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Introduction and motivation Comparitive investigation: Predictive performance of measures of synchronization Statistical validation of seizure predictions: The method of measure profile surrogates Summary and outlook Predictability of epileptic seizures - Content -

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~ 1 % of world population suffers from epilepsy ~ 22 % cannot be treated sufficiently ~ 70 % can be treated with antiepileptic drugs ~ 8 % might profit from epilepsy surgery Exact localization of seizure generating area Delineation from functionally relevant areas Aim: Tailored resection of epileptic focus Predictability of epileptic seizures - Introduction: Epilepsy -

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Intracranially implanted electrodes

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EEG containing onset of a seizure (preictal and ictal) L R

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EEG in the seizure-free period (interictal) L R

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Predictability of epileptic seizures - Motivation I - Open questions: Does a preictal state exist? Do characterizing measures allow a reliable detection of this state? Goals / Perspectives: Increasing the patient‘s quality of life Therapy on demand (Medication, Prevention) Understanding seizure generating processes

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Predictability of epileptic seizures - Motivation II - State of the art: Reports on the existence of a preictal state, mainly based on univariate measures Gradual shift towards the application of bivariate measures Little experience with continuous multi-day recordings No comparison of different characterizing measures Mostly no statistical validation of results

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Predictability of epileptic seizures - Motivation III - Why bivariate measures? Synchronization phenomena key feature for establishing the communication between different regions of the brain Epileptic seizure: Abnormal synchronization of neuronal ensembles First promising results on short datasets: “Drop of synchronization” before epileptic seizures * * Mormann, Kreuz, Andrzejak et al., Epilepsy Research, 2003; Mormann, Andrzejak, Kreuz et al., Phys. Rev. E, 2003

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I. Continuous EEG – multichannel recordings II. Calculation of a characterizing measure III. Investigation of suitability for prediction by means of a seizure prediction statistics - Sensitivity Performance - Specificity IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure -

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Predictability of epileptic seizures - Moving window analysis - Window Chan. 1 Chan. 2

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Predictability of epileptic seizures - Moving window analysis - Window Chan. 1 Chan. 2

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Predictability of epileptic seizures - Moving window analysis - Window Chan. 1 Chan. 2

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Predictability of epileptic seizures - Moving window analysis - Window … Chan. 1 Chan. 2

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sensitive not sensitive not specific For this channel combination: Reliable seperation preictal interictal impossible ! Predictability of epileptic seizures - Example: Drop of synchronization as a predictor - Time [Days]

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Predictability of epileptic seizures - Example: Drop of synchronization as a predictor - Selection of best channel combination : Clearly improved seperation preictal interictal Significant ? Seizure times surrogates Time [Days]

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Introduction and motivation Comparitive investigation: Predictive performance of measures of synchronization Statistical validation of seizure predictions: The method of measure profile surrogates Summary and outlook Predictability of epileptic seizures - Content -

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I. Continuous EEG – multichannel recordings II. Calculation of a characterizing measure III. Investigation of suitability for prediction by means of a seizure prediction statistics - Sensitivity Performance - Specificity IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure -

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I. Database Seizures Time [h]

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I. Continuous EEG – multichannel recordings II. Calculation of a characterizing measure III. Investigation of suitability for prediction by means of a seizure prediction statistics - Sensitivity Performance - Specificity IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure -

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Cross Correlation C max Mutual Information I Indices of phase synchronization based on and using Nonlinear interdependencies S s and H s Event synchronization Q SynchronizationDirectionality Nonlinear interdependencies S a and H a Delay asymmetry q - Shannon entropy (se) - Conditional probabilty (cp) - Circular variance (cv) - Hilbert phase (H) - Wavelet phase (W) II. Bivariate measures - Overview -

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II. Bivariate measures - Cross correlation and mutual information C max I * * C max I ** C max I * *

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II. Bivariate measures - Phase synchronization -

