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Epilepsy as diseases of the dynamics of neuronal networks: models and
predictions
Fernando Lopes da Silva University of Amsterdam, The Netherlands
Brain Research Unit Low Temperature Laboratory
Helsinki University of Technology
April 1st, 2008
Epilepsy as diseases of the dynamics of neuronal networks. Models and
predictions
Basic question:
How does the transition from normal brain activity to “epileptic activity” take
place?
Basic neurophysiology: two different cases, in vivo and in vitro
Principles of interictal-ictal transitions and precursors of seizures
Case 1: Absence seizures:The occurrence of Spike-and-Wave
discharges in the thalamo-cortical system.
Case 2: Temporal Lobe Seizures:
The occurrence of seizure activity in the hippocampus and associated brain areas.
Principles of interictal-ictal transitions and precursors of seizures
Case 1: Absence seizures:The occurrence of Spike-and-Wave
discharges in the thalamo-cortical system.
Case 2: Temporal Lobe Seizures:
The occurrence of seizure activity in the hippocampus and associated brain areas.
Spontaneous absence:
Patient is requested to press a button immediately after a technician did the same.
genetic model. no neurological defects. absences are characterized by behavioral arrest and spike-and-wave discharges (SWDs) in the EEG. pharmacological responses is similar to that of patients with absences.
The WAG/Rij rat as a genetic model of absences seizures
Typical SWDs start and end abruptly
Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, Journal of Neuroscience 2002,22:1480-95
VPM VPL
18.4
8.8
29.3
3.1
9.9
Hindpaw
UpperLip Nose
“FOCUS”
SmIThalamus
B. whole seizure
4.9
A. first 500 msec
VPM
2.9
8.1
11.7
30.0
4.3
6.1
VPL
UpperLipNose
“FOCUS”
SmIThalamus
Hindpaw
20-30
40-5030-4070-80
50-60
60-70Association (%)
Evolution of absence seizures: a summary
Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, J. Neurosci 2002,22:1480-95
Cortico-Cortical. Intra-Thalamic and Cortico-Thalamic relations
The solution was to analyze short EEG epochs
A cortical “focus” of spike-and-wave discharges
• New electrophysiological evidence: extra – and intra- cellular observations
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
The occurrence of SWD in the local ECoG coincides with rhythmic membrane depolarizations superimposed on a tonic hyperpolarization of this layer IV neuron (filled with neurobiotin) (GAER rat)
Polack, Guillemain, Hu, Deransart, Depaulis and Charpier, J. of Neurosci June 2007
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Computational model of the thalamo-cortical neuronal networks
In order to understand this behaviour of the neuronal networks we need a
computational model
Suffczynski, Kalitzin, Lopes da Silva,Dynamics of non-convulsive epileptic phenomena modelled by a bistable neuronal network, Neuroscience 126 (2004) 467–484
Thalamocortical network
© SEIN, 2003Medical Physics Department
Extracellular activity of a RE neuron (yellow) and cortical field potential (green) recorded in the GAERS during a spike and wave discharge
downloaded from Crunelli Research Group:www. thalamus.org.uk
pyramidal cell
GABAergic interneuron
thalamic reticular (RE) neuron
thalamocortical (TC) neuron
In both TC and RE cellsburst firing is provided by IT calcium current
ThalamicReticularNucleus
Thalamo-corticalRelayNucleus
Excitation Inhibition
TC
RE
IN
PY
Time evolution of the neuronal membrane potential:
Synaptic currents
Synaptic conductances are modeled by convolving firing rate frequency with synaptic impulse response
Nonlinear GABA-B synaptic response
Nonlinearity is realized by a sigmoidal function of the form:
Basic equations of the model (1)
The model was realized using the Simulink toolbox of Math Works. Simulations were run using the ode3 integration method with a time step of 1 millisecond duration. Postprocessing was done using Matlab.
Model scheme
© SEIN, 2003
pyramidal cellspopulation
thalamocortical cellspopulation
interneuronalpopulation
thalamic RE cellspopulation
external inputs
burst generationprocess
Suffczynski, Kalitzin, Lopes da Silva,Dynamics of non-convulsive epileptic phenomena modelled by a bistable neuronal network, Neuroscience 126 (2004) 467–484
Example of a bifurcation between two states: “normal” & “seizure” (absence type), both in the model and in EEG real signals.
