introduction and motivation comparitive investigation: predictive performance of measures of...

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 -

~ 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 -

Intracranially implanted electrodes

TBARTBPR TBAL

TBPL

TL TR

FLRFPR

FPLFLL

TLLTLR

RL

RL

RL

EEG containing onset of a seizure (preictal and ictal)

L

R

EEG in the seizure-free period (interictal)

L

R

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 of synchronization” before epileptic seizures *

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

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 -

1 2 3 4 5 6 7 80

0.5

1M

-303

x (t

)

20 40 60 80 100 120 140 160

-303

y (t

)

t [s]

Predictability of epileptic seizures- Moving window analysis -

Window

Chan. 1

Chan. 2

1 2 3 4 5 6 7 80

0.5

1M

-303

x (t

)

20 40 60 80 100 120 140 160

-303

y (t

)

t [s]

Predictability of epileptic seizures- Moving window analysis -

Window

…

Chan. 1

Chan. 2

1 2 3 4 50

0.2

0.4

0.6

0.8

1

Zeit [Tage]

a)

RH

sensitivenot

sensitivenot

specific specific

For this channel combination:

Reliable seperation preictal interictal impossible !

Predictability of epileptic seizures - Example: Drop of synchronization as a predictor -

Time [Days]

1 2 3 4 50

0.2

0.4

0.6

0.8

1

Zeit [Tage]

a)

RH

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]






Summary and outlook






- Specificity



10

15

3

6

17

1

6

5

3

Anfälle

Zeit [Std.]

Pa

tien

t

30 60 90 120 150 180

A

B

C

D

E

F

G

H

I

I. DatabaseSeizures

Time [h]





- Specificity



• Cross Correlation Cmax

• Mutual Information I

• Indices of phase synchronization

based on

and using

• Nonlinear interdependencies Ss and Hs

• Event synchronization Q

Synchronization Directionality

• Nonlinear interdependencies Sa and Ha

• Delay asymmetry q

- Shannon entropy (se)

- Conditional probabilty (cp)- Circular variance (cv)

- Hilbert phase (H)

- Wavelet phase (W)Wcv

Hcv

Wcp

Hcp

Wse

Hse , , , , ,

II. Bivariate measures- Overview -

II. Bivariate measures- Cross correlation and mutual information -

1.0

0.5

0.0

Cmax I

* *

1.0

0.5

0.0

Cmax I

* *1.0

0.5

0.0

Cmax I

**

0 2

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

0

/2

3/2

0 2

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

0

/2

3/2

0 2

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

0

/2

3/2

II. Bivariate measures- Phase synchronization -

II. Bivariate measures- Nonlinear interdependencies -

No coupling:

X

II. Bivariate measures- Nonlinear interdependencies -

Strong coupling:

1 2-4

0

4

Kanal 2

Kanal 1

0

25

Q*

q*

Zeit [s]

II. Bivariate measures- Event synchronization and Delay

asymmetry I -

Time [s]

Chan. 1

Chan. 2





- Specificity



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

-4 -2 0 2 40

0.01

0.02

0.03

0.04

0 0.5 10

0.5

1

Sen

sitiv

ität

1-Spezifizität

III. Seizure prediction statistics: ROC

Sen

siti

vit

y1 - Specificity

-4 -2 0 2 40

0.01

0.02

0.03

0.04

0 0.5 10

0.5

1

ROC-Fläche: 0.86

Sen

sitiv

ität

1-Spezifizität


Sen

siti

vit

y1 - Specificity

ROC-Area

a)

0

0.5

1

ROC-Fläche: 0Se

nsi

tivitä

t

b)

0

0.5

1

ROC-Fläche: 1Se

nsi

tivitä

t

c)

0

0.5

1

ROC-Fläche: -1Se

nsi

tivitä

t

d)

0 0.5 10

0.5

1

ROC-Fläche: -0.003Se

nsi

tivitä

t

1-Spezifizität


ROC-Area

ROC-Area

ROC-Area

ROC-Area

1 - Specificity

Sensi

tivit

ySensi

tivit

ySensi

tivit

ySensi

tivit

y

1 2 3 4 50

0.2

0.4

0.6

0.8

1

Zeit [Tage]

cvHTime Profile : BON , TR08-TR09

0.5 0.6 0.7 0.8 0.90

1

2

3

4

cvH

%

InterPrä

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Se

nsi

tivitä

t

1 - Spezifizität

ROC-Fläche: 0.67

III. Seizure prediction statistics: Example

Sensi

tivit

y1 - Specificity

ROC-Area

Time [days]

e

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






- Specificity



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 surrogatesII. Measure profile surrogates

