Differentiating resting brain states using ordinal symbolic analysis
C. Quintero-Quiroz, Luis Montesano, A. J. Pons, M. C. Torrent, J. García-Ojalvo, C. Masoller
QQuintero-Quiroz et al
Differentiating resting brain states using ordinal symbolic analysis
C. Quintero-Quiroz, Luis Montesano, A. J. Pons, M. C. Torrent, J. Garc´ıa-Ojalvo, and C. Masoller Universitat Polit`ecnica de Catalunya, Departament de F´ısica, Colom 11, 08222 Terrassa, Barcelona,Spain. Bitbrain, Zaragoza, Spain. Department of Experimental and Health Sciences, Universitat Pompeu Fabra,Parc de Recerca Biom`edica de Barcelona, Barcelona, Spain. (Dated: 11 May 2018)
Symbolic methods of analysis are valuable tools for investigating complex time-dependent signals. In partic-ular, the ordinal method defines sequences of symbols according to the ordering in which values appear in atime series. This method has been shown to yield useful information, even when applied to signals with largenoise contamination. Here we use ordinal analysis to investigate the transition between eyes closed (EC) andeyes open (EO) resting states. We analyze two EEG datasets (with 71 and 109 healthy subjects) with dif-ferent recording conditions (sampling rates and number of electrodes in the scalp). Using as diagnostic toolsthe permutation entropy, the entropy computed from symbolic transition probabilities, and an asymmetrycoefficient (that measures the asymmetry of the likelihood of the transitions between symbols) we show thatordinal analysis applied to the raw data distinguishes the two brain states. In both datasets we find that theEO state is characterized by higher entropies and lower asymmetry coefficient, as compared to the EC state.Our results thus show that these diagnostic tools have potential for detecting and characterizing changes intime-evolving brain states.Keywords: time series analysis, ordinal analysis, EEG, brain dynamics
In the “big data” era, many efforts are being de-voted to extracting useful information from com-plex signals. The human brain is one of the mostcomplex systems that one can try to understand.In the last decades, the development and popular-ization of recording techniques such as electroen-cephalography (EEG), magnetoencephalography(MEG) and functional magnetic resonance imag-ing (fMRI), have provided the scientific commu-nity with a huge amount of data: different typesof brain signals, recorded with different spatio-temporal resolution, under different behavioralor cognitive states, from healthy or from dysfunc-tioning subjects. The underlying brain states are,in spite of many efforts, still poorly understood.Here we use a symbolic analysis tool to investi-gate EEG signals recorded from healthy subjectsduring a simple behavioral task: the subjects re-main in resting state with eyes closed (EC state)during an interval of time, and then open theireyes (EO state). We show that symbolic analysisapplied to the raw EEG signals detects the transi-tion and identifies subtle differences between theEC and EO brain states.
I. INTRODUCTION
Changes in brain states detected through the analysisof electroencephalography (EEG) signals can be used fortranslating brain signals into operational commands, andin fact, EEG analysis is one of the techniques used forbrain-computer interfaces. Several methods have been used to detect underlyingchanges in the behavior of dynamical systems from ob-served data, and one of these, ordinal analysis , hasbeen demonstrated to be computationally efficient and toperform well even with very noisy data . Due to theseadvantages, ordinal analysis has been used in the fieldof neuroscience, specifically in the area of epilepsy, fordetecting, anticipating and characterizing seizures .Since the early 1930’s it is well known that alpha wavesdominate the EEGs of healthy individuals when theyare resting with their eyes closed, and that this activ-ity diminishes when their eyes are opened . There-fore, a simple method to detect the Eyes-Closed (EC) toEyes-Open (EO) transition is by using the Fourier spec-trum to estimate the difference of the power of the al-pha frequency components . However, this approachhas the drawback of requiring a certain time-windowfor computing the power spectra. Another approach tostudy the EC-EO transition is to use the synchronizationlikelihood or the mutual information to find changesin the functional brain networks that characterize thetwo brain states. However, constructing functional brainnetworks is computationally demanding, and comparingthem is a challenging task because it is not always possi-ble to discriminate reliably between differences that aredue to constrains imposed by method of network con-struction, or due to genuine changes in brain states .The aim of this paper is to investigate if the ordinal ap-proach can accurately discriminate between EC and EObrain states. In Sec. II we describe the datasets analyzed,in Sec. III we describe the ordinal-pattern methodologyand the quantifiers used to characterize the EC and EOstates. Sec. IV presents the results obtained and Sec. Vsummarizes our conclusions. a r X i v : . [ phy s i c s . d a t a - a n ] M a y uintero-Quiroz et al 2 TABLE I. Description of the datasets used.DTS1 DTS2Sampling rate(Hz) 256 160Time task(seg) 120 60Total points 30720 9600Number of electrodes 16 64Number of subjects 71 109
