Predictability of epileptic seizures
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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.

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Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

Intracranially implanted electrodes


Introduction and motivation comparitive investigation

L

R

EEG containing onset of a seizure (preictal and ictal)


Introduction and motivation comparitive investigation

L

R

EEG in the seizure-free period (interictal)


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window


Introduction and motivation comparitive investigation

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window


Introduction and motivation comparitive investigation

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window


Introduction and motivation comparitive investigation

Chan. 1

Chan. 2

Predictability of epileptic seizures

- Moving window analysis -

Window


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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]


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

I. Database

Seizures

Time [h]


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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 -

*

*

*

*

*

*


Introduction and motivation comparitive investigation

II. Bivariate measures

- Phase synchronization -


Introduction and motivation comparitive investigation

II. Bivariate measures

- Nonlinear interdependencies -

No coupling:

X


Introduction and motivation comparitive investigation

II. Bivariate measures

- Nonlinear interdependencies -

Strong coupling:


Introduction and motivation comparitive investigation

II. Bivariate measures

- Event synchronization and Delay asymmetry I -

Chan. 1

Chan. 2

Time [s]


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

ROC-Area

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: ROC

Sensitivity

ROC-Area

Sensitivity

ROC-Area

Sensitivity

ROC-Area

Sensitivity

ROC-Area

1 - Specificity


Introduction and motivation comparitive investigation

III. Seizure prediction statistics: Example

Time [days]

e

Sensitivity

ROC-Area

1 - Specificity


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

- Results: Measure profiles of phase synchronization -

Channel combination

Time [days]


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

- First evaluation scheme -

Channel combination

Time [days]


Introduction and motivation comparitive investigation

Results: First evaluation scheme

| ROC-Area |

Measures


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

- Second evaluation scheme -

Channel combination

Time [days]


Introduction and motivation comparitive investigation

- Second evaluation scheme -

Channel combination

Time [days]


Introduction and motivation comparitive investigation

- Second evaluation scheme -

Channel combination

Time [days]


Introduction and motivation comparitive investigation

Results: Preictal and interictal distributions

e


Introduction and motivation comparitive investigation

Results: Second evaluation scheme

| ROC-Area |

Measures


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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)


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

Measure profile surrogates

Zeit [Tage]

Time [days]

Time [days]


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

Measure profile surrogates

- Simulated Annealing II -

Temperature

18 channel combinations

(Phase synchronization)

Cost function

Iteration steps


Introduction and motivation comparitive investigation

  • 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


Introduction and motivation comparitive investigation

Measure profile surrogates

- Original autocorrelation functions (Phase sync.) -

Time [days]


Introduction and motivation comparitive investigation

Measure profile surrogates

- Original autocorrelation functions (Phase sync.) -

Time [days]


Introduction and motivation comparitive investigation

Measure profile surrogates

Time [days]


Introduction and motivation comparitive investigation

Measure profile surrogates

Time [days]


Introduction and motivation comparitive investigation

Measure profile surrogates

- Two evaluation schemes -

  • Each channel combination separately

  • Selection of best channel combination


Introduction and motivation comparitive investigation

Results: Phase synchronization

|ROC|


Introduction and motivation comparitive investigation

Results: Event synchronization

|ROC|


Introduction and motivation comparitive investigation

Results: Phase synchronization

|ROC|


Introduction and motivation comparitive investigation

Results: Event synchronization

|ROC|


Introduction and motivation comparitive investigation

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:


Introduction and motivation comparitive investigation

Results

- ES II: Selection of best channel combination -

Phase synchronization

Event synchronization


Introduction and motivation comparitive investigation

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.


Introduction and motivation comparitive investigation

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.


Introduction and motivation comparitive investigation

Results

- ES II: Selection of best channel combination -

Phase synchronization

Event synchronization


Introduction and motivation comparitive investigation

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 |


Introduction and motivation comparitive investigation

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.


Introduction and motivation comparitive investigation

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


Introduction and motivation comparitive investigation

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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