Tensor decompositions for modelling epileptic seizures in EEGBorbála Hunyadi

Daan Camps Maarten De Vos

Laurent Sorber Sabine Van HuffelWim Van Paesschen Lieven De Lathauwer

Outline

• Introductiono Epileptic seizureso EEG

• Tensor decompositionso CPDo BTD

• Signal modelo Oscillatory behaviour o Sum of exponentially damped sinusoids

• Simulation study

• Real EEG examples

• Conclusions

Epilepsy

• Manifestation: o epileptic seizureso severe clinical symptoms

• Epileptic seizure:o abnormal, synchronous

activity of a large group of neurons

o Can be recorded in the EEG

Seizures and EEG

• Repetitive, oscillatory pattern

• Evolution in o Amplitueo Frequencyo Topography

• Expert visual analysiso Determinte seizure type,

epilepsy syndromeo Important for proper

treatment

Seizures and EEG

• Repetitive, oscillatory pattern

• Evolution in o Amplitueo Frequencyo Topography

• Expert visual analysiso Determinte seizure type,

epilepsy syndromeo Important for proper

treatment

• BUT! Artefacts...

6

Nature of EEG

Mixture and

indirect measurement

EEG

Key considerations:Low SNR

Retrieve patterns of interest relying on a structured signal model

Appropriate representation and decomposition

s1

s2

sn

x1

⁞

xm

X = AS

7

Tensor decompositions

= + + ... +

Ta

R

bR

cR

a2

b2

c2

a1

b1

c1

= + + ... +

TI1A1

c1

I2

I3B1T

A

c2

I2B2T

A2

I3 L2I1AR

cR

I2

I3BRTI1I1

I2I3 L

1LR

CPD:

BTD-(L,L,1):

8

Signal model: oscillatory behaviourBTD of wavelet expanded EEG tensors

freq

uenc

ych

anne

l

time

CWT-CPD (Acar 2007, De Vos 2007)

CWT-BTD

9

Signal model: sum of exp. damped sinusoidsBTD of Hankel expanded tensors

chan

nel

hankel

H-BTD (De Lathauwer, 2011)

10

Simulation study

• 3 scenarioso Stationary ictal patterno Ictal pattern with evolving frequencyo Ictal pattern propagating towards remote brain regions

• Ictal pattern superimposed ono background EEG patterno muscle artefact (extracted from healthy EEG)

• Increasing noise levels (SNR: 1-0.1)

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Simulation studyStationary ictal pattern

• sinusoidal CWT-CPD or H-BTD-(1,2,2) is optimal

• CWT-BTD can be useful to model artefact sources

• H-BTD performs best to reconstruct time course

• All models equally good for retrieving the spatial map

12

Simulation studyIctal pattern with evolving frequency

• CWT-BTD or H-BTD is the optimal model (L=?), while CPD cannot capture the frequency evolution

• CWT-BTD retrieves the TF matrices better than CPD (ICWT problem!)

• All models equally good in retrieving the localisation

13

Simulation studyPropagating ictal pattern

• Fit a dipole on the reconstructed EEG

• CWT-BTD-(2,1,2) can reveal both sourceso fit 2 dipoleso fit 1 moving dipole

• CPD retrieves 1 source located in between the 2 simulated sources

14

Clinical examplesSevere artefact

15

Clinical examplesEvolution in frequency

16

Clinical examplesSpatial evolution

17

Conclusion

• CWT-CPDo Model stationary sourceso Onset localisation

• CWT-BTDo Sources with evolving frequency or spatial distributiono High power, complex artefacts

• H-BTDo Seizure with fixed topography with arbitrary time courseo Precise reconstruction of time course

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Future work

• Automatic model selection

• Applications:o Onset localisation:

• automatic model selection is needed• Test on large real EEG dataset

o Seizure detection: • find optimal model with trial-error and use the model to detect

subsequent seizures

19

Thank you!

• Any questions?