EPILEPTIC SEIZURE PREDICTION

Transcription

1 EPILEPTIC SEIZURE PREDICTION Submitted by Nguyen Van Vinh Department of Electrical & Computer Engineering In partial fulfillment of the requirements for the Degree of Bachelor of Engineering National University of Singapore i

2 ABSTRACT This project evaluates performance of seizure prediction based on various characterizing measurements on rat model of human temporal epilepsy. Different approaches are compared in term of the predictive power and prediction interval at different levels of channel consistency. Results obtained show that nonlinear measurements outperform linear measurements in three out of four studied animals. Effects of filtering on prediction performance are also being examined and results show that measurements such as correlation density and correlation dimension are very robust with respect to filtering. The mean prediction time obtained is up to 50 minutes before seizure onsets and the false positive rate is as low as 10%. Finally, prediction scheme using three-channel consistency check generally gives longer prediction intervals. ii

3 ACKNOWLEDGEMENTS I would like to thank my parents for their love and support. I would also like to thank my brother for sharing with me his research experiences. My family is always beside me and gives me courage and motivation to proceed in this project. I would like to thank Dr. Yen for his enthusiastic and excellent supervision during the course of this project. His elaborate guidance help me always on the right track of my research. I also learned from him helpful research experiences and good work ethics. I would like to thank Dr. Tang, Mr. Yongcheng, Ms. Wen Lin and Ms. Ezza from National Neuroscience Institute for giving me invaluable support on the epileptic data. I would also like to thank Mr. Roger and Ms. Yasamin from Biomedical Signal Processing lab for giving me helpful technical supports. iii

4 CONTENTS ACKNOWLEDGEMENTS... iii CONTENTS... iv LIST OF FIGURES... vii LIST OF TABLES... ix LIST OF SYMBOLS AND ABBREVIATIONS...x CHAPTER INTRODUCTION Importance of seizure prediction in epilepsy Clinical applications Project objectives Organization...2 CHAPTER SEIZURE PREDICTION IN EPILEPSY Overview Basic of electroencephalogram Definitions of seizure activity Linear time series analysis Power method Autocorrelation method Nonlinear time series analysis Embedding theory Choosing delay parameters Choosing embedding dimension Kolmogorov entropy Lyapunov exponent iv

5 2.5.6 Correlation density and dimension CHAPTER DATA DESCRIPTION AND EXPERIMENTAL PROCEDURES Data recording Rat model of human epilepsy EEG signal characteristics and filtering Data manipulation and visualization Nonlinear dynamics toolboxes: CHAPTER AUTOMATIC SEIZURE PREDICTION Objectives Detection based on average power calculation Detection based on correlation integral Sliding window analysis Phase space reconstruction Estimation of C(r) Removal of temporal correlation Correlation density Detection based on Kolmogorov entropy Comparison and results CHAPTER SEIZURE PREDICTION Overview Data sets Calculation of characterizing measurements Variance Linear cross-correlation Correlation dimension Prediction scheme and performance indicators v

6 5.4.1 Prediction scheme Receiver operating characteristic curve Prediction intervals Results Measurement profiles Estimated ROC curves Prediction interval Performance at different consistency levels CHAPTER CONCLUSIONS Concluding remarks Future directions REFERENCES vi

7 LIST OF FIGURES Figure Caption Page Fig. 3.1 (A) Six-minute long episode containing seizure at t=230s. (B) Spectrogram of a Fig. 3.2 Fig. 4.1 minute EEG segment, seizure occurs at t=200s (A) Order-2 Butterworth digital filter magnitude response. (B) Original signal and filtered signal Power spectrum of a five-minute EEG signal. (A) Traditional FFT using 512 points (B) FFT using Welch method with 512 segments, 50% overlapping and triangular windowing Fig. 4.2 Detection of seizure using moving average power. Seizure occurs at t=200s 23 Fig. 4.3 Mutual information of a seizure window. Average cycle time = (s/cycle) 24 Fig. 4.4 False nearest neighbor of seizure and non-seizure window. Calculations are performed both on raw and filtered data 26 Fig. 4.5 Phase space reconstruction at m = 7 and τ = 10 sample 27 Fig. 4.6 Fig. 4.7 STP of a 20s EEG segment. Curves from bottom to top correspond to density levels 5%,10%,, 100% (A) Correlation integral of non-seizure and seizure window. (B) Correlation density of one data segment, seizure occurs at t=3600s Fig. 4.8 Kolmogorov entropy calculated for one data segment, seizure occurs at t=3600s 31 Fig. 5.1 Cross-correlation function. (A) Nonseizure window. (B) Seizure window 36 Fig. 5.2 Estimation of correlation dimension from C r. (A) Non-seizure window, D 2 = (B) Seizure window, D 2 = Fig. 5.3 Profile of different measurements from one seizure episodes of HM3, seizure occurs 41 vii

8 at t=3600s Fig. 5.4 Estimated ROC curves for five measurements on raw data sets 43 Fig. 5.5 Estimated ROC curves for five measurements on filtered data sets 43 Fig. 5.6 ANOVA on distributions of areas under ROC curves on for unfiltered data sets 45 Fig. 5.7 ANOVA on distributions of areas under ROC curves for filtered data sets 46 Fig. 5.8 Prediction intervals corresponding to optimal threshold levels on raw data 47 Fig. 5.9 Prediction intervals corresponding to optimal threshold levels on filtered data 47 Fig Prediction performance at different consistency levels on filtered data sets 48 Fig Prediction intervals for different levels of channel consistency on filtered data sets For each column of each plot, from left to right is corresponding to one-channel, two-channel and three-channel consistency levels 50 Fig Optimal settings of k value for different channel consistency levels 50 viii

9 LIST OF TABLES Table Caption Page Table 4.1 Collected episodes from detection algorithm. Seizure episodes contain 60 minutes pre-ictal activities and 10 minutes post-ictal activities. Control data are at least 3 hours before any seizures 32 Table 5.1 Data sets from four mice 35 Table 5.2 Areas under ROC curves of five measurements for raw and filtered data sets 43 ix

10 LIST OF SYMBOLS AND ABBREVIATIONS {x i } 1 N P 0 F s Sk X i m τ dt I τ S m m 0 R m i C t C b KE ml b avg λ i λ max C r D 2 H z δt Time series with N points Power Autocorrelation function Characteristic time Embedding vector Embedding dimension Delay parameter Embedding window Mutual information Average displacement of embedding vector Minimal embedding dimension distance between a vector and its nearest neighbor Separation of the two trajectories at time t Separation of the two trajectories at time step b Maximum likelihood estimator for Kolmogorov entropy The average time step for trajectories divergence Lyapunov exponent in i-th dimension Maximum Lyapunov exponent Correlation integral Correlation dimension Discrete transfer function Theiler window x

11 t s F s C x, y τ C m Sampling time Sampling frequency Linear cross-correlation Maximum correlation coefficient EEG MI FNN KE LA CI COR LP TLE FFT SGE STP VA XC ROC ANOVA Electroencephalogram Mutual information False nearest neighbor Kolmogorov entropy Lyapunov exponent Correlation integral Correlation density Lithium-pilocarpine Temporal lobe epilepsy Fast Fourier Transform Sun Grid Engine Space-time separation plot Variance Cross-correlation Receiver operating characteristic Analysis of variance xi

