Computational model of Temporal Lobe Epilepsy

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1 Computational model of Temporal Lobe Epilepsy Piotr Mirowski From Wendling et al, 2000, 2002, 2005 CBLL meeting, February 6, 2008 [Wendling et al, 2002] 1

2 Brain anatomy and temporal lobe Frontal lobe Hippocampus (Temporal lobe) Emotion, behaviour Long-term memory Spatial navigation Parietal lobe Occipital lobe Temporal lobe Cerebellum Amygdala (Temporal lobe) Processing Memory Emotional reactions [Suffczynski, 2000, Wendling et al, 2005] 2

3 Random facts about epilepsy Epilepsy Chronic illness Affects 1% to 2% of world population 40% of patients refractory to medication Resective surgery as a treatment Partial ( focal ) Impairment of consciousness or perception Generalized: Absence ( petit mal ) Impairment of consciousness Abrupt start and termination, short duration Unpredictable (?) Generalized: Tonic-clonic ( grand mal ) Rhythmic muscle contractions Loss of consciousness Sometimes aura for other seizures Temporal Lobe Epilepsy Epileptogenic focus localized in: hippocampus or amygdala [Kwan et al, 2000, Suffczynski, 2000, Suffczynski et al, 2006, Wendling et al, 2005] 3

4 ElectroEncephaloGraphy (EEG) Scalp EEG [Suffczynski, 2000, wikipedia.org] 4

5 Intra(cranial/cerebral) EEG Strip electrodes Depth electrodes Grid electrodes [EEG database at Albert-Ludwigs-Universität in Freiburg, Germany] 5

6 Normal EEG rhythms Slow-wave sleep in adults Babies Adults: drowsiness, arousal, meditation Young children Dominant α wave: closing eyes, relaxation μ rhythm in sensorimotor cortex Active concentration Communication between populations of neurons for cognitive or motor task Biological artifacts: eye movement muscles electrocardiogram (EKG)... External artifacts: poor grounding (50 or 60Hz hum) electrode impedance change... [Suffczynski, 2000] Artifact removal: e.g. ICA 6

7 Pathological EEG activity Tonic-clonic epilepsy Partial epilepsy Change in brain before seizure Normal Interictal Spiking Preictal Low-amplitude High-frequency Onset Seizure Ictal Absence epilepsy Spike and Wave Spontaneous [Wendling et al, 2002, Suffczynski, 2000] 7

8 Synapses and Post-Synaptic Potentials excitatory slow inhibitory (dentritic) fast inhibitory (somatic) [Suffczynski, 2000, et al, 2006] 8

9 Temporal Lobe Epilepsy model Excitation y2(t) y1(t) y0b(t) y3(t) Excitatory input noise y0a(t) y0c(t) Slow Dentritic Inhibition Excitation y4(t) Pyramidal cells (in hippocampus or in 80% of cortex) Transmit information to other parts of brain Major excitatory neurons [Wendling et al, 2002, wikipedia.org] Fast Somatic Inhibition 9

10 Temporal Lobe Epilepsy model Excitatory interneurons y0a(t) y1(t) Pyramidal y2(t) y0b(t) Slow inh. interneurons y4(t) y3(t) Ck = number of synaptic connections Gaussian white noise p(t) y0c(t) EEG = y1(t) y2(t) y3(t) Fast inh. interneurons [Wendling et al, 2002] 10

11 At synapses, post-synaptic EPSP or IPSP from afferent pre-synaptic pulse densities 2nd order ODE Dampened forced oscillator Afferent Post-synaptic pulse density x membrane potential y y t =W t e wt 2 y y =C W w x t 2 w w 2 y t k 2 t t Synaptic gain W (mv): Excitatory: W=A (TBD) Slow inhibitory: W=B (TBD) Fast inhibitory: W=G (TBD) Impulse responses (solutions y for a Dirac at time t=0) Time constant w (Hz): Excitatory: w=a=100hz Slow inhibitory: w=b=50hz Fast inhibitory: w=g=200hz 11

