Acta Polytechnica Acta Polytechnica 53(2):94–97, 2013 © Czech Technical University in Prague, 2013 available online at http://ctn.cvut.cz/ap/ PREDICTIVE MODELS IN DIAGNOSIS OF ALZHEIMER’S DISEASE FROM EEG Lucie Tylovaa,∗, Jaromir Kukala, Oldrich Vysatab a Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Department of Software Engineering in Economy, Trojanova 13, 120 00 Praha 2, Czech Republic b Department of Computing and Control Engineering, Faculty of Chemical Engineering, Institute of Chemical Technology in Prague ∗ corresponding author: tylovluc@fjfi.cvut.cz Abstract. The fluctuation of an EEG signal is a useful symptom of EEG quasi-stationarity. Linear predictive models of three types and their prediction error are studied via traditional and robust measures. The resulting EEG characteristics are applied to the diagnosis of Alzehimer’s disease. Our aim is to decide among: forward, backward, and predictive models, EEG channels, and also robust and non-robust variability measures, and then to find statistically significant measures for use in the diagnosis of Alzheimer’s disease from EEG. Keywords: Alzheimer’s disease, EEG, linear predictive model, quasi-stationarity, robust statistics, multiple testing, FDR. 1. Introduction Dementia is a set of clinical symptoms, e.g., memory loss and communicative difficulties. Two main cat- egories are cortical and subcortical dementias. The most important cortical dementia, which accounts for about 50 % of the cases, is Alzheimer’s disease. In patients with Alzheimer’s disease, brain cells die quickly and the chemistry and structure of the brain is changed. EEG is used to study and detect abnor- malities caused by dementia. Biological rest is an endogenously dynamic process. Transient EEG events identify and quantify brain elec- tric microstates as time epochs with a quasi-stable field topography [1]. We can assume better predictability inside microstates, lower predictability during changes between microstates. Higher fluctuations of EEG pre- dictability may be connected with higher frequency of microstate changes. Falk et al. [2] analysed an EEG signal via its enve- lope. They first constructed the modulation spectrum and found the region of significant spectral peaks (SP). This technique achieves accuracy 81.3 % with sensi- tivity 85.7 % and specificity 72.7 %. After the Hilbert transform, they also calculated the percentage mod- ulation energy (PME) with better accuracy 90.6 %, sensitivity 90.5 %, and specificity 90.9 %. Another approach was used by Ahmadlou et al. [3]. The first step in their approach was based on wavelet decomposition. The resulting patterns were processed by the Visibility Graph Algorithm (VGA). The power spectrum of the VGA structures was used for fea- ture extraction. Two types of classifier (RBFNN, PCA-RBFNN) were used for the final decision. The accuracy was 96.50 % with sensitivity 100 % and speci- ficity 87.03 % in the case of RBFNN. PCA-RBFNN increased the accuracy to 97.75 % with sensitivity 100 % and specificity 91.08 %. 2. Models The main hypothesis of this work is that predictability of the brain activity differs between groups of patients with Alzheimer’s disease (AD) and normal controls (CN). The activity of the human brain is measured via multichannel EEG, which produces a time series. On the basis of the quasi-stationarity of the EEG signal, the time series were decomposed into non-overlapping segments of constant length. Each segment of a given EEG channel and of each patient produced a short time series, the properties of which were studied via linear autoregressive models of three types. 