It isis more conplex. In oraer to look into the differenceobvious that the ACD of the aloholic is larger thanmore clearly , we subtracted the ACD of the controlthat of the control at the same electrode. Since thefrom that of the alcoholic at the same electrode andcorrelation dimension is the relative measure of thegot the result SACD. Fig. 8 shows that all of thecomplexit万为数据given system' s dynamic591, theSACDs are greater than 0 and most of them are beProgress in Natural Science Vol. 12 No.12 2002919tween 0.2 and 1. It means that the difference of theof the alcoholic is larger than that of the control atACD between the alcoholic and the control is obvious ,most electrodes ,i.e. the brain dynamics of the alco-i. e. the difference between the two kinds of subjectsholic is less steady.is distinct. The SACDs at electrode CP2，PZ andCP4 are all more than 1. The difference is especiallydistinct at these electrodes.1.5厂w.0|-2一六230 4C50 60 70ElectrodeFig. 10. The SSV-electrode plot.3(40506070.2.3 ConclusionFig.8. The SACD- lectrde plot.In this study the nonlinear dynamical analysis isThe sample variance( SV )is a proper characteri-applied to the EEGs of the alcoholic and the control.zation of the distributing degree of the samples. ByWe characterize the differences between the two kindscomputing the SVs , the distributing degree of D2s isof subjects by comparing the complexity and the sta-obtained. Plotting the SV- electrode curves of the twobility of the EEG. Compared with that of the con-kinds of subjects , Fig. 9 is obtained.trol , the brain dynamics of the alcoholic is more com-plex and less steady.AlcoholicReferences1 Babloyantz, A. et al. Low dimensional chaos in an instance ofepilepsy. Proc. Nat. Acad. Sci. USA , 1986 ,83 :3513.z 2F? Molinali ,L. et al. Once more :dimension and Lyapunov exponentsfor the human EEG. In : Nonlinear Dynamical Analysis of EEG ,Jansen,B.H. et al. Singapore : World Scientific , 1993 , 140.3 Packard ,N.H. et al. Gometry from a time series. Physical Re-00203040506070view Letters , 1980 ,45 :712.Grassberger ,P. et al. Characterization of strange attractors. Phys-ical Review Letters , 1983 ,50 :346.Fig. 9. The SV-electrode curves of the alooholic and the control.Rosenstein ,M. T. et al. Recconstruction expansion as a geometry-based framework for choosing proper delay times. Physica D ,Fig. 9 shows that most of the SVs of the control1994 ,73 :82.are smaller than 1. 5，and that especially most of) Lai,Y.C. et al. Effective scaling regime for computing the corre-lation dimension from chaotic time series. Physica D, 1998 ,115 :them are smaller than 1. On the contrary , the SVs ofthe alcoholic are relatively larger. For most of elec-Cao,L. Y. Practical method for determining the minimum embed-trodes , the SV of the alcoholic is larger than that ofding of a scalar time series. Physica D , 1997 , 100 :43.the control at the same electrode. We also subtracted8 Zhang ,X. L. et al. Event related potentials during object recogni-tion tasks. Brain Research Bulletin , 1995 ,38( 6 ):531.the SV of the control from that of the alcoholic at theStam,C.J. et al. Use of non- linear EEG measures to characterizesame electrode , and got the value SSV , and then plotEEG changes during mental activity. Electroencephalography andFig. 10. It is obvious that most of the SSVs are largerClinical Neurophysiology , 1996 , 99 :214.than 0. It implies that the distributing degree of D2s中国煤化工MYHCNMHG