12 CHAPTER 1 INTRODUCTION 1.1 Importance of seizure prediction in epilepsy Epilepsy is one of the most common serious neurological disorders which affect 0.8% of the human population [1]. One-third of patients remain refractory to drug therapy and surgery is usually not applicable. The most devastating aspect of epilepsy is the unpredictability of seizure onset, which affects patient safety and the management of medications. The ability to predict seizure onsets can help 25 million patients with alternative treatment paradigms. Effective prediction scheme also enables timely clinical interventions, thus reduce anti-epilepsy drugs used and their various side-effects. 1.2 Clinical applications In the last two decades, there was a substantial interest in the field of epileptic seizure prediction among the medical community. In order to capture the characteristics and transitions of brain activities before and during ictal states, electroencephalogram (EEG) was the most useful measurement. The development in time series analysis theories, especially the introduction of novel concepts on nonlinear systems into studies of human brain dynamics and EEG measurement has enabled imminent seizures to be anticipated up to minutes before onsets. One example application of prediction schemes for clinical use is the development of implanted neuroprosthetis devices for epilepsy treatment. In an on-going study at New York University [2], a hybrid neuroprosthesis device combining electrophysiological and pharmacological components is developed to correct abnormal neural functions. In this study, a simple and fast 1

13 computational scheme was implemented to recognize abnormal epileptiform EEG signals prior to clinical seizure. The device then activates pharmacological unit to deliver anti-epilepsy drugs and correct neural abnormalities. In another study by NeuroPace Company [3], the so-called RNS system, which is currently on clinical trials, is developed to detect and suppress seizures by brain stimulation. The RNS is implanted in the brain and is designed to continuously monitor electrical activities from the brain dynamics. Once the signature of seizure onset is detected, the device produces brief and mild electrical stimulation to suppress upcoming seizure. 1.3 Project objectives With the aforementioned importance and promising clinical applications, it is desirable to have a general assessment on performance of different seizure prediction schemes. In this project, different anticipation methods are to be implemented and compared to give an insight of pros and cons of different approaches. With the availability of large amount of epileptic EEG signals from rat models, statistically reliable results on performances of prediction algorithms are also to be obtained to provide hints for future diagnostic and therapeutic applications in epileptic patients. The project also aims at studying the real, complex and nonlinear dynamical system of human brain which might have useful implication for treating other neurological disorders 1.4 Organization The content presented in this thesis is mainly focused on the application of time series theories for data analysis. It also discusses computational schemes proposed and implemented, experimental results obtained and observations made based on those results. The composition of this thesis is as follows: 2

14 Chapter 2 provides a review of epileptic seizure prediction, addresses achievements made recently by the academic community and some challenging problems remain unsolved. Chapter 3 explains in detail the project settings and executions as well as basic information about epileptic rat model. Chapter 4 explains the implementation of automatic detection algorithm and the building of seizure and control EEG episodes for applying various prediction algorithms. Chapter 5 provides implementation and evaluation prediction algorithms using both linear and nonlinear approaches. the research. Chapter 6 summarizes results obtained from this study and suggests future directions for 3

15 CHAPTER 2 SEIZURE PREDICTION IN EPILEPSY 2.1 Overview Since 1980s, computer-based instrumental and analytical methods had been used in the studies of EEG. There were some early studies in the field of epilepsy that reported successful application of frequency-domain analysis and auto-regressive models into the problem of seizure prediction. However, these methods were either difficult to evaluate or the anticipation periods obtained were limited to only few seconds. Since 1990s, when theories and concepts of nonlinear dynamics were introduced to the study of complex brain system, numerous studies in the field reported the possibility to anticipate up to minutes or even hours prior to seizure onsets. Even though these results suggest promising perspective for epileptic patients, all different methods proposed bare certain limitations and there are still no standard rules for detecting pre-ictal states. The main reason for this is due to the unknown nature of underlying processes that lead to seizures. On the one hand, it s contentious that whether these underlying processes are stochastic or deterministic. Before the introduction of nonlinear dynamics theories in 1980s, there re basically classes of processes conceived: Deterministic processes: periodic (or quasi-periodic) processes (apart from transients), which can be completely described by their Fourier spectrum Stochastic processes: have broad-banded Fourier power spectrum and contain pure randomness as driving forces 4

16 However, when nonlinear dynamics theories (or chaos theory ) came in, it is argued that there are irregular, non-periodic time series which are nevertheless completely deterministic. In particular, EEG time series is thought to be of this type of process by the scientist supporting this chaos theory. Initial attempts in seizure prediction employed the statistical theory of stochastic processes but didn t obtain prominent results. Meanwhile, nonlinear techniques have been used more and more extensively in epilepsy studies to establish promising prediction algorithms, some of which are currently being used in clinical trials. However, the validity of nonlinear approach is still debatable. Moreover, different methods are implemented in different project settings, with data sets that might be completely different in nature. Hence, any general comparison between the linear and nonlinear techniques for seizure prediction will tend to be subjective and inconclusive. On the other hand, even when the assumption of deterministism is valid, it is almost impossible to provide information about the future state of a process, given its present and past information. For EEG time series, it is often observed that the underlying process exhibits a chaotic behavior in which any minute perturbations will be propagated exponentially to the future states. Thus, with the finite computational precision of digital computers, it is impossible to tell exactly about the future state from past and present state information. The only feasible approach in the field of seizure prediction is to look for a general signature of upcoming seizure, and some scientists also try to prove the existence of the so-called pre-ictal state. 2.2 Basic of electroencephalogram In most of epilepsy studies, EEG signal is used to measure, characterize and detect seizures. There are standard EEG, which is used in clinical applications, and invasive EEG signal recorded from implanted electrodes. EEG can be thought of as a linear summation of all 5

17 neuronal activities in the brain. However, nonlinear processes still manifest within EEG recordings due to the nonlinear properties of individual neuronal response and the complicated neuronal interaction. Since clinical recording represents the aggregate activities of over one million neurons, it tends to be blind to details of small-scale processes occurring at the seizure onset. Hence, it is often more convenient to use invasive EEG which can capture the systematic change of small-scale processes at seizure onset and less likely to suffer from unwanted noises. 2.3 Definitions of seizure activity There are two defining terms for epileptic seizure: Clinical seizure: a change in observable behavior associated with a diminished adaptive response to the environmental input, and electrical abnormalities in the cortex Electrographic seizure: paroxysmal abnormal cortical electrical activity. Electrographic seizure does not have to involve changes in observable behavior nor loss of adaptive skills. In this study, prediction of seizures is associated with the definition of electrographic seizure, even though most of the time seizures are verified by obvious change in subject s behavior as well. The ictal period is defined as the epoch between seizure onset and offset. Interictal period is the epoch between seizures. During the interictal period, two hypothetical states occur: the preictal (prior to the seizure onset) and the postictal (after the seizure onset). The hypothesized processes during preictal state leading to seizure is referred to as ictogenesis. The detection of ictogenesis can therefore help predict seizure onset. 2.4 Linear time series analysis 6