Phase portraits of the system under non-epileptic and epileptic conditions
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
One prediction is that for this kind of seizures the transition occurs randomly;
What are the predictions of the model of type 1 with respect to the dynamics of absence seizures?
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• This prediction was tested by calculating the distributions of durations and of intervals inter-paroxysms.
Distribution of Durationseither of paroxysmal events or of inter-
paroxysmal events
© SEIN, 2003Medical Physics Department
Probability of termination in unit time : p
Probability of survival of unit time : 1- p
Process durationN
um
ber
of
pro
cess
es
Exponential distributionof process durations
P(t) = (1-p)(1-p)….(1-p)p1 - p = e-λ p = 1 - e-λ
P(t) = (1 - e-λ)e-λt
e-λ 1 - λP(t) = λe-λt
Termination of a process is random in time with
constant probabilitysimple calculation
In common language:
In math language:
0 10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
λe-λt
log
time
Prediction
Distributions of epochs duration
© SEIN, 2003Medical Physics Department
Suffczynski P, Lopes da Silva FH, Parra J, Velis DN, Bouwman BM, van Rijn CM, van Hese P, Boon P, Khosravani H, Derchansky M, Carlen P, Kalitzin S. Dynamics of epileptic phenomena determined from statistics of ictal transitions. IEEE Trans Biomed Eng. 2006 Mar;53(3):524-32.
Quasi- exponential (a ~ 1) distribution of SWDs in rat (WAG/Rij)
Quasi-exponential distribution of duration of 3 Hz paroxysms in a patient with absence non-
convulsive seizures during the night
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
But ….
Does it hold in all similar cases?
Not exactly….
Gamma distribution of SWDs duration of GAER rats
Gamma distribution of SWDs duration of GAER rats
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Thus, what do we have to modify in the model?
It is necessary to include a ‘use-dependent parameter’, i.e. a parameter that changes as a seizure progresses.
,
/1 xeCxy
/1 xeCxy A value of α=1 indicates that the termination of ictal epochs is consistent with a Poisson process.
A value of α>1 indicates that one or more parameters change gradually after seizure initiation, which facilitates a transition back to the normal state. This may be mediated by a GABA dependent process since it is GVG (Vigabatrin) sensitive.
Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM.
Eur J Neurosci. 2007 May;25(9):2783-90.
Serendipity
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• The most likely hypothesis is that this effect depends on “use-dependent” changes in the dynamics of GABA
receptors.
Possible “use-dependent” candidate process:
In Conclusion:
The absence types of epilepsy seizures follow a bifurcation dynamical scenario: they display jump transitions
(Model type 1).
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Case 1: Absence seizures:The occurrence of Spike-and-Wave
discharges in the thalamo-cortical system.
Case 2: Temporal Lobe Seizures:
The occurrence of seizure activity in the hippocampus and associated brain areas.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Case 1: Absence seizures:The occurrence of Spike-and-Wave
discharges in the thalamo-cortical system.
Case 2: Temporal Lobe Seizures:
The occurrence of seizure activity in the hippocampus and associated brain areas.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
An example from basic neurophysiology shows what the properties of a pre-ictal state may be.
Disinhibition-induced synchronization of CA3 population firing
(perfusion with 10 um bicucculine)
After 2 min 6 min 7.5 min
Convol. Gauss 100 ms (black) & 1600 ms (red)
Sliding variance index
Var(t)=mean((f-F)2)
Mean amplitude of action potentials
1st Epileptiform discharge
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Cohen et al (2006) experiments show the existence of what may be called a precursor state.
These results imply that in this case there exists a pre-ictal state with special properties.
The sliding variance index = mean [(f – F)2] starts to change several minutes before the first epileptiform spike is detected.
