1. Tensor decompositions for modelling epileptic seizures in EEG Borbála Hunyadi Daan CampsMaarten De Vos Laurent SorberSabine Van Huffel Wim Van Paesschen Lieven De Lathauwer

2. Outline Introduction o Epileptic seizures o EEG Tensor decompositions o CPD o BTD Signal model o Oscillatory behaviour o Sum of exponentially damped sinusoids Simulation study Real EEG examples Conclusions

3. Epilepsy Manifestation: o epileptic seizures o severe clinical symptoms Epileptic seizure: o abnormal, synchronous activity of a large group of neurons o Can be recorded in the EEG

4. Seizures and EEG Repetitive, oscillatory pattern Evolution in o Amplitue o Frequency o Topography Expert visual analysis o Determinte seizure type, epilepsy syndrome o Important for proper treatment

5. Seizures and EEG Repetitive, oscillatory pattern Evolution in o Amplitue o Frequency o Topography Expert visual analysis o Determinte seizure type, epilepsy syndrome o Important for proper treatment BUT! Artefacts...

6. 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 s1s1 s2s2 snsn x1 xmx1 xm X = AS

7. 7 Tensor decompositions = + +... + T aRaR bRbR cRcR a2a2 b2b2 c2c2 a1a1 b1b1 c1c1 T I1I1 A1A1 c1c1 I2I2 I3I3 B1TB1T A c2c2 I2I2 B2TB2T A2A2 I3I3 L2L2 I1I1 ARAR cRcR I2I2 I3I3 BRTBRT I1I1 I1I1 I2I2 I3I3 L1L1 LRLR CPD: BTD-(L,L,1):

8. 8 Signal model: oscillatory behaviour BTD of wavelet expanded EEG tensors frequency channel time CWT-CPD (Acar 2007, De Vos 2007) CWT-BTD

9. 9 Signal model: sum of exp. damped sinusoids BTD of Hankel expanded tensors channel hankel H-BTD (De Lathauwer, 2011)

10. 10 Simulation study 3 scenarios o Stationary ictal pattern o Ictal pattern with evolving frequency o Ictal pattern propagating towards remote brain regions Ictal pattern superimposed on o background EEG pattern o muscle artefact (extracted from healthy EEG) Increasing noise levels (SNR: 1-0.1)

11. 11 Simulation study Stationary 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. 12 Simulation study Ictal 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. 13 Simulation study Propagating ictal pattern Fit a dipole on the reconstructed EEG CWT-BTD-(2,1,2) can reveal both sources o fit 2 dipoles o fit 1 moving dipole CPD retrieves 1 source located in between the 2 simulated sources

14. 14 Clinical examples Severe artefact

15. 15 Clinical examples Evolution in frequency

16. 16 Clinical examples Spatial evolution

17. 17 Conclusion CWT-CPD o Model stationary sources o Onset localisation CWT-BTD o Sources with evolving frequency or spatial distribution o High power, complex artefacts H-BTD o Seizure with fixed topography with arbitrary time course o Precise reconstruction of time course

18. 18 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. 19 Thank you! Any questions?