18 Various linear methods have been used in studies of epilepsy. Some of these methods use the calculation of power and the autocorrelation function as explained below Power method A simple and intuitive approach is to calculate the total power of the time series. In this method, the power P o of demeaned time series window {x i } 1 N is calculated as follows: N P o = 1 N x i 2 i=1 (2.1) By monitoring the power index over time, Litt et al. (2001) [4] detected an increase in energy in adult patients several hours prior to a seizure onset. Similarly, van Drongelen et al. (2003) [5] used this method to predict seizures in pediatric patients up to 45 minutes. Since the data is demeaned, the power index mentioned can also be thought of as the variance of the time series. Hence, this method is equivalent to the method of running variance (VA) used by McSharry et al. (2003) [6]. McSharry and co-workers used the running variance technique to compare with a nonlinear approach using correlation integral, which will be addressed later Autocorrelation method Autocorrelation function represents the similarity between observations as a function of the time separation between them. For a time series x N i 1, the correlation function at time lag s is defined as: F s = 1 N s N s j =1 x j x(j s) (2.2) 7

19 By calculating the autocorrelation function of a time series segment, we may detect any substantial spectral change occurring before and during seizure onset. Martinerie et al. (1998) [1] used this method to examine the epileptiform signal from 11 patients. In this study, by monitoring the characteristic time Sk such that F(Sk) = 1/e over time, Martinerie and coworkers showed that the autocorrelation method can help detect well the seizure onset but provide no significant anticipatory signs of the transition. 2.5 Nonlinear time series analysis This section provides the application of nonlinear dynamics concepts into the analysis of EEG time series. The important background of the embedding theory will be explained, followed by various nonlinear metrics that have been used for characterizing and predicting seizures Embedding theory As EEG time series is only a scalar measurement from the multi-dimensional brain dynamics, much of important information about the system transitions has been hidden due to the projection into low-dimension space. Thus, it is desirable to have a mechanism to reconstruct the original state-space from observable scalar time series. The reconstruction procedure is done by using the important theory so-called the method of delay by Taken (1981) [7]. In this N method, the embedding of a time series x i 1 is done by creating a set of vector X i such that: X i = x i, x i+τ, x i+2τ, x i+3τ,, x i+ m 1 τ dt (2.3) where m is the embedding dimension, τ is the delay in number of samples, and dt is the embedding window: dt = m 1 τ. According to Taken s theory [7], a reconstruction will preserve system s invariants if m is greater than twice the topological dimension of the original system. However, Taken s theory 8

20 assumed that there is an infinite amount of noise-free data and did not provide any hints about the choice of embedding parameters m and τ. Hence, we need to follow some procedures to choose good embedding parameters, which are critical in practical applications Choosing delay parameters Choice of dt There are several methods for choosing the delay parameters. An important condition for good embedding delay window dt is that it should not be too large so that the first and the last element of the embedding vector X i are practically uncorrelated (large dt means trajectories x i along the embedding vector tend to wrap around the state space attractor). On the other hand, dt should be large enough to cover the dominant frequency range in the signal. One simple way is to choose dt such that the autocorrelation function F(s) (section 2.4.2) first drops below a certain fraction of its initial value. However, it is argued that autocorrelation approach is inconsistent due to ill-defined relation between temporal measurement reflected by F s and spatial distribution of the reconstructed attractor. Another approach for choosing dt is to use mutual information of the time series. For a time series x N i i=1, mutual information at a time lag τ is defined as: I τ = P x n, x n + τ log 2 P x n, x n + τ P x n P x n + τ x n,x n+τ (2.4) In general, I(τ) measure includes both the linear and nonlinear dependence within the signal at a time lag τ. It is thus recommended to choose dt corresponding to the first local minimum of I(τ) so that x(i) and x(i + dt) are independent enough. The problem with this method is computational costs and difficulties in finding the extrema. It is also argued by 9

21 Martinerie et al. (1992) [8] that this approach does not guarantee giving the optimal embedding window for estimation of correlation dimension. Choice of τ Since τ is related to the embedding window dt and the embedding dimension m, it is often that dt and m are chosen first, and then τ is obtained using m 1 τ = dt. However, there are cases where τ is normalized to 1 samples for convenience, as in the approach of Schouten et al. (1994a) [9]. On the other hand, it is argued by Rosenstein et al. (1993) [10] that the choice of τ is more important and they suggested a scheme for choosing τ based on a geometrical perspective. In this approach, τ is chosen to maximize the average displacement S m of embedding vectors from their original location on the line of identity in the phase space: N m 1 S m τ = 1 2 x i + jτ x i N i=1 j =1 (2.5) Choosing embedding dimension One popular approach to determine a proper embedding dimension is to look at the fraction of false nearest neighbors (FNN) in the phase space. Suppose the minimal embedding N dimension for a given time series x i i=1 is m 0. This means in m 0 -dimensional delay space, the reconstructed attractor is a one-to-one mapping of the original attractor and thus the fraction of FNN is small. Therefore, a proper embedding dimension should result in a small fraction of FNN and any higher embedding dimensions would cause little variance in FNN calculation. Specifically, let R m (i) be the distance between vector X i and its nearest neighbor in m- 10

22 dimensional space. Relative distance change from embedding dimension m to m + 1 is then defined as: ΔR m i = 2 2 R m +1 i R m i 2 R m i (2.6) If ΔR m i exceeds certain threshold then its neighbor is marked as a false neighbor. The plot of fraction of FNN gives hint to how good an embedding dimension is Kolmogorov entropy A nonlinear metric that has been used to detect the preictal activities is the calculation of Kolmogorov entropy (KE). It measures the rate at which information about the state of a system is lost and can be estimated by monitoring two initially nearby trajectories in the attractor. The time interval t required for the two trajectories to diverge beyond a threshold distance satisfies the distribution:,where C(t) is the separation of the two trajectories. C t e KEt (2.7) For digital signal with sampling time Ts, this relationship becomes:,where b is the time step for trajectory divergence. C b e KEt sb (2.8) It is showed by Schouten et al. (1994b) [11] that the maximum likelihood estimator for Kolmogorov entropy KE ml is as follows: KE ml = 1 T s log b avg (bits/second) (2.9) 11

23 in which b avg is the average time step for trajectories divergence. Using KE calculation, van Drongelen et al. (2003) [5] reported detection of preictal activities up to 30 minutes before a seizure onset. In this study, the authors monitored the trend of KE, a significant decrease of which will likely to inform an upcoming seizure Lyapunov exponent Lyapunov exponent (LE) represents the convergence and divergence of trajectories in each dimension of the attractor. On the one hand, for an attractor to exists, there must be attraction (convergence) of trajectories into its space. On the other hand, for a chaotic phase space, there must be at least one dimension in which the initially nearby trajectories diverge. For a dimension i-th, the corresponding LE λ i >0 indicates divergence and λ i < 0 indicates convergence in that dimension. In term of seizure prediction, it is often of our interest to look at the maximum LE, which has to be positive for a chaotic phase space. For a given time series segment x N i i=1, the maximum LE is estimated as: λ max = 1 N α α λ ij (2.10) where λ ij is local LE and N α is the total number of those exponents. λ ij (bits/second) are obtained from the divergence of neighboring trajectories X i = X(t i ) and X j = X(t j ) after a set time scale Δt: λ ij = 1 Δt log 2 X t i + Δt X t j + Δt X t i X t j (2.11) 12

