[Wendling et al, 2002] 1

Computational model of Temporal Lobe EpilepsyPiotr MirowskiFrom Wendling et al, 2000, 2002, 2005

CBLL meeting, February 6, 2008

[Suffczynski, 2000, Wendling et al, 2005] 2

Brain anatomy and temporal lobe

Occipitallobe

Parietallobe

Temporallobe

Frontallobe

Cerebellum

Hippocampus (Temporal lobe)Emotion, behaviourLong-term memorySpatial navigation

Amygdala (Temporal lobe)ProcessingMemoryEmotional reactions

[Kwan et al, 2000, Suffczynski, 2000, Suffczynski et al, 2006, Wendling et al, 2005] 3

Random facts about epilepsy

Generalized: Tonic-clonic (“grand mal”)Rhythmic muscle contractionsLoss of consciousness

Generalized: Absence (“petit mal”)Impairment of consciousnessAbrupt start and termination, short durationUnpredictable (?)

EpilepsyChronic illnessAffects 1% to 2% of world population40% of patients refractory to medicationResective surgery as a treatment

Partial (“focal”)Impairment of consciousnessor perceptionSometimes aura for other seizures

Temporal LobeEpilepsyEpileptogenic focuslocalized in:hippocampusor amygdala

[Suffczynski, 2000, wikipedia.org] 4

ElectroEncephaloGraphy (EEG)

Scalp EEG

[EEG database at Albert-Ludwigs-Universität in Freiburg, Germany] 5

Intra(cranial/cerebral) EEG

Strip electrodes

Depth electrodes

Grid electrodes

[Suffczynski, 2000] 6

Normal EEG rhythmsSlow-wave sleep in adultsBabies

Adults: drowsiness, arousal, meditation Young children

Dominant α wave: closing eyes, relaxationμ rhythm in sensorimotor cortex

Active concentration

Communication between populations of neurons for cognitive or motor task

Biological artifacts: eye movementmuscleselectrocardiogram (EKG)...

External artifacts: poor grounding (50 or 60Hz hum)electrode impedance change...

Artifact removal:e.g. ICA

[Wendling et al, 2002, Suffczynski, 2000] 7

Pathological EEG activity

NormalInterictal

SpikingPreictal

Low-amplitudeHigh-frequency

OnsetSeizure

Ictal

Absence epilepsySpike and WaveSpontaneous

Tonic-clonic epilepsyPartial epilepsyChange in brain before seizure

[Suffczynski, 2000, et al, 2006] 8

Synapses and Post-Synaptic Potentials

excitatory

slow inhibitory(dentritic)

fastinhibitory(somatic)

[Wendling et al, 2002, wikipedia.org] 9

Temporal Lobe Epilepsy model

y1(t)

y0a(t)y0b(t)

y0c(t)

y2(t)

y3(t)

y4(t)

Excitation

Excitation

FastSomatic

Inhibition

SlowDentriticInhibition

Excitatoryinput noise

Pyramidal cells(in hippocampus or in 80% of cortex)Transmit information to other parts of brainMajor excitatory neurons

[Wendling et al, 2002] 10

Temporal Lobe Epilepsy model

y1(t)

y0a(t)

y0b(t)

y0c(t)

y2(t)

y3(t)y4(t)

PyramidalPyramidal

ExcitatoryExcitatoryinterneuronsinterneurons

Slow Slow inh. inh. inter-inter-neuronsneurons

Fast Fast inh. inh. inter-inter-neuronsneurons

Ck = number of synaptic connections

Gaussian white noise p(t)

EEG =y1(t) – y2(t) – y3(t)

[Wendling et al, 2000, 2002, 2005] 11

At synapses, post-synaptic EPSP or IPSPfrom afferent pre-synaptic pulse densities

Post-synaptic membrane potential y

Afferentpulse density x

2nd order ODEDampened forced oscillator

Impulse responses(solutions y for a Dirac at time t=0)