2.1. Predictive model Let m be the length of a segment. Let n be the model size as a number of parameters. Let x1, . . . ,xm be an EEG [4] data segment. The linear predictive model has the form xk = n∑ i=1 aixk−i + ek, , (1) for k = n+1, . . . ,m, where ek is the model error in the k-th measurement and ai is the model parameter for i = 1, . . . ,n. Formula (1) represents the traditional AR (autoregressive) model [5]. 2.2. Back-predictive model The predictive AR model (1) can also be used in the opposite time direction. The resulting model is xk = n∑ i=1 aixk+i + ek, (2) 94 http://ctn.cvut.cz/ap/ vol. 53 no. 2/2013 Predictive Models in Diagnosis of Alzheimer’s Disease from EEG Ch Predictive Back-predictive Symmetric STD MAD1 MAD2 STD MAD1 MAD2 STD MAD1 MAD2 1 0.1027 0.0402 0.0314 0.0711 0.0338 0.0270 0.0503 0.0131 0.0074 2 0.0065 0.0016 6.52·10−4 0.0031 0.0012 5.06·10−4 0.0015 2.16·10−4 6.00·10−5 3 0.0121 0.0038 0.0014 0.0141 0.0035 0.0013 0.0172 0.0010 2.24·10−4 4 0.1408 0.0612 0.0337 0.1470 0.0540 0.0308 0.0635 0.0081 0.0029 5 0.2551 0.1906 0.1277 0.2573 0.1690 0.1141 0.2063 0.0867 0.0441 6 0.0643 0.0476 0.0275 0.0647 0.0391 0.0223 0.0417 0.0165 0.0064 7 0.0279 0.0192 0.0103 0.0232 0.0166 0.0086 0.0288 0.0214 0.0091 8 0.0917 0.1619 0.1290 0.0947 0.1474 0.1152 0.0572 0.0908 0.0664 9 0.1780 0.2093 0.1512 0.1815 0.1797 0.1308 0.1862 0.0832 0.0504 10 0.6823 0.8572 0.8429 0.7739 0.8309 0.8136 0.6093 0.6226 0.5553 11 0.2358 0.1763 0.1203 0.2218 0.1540 0.1046 0.1234 0.0527 0.0255 12 0.0910 0.0598 0.0467 0.0924 0.0545 0.0446 0.0359 0.0285 0.0216 13 0.1183 0.2376 0.1806 0.0953 0.2120 0.1607 0.0997 0.1113 0.0602 14 0.1027 0.1964 0.1744 0.1114 0.1779 0.1595 0.0706 0.0827 0.0558 15 0.2297 0.2925 0.2539 0.2363 0.2521 0.2174 0.1673 0.1517 0.0985 16 0.4478 0.5942 0.5282 0.4009 0.5395 0.4806 0.3636 0.3136 0.2170 17 0.0680 0.1197 0.1094 0.0437 0.1070 0.0965 0.0288 0.0304 0.0175 18 0.0418 0.0634 0.0595 0.0545 0.0694 0.0654 0.0296 0.0299 0.0219 19 0.2875 0.3889 0.3288 0.2483 0.3431 0.2868 0.1506 0.1568 0.1025 Table 1. Traditional fluctuation measures. where ek is again the model error, but for k = 1, . . . ,m−n. 2.3. Symmetric model The third AR model is symmetric, and thus with lower prediction error for smooth signals. Supposing n is even, the adequate model is xk = n/2∑ i=1 aixk−i + n/2∑ i=1 an/2+ixk+i + ek, (3) where ek is the model error for k = n/2 + 1, . . . ,m− n/2. 2.4. Model error The three AR models above are easily comparable, because they produce an overdetermined system of M = m−n linear equations for n unknown variables a1, . . . ,an. The unknown parameters a1, . . . ,an were estimated by the method of least squares (LSQ) [6] and the residues r1, . . . ,rM are determined as the difference between an observed value and a predicted value. The estimate of the prediction error inside the given segment is se = √ ∑M i=1 ri 2 M −n . (4) 3. Fluctuation of the model error Three basic characteristics were used to characterize EEG fluctuations: the standard deviation (STD), the mean of the absolute differences from the mean value (MAD1), and the mean of the absolute differences from the median value (MAD2). However, these char- acteristics are excessively sensitive to outlier values. We preferred robust