24 Recently, Isemidis et al. (2005) [12] used the approach of LE to obtain promising results in seizure prediction. The scientists were able to predict 91.3% of 23 impending seizures on human EEG, with prediction interval of approximately 89 minutes and low false warning rate. In this approach, the statistical difference between LE calculations of different channels was examined. Seizures are argued to be associated with systematic entrainment of LE calculation, thus a significant drop in the statistical difference can help anticipate seizure onset Correlation density and dimension Measures of dimensionality are often used to characterize the attractor geometry. For seizure prediction, correlation dimension D 2 is often refered to. The dimension can be derived from the so-called correlation integral (CI), which is defined as: C r = with Θ(x) is the Heaviside function. 1 N N 1 i j Θ r X i X j (2.12) The correlation integral C(r) at a particular length scale r represents the probability of finding two vectors X i and X j whose distance is less than r. Intuitively, this measures the particle density of the attractor. For a large number of points N in the time series segment, C(r) follows the power law: C(r) r D 2 (2.13) Thus, D 2 can be estimated by calculating the slope in the plot of logc(r) vs logr. In practical situation, the plot of logc(r) is not exactly a straight line, with noise effects usually occur at small length scales and saturation effect at large length scale. Therefore, the choice of length scales at which D 2 can be estimated from (so-called the scaling region) is critical. 13

25 Schouten et al. [9] proved that in the present of noise, the correlation integral C(r) is effectively zero below a length scale threshold r n. The correlation integral is then follows the modified form of power law: C r = r r n 1 r n D 2 (2.14) where r n r 1 is the normalized length scale. According to this approach, the dimension can then be estimated by doing a nonlinear curve fitting with nonlinear parameters r n and D 2. Due to the difficulties in finding proper scaling region, as well as the dependence of D 2 estimation upon embedding parameters, estimated values are not guaranteed to be the exact geometrical dimension of the attractor. However, the discriminative power of D 2 estimate can still be employed to predict seizures. For example, Lehnertz and Elger (1998) [13] used a modified version of D 2 estimate to predict up to 5.25 minutes before seizures. Similarly, in stead of looking for the exact estimation of D 2 to detect pre-ictal activities, some research groups actually focus on the correlation integral for seizure prediction. Martinerie and co-workers [1] monitored the correlation density (COR) - value of C(r) calculated at a fixed length scale r = r 0 over time - to look for pre-ictal states. By using this correlation density measurement, they were able to anticipate seizures at the average time interval of 2.5 minutes and concluded that this method outperforms the method of autocorrelation applied on the same data set. In another study, Lerner (1996) [14] showed that the method of correlation density is robust with respect to embedding parameters and noise effects. 14

26 CHAPTER 3 DATA DESCRIPTION AND EXPERIMENTAL PROCEDURES 3.1 Data recording In this project, seizure prediction algorithms are examined based on invasive EEG recordings on rat model of human temporal epilepsy. The experiment was performed at National Neuroscience Institute. Multi-channel EEG recording from the amygdalo-hippocampal complex of animal brain was transmitted via a wireless link and collected by PowerLab hardware. The data was then amplified, digitalized at 2000 Hz sampling frequency and converted into MATLAB format for further processing, which is the main task in this project. The availability of long EEG recording (from 15 to 30 days) of subjects studied is a crucial advantage since not many researches in the field have been able to perform on large amount of data and come up with statistically significant conclusions. In addition to EEG signals, there are recorded videos available for determining any abrupt changes in clinical behavior and verifying seizure activities. 3.2 Rat model of human epilepsy Due to ethical constraints in experimentation with human brain, a rat model is being used to study epilepsy. In order to access performance of epileptic seizure prediction algorithms, a chronic epilepsy model should satisfy the following criteria: The model should be simple and inexpensive so that a large number of subjects can be generated for studying 15

27 The model should allow long-term recording and monitoring. The animal should survive the acute epileptogenic insult used to induce epilepsy. Seizure generated should be discrete and countable. The model should simulate at least one form of human epilepsy in term of clinical behaviors and electrographic characteristics. In this project, lithium-pilocarpine (LP) model of acute status epilepticus in rats is implemented to simulate the intractable temporal lobe epilepsy (TLE) in human. It has been proved seizures generated from LP model are similar to TLE seizures in term of electrographic characteristics. Since TLE is among the most common intractable epilepsy, observation from analysis based on LP model can give valuable contribution to our understanding of human epilepsy. The underlying mechanism of epileptic seizures involves abnormal discharge and synchronization of neurons to a great extent. Prediction algorithms should capture these activities during pre-ictal periods in order to effectively anticipate seizure onsets. 3.3 EEG signal characteristics and filtering The EEG signal collected has amplitude range from -1.5 V to 1.5 V, dominant frequency from 0.5 to 100 Hz as can be seen from the spectrogram below. Even though seizures are clearly visible in the epileptiform signal shown, there are many other cases where it is not obvious to tell whether there is a seizure at one point by simply looking at the waveform itself. In these cases, it is necessary to refer to the recorded videos to check for the present of dramatic clinical behaviors. 16

28 (A) (B) Figure 3.1. (A) Six-minute long episode containing seizure at t=230s. (B) Spectrogram of a 10-minute EEG segment, seizure occurs at t=200s. In general, seizure activities often associate with an increase in power of lower frequency components. However, there also exists a lot of noise at lower frequency due to scratching activities of studied subjects during and after seizures. Especially, there are some occasions during recording time that the electrode contacts are loosened. These phenomena cause signal to be contaminated with artifacts, either in one or multiple channels. In addition, since data are sampled at high frequency, there are also high frequency components within the signal. These high frequency components give little information about the seizures and preictal activities and it is desirable to eliminate these signals as well. Finally, from the FFT of EEG data, it is observed that the baseline artifact is at 117 Hz and multiples of it. In this project, bandpass filter is applied to remove movement artifacts as well as high frequency component. Prediction algorithms are also performed on original unfiltered signal for comparison. The bandpass filter is designed to have low and high cut-off frequency at 10 and 99 Hz respectively using order-2 Butterworth digital filter. In general, a Butterworth filter is characterized by a magnitude response that is maximally flat in the pass band and monotonic 17

29 overall. Even though Butterworth filter sacrifices roll-off steepness for monotocity in the passand stopbands, the filter s overall performance is acceptable since steep roll-off is not an important criterion in our case here. Specifically, the digital filter is designed using MATLAB Filter Design Toolbox. The transfer function of this filter is given as: H z = z z 4 (3.1) z z z z 4 The magnitude response is shown in figure 3.2.A below. For time series analysis, since it is desirable that filtering of the signal does not result in any phase distortion, zero-phase digital filtering algorithm is being used in combination with designed Butterworth filter. In this algorithm, the Butterworth filter is first applied in the forward direction. The algorithm then reverses the filtered sequence and runs it back through the filter. Hence, the result has precisely zero-phase distortion, the magnitude is the square of Butterworth filter s magnitude response and the overall filter order is doubled. A comparison of original signal versus the filtered signal is being shown in figure 3.2.B below. (A) (B) Figure 3.2. (A) Order-2 Butterworth digital filter magnitude response. (B) Original signal and filtered signal 3.4 Data manipulation and visualization 18