II. DATASETS
We use two EEG datasets with different number of sub-jects and recording conditions, which are summarized inthe Table I. Dataset one (DTS1) was collected by the Bit-brain company . The EEG signals were recorded from71 healthy subjects that remained with eyes closed andeyes open during a period of two minutes each. Datasettwo (DTS2), which is freely available , consists ofEEG recordings of 109 subjects performing the sametask, in this case for a period of one minute in each ofthe two states.We removed the artifacts related to eye blinking fol-lowing the standard procedure: we applied the Indepen-dent Component Analysis (ICA) using the function ICAfrom the MNE library on Python and filtered out thecomponent related to the blinks (see Fig. 1).It is well known that alpha waves are a dominant com-ponent in EEG signals during eyes closed conditions, andare reduced when the eyes are open . Therefore, inorder to determine whether changes detected through or-dinal analysis are only due to the change of the strengthof alpha waves, we analyze and compare the results ob-tained from the raw time series, and from filtered timeseries where both eye blinking artifacts and the frequencycomponent of the alpha band were removed (by using aband pass filter between 14 and 31 Hz, see Fig. 2). III. METHODS
We apply ordinal analysis in non-overlapping windowsof 1 second , and thus, the number of data points inthe window, w , is equal to 256 for DTS1 and to 160for DTS2. Then, for each electrode i , the time-series, x i ( t ) = { x (1) , x (2) , · · · , x ( w ) } is transformed into asequence of symbols, s i ( t ), by using the ordinal rule ,explained in what follows.To define the ordinal patterns we consider vectorsof dimension D formed by consecutive data points, i.e. { x ( j ) , x ( j + 1) , · · · , x ( j + D − } , and then assign a sym-bol according to the ordinal relationship (from the largestto the smallest value) of the D entries in the vectors. Forexample, with D = 2 there are 2 ordinal patterns ( D !): x ( t j ) < x ( t j +1 ) corresponding to the ordinal pattern ‘01’and x ( t i ) > x ( t i +1 ) corresponding to the ordinal pattern‘10’. Then we computed the frequency of occurrence of the D! different patterns in the signal of electrode i , andby averaging over all the electrodes, computed the prob-ability of each pattern.Then, the permutation entropy (PE) is calculated as:PE = − (cid:88) j p π j ln p π j (1)where p π j is the probability of pattern π j along all theelectrodes. In this way, the PE is a measure of the en-tropy of the brain EEG signals, in the given time win-dow. If the EEG signals are generated by fully randomprocesses, all symbols are equally probable and the PEis maximum, P E = ln( D !).Additional diagnostic tools were proposed by Masoller et al. , which are based in the transition probabilities(TPs) between consecutive symbols defined from non-overlapping data values. The transition probability frompattern π a to pattern π b is the relative number of timespattern π a is followed by pattern π b , in the sequence s ( t ): M a,b = (cid:80) w − t N [ s ( t ) = π a , s ( t + 1) = π b ] (cid:80) w − t N [ s ( t ) = π a ] . (2)With this definition, the transition probabilities arenormalized such that (cid:80) b M ab = 1. Then, exploit-ing this normalization, an entropy can be associatedto the transition probabilities of each pattern as s a = − (cid:80) b M ab ln M ab , and its average s n = (cid:80) a s a D ! , (3)is another measure of the entropy of the EEG signal. Ifa signal is generated by fully random processes, all tran-sition probabilities will be equal and thus, s a = ln( D !)for all π a , and s n = ln( D !). In addition, we calculate thetransition asymmetry coefficient , a c = (cid:80) a (cid:80) b (cid:54) = a | M ab − M ba | (cid:80) a (cid:80) b (cid:54) = a ( M ab + M ba ) , (4)which is equal to zero if transition probabilities are fullysymmetric ( M ab = M ba for all π a , π b ), and equal to oneif they are fully asymmetric (either M ab = 0 or M ba = 0,for all π a , π b ). If the EEG signals are generated by fullyrandom processes, then the transition probabilities willbe all equal and a c = 0.In the following section the analysis is performed withnon overlapping patterns of length D = 4 (similar re-sults were found with D = 3). There are 4! = 24 possiblepatterns and 24 ×
60 80 100 120 140 160 18012345678910111213141516 time (s)