Randomizationof measure profiles

Randomizationof seizure times

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

1 2 3 4 5

TL01-TL02

TL02-TL03

TL03-TL04

TL04-TL05

TL05-TL06

TL06-TL07

TL07-TL08

TL08-TL09

TL09-TL10

TR01-TR02

TR02-TR03

TR03-TR04

TR04-TR05

TR05-TR06

TR06-TR07

TR07-TR08

TR08-TR09

TR09-TR10

Zeit [Tage]

Ka

na

lko

mb

ina

tion

- Results: Measure profiles of phase synchronization -

Time [days]

Channel co

mbin

ati

on

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 -


1 2 3 4 5

TL01-TL02

TL02-TL03

TL03-TL04

TL04-TL05

TL05-TL06

TL06-TL07

TL07-TL08

TL08-TL09

TL09-TL10

TR01-TR02

TR02-TR03

TR03-TR04

TR04-TR05

TR05-TR06

TR06-TR07

TR07-TR08

TR08-TR09

TR09-TR10

Zeit [Tage]

Ka

na

lko

mb

ina

tion

- First evaluation scheme -

Time [days]

Channel co

mbin

ati

on

0

0.2

0.4

0.6

0.8

1

Cmax

I seH

cpH

cvH

seW

cpW

cvW S

sH

sQ S

aH

aq

Maße

| RO

C-F

läch

e |

n.s.p = n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s. n.s.

Results: First evaluation scheme |

RO

C-A

rea |

Measures

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 -


1 2 3 4 5

TL01-TL02

TL02-TL03

TL03-TL04

TL04-TL05

TL05-TL06

TL06-TL07

TL07-TL08

TL08-TL09

TL09-TL10

TR01-TR02

TR02-TR03

TR03-TR04

TR04-TR05

TR05-TR06

TR06-TR07

TR07-TR08

TR08-TR09

TR09-TR10

Zeit [Tage]

Ka

na

lko

mb

ina

tion

- Second evaluation scheme -

Time [days]

Channel co

mbin

ati

on

0 10

0.01

0.02

0.03 TL01-TL02

0 10

0.02

0.04

0.06

0.08TL02-TL03

0 10

0.01

0.02

0.03 TL03-TL04

0 10

0.02

0.04 TL04-TL05

0 10

0.02

0.04

0.06 TL05-TL06

0 10

0.02

0.04

TL06-TL07

0 10

0.02

0.04

0.06

0.08 TL07-TL08

0 10

0.02

0.04

TL08-TL09

0 10

0.02

0.04

0.06 TL09-TL10

0 10

0.01

0.02

0.03 TR01-TR02

0 10

0.02

0.04

TR02-TR03

0 10

0.05

0.1

TR03-TR04

0 10

0.05

0.1

TR04-TR05

0 10

0.02

0.04

TR05-TR06

0 10

0.02

0.04

0.06

0.08 TR06-TR07

0 10

0.02

0.04

TR07-TR08

0 10

0.02

0.04

TR08-TR09

0 10

0.02

0.04

0.06

0.08TR09-TR10

1 1.5 2-1

0

1

InterPrä

Results: Preictal and interictal distributions

e

0

0.2

0.4

0.6

0.8

1

| RO

C-F

läch

e |

Cmax

I seH

cpH

cvH

seW

cpW

cvW S

sH

sQ S

aH

aq

Maße

.05p = .05 .05 .05 .05 .05 .05 .05 n.s. n.s. n.s. .05 n.s. .05

Results: Second evaluation scheme|

RO

C-A

rea |

Measures

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






Summary and outlook


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

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 -

I. Continuous EEG multi channel recordings

II. Calculation of characterizing measures




- Patient A (18 channel combinations)

- Phase synchronization und event synchronization Q

- ROC, same optimization, for every channel combination

- Method of measure profile surrogates

Hcv

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 surrogatesII. Measure profile surrogates

Randomizationof measure profiles

Randomizationof seizure times

0

0.5

1Ori)

0

0.5

1S1)

0

0.5

1S2)

0

0.5

1S3)

1 2 3 4 50

0.5

1

Zeit [Tage]

S4)

Measure profile surrogates

Zeit [Tage]

Time [days]

Time [days]

• 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:

104

105

106

107

10-6

10-5

Tem

pera

tur

104

105

106

107

10-5

10-4

10-3

10-2

Iterationsschritte

Kos

tenf

unkt

ion

Measure profile surrogates- Simulated Annealing II -

18 channel combinations(Phase synchronization)

Cost

funct

ion

Tem

pera

ture

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

1

0

0 1

)(

N

nnn xx

NC

max

1

)]()([

OriSurr CCE

1 2 3 4-1

-0.5

0

0.5

1

Zeit [Tage]