30 Due to the availability of large amount of data, it s desirable to have efficient data handling and visualization methods. The current database consists of 250 GB data with over 650 files for 6 animals, including both multi-channel and single-channel EEG. Data collected from experiment are first needed to be converted into MATLAB readable format. This is done by setting up an automatic workflow on MAC computer to repeat similar tasks and convert files automatically. UNIX shells are used to perform daily multiple-file manipulation routines such as listing, renaming or removing. For batch processing, MATLAB codes are compiled into UNIX executables and UNIX shell scripts are used to call these executables and submit batch jobs to the Sun Grid Engine (SGE). SGE is an open-source batch-queuing system used in High Performance Computing cluster to accept, schedule, dispatch and manage the remote and distributed execution of large number of standalone, parallel jobs. By using SGE, we can perform calculation on multiple data files at the same time, thus reduce the computation time for each kind of analysis. Computational results obtained are then plotted out and combined into single movie files so that hundreds of data files can be reviewed and analyzed in few minutes. 3.5 Nonlinear dynamics toolboxes: In this project, besides the use of MATLAB, some chaos toolboxes are also being used to either perform nonlinear analysis or double-check with algorithms implemented. RRCHAOS is a freely available, menu-driven software that supports various nonlinear dynamics analysis. Several features of RRCHAOS are calculation of mutual information, correlation dimension, Kolmogorov entropy and nonlinearity test. However, the program is only capable of perform calculation on a small amount of data and impossible to do batch processing on huge data set. Thus, this is mainly used for verifying algorithms implemented. 19

31 TISEAN package is a freely available C-source toolbox that also supports various nonlinear dynamics analysis. A convenience feature of TISEAN is that it allows calculation to be performed from UNIX shell command line. Thus, it is possible to use calculation of TISEAN directly for batch processing. Several features of TISEAN include calculation of Lyapunov exponent, false nearest neighbor and correlation dimension. 20

32 CHAPTER 4 AUTOMATIC SEIZURE PREDICTION 4.1 Objectives The aim of having an automatic seizure detection algorithm is to build a data library with large amount of seizure and control (non-seizure) episodes for later study of prediction algorithms. Given a huge amount of data available, it is impractical to go through each data file to determine seizure activities and manually clip out data episodes. Hence, a detection algorithm is to be developed to scan through the whole database, determine suspicious seizure activities and cut out the detected data segment with desired duration of pre-ictal and post-ictal activities. Based on suspicious point detected, the detection algorithm also needs to clip out potential interictal activities to build control episodes. Returned episodes are then to be verified by either referring to the videos or examining the signal waveform, which takes much less time that manually scan through each data files. Detection algorithm should be computationally fast and efficient in term of detecting seizure points. The following discussed detection algorithms performed on unfiltered data at the very initial stage of this project. 4.2 Detection based on average power calculation As mentioned in section 3.3, it is observed that when a seizure occurs, there is a rise in power at lower frequency components. Especially, from experimental observation, this power increase phenomenon is most visible at the frequency range from 2 to 7 Hz (given data are raw, unfiltered signal). Indeed, as shown in figure 4.1, for a five-minute EEG segment, the spectrum 21

33 is dominated by power of low frequency components from 2 to 7 Hz. Hence, initial approach is to examine the average power within this range of frequency over time to detect seizure. (A) (B) Figure 4.1. Power spectrum of a five-minute EEG signal. (A) Traditional FFT using 512 points. (B) FFT using Welch method with 512 segments, 50% overlapping and triangular windowing In detail, sliding window analysis is used to monitor the average power within the range of 2 to 7 Hz over time. For each window consisting of 1024 samples (0.512 seconds), the FFT is calculated. The energy of signal within 2 to 7 Hz is then computed by calculating the area under the curve of FFT plot for frequencies from 2 to 7 Hz. The average power is then obtained by dividing the energy by total length of the frequency range. As plotted in figure 4.2, the average power index is abruptly increased at the seizure, which occurs at t = 200s in this ten-minute EEG segment. Given this average power calculation, seizures are then can be detected by setting a heuristic threshold for power such that the epileptic seizure activities can stand out from the nonseizure activities. 22

34 Figure 4.2. Detection of seizure using moving average power. Seizure occurs at t=200s 4.3 Detection based on correlation integral Sliding window analysis As in the case of detection using power calculation, sliding window analysis is being used to monitor a calculated metric overtime for seizure detection. However, in the case of nonlinear metric, the choice of window to be analyzed needs more careful consideration. First of all, since EEG is non-stationary over a long time period, the window length should be small enough so that the underlying process s characteristics do not change much within one analyzed window. It has been commonly agreed that EEG signal can be regarded as quasi-stationary for window length from 10 to 40 seconds [1]. On the other hand, chosen window length should be long to reduce computational times. Hence, the window length of 20 seconds is chosen in this project for calculation of nonlinear metrics. In addition, to be able to capture the temporal changes, sliding windows are overlapping for 18 seconds. Thus, there is one calculated metric for every 2 seconds Phase space reconstruction 23

35 In this project, the embedding window length dt for phasespace reconstruction is determined based on the calculated mutual information of seizure window. Embedding dimension m is chosen based on fraction of false nearest neighbor. The time delay τ is then obtained from dt and m. Choice of dt As mentioned in section 2.5.2, mutual information I(τ) of an EEG window measures both the linear and nonlinear dependence within the signal at a time lag τ. Even though it is still argueable that whether this approach can give optimal embedding window length or not, the method gave acceptable dt for phasespace reconstruction and nonlinear metric calculation from experimental observations on this data set (the observed scaling region of correlation integral, which will be discussed later). I(τ) Cycles Figure 4.3. Mutual information of a seizure window. Average cycle time = (s/cycle) As mentioned in section 2.5.2, it is recommended to choose dt corresponding to the first local minimum of MI. Shown in figure 4.3 is the MI calculated using menu-driven software called RRCHAOS. The EEG signal is from a seizure window and local minima of MI are circled 24

36 as shown. It should be noted that RRCHAOS calculating MI based on the average cycle time, which is twice the average duration of zero-crossing intervals in one EEG window. From this result, we obtain the dt in number of samples as: dt = 2.73 cycles s/cycle 2000 samples/second = 60 (samples) Choice of m From section 2.5.2, we know that good choice of m should results in small fraction FNN. On the other hand, if m is too big, some details of nonlinear metrics at the ictal state is lost. For example, referring to correlation dimension D2, it is observed that at seizure onset D2 drop abruptly. However, large embedding dimension causes estimated D2 increase, thus makes D2 value at ictal state possibly indistinguishable from at non-ictal state. Therefore, choice of m is based on FNN of a seizure window and should not be too large. Figure 4.4 shows FNN fraction calculated using TISEAN software. One observation is that the FNN fraction is much smaller for filtered signal and at ictal state. Our choice of m will be based on FNN of filtered signal and at ictal state. From the figure, embedding dimension m = 7 gives acceptably low FNN fraction. We can verify this value of m by making use of correlation dimension estimated on the same data using RRCHAOS. Indeed, at this seizure window, the dimension is estimated as approximately 3 using Taken s estimator for D2. Thus, according to Taken s theory [7], embedding should be at least = 7 to preserve the system invariants in the reconstructed phase space. This is consistent with our choice of m = 7. 25

37 Figure 4.4. False nearest neighbor of seizure and non-seizure window. Calculations are performed both on raw and Choice of τ filtered data. Given dt = 60 and m = 7, we can obtain the value for τ: τ = m 1 τ = dt dt m 1 = 60 = 10 (samples) 7 1 From the chosen value for m, τ, the phase space is reconstructed as illustrated in figure 4.5 below. The bottom plots show the projection of recontructed space onto a 3-dimensional space. It is observed that at the seizure state, the embedding vectors in the reconstructed phase space distributed evenly all over the phase space, which is due to the synchronization of neural activities. 26