FIG. 1. Example of Independent Component Analysis (ICA) related to eye blinks in the EEGs, for a given subject of DTS1.Left: spatial contribution of the selected ICA component, ploted in red in the left panel. Right: all the individual componentsobtained from the ICA function, in red the component related to the eye blinks, shown in the left panel. -2 -1 M a g n i t u d e RawFilt
60 80 100 120 140 160 18012345678910111213141516 time (s)
FIG. 2. Filtering of the alpha band from the ICA data. The left panel displays the power spectrum of the EEG of a subjectbefore (blue line) and after (green line) filtering. The right top panel displays the post-processed EEG’s time-series (after thefiltering), the vertical line indicates the time of the eyes closed – eyes open transition. The subject is the same as in Fig. 1. that the TP-based diagnostic tools, s and a c , can alsodetect changes in datasets. As a measure of statisticalsignificance we calculate the p -value using Welch’s t-testand consider, as null hypothesis, that the signals repre-sent the same state. IV. RESULTS
We begin by calculating the PE for the raw, unfilteredtime series. Figure 3 displays the results obtained fromDTS1 and DTS2 and we can see that there is a significantdifference between the PE values of the eyes-closed andeyes-open states. The entropy is computed for each sub-ject, and then is averaged over all the subjects (71 or 109,depending on the dataset). The shaded area representsone standard deviation of the PE values of all subjects,and we note that there is large variability, thus, the PEvalue does not allow a full discrimination between the twostates. We note that the average PE value is slightly dif-ferent for the two datasets, which is attributed to the fact that they have different spatial and temporal resolution.We also note that the average value of the PE is signifi-cantly different from the maximum possible value (whichoccurs when the patterns are equally probable, and for D = 4, PE max = ln 24 = 3 . ), allow for a betterdiscrimination of the two states.Comparing with the results obtained from the filteredtime series, displayed in Fig. 4, we note that the PEvalues remain almost unchanged, which suggests that thePE captures changes in brain dynamics which are not dueto the change in the strength of alpha oscillations duringthe EC-EO transition.Figure 5 displays the TP-based measures, s and a c ,uintero-Quiroz et al 4 FIG. 3. Permutation entropy, Eq. 1, from raw time series ofDTS1 (top) and DTS2 (bottom). In DTS1 the subjects opentheir eyes at 120 s; in DTS2, at 60 s. The blue line indicatesthe mean value of the PE for all the subjects, and the shadedarea indicates one standard deviation of the PE values.
FIG. 4. Permutation entropy, Eq. 1, computed from filteredtime series of DTS1 (top) and DTS2 (bottom). using the DST2 (similar results were found in DST1),although there is a clear transition around 60s in themean values, the dispersion in the values of the differentsubjects is higher than in the PE analysis (likely due tothe limited length of the time series, which does not allowa precise estimation of the TPs).In Fig. 6 (for DTS1) and Fig. 7 (for DTS2) we presentthe topographic visualization for the different electrodes,of the PE value averaged over all the subjects, for theEC and EO conditions. We also present the difference ofPE values (PE-open - PE-closed), and the p -value. The s n a c FIG. 5. The entropy defined from the transition probabilities,Eq. 3, and the asymmetry coefficient, Eq. 4, computed for theDTS2. results are consistent for the two datasets, the discrep-ancies are due to their different spatial resolution. Wealso note the low p-values obtained, which confirm thesignificance of the uncovered differences.
V. CONCLUSIONS
We have used ordinal time series analysis to investigateEEG signals recorded under eyes-closed (EC) and eyes-open (EO) resting conditions. We have analyzed twodatasets with different spatial and temporal resolutions,and contrasted the results of the analysis of raw time se-ries and filtered time series (where eye blinking artifactswere removed and the alpha frequency band was filteredout). We used three diagnostic measures, the permu-tation entropy, PE, which is computed from the prob-abilities of the ordinal patterns, and two measures, thetransition entropy and the asymmetry coefficient, whichare computed from the transition probabilities betweenpatterns.We have found, in both datasets, that the EO stateis characterized by higher entropy values, accompaniedby a lower asymmetry coefficient, with respect to the ECstate. We have also identified which brain regions aremore important for distinguishing the two states. No sig-nificant difference was detected between the raw data andthe pre-processed data, which suggests that the ordinalmethod can be directly applied to EEG signals, avoidingthe need of data pre-processing. Thus, ordinal analysiscan be a computationally efficient tool, which could pro-vide extra valuable information for new brain-computerinterface protocols.