Synaptic gain W (mV):Excitatory: W=A (TBD)Slow inhibitory: W=B (TBD)Fast inhibitory: W=G (TBD)

Time constant w (Hz):Excitatory: w=a=100HzSlow inhibitory: w=b=50HzFast inhibitory: w=g=200Hz

∂2 y∂ t2

=C kW w x t −2w∂ y∂ t

−w2 y t y t =W t ew t

[Wendling et al, 2000, 2002, 2005] 12

In the axon, efferent pulse densityfrom post-synaptic membrane potential

x t =S y t =2e0

1er y0− y t

x t =S ∑k=1

Ny k t

Post-synaptic membrane potential y

Afferentpulse density x

x(t) y(t)

[Wendling et al, 2000, 2002, 2005] 13

1st order Euler discretization

y(t+Δt)

z(t+Δt)

y(t)

z(t)

p(t)

x(t)

Layer of 2 linear nodes

∂ z∂ t

=C kW w x t −2w z t −w2 y t

∂ y∂ t

=z t

z t t −z t t

=C kW w x t −2w z t −w2 y t

y t t − y t t

=z t

∂2 y∂ t2

=C kW w x t −2w∂ y∂ t

−w2 y t

z t t =1−2 t w z t t C kW w x t − t w2 y t

y t t =1 y t t z t adaptable

[Wendling et al, 2000, 2002, 2005] 14

Artificial Neural Network model

x t =S y t =2e0

1er y0− y t

y(t+Δt)

z(t+Δt)

y(t)

z(t)

p(t)

x(t)

Layer of 2 linear nodes

x t =S ∑k=1

Ny k t

Only adaptable parameter: WExcitatory: W=A (TBD)Slow inhibitory: W=B (TBD)Fast inhibitory: W=G (TBD)

[Wendling et al, 2000, 2002, 2005] 15

Artificial Neural Network model

x t =S y t =2e0

1er y0− y t

y(t+Δt)

z(t+Δt)

y(t)

z(t)

p(t)

x(t)

Layer of 2 linear nodes

x t =S ∑k=1

Ny k t pyramidal

exc. interneurons

slow inh. interneurons

fast inh. interneurons

exc. noise

EEG

y0a , z0a , y0b , z0b , y0c , z0c , y1, z1, y 2, z2, y3, z3, y4, z4, p

y0a , z0a , y0b , z0b , y0c , z0c , y1, z1, y 2, z2, y3, z3, y4, z4

Input:

Output:

y1− y2− y3

Only adaptable parameter: WExcitatory: W=A (TBD)Slow inhibitory: W=B (TBD)Fast inhibitory: W=G (TBD)

[Wendling et al, 2000, 2002, 2005] 16

Activity mode I:normal background (interictal)

[Wendling et al, 2000, 2002, 2005] 17

Activity mode II:sporadic spikes (transition to preictal)

[Wendling et al, 2000, 2002, 2005] 18

Activity mode III:sustained spike discharge (preictal)

[Wendling et al, 2000, 2002, 2005] 19

Activity mode IV:slow rhythmic activity (before onset or ictal)

[Wendling et al, 2000, 2002, 2005] 20

Activity mode V:low-voltage rapid activity (onset)

[Wendling et al, 2000, 2002, 2005] 21

Activity mode VI:slow quasi-sinusoidal, seizure (ictal)

[Wendling et al, 2000, 2002, 2005] 22

Time-varying excitation and inhibition parameters EXC, SDI, FSI

Hypothesis developed in Wendling et al, 2000, 2002, 2005 and Suffczynski et al, 2006:

The transition from interictal to ictal activity in the Temporal Lobe Epilepsyis a time-varying interaction between neuronal populations in the hippocampus:excitatory pyramidal cells (excitation gain EXC(t))local inhibitory interneurons mediating slow synapses (inhibition gain SDI(t))local inhibitory interneurons mediating fast synapses (inhibition gain FSI(t))