38 4.3.3 Estimation of C(r) Figure 4.5. Phase space reconstruction at m = 7 and τ = 10 samples To estimate C(r), the data is first demeaned and normalized to the average absolute deviation of signal. From chosen embedding parameters, a phase space is reconstructed from the N scalar signal x i i=1 using the method of delay. Next, a large number of random pairs were chosen to generate the histogram of distances of each pairs of point in the reconstructed phase space. From the distance histogram, we can compute the cumulative histogram and normalize to the maximum value to get the profile of C(r) over different length scales r Removal of temporal correlation In the calculation of correlation integral and correlation dimension later on, it is important that the estimations base only on geometrical correlation and any temporal correlation should be removed. Space-time separation plot (STP) is used to determine the lower bound of time distance 27

39 between two randomly chosen vectors X i and X j so that they are temporally uncorrelated. The STP shows lines of constant probability density of a point to be ε neighbor of the current point if its temporal distance is δt. As seen from figure below, at large temporal distance δt, point density is not dependent on temporal distance. Thus, time distance (so- called Theiler window) is chosen to be at δt = 500 (samples) to remove temporal correlation without significant lost of statistics in the estimations of C(r)and D. Distance Time separation (samples) Figure 4.6. STP of a 20s EEG segment. Curves from bottom to top correspond to density levels 5%,10%,, 100% Correlation density Correlation density is obtained from correlation integral by calculating C(r) at a fixed length scale r = r 0. Intuitively, the correlation density represent the particle density in reconstructed phase space at a given length scale. The length scale r 0 is chosen to be within the scaling region. As shown in figure 4.7.A, the scaling region can be observed from length scale 0.5 to 0.8. Within this region, C(r) graph is approximately a straight line. This also helps verify that our embedding parameters are acceptable and it is possible to estimate the correlation dimension using this set of parameters. Figure 4.7.B shows the profile of correlation density 28

40 calculated at r 0 = 0.7 using sliding window analysis. It can be seen clearly that correlation density increases abruptly at seizure onset. This is due to the fact that at seizure state, embedding vectors are distributed very evenly over the phase space, making the average particle density observed at one particular length scale decrease. However, in our approach of estimating C r, we normalized the data to average maximum deviation. Thus, the value of C(r) increases instead of decreases (seizure discreminative power still remains the same). Detection algorithm can then be developed by setting a heuristic threshold for correlation density above which we can define a possible seizure. (A) (B) Figure 4.7. (A) Correlation integral of non-seizure and seizure window. (B) Correlation density of one data segment, seizure occurs at t=3600s 4.4 Detection based on Kolmogorov entropy In this project, Kolmogorov entropy is estimated by following the approach of Schouten et al. [11] using the maximum likelihood estimator given by equation

41 According to this approach, the data is first demeaned and normalized as in the case of correlation dimension. For data being rescaled this way, we can use unit 1 as our trajectory divergence threshold. In other words, the trajectories are said to be divergent if their distance is greater than 1. Next step, number of cycles in the original time series is estimated as half of the number of zero-crossings. Number of samples per cycle m is then calculated. Here m can be thought of as similar to our embedding dimension as in the case of phase space reconstruction. The only difference is that in this approach of estimating KE, we use simplified τ = 1, thus m dt is the time interval over which the trajectory x i traverses and is being used to determine whether a pair of trajectories x i and x j are independent or not. Next, a pair of samples in the data is randomly chosen at time step i and j. If i j m then they are considered independent. Also, let us define the maximum norm d = max ( x i+k x j +k ) for 0 k m 1. If d 1 then we consider the two trajectories are nearby (in general d should less than the mean absolute deviation, but since we already rescaled the data, our threshold is 1). Finally, having chosen a pair of independent, nearby trajectories, we monitor the number of time step such that the two trajectories diverge (maximum norm greater than 1). By generating a large number of such pair, we can estimate the average time step b avg which is required for the 2 randomly chosen independent and nearby trajectories to diverge. From b avg, we can obtain the estimation of KE based on the maximum likelihood estimation. Figure 4.8 show the calculation of KE for 70-minute data episodes containing seizure at t=3600s. It is observed that at ictal state, KE drops abruptly due to the discharge of neuronal activities. Indeed, at this state, because of synchronization of a large amount of neurons, the phase space is in its very ordered state and thus not much information is being lost due to 30

42 projection into lower dimension. Similar to the two previous detection algorithms, we can detect suspicious ictal activities by manually setting a threshold below which a detected point is defined. Figure 4.8. Kolmogorov entropy calculated for one data segment, seizure occurs at t=3600s. 4.5 Comparison and results Among the three methods, the linear approach is the simplest and fastest one. However, it is observed that power calculation tends to be very sensitive to movement artifacts, which results in large false detection percentage. In addition, power calculation also can not detect the seizure points as precisely as the other two. In term of discriminative power, methods based on CI and KE are equivalent. However, KE method is simpler to implement and run much faster than CI method. Thus, KE method is mainly used for seizure detection and building episode library. Table 4.1 below summarizes the results obtained based on KE calculation. 31

43 Mice Seizure episodes Control episodes Detection Sensitivity False detection HM3 41 (total 60) % 11 HM5 13 (total 26) 93 50% 6 Table 4.1. Collected episodes from detection algorithm. Seizure episodes contain 60 minutes pre-ictal activities and 10 minutes post-ictal activities. Control data are at least 3 hours before any seizures Since the data are multi-channel EEG recordings, it is useful to exploit all calculations in three channels to have a robust and reliable detection. Here, the detection algorithm checks for consistency between detected points in each single channel. Indeed, for a detected seizure point to be defined, it must show detection in at least two channels that are at most 90 seconds apart (normal duration of a seizure is one and a half minute). Once a seizure point is detected, the detection algorithm then proceeds to clip out the data segment that contain that seizure point with specified duration of preictal and postictal activities. In detail, duration of signal before seizure point is set to be one hour, and signal after seizure point is set to 10 minutes. If there is another seizure occurring at any time within the 1-hour preseizure interval, the algorithm will skip the current detected point. The purpose of skipping nearby seizures is to have reasonably long preseizure activities to observe systematic transition of the brain toward the ictal state. Due to this setting, detection algorithm effectively ignored nearby seizure and only returns a portion of total number of seizures in the data set, as shown in table 4.1. Also, there are several false detections, which is mainly due to movement artifacts within the signal. Based on the detected seizure points, the detection will then traverse through the whole data set again to clip out control episodes. The control episodes are chosen based on the criteria that they should be at least 2 hours before any seizures. This criterion is to make sure that the control episodes will not contain any preictal activities and thus will represent the very normal 32

44 state of the brain. Finally, duration of control episodes are set to be equal to seizure episodes for the ease of comparison. 33