Bear, Connors, Paradiso, Neuroscience 1996
Temporal lobe
Many factors affect network stability
Loss ofconnectionsDormantCells
FeedbackInhibition
FeedforwardInhibition
Sprouting
Excitation
Modulatory inputAcetylcholineNoradrenaline
Inhibitoryinterneurons
Inhibitoryinterneurons
Pyramidalneurons
Synaptic strength(plasticity,LTP, LTD)
Output
Ephaptic interactions
Gap-junctions
Input
IntrinsicCurrents
Apoptosisnecrosis of
specificcells
X
Input
Input
Neuronal models and the routes to seizures
The 2nd case:
a simplified model of a Hippocampal network:
“Epileptic fast activities can be explained by a model of impaired GABAergic dendritic inhibition”F. Wendling, F. Bartolomei, J.J. Bellanger and P. Chauvel.
European Journal of Neuroscience 2002
Detail of the model: interaction between different types of inhibitory interneurons and principal (pyramidal) cells.
Fast
slow
Hippocampal EEG pre-ictal and transition to ictal
Simulated EEG
Hippocampal Neuronal Population Model
Fast IN
Slow IN
Simulated EEG
Slow dendritic inhibition B
Fast somatic inhibition G
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Theoretically we may consider that the transition to an epileptic seizure can occur according to 2 models:
1. Bi- (or multi-stable) systems where jumps between two or more pre-existing attractors can take place, caused by stochastic fluctuations (noise) of any input – Case 1.
2. Parametric alteration, or deformation, that may be caused by an internal change of conditions or an external stimulus (sensory in reflex epilepsies) - Case 2.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• The main question in cases of the second type is how to detect the special properties of the pre-ictal state.
Many analytical methods have been proposed. Some of these are based on recording spontaneous neuronal activities.
Here I will consider only those methods that use a probe – i.e. a given stimulation protocol - in order to estimate changes in the excitability state of the neuronal networks that may be characteristic of this pre-ictal state.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• With respect to Case 2 we have to note that some seizures, even of the Absence type, may be triggered by an appropriate external stimulus, namely by way of intermittent light stimulation.
For example Intermittent light stimulation can be used as a probe to assess the changes in excitability state of the networks.
Magnetoencephalography (MEG) at the Free University in Amsterdam
• Whole-head CTF system
• 151 MEG sensors
• Axial gradiometers– 3rd order– 5 cm baseline
IPS (10 Hz), EO, 9 yr, F
1 2 3 4 5 6 7 8 9 10 11 12
lk
lklkd
XXdAAN
AXD,
),(1
}),({ ,
2
,
)( k
klk
lkd AAAN ,
Mean correlation distance
Phase coherency index
max
}),({1}),({
D
AXDAXC
})),({(sup ,max AXDD AX
Theoretical background (Stiliyan Kalitzin)
X - sequence of phases; A - sequence of weights
X1 X2
X3
d(X2,X3)
Parra, Kalitzin, Iriarte, Blanes, Velis and Lopes da Silva, Gamma-band phase clustering and photosensitivity: Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain. 2003 May;126(Pt 5):1164-72.
A
B
A: Phase coherency analyses – PCI; ,B: Amplitude analysesPPR & Absence seizure follows a period of IPS
IVD,10Hz stim, EO
Hz
MEG sensors
We found that the most reactive frequency band was the gamma band.
PCI
PCI
Distribution over the scalp of Phase clustering index (PCI) in the gamma
frequency band
Gamma oscillations and seizures
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• This finding led us to investigate whether PCI of EEG signals in other cases, namely of patients with mesial temporal lobe epilepsy could also have a predictive value using another kind of probe.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Implantation layout and electrode bundles: subdural reeds and
Intracerebral electrodes aimed at the head of the hippocampus and the midportion of the body of the hippocampus.
Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.
Direct intra-cerebral electrical stimulation using
a carrier frequency modulation probe
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Bilateral electrical stimulation [20 Hz, 800 μA, duration 5 sec] stimulated electrodes are HCL K4 and HCL K5 on the left hippocampus, and HCR H4 and HCR H5 on the right.
Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.
The relative phase clustering index (rPCI) is computed for all signals and all stimulated epochs
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Statistics of the interictal rPCI values for 18 Traces of 6 patients; grouped according to whether the electrodes were at the Site of Seizure Onset (SOS) or near to it, or not (non-SOS).
Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.
rPCI as function of time preceding a seizure
Values of rPCI en route to a seizure combined for all sites
rPCI > 0.6 – Seizure occurring <2h, accuracy >80%;
0.1>rPCI<0.3 – seizure expectancy within 15-30h, accuracy >80%.
Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, Clin. Neurophysiol. 2005, 116: 718 – 728.
Seizure anticipation
signal variable
Seizure risk assessment
seizure anticipation
control parameters
interictal state seizure state
bifurcation point
Low risk High risk
11.5
20 20 40 60 80 100
0
2
4
6
8
10
12
14
16
patient
cont
rol
para
met
ers
time
intervention or warning
measurement
Pre-ictal
Special properties?
Counter-stimulation is capable of annihilating the transition to the paroxysmal oscillation
Negative stimulus
Positive stimulus
• Is it possible to anticipate the occurrence of
epileptic seizures by means of (chronic) ICES in
some refractory epileptic syndromes?
?• Is it possible to prevent/to abort the occurrence of
epileptic seizures by means of (chronic) ICES in
refractory epileptic syndromes?
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Questions and Answers
Bifurcation dynamical model: jump transition – Case 1.
Deformation model: gradual transition – Case 2.
In Conclusion: there are 2 main classes of models that may explain the transition to an epileptic seizure
Bifurcation dynamical model: jump transition between two (or more) pre-existing attractors – Case 1.
Deformation model: gradual transition; in this case brain properties are assumed to change such that a new seizure state – or attractor – is either formed or is made more prominent in the pre-ictal state – Case 2.
In Conclusion: there are 2 main classes of models that may explain the transition to an epileptic seizure
Both models assume the existence of attractors that correspond to a seizure state
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Collaborators from the Department of Medical Physics of the Institute of Epilepsy SEIN (“Meer en Bosch”, Heemstede) and Center of NeuroSciences, University of Amsterdam):Stiliyan Kalitzin, Piotr Suffczynski Jaime Parra.Elan Ohayon Fernando Lopes da SilvaDimitri Velis
Details are described in Kalitzin, Parra, Velis, and Lopes da Silva, (2002) Enhancement of Phase Clustering in the EEG/MEG Gamma Frequency Band Anticipates Transitions to Paroxysmal Epileptiform Activity in Epileptic Patients With Known Visual Sensitivity.IEEE Transactions on BioMedical Engineering, 49 (11), 1279-85.
Parra, Kalitzin, Iriarte, Blanes, Velis and Lopes da Silva, (2003)Gamma-band phase clustering and photosensitivity: Is there an underlying mechanism common to photosensitive epilepsy and visual perception? Brain, 126(Pt 5):1164-72.
Lopes da Silva FH, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. Dynamical diseases of brain systems: different routes to epileptic seizures. IEEE Trans Biomed Eng. 2003 May;50(5):540-8.
Principles of interictal-ictal transitions and precursors of seizures
Principles of interictal-ictal transitions and precursors of seizures
Kalitzin, Velis, Suffczynski, Parra, Lopes da Silva, (2005) Electrical brain-stimulation paradigm for estimating the seizure onset site and the time to ictal transition in temporal lobe epilepsy. Clin Neurophysiol, 116(3):718-28.
Suffczynski P, Lopes da Silva FH, Parra J, Velis DN, Bouwman BM, van Rijn CM, van Hese P, Boon P, Khosravani H, Derchansky M, Carlen P, Kalitzin S. Dynamics of epileptic phenomena determined from statistics of ictal transitions. IEEE Trans Biomed Eng. 2006 Mar;53(3):524-32.
Kalitzin SN, Parra J, Velis DN, Lopes da Silva FH Quantification of unidirectional nonlinear associations between multidimensional signals.IEEE Trans Biomed Eng. 2007 Mar;54(3):454-61.
Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM. GABAergic mechanisms in absence epilepsy: a computational model of absence
epilepsy simulating spike and wave discharges after vigabatrin in WAG/Rij rats.Eur J Neurosci. 2007 May;25(9):2783-90.
Ohayan, EL, Kwan, HC, McIntyre Burnham, W, Suffczynski, P, Lopes da Silva, FH and Kalitzin, S, Adaptable Internittency and autonomous Transitions in Epilepsy and Cognition, Proceedings of the the 1st International Conference on Cognitive Neurodynamics – 2007, Shanghai.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
• Not only intermittent light stimulation may trigger this kind of epileptic seizures; also other forms of visual stimuli may do the same, such as Pokémon video.