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II. Bivariate measures - Nonlinear interdependencies - No coupling: X

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II. Bivariate measures - Nonlinear interdependencies - Strong coupling:

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II. Bivariate measures - Event synchronization and Delay asymmetry I - Time [s] Chan. 1 Chan. 2

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I. Continuous EEG – multichannel recordings II. Calculation of a characterizing measure III. Investigation of suitability for prediction by means of a seizure prediction statistics - Sensitivity Performance - Specificity IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure -

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III. Seizure prediction statistics - Steps of analysis - Measure profiles of all neighboring channel combinations Statistical approach: Comparison of preictal and interictal amplitude distributions Measure of discrimination : Area below the Receiver-Operating-Characteristics (ROC) - Curve Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity

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III. Seizure prediction statistics: ROC Sensitivity 1 - Specificity ROC-Area

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III. Seizure prediction statistics: ROC ROC-Area 1 - Specificity Sensitivity

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III. Seizure prediction statistics: Example Sensitivity 1 - Specificity ROC-Area Time [days] e

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For each channel combination 2 * 4 * 2 = 16 combinations III. Seizure prediction statistics - Parameter of analysis - Smoothing of measure profiles (s = 0; 5 min) Length of the preictal interval (d = 5; 30; 120; 240 min) ROC hypothesis H - Preictal drop(ROC-Area > 0, ) - Preictal peak (ROC-Area < 0, ) Optimization criterion for each measure: Best mean over patients Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

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I. Continuous EEG – multichannel recordings II. Calculation of a characterizing measure III. Investigation of suitability for prediction by means of a seizure prediction statistics - Sensitivity Performance - Specificity IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure -

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IV. Statistical Validation - Problem: Over-optimization - Given performance: Significant or statistical fluctuation? Good measure: „Correspondence“ seizure times - measure profile To test against null hypothesis: Correspondence has to be destroyed I. Seizure times surrogates II. Measure profile surrogates Randomization of measure profiles Randomization of seizure times

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IV. Statistical Validation - Seizure times surrogates - Random permutation of the time intervals between actual seizures: Seizure times surrogates Calculation of the seizure prediction statistics for the original as well as for 19 surrogate seizure times ( p=0.05) Andrzejak, Mormann, Kreuz et al., Phys Rev E, 2003

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- Results: Measure profiles of phase synchronization - Time [days] Channel combination

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Discrimination of amplitude distributions Interictal Preictal 1.Global effect: All Interictal All Preictal (1) 2.Local effect: Interictal per channel comb Preictcal per channel comb (#comb) Results - Evaluation schemes - Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

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- First evaluation scheme - Time [days] Channel combination

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Results: First evaluation scheme | ROC-Area | Measures

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Discrimination of amplitude distributions Interictal Preictal 1.Global effect: All Interictal All Preictal (1) 2.Local effect: Interictal per channel comb Preictcal per channel comb (#comb) Results - Evaluation schemes - Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

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- Second evaluation scheme - Time [days] Channel combination

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- Second evaluation scheme - Time [days] Channel combination

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- Second evaluation scheme - Time [days] Channel combination

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Results: Preictal and interictal distributions e

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Results: Second evaluation scheme | ROC-Area | Measures

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Predictability of epileptic seizures - Summary I: Comparison of measures - General tendency regarding predictive performance: - Phase synchronization based on Hilbert Transform - Mutual Information, cross correlation - … - Nonlinear interdependencies Measures of directionality among measures of synchronization No global effect, but significant local effects

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Introduction and motivation Comparitive investigation: Predictive performance of measures of synchronization Statistical validation of seizure predictions: The method of measure profile surrogates Summary and outlook Predictability of epileptic seizures - Content - * Kreuz, Andrzejak, Mormann et al., Phys. Rev. E (2004)

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Mostly not sufficient data for „Out of sample“ – study (Separation in training- and test sample) „In sample“ – Optimization (Selection) (Best parameter, best measure, best channel, best patient, …) Statistical fluctuations difficult to estimate Seizure prediction - Problem : Statistical validation -