45 CHAPTER 5 SEIZURE PREDICTION 5.1 Overview This section explains seizure prediction algorithm based on various measurements that were implemented. These measurements include linear metrics such as variance (VA), linear cross-correlation (XC) and nonlinear metrics such as Kolmogorov entropy (KE), correlation dimension (D 2 ) and correlation density (COR). For each studied animal, the control data set is divided into two groups: the first group is used to compute the distribution of characterizing measurements (VA, KE, etc) while the second group is used for testing the prediction algorithm and estimating the false positive rate. On the other hand, seizure data set of each animal is used to determine the sensitivity of prediction algorithm. Performances of prediction based on different measurements are then compared in term of mean prediction interval and predictive power (through the calculation of area under receiver operating characteristic curve). Comparison is also made on filtered versus unfiltered data sets. Finally, performances are assessed at different level of channel consistency to determine which criterion gives the best prediction interval and predictive power. 5.2 Data sets As mentioned earlier, the current EEG data from NNI lab comprises six animals, including four multi-channel and two single-channel data sets. Since it s often more convenient to study multichannel time series, the single-channel EEG are set aside and not yet been studied in this project. Among the four multi-channel data sets, data episodes for mice HM3 and HM5 34

46 are obtained mainly from the detection algorithm as described above (with some later manual manipulation and verification). Due to the time constrain, data episodes for mice HM7 and HM8 are obtained directly from a manually specified list of seizure onsets (the procedures are still automatic; the only difference is that seizure onsets are prescribed instead of obtained from KE calculations). The completed data sets for studying prediction are summarized in the table below. Mice HM3 HM5 HM7 HM8 Control episodes Seizure episodes Table 5.1. Data sets from four mice For HM3, HM5 and HM8, each data episode has one hour of preictal activities and ten minutes of postictal activities. However, for HM7, since most of seizures occur very close to each other, slightly shorter preictal duration is chosen (50 minutes) such that more seizures can be studied. Data episodes are then band-passed from Hz and prediction performances are studied for both original and filtered data. 5.3 Calculation of characterizing measurements In addition to some measurements used to characterize the transition of processes underlying EEG signal such as KE and correlation density (chapter 4), we discuss here some additional measurements that can be used to predict seizures Variance Similar to the approach of McSharry et al. (2003) [6], the variance of an EEG segment N x i i=1 with mean x is calculated as: 35

47 VA = 1 N N i=1 x i x 2 (5.1) Linear cross-correlation The idea of using linear cross-correlation (XC) is to quantify the similarity of two signals N N x i i=1 and y i i=1 from different recording channels. By definition, the normalized crosscorrelation of the two time series at time delay τ is defined as: C x, y τ = N τ 1 x N τ i+τ y i τ 0 i=1 C x, y τ τ < 0 (5.2) The maximum correlation coefficient is then computed to characterize the similarity of the two channels [3]: C m = max τ C x, y τ C x, x 0. C y, y 0 (5.3) From the definition, C m is always in the range of [0,1].A high value of C m indicates that the two signals have a similar course in time, while C m 0 means the two signals are highly dissimilar. (A) Figure 5.1. Cross-correlation function. (A) Nonseizure window. (B) Seizure window (B) 36

48 5.3.3 Correlation dimension Since D 2 represents the system complexity, it is useful to monitor the dimension over time to detect reduced complexity of the brain dynamic before seizure onset. The dimension is estimated from the distribution of correlation integral C(r) using procedures proposed by Schouten et al. [9] as explained in section The dimension is obtained by fitting C(r) curve to a straight line and calculating the slope. (A) (B) Figure 5.2. Estimation of correlation dimension from C(r). (A) Non-seizure window, D 2 = (B) Seizure window, D 2 = Figure 5.2 above shows the estimated D 2 for a non-seizure and seizure window. The C(r) curve is fitted to a straight line for length scale from r 1 = 0.5 to r 2 = 1. The lower limit of length scale is choosen since C(r) at small length scale is often contaminated by dynamic noise that is intrinsic in the system. On the other hand, it is also convenient to choose the upper bound for the scaling distance r. This is due to the fact that the scaling relationship C r r D 2 only holds for sufficiently small r. Moreover, when r is large, the correlation intergral is dominated by the saturation effect since C r 1. Since we are dealing with rescaled data, a threshold of r 2 = 1 37

49 is chosen. As shown in figure 5.2, correlation dimension of the brain dynamic drops significantly at seizure onset, indicating a decrease in system s complexity due to abnormal discharge activities of neural network. 5.4 Prediction scheme and performance indicators Prediction scheme The first step in prediction procedures is to compute a control distribution of characterizing measurements (VA, XC, etc). For each measurement, the number of control episodes equal to that of seizure episodes is used for testing the prediction algorithm, leaving the rest for computing the control distribution. For example, with D 2 being used for prediction on HM3 data set, calculation of D 2 on 41 control episodes is used for testing the prediction algorithm (since there are 41 seizure episodes), leaving the remaining 58 for computing the control distribution of D 2. In order to detect preictal activities, sliding window analysis on the calculated characterizing measurements with window length of 5 minutes and overlapping of 1 minute is being used. For each analyzed window, the distribution of the characterizing measurement being used is obtained and the mean of that distribution is calculated. This mean value is then compared with the mean of a control distribution calculated previously. Depending of the specific measurement being used, a preictal activity is defined when the mean of analyzed window is critically less than or greater than that of the control distribution. Specifically, if u is the mean of analyzed window and u 0, s 0 are the mean and standard deviation of the control distribution, then we are comparing u with either u 0 + ks 0 or u 0 ks 0, depending on whether the measurement is increasing or decreasing before seizure onset. We vary k from 0 to 3, with a 38

50 step of 0.25 each time, to obtain different combinations of predition sensitivity and specificity. For k = 0, it is simply the comparison of the means. Meanwhile, for k = 3, it is equivalent to the 3-sigma rule, which states that we can conclude with 95% confidence that the mean value u belongs to a different distribution than the control one if it exceeds 3 times the standard deviation from the baseline level u 0. The above criteria for detecting preictal activities is then applied to seizure episodes and testing control episodes to calculate the sensitivity and specificity corresponding to a particular setting of k value. Comparisons are then made on performance of different measurements on filtered and raw data sets at different level of consistency between channels. We use here the term channel consistency to refer to the degree of how well calculated results at a time instance on different channels agree with each other. Thus, one-channel consistency means a preictal activity is detected whenever there is at least one channel shows preictal detection. Similarly, two-channel consistency requires the agreement of at least two channels, and threechannel consistency means all channels have to show detection for a preictal activity to be defined. For the comparison of different measurements on filtered and raw data sets, threechannel consistency is being used. Meanwhile, for comparison of performance at different consistency levels, filtered data sets are being used Receiver operating characteristic curve One of the best ways to compare the discriminative power of prediction algorithm based on different measurements is the use of receiver operating characteristic (ROC) curve. By definition, the ROC curve is the plot of sensitivity versus one minus specificity corresponding to different setting of the threshold value. Sensitivity and specificity are defined as: 39