measures of EEG fluctuations: the median of the absolute differences from the median (MAD3), the interquartile range (IQR), and the first quartile of the absolute mutual differences (MED). Let N be the number of EEG signal segments. Let s = (s1,s2, . . . ,sN ) be the vector of errors (4) in all segments. Let Q1, Q2, Q3, E be the first, the second, and the third quartile and mean value functions. The fluctuation criteria are defined as STD = (E(s − E(s))2)1/2, (5) MAD1 = E(|s − E(s)|), (6) MAD2 = E(|s − Q2(s)|), (7) MAD3 = Q2(|s − Q2(s)|), (8) IQR = Q3(s) − Q1(s), (9) MED = Q1(|si −sj|). (10) We obtained the STD, MAD1, MAD2, MAD3, IQR, and MED values of the model fluctuations of each channel for all AD and CN patients. The null hy- pothesis H0: µAD = µCN was tested via a two-sample t-test [7] against the alternative HA: µAD 6= µCN. Here, µAD = E ln fluctuation (5–10) for AD group and µCN = E ln fluctuation (5–10) for CN group. 4. Experimental part Groups of 26 AD and 139 CN patients were used for testing. We used the international 10–20 electrode sys- tem with constant sampling frequency 200 Hz. A pre- dictive model (1), a back-predictive model (2), and a 95 L. Tylova, J. Kukal, O. Vysata Acta Polytechnica Ch Predictive Back-predictive Symmetric STD MAD1 MAD2 STD MAD1 MAD2 STD MAD1 MAD2 1 0.0029 0.0265 0.0018 0.0035 0.0236 0.0021 2.6·10−4 0.0025 2.3·10−4 2 6.9·10−6 6.2·10−5 4.8·10−6 1.0·10−5 5.1·10−5 4.8·10−6 3.9·10−7 3.0·10−6 5.1·10−7 3 3.5·10−6 6.5·10−5 3.5·10−6 1.7·10−6 4.2·10−5 3.7·10−6 1.8·10−7 1.6·10−6 3.0·10−7 4 2.4·10−4 0.0019 2.2·10−4 6.6·10−4 0.0026 3.4·10−4 4.8·10−6 4.6·10−5 9.1·10−6 5 0.0017 0.0124 0.0022 0.0038 0.0170 0.0025 1.4·10−4 0.0015 2.1·10−4 6 2.9·10−4 0.0047 4.1·10−4 2.9·10−4 0.0039 3.2·10−4 2.4·10−5 2.4·10−4 3.2·10−5 7 2.4·10−4 0.0025 1.9·10−4 1.7·10−4 0.0019 1.7·10−4 2.9·10−4 0.0014 2.6·10−4 8 0.0478 0.0787 0.0390 0.0495 0.0679 0.0406 0.0174 0.0384 0.0204 9 0.0159 0.0490 0.0127 0.0130 0.0387 0.0123 0.0013 0.0066 0.0023 10 0.8614 0.6785 0.7914 0.8522 0.6462 0.7958 0.3281 0.2948 0.3613 11 0.0038 0.0227 0.0034 0.0021 0.0151 0.0031 1.8·10−4 0.0015 2.4·10−4 12 0.0054 0.0182 0.0082 0.0066 0.0201 0.0121 0.0051 0.0100 0.0083 13 0.0177 0.0722 0.0212 0.0201 0.0730 0.0219 7.0·10−4 0.0085 6.9·10−4 14 0.0713 0.1341 0.0873 0.0676 0.1056 0.0885 0.0040 0.0180 0.0053 15 0.0877 0.1351 0.0791 0.0581 0.0994 0.0631 0.0028 0.0139 0.0050 16 0.2547 0.2882 0.2583 0.2338 0.2464 0.2512 0.0131 0.0368 0.0195 17 0.0307 0.0740 0.0359 0.0277 0.0676 0.0338 4.3·10−4 0.0038 4.7·10−4 18 0.0511 0.1400 0.0317 0.0451 0.1313 0.0375 0.0032 0.0257 0.0033 19 0.0491 0.1666 0.0492 0.0448 0.1625 0.0439 0.0017 0.0253 0.0021 Table 2. Robust fluctuation measures. Predictive Back-predictive Symmetric MAD3 3 3 2, 3, 4 IQR 2, 3 MED 2, 3 2, 3 2, 3 Table 3. Significant channels. symmetric model (3) were identified, and the model errors (4) and their fluctuations were studied for seg- ment length m = 150 and model size n = 50. The number of EEG segments varied patient-by-patient and satistisfied the inequality 352 ≤ N ≤ 762. The significance level for the testing was α = 0.001. The hypotheses of mean equity were tested on 19 EEG channels, three predictive models, and six fluctuation characteristics. This is a kind of multiple testing, with 342 potentially dependent tests. The standard False Discovery Rate (FDR) methodology [8] was used to eliminate the acceptance of a false hypothesis. The corrected critical value