International Workshop on Advanced Epilepsy Treatment - CADET 2009 – 28-30 March, 2009 Kitakyushu Science & Research Park, Kitakyushu, Japan Realistic modeling and interpretation of depth-EEG signals recorded during inter-ictal to ictal transition in temporal lobe epilepsy F. Wendling INSERM U642 - University of Rennes Laboratory of Signal and Image Processing Rennes – France http://perso.univ-rennes1.fr/fabrice.wendling/ 1 LTSI
Epilepsies - Neurological disorder characterized by recurrent seizures - Excessive firing in neuronal cells, abnormally-high synchronization processes in neuronal networks - Imbalance between excitation- and inhibition-related processes - Poorly understood mechanisms of: - epileptogenesis ( property of a neuronal tissue to become epileptic) - ictogenesis ( transition from interictal to ictal activity ) Development of models Development of numerous techniques allowing for the observation of neuronal activity 2
Electrophysiological observations Human Organ Brain - Local field activity (intracerebral EEG, ECoG) Cerebral region - Global activity (scalp EEG, MEG) Cerebral structure Experimental models (animals) Neuronal population - Field activity Cell - Cellular activity (1 or a few cells) Neuron Seizure Seizure start termination Deep EC Cerveau isolé … … Superficial EC SEEG exploration SEEG exploration SEEG exploration SEEG exploration SEEG exploration SEEG exploration … … Klaus Goldbrandsen 5 s Neurological Institute Preictal Background Ictal burst Fast onset Ictal burst Carlo Besta, Milan activity activity activity activity activity M. de Curtis (slower frequency) 3 Intracerebral multiple lead electrodes Intracerebral multiple lead electrodes Intracerebral multiple lead electrodes Epilepsy Unit, CHR La timone, Marseille (lead: ∅ 0.8 mm, L 2mm) (lead: ∅ 0.8 mm, L 2mm) (lead: ∅ 0.8 mm, L 2mm)
Objective of this work: “To interpret” depth-EEG signals A difficult issue: � Observations are incomplete - In time: epilepsy = progressive disease, observation window is limited - In space: spatial undersampling, some structures can not be recorded (difficult access) � Pathophysiological mechanisms occur at different temporal scales - Epileptic « spikes »: a few hundred of ms - Seizures: a few tens of seconds up to several minutes ( prediction? ) - Frequency of seizures : a few/day up to a few/month ( regulations ?) � Complexity of recorded systems (specific cytoarchitectonics , nonlinear mechanisms, different spatial scales , short/long term plasticity ) Depth-EEG is a non-stationary signal with transient events and ruptures of dynamics (more or less abrupt) 4
Interictal and pre-onset activity (TLE) Depth-EEG 5 sec Amygdala Ant. hippocampus Post. hippocampus Entorhinal cortex 5
Seizure onset Depth-EEG 5 sec Amygdala Ant. hippocampus Post. hippocampus Entorhinal cortex 6
Ictal activity Depth-EEG 5 sec Amygdala Ant. hippocampus Post. hippocampus Entorhinal cortex 7
Interictal / ictal transition Amygdala Ant. hippocampus Post. hippocampus Entorhinal cortex 8
Power spectral densities Ant. hip. Post. hip. 9
Power spectral densities Interictal Onset Ictal Ant. hip. PSD PSD PSD PSD PSD PSD (V²/Hz) (V²/Hz) (V²/Hz) (V²/Hz) (V²/Hz) (V²/Hz) f (Hz) f (Hz) f (Hz) f (Hz) f (Hz) f (Hz) Post. hip. Ant. hip. Post. hip. 10
Time-frequency representation HIP 5 s ? Frequency (Hz) 11 Time (s) Approach : physiological modeling of depth-EEG signals
Models used in the study of epileptic phenomena F. Wendling, Computational models of epileptic activity: a bridge between observation and pathophysiolocial interpretation , Expert Review of Neurotherapeutics (2008) 12
Why a ‘population-oriented’ approach ? • Main figures: - Cerebral cortex : 10 billions of neurons - Each neuron is connected to a large number of neurons (100 to 100 000 synapses/neuron) • Interactions between subpopulations of cells Ensemble dynamics ( positive or negative loops, feedback/feedforward) • EEG dynamics - reflection of these ensemble interactions - summation of PSP generated by a large number of cells activated quasi-synchronously 13
Background • Population models : Wilson & Cowan (1972), Freeman (~1970), Lopes da Silva (~1970), Jansen (1993, 1995), Wendling (2000), Suffczynski (2001), and others � Main features - Relevant variable: firing-rate - Synaptic inputs sum linearly into the soma (mean-field approximation) - Firing-rate computed from the total current delivered by synaptic inputs 14 W.J. Freeman, Tutorial on neurobiology: From single neurons to brain chaos , Int. J. Bif. Chaos, 1992