ACKNOWLEDGMENTS
This work was supported in part by ITN NETT(FP7 289146), the Spanish MINECO (FIS2015-66503and FIS2015-66503-C3-2-P) and the program ICREAACADEMIA of Generalitat de Catalunya.uintero-Quiroz et al 5 a) b) c) d) e) f) g) h) FIG. 6. Topographic visualization of the analysis of the raw (top row) and filtered (lower row) EEG signals of DTS1, averageover the subjects. Panels a) and e) display the permutation entropy for EC conditions; b) and f) for EO conditions; c) and g)display the difference of the PE values; d) and h) display the p value. a) b) c) d) e) f) g) h) FIG. 7. As in Fig. 6, but for the dataset DTS2. C. Bandt and B. Pompe, Phys. Rev. Lett. , 174102 (2002). Y. Cao, W.-w. Tung, J. Gao, V. A. Protopopescu, and L. M.Hively, Physical review E , 046217 (2004). C. Masoller, Y. Hong, S. Ayad, F. Gustave, S. Barland, A. J.Pons, S. G´omez, and A. Arenas, New Journal of Physics ,023068 (2015). M. Zanin, L. Zunino, O. A. Rosso, and D. Papo, Entropy ,1553 (2012). C. Quintero-Quiroz, S. Pigolotti, M. C. Torrent, and C. Masoller,New Journal of Physics , 093002 (2015). J. Li, J. Yan, X. Liu, and G. Ouyang, Entropy , 3049 (2014). N. Nicolaou and J. Georgiou, Expert Systems with Applications , 202 (2012). E. Olofsen, J. Sleigh, and A. Dahan, British journal of anaes-thesia , 810 (2008). A. A. Bruzzo, B. Gesierich, M. Santi, C. A. Tassinari, N. Bir-baumer, and G. Rubboli, Neurological sciences , 3 (2008). X. Li, G. Ouyang, and D. A. Richards, Epilepsy research , 70(2007). I. Veisi, N. Pariz, and A. Karimpour, in
Bioinformatics andBioengineering, 2007. Proceedings of the 7th IEEE InternationalConference on (IEEE, 2007) pp. 200–203. X. Ren, Q. Yu, B. Chen, N. Zheng, and P. Ren, in
DesignAutomation Conference (ASP-DAC), 2015 20th Asia and SouthPacific (IEEE, 2015) pp. 20–21. J. R. Smith, The Pedagogical Seminary and Journal of GeneticPsychology , 455 (1938). uintero-Quiroz et al 6 H. H. Jasper, Science (1936). E. D. Adrian and B. H. Matthews, Brain , 355 (1934). H. Berger, Archiv f¨ur Psychiatrie und Nervenkrankheiten , 231(1933). R. J. Barry, A. R. Clarke, S. J. Johnstone, C. A. Magee, andJ. A. Rushby, Clinical Neurophysiology , 2765 (2007). R. J. Barry and F. M. De Blasio, Biological psychology , 293(2017). S.-H. Jin, W. Jeong, D.-S. Lee, B. S. Jeon, and C. K. Chung,Journal of neurophysiology , 1455 (2014). B. Tan, X. Kong, P. Yang, Z. Jin, and L. Li, Computa-tional and mathematical methods in medicine (2013),10.1155/2013/976365. B. C. Van Wijk, C. J. Stam, and A. Daffertshofer, PloS one ,e13701 (2010). T. A. Schieber, L. Carpi, A. D´ıaz-Guilera, P. M. Pardalos, C. Ma-soller, and M. G. Ravetti, Nat. Commun. , 13928 (2017). Bitbrain Technologies, “http://bitbrain.tech/,”. G. Schalk, D. J. McFarland, T. Hinterberger, N. Birbaumer, andJ. R. Wolpaw, IEEE Transactions on biomedical engineering ,1034 (2004). A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C.Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C.-K. Peng, andH. E. Stanley, Circulation , e215 (2000). A. Gramfort, M. Luessi, E. Larson, D. A. Engemann,D. Strohmeier, C. Brodbeck, L. Parkkonen, and M. S.H¨am¨al¨ainen, Neuroimage , 446 (2014). A. Gramfort, M. Luessi, E. Larson, D. A. Engemann,D. Strohmeier, C. Brodbeck, R. Goj, M. Jas, T. Brooks,L. Parkkonen, et al. , Frontiers in neuroscience , 267 (2013). U. Parlitz, S. Berg, S. Luther, A. Schirdewan, J. Kurths, andN. Wessel, Computers in Biology and Medicine42