was determined as αFDR = 4.8347 · 10−6. The t-test results (pvalue) for traditional measures are included in Tab. 1. Results for robust measures are collected in Tab. 2. Bold font was used for a pvalue below the critical probability αFDR. The null hypothesis was rejected only in chan- nels 2, 3, 4, which correspond to the frontal domain of the human brain. Only three robust fluctuation characteristics are significant: ln MAD3, ln IQR, and ln MED. The second channel is significant only for ln MED or symmetrical prediction. The third channel is significant only for ln MED, ln MAD3 or symmetric prediction. The fourth channel is significant only for ln MAD3 together with symmetrical prediction. Tab. 4 summarizes the results. The best pvalue = 1.8885 · 10−7 was obtained on the third channel for the symmetric model and the ln MAD3 criterion. Figure 1 shows its Receiver oper- ating characteristic (ROC) curve [9]. The area under the curve (AUC) is 0.77, which evaluates the model as good. The boxplot in Fig. 2 displays the differences between AD and CN patients. 5. Discussion While the autoregressive model is linear and requires a stationary signal, the higher fluctuation of the model error in Alzheimer’s subjects may reflect a different structure of brain microstates than in healthy subjects. It may reflect alterations in the brain anatomical cortical connectivity in resting-state networks. In contrast to applying robust methods and filters, the autoregressive linear model offers a simple and traditional solution that provides results with a suffi- cient level of significance. These results could also be influenced by the small group of testing data. 96 vol. 53 no. 2/2013 Predictive Models in Diagnosis of Alzheimer’s Disease from EEG 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 − sp se Figure 1. ROC for ln MAD3 6. Conclusion Using a symmetric predictive model of the EEG sig- nal and MAD3, IQR, and MED robust measures of predictive error fluctuations, we recognize significant differences between AD and CN groups in the case of frontal electrodes, which are represented by the second, the third, and the fourth channel of EEG. This result is directly applicable to the diagnosis of Alzheimer’s disease. The accuracy of our method is 63.64 % with sensitivity 84.62 % and specificity 59.71 %. However, methods based on the modula- tion spectrum and the Hilbert transform [2] or on the Visibility Graph Algorithm [3] are better in accuracy, sensitivity, and specificity. Acknowledgements This paper was created with support from CTU in Prague grant SGS11/165/OHK4/3T/14. References [1] Musso, F., Brinkmeyer, J., Mobascher, A., Warbrick, T., Winterer, G., Spontaneous brain activity and EEG −7.5 −7 −6.5 −6 −5.5 −5 −4.5 −4 −3.5 AD CN ln M A D 3 Figure 2. Boxplot diagram for ln MAD3 microstates. 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[8] Benjamini, Y., Hochberg, Y., Controlling the false discovery rate: A practical and powerful approach to multiple testing, Journal of the Royal Statistical Society, Vol.57, No.1, 1995, pp. 289-300. [9] Fawcett, T., An Introduction to ROC Analysis, Pattern Recognition Letters, Vol.27, No.8, 2006, pp. 861-874. 97 Acta Polytechnica 53(2):94--97, 2013 1 Introduction 2 Models 2.1 Predictive model 2.2 Back-predictive model 2.3 Symmetric model 2.4 Model error 3 Fluctuation of the model error 4 Experimental part 5 Discussion 6 Conclusion Acknowledgements References