Example : Freeman ’s model (1/2) Olfactory system ( receptors → olf. bulb → Ant olf. nucleus → prepyiform cortex ) 2nd order ordinary differential equation 15
Example : Freeman ’s model (2/2) W.J. Freeman, Simulation of chaotic EEG patterns with a Dynamic Model of the 16 Olfactory System , Biol. Cyb., 1987
Neuronal population model : basic principles Neuronal population « Pulse-to-Wave » (linear transfer function) Afferent APs � PSP Main cells input (Pyramidal) From other subset(s) of cells From other subset(s) of cells Inhibitory « Wave-to-Pulse » interneurons (nonlinear function) PSP � APs excitatory inhibitory To other subset(s) of cells To other subset(s) of cells Wendling F, Chauvel P, “Transition to ictal activity in Temporal Lobe Epilepsy: insights from macroscopic models”, in Computational Neuroscience in Epilepsy ,. I. Soltesz & K. Staley eds., 2008 17
Pulse-to-wave and wave-to-pulse conversion operations - Pulse to wave : the average membrane potential results from passive integration of PPS’s related to afferent AP’s (mainly at the dendrites) → represented by a second order transfer function of impluse − = at response given by (excitatory case) h ( t ) u ( t ). Aate e = z ( t ) z ( t ) & PSP AP h e (t) 1 2 = − − z ( t ) Aa x ( t ) 2 a z ( t ) a z ( t ) & 1 1 - Wave to pulse : the average density of action potentials fired by the neurons depends on a nonlinear transform of the average membrane potential (threshold + saturation effect) → represented by the sigmoid function 2 e = 0 S ( v ) AP S(v) PSP − + r ( v v ) 1 e 0 18
Pulse-to-wave and wave-to-pulse conversion operations - Pulse to wave : the average membrane potential results from passive Average EPSP integration of PPS’s related to afferent AP’s (mainly at the dendrites) Average IPSP → represented by a second order transfer function of impluse Average potential (mv) − = at response given by (excitatory case) h ( t ) u ( t ). Aate e = z ( t ) z ( t ) & PSP AP h e (t) 1 2 = − − z ( t ) Aa x ( t ) 2 a z ( t ) a z ( t ) & 1 1 t (ms) - Wave to pulse : the average density of action potentials fired by the neurons depends on a nonlinear transform of the average membrane potential (threshold + saturation effect) S ( v ) ( v 0 , e 0 ) → represented by the sigmoid function 2 e = 0 S ( v ) AP S(v) PSP − + r ( v v ) 1 e 0 v (mV) 19
Block diagram, equations and generated signals Nonlinear dynamical system (ODEs) = & ( ) y t y ( ) t input Main cells Main cells 0 3 C 2 S(v) h e (t) C 1 = − − − (Pyramidal) (Pyramidal) 2 y & ( ) t AaS y ( y ) 2 ay ( ) t a y ( ) t 3 1 2 3 0 + p(t) = + y t & ( ) y ( ) t h e (t) EPSP EPSP 1 4 + { } S(v) = + − − 2 & ( ) y t Aa p t ( ) C S C y [ ( )] t 2 ay ( ) t a y t ( ) - Model output 4 2 1 0 4 1 h i (t) Inhibitory Inhibitory excitatory excitatory = y & ( ) t y t ( ) IPSP IPSP 2 5 interneurons interneurons inhibitory inhibitory { } C 4 S(v) h e (t) C 3 = − − 2 & ( ) y t Bb C S C y ( ( ) t 2 by t ( ) b y ( ) t 5 4 3 0 5 2 20
Block diagram, equations and generated signals Nonlinear dynamical system (ODEs) input Main cells Main cells C 2 S(v) h e (t) C 1 (Pyramidal) (Pyramidal) + p(t) + h e (t) EPSP EPSP + S(v) - Model output h i (t) Inhibitory Inhibitory excitatory excitatory IPSP IPSP interneurons interneurons inhibitory inhibitory C 4 S(v) h e (t) C 3 Simulated signal (~LFP) Amplitude (a.u) Time (s) 21
Single population model Main cells (Pyramidal) � Model configuration : Single population + progressive increase of Inhibitory interneurons the E/I ratio (excitation/inhibition) � Similarity with real intracerebral EEG signals 22 Wendling et al., Biol. Cyb., 2000
Model of multiple coupled populations 23
Influence of couplings � Model configuration : 3 populations, unidirectional couplings: isolated spikes propagate from P1 to P3 � Introduction of a recurrent connection: isolated spikes sustained discharges of spikes � Real intracerebral EEG signals recorded during seizure (TLE) 24 Wendling et al., Biol. Cyb., 2000
Exemple of model simulation 2 1 Legends Legends E/I + : increase of the Excitation/Inhibition ratio E/I + : increase of the Excitation/Inhibition ratio C+ : increase of the coupling from P1 to P2 C+ : increase of the coupling from P1 to P2 25
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