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...
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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):
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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
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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
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Clinical examplesSevere artefact
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Clinical examplesEvolution in frequency
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Clinical examplesSpatial evolution
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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
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Thank you!
• Any questions?