12 In the axon, efferent pulse density from post-synaptic membrane potential x(t) y(t) x t =S y t = 2 e0 1 e r y 0 y t Post-synaptic membrane potential y Afferent pulse density x x t =S N k =1 y k t 12

13 st 1 order Euler discretization 2 y y 2 =C W w x t 2 w w y t k 2 t t y =z t t z =C k W w x t 2 w z t w 2 y t t y t t y t = z t t z t t z t =C k W w x t 2 w z t w 2 y t t y t t =1 y t t z t adaptable z t t = 1 2 t w z t t C k W w x t t w 2 y t Layer of 2 linear nodes z(t) y(t) y(t+δt) x(t) z(t+δt) p(t) 13

14 Artificial Neural Network model x t =S y t = x t =S 2 e0 1 e N k =1 r y 0 y t y k t Only adaptable parameter: W Excitatory: W=A (TBD) Slow inhibitory: W=B (TBD) Fast inhibitory: W=G (TBD) Layer of 2 linear nodes z(t) y(t) y(t+δt) x(t) z(t+δt) p(t) 14

15 Artificial Neural Network model exc. noise exc. interneurons x t =S y t = pyramidal x t =S EEG 2 e0 1 e N k =1 r y 0 y t y k t y 1 y 2 y 3 slow inh. interneurons Only adaptable parameter: W Excitatory: W=A (TBD) Slow inhibitory: W=B (TBD) Fast inhibitory: W=G (TBD) fast inh. interneurons Input: y 0a, z 0a, y 0b, z 0b, y 0c, z 0c, y1, z 1, y 2, z 2, y 3, z 3, y 4, z 4, p Output: y 0a, z 0a, y 0b, z 0b, y 0c, z 0c, y1, z 1, y 2, z 2, y 3, z 3, y 4, z 4 Layer of 2 linear nodes z(t) y(t) y(t+δt) x(t) z(t+δt) p(t) 15

16 Activity mode I: normal background (interictal) 16

17 Activity mode II: sporadic spikes (transition to preictal) 17

18 Activity mode III: sustained spike discharge (preictal) 18

19 Activity mode IV: slow rhythmic activity (before onset or ictal) 19

20 Activity mode V: low-voltage rapid activity (onset) 20

21 Activity mode VI: slow quasi-sinusoidal, seizure (ictal) 21

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 Epilepsy is 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 spectrogram 3) 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 22

23 Activity maps (article) seizure (ictal) low-votage high-frequency (onset) slow rhythmic (before onset) sustained spikes (preictal) sporadic spikes (preictal) background (interictal) 23

24 Activity maps (reproduced) seizure (ictal) low-votage high-frequency (onset) slow rhythmic (before onset) sustained spikes (preictal) sporadic spikes (preictal) background (interictal) 24

25 Simulation of a seizure onset (reproduced) 25

26 Simulation of a seizure onset (reproduced) seizure (ictal) low-votage high-frequency (onset) slow rhythmic (before onset) sustained spikes (preictal) sporadic spikes (preictal) background (interictal) 26

27 Epileptic parameter identification on 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 simulation 3) Measure fitness of each individual 4) 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 [EEG database at Albert-Ludwigs-Universität in Freiburg, Germany] 27

28 Comparisons of real and simulated EEG (real and simulated, article) EEG recorded in hippocampus of TLE patients 28

29 Comparisons of real and simulated EEG (reproduced, based on FDM pat4, sz2) 29

30 Comparison of real and simulated EEG (real, from FDM pat4, sz2) 30

31 References EEG database at Albert-Ludwigs-Universität in Freiburg, Germany https://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 , Kwan and Brodie, Early Identification of Refractory Epilepsy, New England Journal of Medicine, vol.342, pp , 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, 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 , 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 of Neuroscience, vol.15, no.9, pp , 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 ,

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