tensor decompositions for modelling epileptic seizures in eeg borbála hunyadi daan campsmaarten de...

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)

11

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

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

Thank you!

• Any questions?