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I. Continuous EEG multi channel recordings II. Calculation of characterizing measures III. Investigation of suitability for prediction by means of a seizure prediction statistics IV. Estimation of statistical significance Predictability of epileptic seizures - Procedure - - Patient A (18 channel combinations) - Phase synchronization und event synchronization Q - ROC, same optimization, for every channel combination - Method of measure profile surrogates

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IV. Statistical Validation - Problem: Over-optimization - Given performance: Significant or statistical fluctuation? Good measure: „Correspondence“ seizure times - measure profile To test against null hypothesis: Correspondence has to be destroyed I. Seizure times surrogates II. Measure profile surrogates Randomization of measure profiles Randomization of seizure times

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Measure profile surrogates Zeit [Tage] Time [days]

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Formulation of constraints in cost function E Minimization among all permutations of the original measure profile Iterative scheme: Exchange of randomly chosen pairs Measure profile surrogates - Simulated Annealing I - Schreiber, Phys. Rev. Lett., 1998 Cooling scheme (Temp. T→0), abort at desired precision Probability of acceptance:

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Measure profile surrogates - Simulated Annealing II - 18 channel combinations (Phase synchronization) Cost function Temperature Iteration steps

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Measure profile surrogates - Simulated Annealing III - Properties to maintain: Recording gaps are not permuted Ictal and postictal intervals are not permuted Amplitude distribution Permutation Autocorrelation Cost function

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Measure profile surrogates - Original autocorrelation functions (Phase sync.) - Time [days]

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Measure profile surrogates - Original autocorrelation functions (Phase sync.) - Time [days]

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Measure profile surrogates Time [days]

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Measure profile surrogates Time [days]

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Measure profile surrogates - Two evaluation schemes - Each channel combination separately Selection of best channel combination

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Results: Phase synchronization |ROC|

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Results: Event synchronization |ROC|

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Results: Phase synchronization |ROC|

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Results: Event synchronization |ROC|

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Results - Each channel combination separately - Phase synchronization: Event synchronization: Nominal size: p = 0.05 (One-sided test with 19 surrogates) Independent tests: q = 18 (18 channel combinations) At least r rejections: Significant, Null hypothesis rejected !

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Results - ES II: Selection of best channel combination - Event synchronization Phase synchronization

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Measure profile surrogates - Two Evaluation schemes - Each channel combination separately Null hypothesis H 0 I : Measure not suitable to find significant number of local effects predictive of epileptic seizures. Null hypothesis H 0 II : Measure not suitable to find maximum local effects predictive of epileptic seizures. Selection of best channel combination

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Measure profile surrogates - Two Evaluation schemes - Each channel combination separately Null hypothesis H 0 I : Measure not suitable to find significant number of local effects predictive of epileptic seizures. Null hypothesis H 0 II : Measure not suitable to find maximum local effects predictive of epileptic seizures. Selection of best channel combination

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Results - ES II: Selection of best channel combination - Event synchronization Phase synchronization

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Results - Selection of best channel combination - Significant! Null hypothesis H 0 II rejected Not significant! Null hypothesis H 0 II accepted Event synchronization Phase synchronization | ROC-Area |

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Measure profile surrogates - Summary II: Measure profiles surrogates - Method for statistical validation of seizure predictions Test against null hypothesis Level of significance Estimating the effect of „In sample“ – optimization Phase synchronization more significant than event synchronization. Given example: Discrimination of pre- and interictal intervals:

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Introduction and motivation Comparitive investigation: Predictive performance of measures of synchronization Statistical validation of seizure predictions: The method of measure profile surrogates Summary and outlook Predictability of epileptic seizures - Content -

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Predictability of epileptic seizures - Summary and outlook - Retrospective investigation: Evidence of significant changes before seizures Measures good enough for prospective application ???

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