C ( )

Measure profile surrogates- Original autocorrelation functions (Phase sync.) -

Time [days]

1 2 3 4-1

-0.5

0

0.5

1

Zeit [Tage]

C (

)Measure profile surrogates

- Original autocorrelation functions (Phase sync.) -

Time [days]

0

0.5

1Ori)

0

0.5

1S1)

0

0.5

1S2)

0

0.5

1S3)

1 2 3 4 50

0.5

1

Zeit [Tage]

S4)

Measure profile surrogates

Time [days]

Measure profile surrogates- Two evaluation schemes -

• Each channel combination separately

• Selection of best channel combination

0

1 TL01-TL02

0

1 TL02-TL03

0

1 TL03-TL04

0

1 TL04-TL05

0

1 TL05-TL06

0

1 TL06-TL07

0

1 TL07-TL08

0

1 TL08-TL09

0

1 TL09-TL10

0

1 TR01-TR02

0

1 TR02-TR03

0

1 TR03-TR04

0

1 TR04-TR05

0

1 TR05-TR06

0

1 TR06-TR07

0

1 TR07-TR08

0

1 TR08-TR09

0

1 TR09-TR10

Results: Phase synchronization

|ROC|

0

1 TL01-TL02

0

1 TL02-TL03

0

1 TL03-TL04

0

1 TL04-TL05

0

1 TL05-TL06

0

1 TL06-TL07

0

1 TL07-TL08

0

1 TL08-TL09

0

1 TL09-TL10

0

1 TR01-TR02

0

1 TR02-TR03

0

1 TR03-TR04

0

1 TR04-TR05

0

1 TR05-TR06

0

1 TR06-TR07

0

1 TR07-TR08

0

1 TR08-TR09

0

1 TR09-TR10

Results: Event synchronization

|ROC|

0

1 TL01-TL02

0

1 TL02-TL03

0

1 TL03-TL04

0

1 TL04-TL05

0

1 TL05-TL06

0

1 TL06-TL07

0

1 TL07-TL08

0

1 TL08-TL09

0

1 TL09-TL10

0

1 TR01-TR02

0

1 TR02-TR03

0

1 TR03-TR04

0

1 TR04-TR05

0

1 TR05-TR06

0

1 TR06-TR07

0

1 TR07-TR08

0

1 TR08-TR09

0

1 TR09-TR10

Results: Phase synchronization

|ROC|

0

1 TL01-TL02

0

1 TL02-TL03

0

1 TL03-TL04

0

1 TL04-TL05

0

1 TL05-TL06

0

1 TL06-TL07

0

1 TL07-TL08

0

1 TL08-TL09

0

1 TL09-TL10

0

1 TR01-TR02

0

1 TR02-TR03

0

1 TR03-TR04

0

1 TR04-TR05

0

1 TR05-TR06

0

1 TR06-TR07

0

1 TR07-TR08

0

1 TR08-TR09

0

1 TR09-TR10

Results: Event synchronization

|ROC|

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 !

kqkq

rk

ppk

qP

)1(

0000011.0)8( rP

0015.0)5( rP

-1

0

1 Phasensynchronisationa)

RO

C-A

rea

-1

0

1 Event Synchronisationb)

RO

C-A

rea

Results- ES II: Selection of best channel combination -

Event synchronization

Phase synchronization

Measure profile surrogates- Two Evaluation schemes -

• Each channel combination separately

Null hypothesis H0 I :

Measure not suitable to find significant number of local effectspredictive of epileptic seizures.

Null hypothesis H0 II :

Measure not suitable to find maximum local effectspredictive of epileptic seizures.

• Selection of best channel combination

-1

0

1 Phasensynchronisationa)

RO

C-A

rea

-1

0

1 Event Synchronisationb)

RO

C-A

rea

Results- ES II: Selection of best channel combination -



0

1 Phasensynchronisation

RO

C-F

läch

e

0

1 Event Synchronisation

RO

C-F

läch

eResults

- Selection of best channel combination -

Significant!Null hypothesis H0

II rejected

Not significant!Null hypothesis H0

II accepted



| R

OC

-Are

a |

| R

OC

-Are

a |

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:






Summary and outlook


Predictability of epileptic seizures- Summary and outlook -

Retrospective investigation: Evidence of significant changes before seizures

Measures good enough for prospective application ???

introduction and motivation comparitive investigation: predictive performance of measures of...

Documents

epilepsy slide

r slide

brain epileptic seizure

window analysis window

seizure preictal

predictor time days

preictal state

seizurefree period interictal