51 Sensitivity = Specificity = True Positive True Positive + False Negative True Negative True Negative + False Positive (5.4) In words, it means that we can obtain the prediction sensitivity by simply counting how many percent of total seizure episodes that the preictal activities are correctly detected before seizure onsets. On the other hand, we can obtain false positive from the percentage of false prediction among testing control episodes and compute the specificity as 1 false positive. The area under ROC curve can be used to quantify the discriminative power of a characterizing measurement. Larger area under ROC curve indicates a good predictive performance, while an area of approximately 0.5 indicates the measurement has no discriminative power. In general, we are looking for the point on ROC curve that is closest to the top left point of the ROC plot ((x,y)=(0,1)), which corresponds to the optimal trade-off between sensitivity and false positive. For the significance of the estimated ROC curves, the control episodes used for calculating control distribution are drawn randomly from the original set of control episodes. The estimation of ROC is then repeated 10 times, each time with a different random subset of control episodes for calculating control distribution, to obtain a distribution of areas under ROC curve for each measurement. In order to compare the various distributions of areas under ROC curves for different measurements, analysis of variance (ANOVA) is being used. A one-way ANOVA is used first to test if the mean of five different area distributions are equal. If the means of these distributions are different and the distributions are normal, the parametric multiple comparison test is then used to determine which pairs of means are significantly different and which are not. 40

52 5.4.3 Prediction intervals Another importance performance specification of a prediction algorithm is how far in advance we can predict seizure. Prediction interval is defined as the duration from the earliest detected preictal event to the seizure onset within a seizure episode. For illustration purpose, the results of prediction intervals shown will be corresponding to the optimal value of k for determining the amplitude threshold as described above. From seizure episodes that contain preictal events correctly detected before seizure onsets with a particular setting of k value, the mean and standard deviation of prediction interval is calculated. 5.5 Results Measurement profiles Figure 5.3 shows the profiles of different measurements obtained by using sliding window analysis. Figure 5.3. Profile of different measurements from one seizure episodes of HM3, seizure occurs at t=3600s 41

53 The window length for calculating these measurements is chosen to be 20s and overlapping 2s. It is well-known that EEG signal is quasi-stationary for window length of 10s to 40s [1], thus measured quantities can be considered unchanged within one analyzed window. From experimental observation, seizure onset is associated with critical increases in VA and XC and COR and decreases in D 2 and KE. For linear metrics, only abrupt change at seizures onset is seen and there is no clear indication of a preictal state reflected from the calculation of these measurements. On the other hand, calculation of nonlinear metrics such as D 2, KE and COR exhibit some precursors of seizure onset that can be used for prediction. Indeed, as shown in figure 5.3, preictal activities is associated with a systematic decrease in D 2 and increase in COR. Calculation on KE showed a decreasing trend before seizure onset, but this trend is also abundant in control episodes and thus does not characterize preictal activities very well Estimated ROC curves The ROC curves for different methods on raw and filtered data sets are shown in figure 5.4 and figure 5.5. Table 5.2 summarizes the estimated areas for all measurements on raw and filtered data sets. In general, most of the measurements have the areas under ROC curves considerably higher than 0.5. Nonlinear metrics performed well for all data sets, while linear metrics does not show significant predictive power for data sets of HM5 and HM8. Especially, predictions based on D 2 and COR always give the top performance for all studied animals. Areas for these measurements range from 0.73 to 0.87, which indicates a good discrimination of preictal and interictal activities. 42

54 Mice\Metric COR D 2 KE VA XC HM Raw data HM HM HM HM Filtered data HM HM HM Table 5.2: Areas under ROC curves of five measurements for raw and filtered data sets In term of filtering effects, performances of COR and D 2 are very robust while those of KE, VA and XC are more volatile. For all studied animals, areas of COR and D 2 show little changes after filtering. Whereas, for KE, VA and XC, performances after filtering are improved in some data sets but worsened in the others. This may be because these measurements are more dependent on low frequency components in the signal that have already been filtered out. Figs. 5.6 and 5.7 show the results of multiple comparison test on area distributions for raw and filtered data sets. The test is using parametric T-test since areas are normally distributed. In 3 out of 4 raw data sets (HM5, HM7 and HM8), the distribution means of areas for D 2 and COR are significantly higher than those of VA and XC. In addition, these two nonlinear measurements also performed significantly better than KE for 2 out of 4 raw data sets (HM7 and HM8). For filtered data sets, areas of all nonlinear measurements are significantly higher than those of linear measurements in 3 out of 4 animals (HM5, HM7, HM8). 43

55 Figure 5.4. Estimated ROC curves for five measurements on raw data sets Figure 5.5. Estimated ROC curves for five measurements on filtered data sets 44

56 (A) HM3 (B) HM5 (C) HM7 (D) HM8 Figure 5.6. ANOVA on distributions of areas under ROC curves for unfiltered data sets. 45

57 (A) HM3 (B) HM5 (C) HM7 (D) HM8 Figure 5.7. ANOVA on distributions of areas under ROC curves for filtered data sets. 46

58 In all cases, we observe that the sensitivity is very low for large value of deviation factor k. The percentage of seizures correctly predicted at a threshold level specified by k = 3 (corresponding to a significance level of 0.05) is no more than 10% at all time. This means even though measurements do exhibit significant predictive power, the difference between preictal and interictal is not statistically significant for most seizures. Thus, results obtained from ROC curve estimations can not be used as a statistical validation for the existence of the hypothesized preictal state Prediction interval Figures 5.8 and 5.9 shows the mean and standard deviation of the prediction intervals for raw and filtered data sets. The prediction time is calculated at the threshold level corresponding to the points on ROC curves that are closest to the top left corner point. From figure 5.8 and 5.9, we observe that prediction intervals are in the range from 20 to 50 minutes before seizure onsets. Nonlinear measurements often predict more than 40 minutes before seizure onsets, while the prediction intervals for linear measurements are usually from 20 to 40 minutes. Overall, filtering does not affect much the prediction intervals of various measurements. 47

59 Figure 5.8. Prediction intervals corresponding to optimal threshold levels on raw data Figure 5.9. Prediction intervals corresponding to optimal threshold levels on filtered data 48

60 5.5.4 Performance at different consistency levels Figure 5.10 shows the estimated areas under ROC curves of different measurements using one-channel, two-channel and three-channel consistency check. It is observed that performances based on the consistency of all three channels are actually better than those based on one-channel consistency in 3 animals (HM3, HM5 and HM8). This is due to the fact that when using local information of each channel, the prediction algorithms are generally more volatile with respect to the fluctuation of measurements, which is caused by either preictal activities or noises. For HM3, HM5 and HM8 data sets, when there are lots of measurement fluctuations in control episodes due to noises. Thus, by using local information of each channel, we actually increase the false positive much more than we increase the sensitivity. On the other hand, in the case of HM7, the control episodes are very clean of such fluctuations and the use of one-channel consistency does not affect the false positive. Meanwhile, using local information in single channels helps increase sensitivity with preictal activities before seizures. Thus, for this particular data set, performance using one-channel consistency is better than that of threechannel consistency. Finally, for all cases, two-channel consistency gives a good compromise between the other two schemes. In term of prediction intervals, a comparison of the prediction times at different channel consistency levels is shown in figure In general, prediction intervals using three-channel consistency level are the highest, mainly because the optimal k values are smaller as compared to those in the other consistency levels. Indeed, as shown in figure 5.12, optimal k is highest when using single channel information and lowest when using three-channel consistency. This is because when using single channel, the prediction algorithm is more volatile to fluctuations of 49

61 measurements and a greater value of k is needed to obtain an optimal trade-off between sensitivity and false possitive rate. Figure Prediction performance at different consistency levels on filtered data sets Figure Prediction intervals for different levels of channel consistency on filtered data sets For each column of each plot, from left to right is corresponding to one-channel, two-channel and three-channel consistency levels. 50