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Introduction and motivation Comparitive investigation:

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Predictability of epileptic seizures

- Content -

- 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

- Introduction: Epilepsy -

- ~ 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 ofepileptic focus

Intracranially implanted electrodes

L

R

EEG containing onset of a seizure (preictal and ictal)

L

R

EEG in the seizure-free period (interictal)

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

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

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 ofsynchronization” before epileptic seizures *

* Mormann, Kreuz, Andrzejak et al., Epilepsy Research, 2003; Mormann, Andrzejak, Kreuz et al., Phys. Rev. E, 2003

Predictability of epileptic seizures

- Procedure -

Continuous EEG – multichannel recordings

Calculation of a characterizing measure

Investigation of suitability for prediction by means of a seizure prediction statistics

- Sensitivity

Performance

- Specificity

Estimation of statistical significance

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

…

Window

Reliable seperation preictal interictal impossible !

Predictability of epileptic seizures

- Example: Drop of synchronization as a predictor -

Time [Days]

For this channel combination:

sensitive

not

sensitive

not

specific

specific

Clearly improved seperation preictal interictal

Significant ? Seizure times surrogates

Predictability of epileptic seizures

- Example: Drop of synchronization as a predictor -

Selection of best channel combination :

Time [Days]

Predictability of epileptic seizures

- Content -

- 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

- Procedure -

Continuous EEG – multichannel recordings

Calculation of a characterizing measure

Investigation of suitability for prediction by means of a seizure prediction statistics

- Sensitivity

Performance

- Specificity

Estimation of statistical significance

I. Database

Seizures

Time [h]

Predictability of epileptic seizures

- Procedure -

Continuous EEG – multichannel recordings

Calculation of a characterizing measure

Investigation of suitability for prediction by means of a seizure prediction statistics

- Sensitivity

Performance

- Specificity

Estimation of statistical significance

II. Bivariate measures

- Overview -

Synchronization

Directionality

- Cross Correlation Cmax
- Mutual Information I
- Indices of phase synchronization
- based on
- and using
- Nonlinear interdependencies SsandHs
- Event synchronization Q

- - Shannon entropy (se)
- - Conditional probabilty (cp)
- Circular variance (cv)

- Hilbert phase (H)

- Wavelet phase (W)

- Nonlinear interdependencies SaandHa
- Delay asymmetry q

Cmax

I

Cmax

I

Cmax

I

1.0

1.0

1.0

0.5

0.5

0.5

0.0

0.0

0.0

II. Bivariate measures

- Cross correlation and mutual information -

*

*

*

*

*

*

II. Bivariate measures

- Phase synchronization -

II. Bivariate measures

- Nonlinear interdependencies -

No coupling:

X

II. Bivariate measures

- Nonlinear interdependencies -

Strong coupling:

II. Bivariate measures

- Event synchronization and Delay asymmetry I -

Chan. 1

Chan. 2

Time [s]

Predictability of epileptic seizures

- Procedure -

Continuous EEG – multichannel recordings

Calculation of a characterizing measure

Investigation of suitability for prediction by means of a seizure prediction statistics

- Sensitivity

Performance

- Specificity

Estimation of statistical significance

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

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

ROC-Area

1 - Specificity

III. Seizure prediction statistics: ROC

Sensitivity

ROC-Area

Sensitivity

ROC-Area

Sensitivity

ROC-Area

Sensitivity

ROC-Area

1 - Specificity

III. Seizure prediction statistics: Example

Time [days]

e

Sensitivity

ROC-Area

1 - Specificity

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, )

For each channel combination 2 * 4 * 2 = 16 combinations

Optimization criterion for each measure:Best mean over patients

Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

Predictability of epileptic seizures

- Procedure -

Continuous EEG – multichannel recordings

Calculation of a characterizing measure

Investigation of suitability for prediction by means of a seizure prediction statistics

- Sensitivity

Performance

- Specificity

Estimation of statistical significance

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

Randomization

of seizure times

Randomization

of measure profiles

I. Seizure times surrogates

II. Measure profile surrogates

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

- Results: Measure profiles of phase synchronization -

Channel combination

Time [days]

Results

- Evaluation schemes -

- Discrimination of amplitude distributions Interictal Preictal
- Global effect:
- All Interictal All Preictal (1)
- Local effect:
- Interictal per channel comb Preictcal per channel comb (#comb)

Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

- First evaluation scheme -

Channel combination

Time [days]

Results: First evaluation scheme

| ROC-Area |

Measures

Results

- Evaluation schemes -

- Discrimination of amplitude distributions Interictal Preictal
- Global effect:
- All Interictal All Preictal (1)
- Local effect:
- Interictal per channel comb Preictcal per channel comb (#comb)

Mormann, Kreuz, Rieke et al., Clin Neurophysiol 2005

- Second evaluation scheme -

Channel combination

Time [days]

- Second evaluation scheme -

Channel combination

Time [days]

- Second evaluation scheme -

Channel combination

Time [days]

Results: Preictal and interictal distributions

e

Results: Second evaluation scheme

| ROC-Area |

Measures

Predictability of epileptic seizures

- Summary I: Comparison of measures -

- No global effect, but significant local effects

- General tendency regarding predictive performance:
- Phase synchronization based on Hilbert Transform

- Mutual Information, cross correlation

- …

- Nonlinear interdependencies

- Measures of directionality among measures of synchronization

Predictability of epileptic seizures

- Content -

- 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

* Kreuz, Andrzejak, Mormann et al., Phys. Rev. E (2004)

Seizure prediction

- Problem : Statistical validation -

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

Predictability of epileptic seizures

- Procedure -

Continuous EEG multi channel recordings

Calculation of characterizing measures

Investigation of suitability for prediction by means of a seizure prediction statistics

Estimation of statistical significance

- Patient A (18 channel combinations)

- Phase synchronization und event synchronization Q

- ROC, same optimization, for every channel combination

- Method of measure profile surrogates

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

Randomization

of seizure times

Randomization

of measure profiles

I. Seizure times surrogates

II. Measure profile surrogates

Measure profile surrogates

Zeit [Tage]

Time [days]

Time [days]

Measure profile surrogates

- Simulated Annealing I -

- Formulation of constraints in cost function E
- Minimization among all permutations of the original measure profile
- Iterative scheme:Exchange of randomly chosen pairs

Probability of acceptance:

- Cooling scheme (Temp. T→0), abort at desired precision

Schreiber, Phys. Rev. Lett., 1998

Measure profile surrogates

- Simulated Annealing II -

Temperature

18 channel combinations

(Phase synchronization)

Cost function

Iteration steps

- 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

Measure profile surrogates

- Original autocorrelation functions (Phase sync.) -

Time [days]

Measure profile surrogates

- Original autocorrelation functions (Phase sync.) -

Time [days]

Measure profile surrogates

Time [days]

Measure profile surrogates

Time [days]

Measure profile surrogates

- Two evaluation schemes -

- Each channel combination separately

- Selection of best channel combination

Results: Phase synchronization

|ROC|

Results: Event synchronization

|ROC|

Results: Phase synchronization

|ROC|

Results: Event synchronization

|ROC|

Results

- Each channel combination separately -

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 !

Phase synchronization:

Event synchronization:

Results

- ES II: Selection of best channel combination -

Phase synchronization

Event synchronization

Measure profile surrogates

- Two Evaluation schemes -

- Each channel combination separately

Null hypothesisH0 I:

Measure not suitable to find significant number of local effects

predictive of epileptic seizures.

- Selection of best channel combination

Null hypothesisH0 II:

Measure not suitable to find maximum local effects

predictive of epileptic seizures.

Measure profile surrogates

- Two Evaluation schemes -

- Each channel combination separately

Null hypothesisH0 I:

Measure not suitable to find significant number of local effects

predictive of epileptic seizures.

- Selection of best channel combination

Null hypothesisH0 II:

Measure not suitable to find maximum local effects

predictive of epileptic seizures.

Results

- ES II: Selection of best channel combination -

Phase synchronization

Event synchronization

Results

- Selection of best channel combination -

Phase synchronization

Significant!

Null hypothesis H0 II rejected

| ROC-Area |

Event synchronization

Not significant!

Null hypothesis H0 II accepted

| ROC-Area |

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

- Given example:
Discrimination of pre- and interictal intervals:

Phase synchronization more significant than event synchronization.

Predictability of epileptic seizures

- Content -

- 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

- Summary and outlook -

Retrospective investigation: Evidence of significant changes before seizures

Measures good enough for prospective application ???