How to identify EXC(t), SDI(t), FSI(t)?1) Run simulation for a given triplet (EXC, SDI, FSI)2) Compute spectrogram3) Calculate features:

power spectrum in theta band (1Hz – 4Hz)power spectrum in alpha band (4Hz – 12Hz)power spectrum in beta and gamma band (12Hz – 100Hz)amplitude oscillations

4) Compare feature vectors between target and realization or two realizations

[Wendling et al, 2000, 2002, 2005] 23

Activity maps (article)

background(interictal)

sporadicspikes(preictal)

sustainedspikes(preictal)

slow rhythmic(before onset)

low-votagehigh-frequency(onset)

seizure(ictal)

[Wendling et al, 2000, 2002, 2005] 24

Activity maps (reproduced)

background(interictal)

sporadicspikes(preictal)

sustainedspikes(preictal)

slow rhythmic(before onset)

low-votagehigh-frequency(onset)

seizure(ictal)

[Wendling et al, 2000, 2002, 2005] 25

Simulation of a seizure onset (reproduced)

[Wendling et al, 2000, 2002, 2005] 26

Simulation of a seizure onset (reproduced)

background(interictal)

sporadicspikes(preictal)

sustainedspikes(preictal)

slow rhythmic(before onset)

low-votagehigh-frequency(onset)

seizure(ictal)

[EEG database at Albert-Ludwigs-Universität in Freiburg, Germany] 27

Epileptic parameter identificationon real data from TLE patients

How to identify EXC(t), SDI(t), FSI(t)?

Genetic Algorithms (stochastic optimization)e.g. population of 60 individuals, 20 generations

1) Run simulation for each triplet (EXC, SDI, FSI)2) Compare feature vectors between target and simulation3) Measure fitness of each individual4) Mutations and cross-over at each generation

Depth electrode implantation in

patient 4 (FDM database)female, 38 y.o.

TLE with partial and tonic-clonic seizures

[Wendling et al, 2000, 2002, 2005] 28

Comparisons of real and simulated EEG(real and simulated, article)

EEG recorded in hippocampus of TLE patients

[Wendling et al, 2000, 2002, 2005] 29

Comparisons of real and simulated EEG(reproduced, based on FDM pat4, sz2)

[Wendling et al, 2000, 2002, 2005] 30

Comparison of real and simulated EEG(real, from FDM pat4, sz2)

31

ReferencesEEG database at Albert-Ludwigs-Universität in Freiburg, Germanyhttps://epilepsy.uni-freiburg.de/freiburg-seizure-prediction-project

Jansen, B.H., and Rit, V.G., “Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns”, Biological Cybernetics, vol.73, pp.357-366, 1995.

Kwan and Brodie, Early Identification of Refractory Epilepsy, New England Journal of Medicine, vol.342, pp.314-319, 2000.

Suffczynski, P., Wendling, F., Belanger, J.J., and Lopes da Silva, F.H., “Some Insights Into Computational Models of (Patho)Physiological Brain Activity”, Proceedings of the IEEE, vol.94, no.4, 2006.

Wendling, F., Bellanger, J. J., Bartolomei, F., and Chauvel, P., “Relevance of nonlinear lumped parameter models in the analysis of depth-EEG epileptic signals”, Biological Cybernetics, vol.83, pp.367–378, 2000.

Wendling, F., Bartolomei, F., Bellanger, J. J., and Chauvel, P., “Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition”, European Journal ofNeuroscience, vol.15, no.9, pp.1499–1508, 2002.

Wendling, F., Hernandez, A., Bellanger, J. J., Chauvel, P., and Bartolomei, F., “Interictal to Ictal Transition in Human Temporal Lobe Epilepsy: Insights from a Computational Model of Intracerebral EEG”, European Journal of Neuroscience, vol.15, no.9, pp.1499–1508, 2002.