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Parra J, Kalitzin SN, Stroink H, Dekker E, de Wit C, Lopes da Silva FH. Parra J, Kalitzin SN, Stroink H, Dekker E, de Wit C, Lopes da Silva FH. Removal of epileptogenic sequences from video material: the role of color. Neurology. 2005; 64(5):787-91Removal of epileptogenic sequences from video material: the role of color. Neurology. 2005; 64(5):787-91 ..
Finding of a value of α<1 suggests that seizure initiation occurs according to a random-walk process. In this case the distribution has a fast decay followed by a long tail.
Inter-ictal epochs
Bouwman BM, Suffczynski P, Lopes da Silva FH, Maris E, van Rijn CM. Eur J Neurosci. 2007 May;25(9):2783-90.
Principles of interictal-ictal transitions and precursors of seizures
A value of α<1 reveals that the probability of a transition to a seizure is not constant and it is larger immediately after one seizure and thereafter decreases over time.
Such properties are characteristic of a random-walk process.
Because in a random-walk scenario the probability ofseizure initiation is highest immediately after termination of the previous seizure, this kind of dynamic results in a grouping of seizures, i.e., in the appearance of clusters of ictal episodes separated by long interictal periods
Epilepsy as diseases of the dynamics of neuronal networks. Models and predictions
Alternate or 3rd model: autonomous intermittent transitions between 2 (or more) phases without the occurrence of a perturbation neither from the environment or from any change in network properties.
This intermittency model must be further analyzed in real cases.
Principles of interictal-ictal transitions and precursors of seizures
Proceedings of the the 1st International Conference on Cognitive Neurodynamics – 2007, Shanghai.
Adaptable Intermittency and Autonomous Transitions in Epilepsy and Cognition
Elan Liss Ohayon 1, Hon C. Kwan 2, W. McIntyre Burnham 1,2, Piotr Suffczynski 3, Fernando H. Lopes da Silva 4,5, Stiliyan Kalitzin 5
1University of Toronto Epilepsy Research Program, 2Department of Physiology, Toronto, Canada, 3Institute of Experimental Physics, Warsaw University, Warsaw, Poland, 4Swammerdam Institute for Life Sciences, University of Amsterdam, The Netherlands, 5Dutch Epilepsy Clinics Foundation (SEIN), Heemstede, The Netherlands
Transfer between firing rate and membrane potential
Transfer function for the burst firing mode
Where GB is the maximal firing rate within a burst, variables ninf(V) and minf(V) are static sigmoidal functions that describe the fractions of neurons that are deinactivated or activated, respectively. Expressions (9) and (10) describe the time delay of IT inactivation.
Basic equations of the model (2)
Wendling’s model of Hippocampal network
Simulated signals Real EEG signals
Cortico-Cortical Associations: Bilaterally Symmetric Sites
1
11 9 75 3
13
2
8 6 4
14 12 10
C.
1
3
5
7
9
11
13
2
4
6
8
10
12
14
Cx left
Cx right
A.
B.1 mV
1 s
D.
Meeren, Pijn, van Luijtelaar, Coenen and Lopes da Silva, J. Neurosci 2002,22:1480-95
A cortical “focus” of spike-and-wave discharges
SWDs are initiated in the facial somatosensory cortex in GAERS and propagate to other cortical areas and to the thalamus.
Polack, Guillemain, Hu, Deransart, Depaulis and Charpier,
J. of Neurosci June 2007
Bifurcation diagram
© SEIN, 2003Medical Physics Department
onlyparoxysmal
normaland
paroxysmal
onlynormal
Input
Normal activity - steady state
Paroxysmal activity - limit
cycle
Input distribution
Occurrence of transition to “epileptic seizure” mode: parameter sensitivity
Active observation: stimulation with “carrier frequency” Phase clustering index (PCI)
Complex amplitudes
kkf
kkf
f Z
Z
||
ffkkffk
kf AZZ ||||
Repetitive stimulus
kfZ
S. Kalitzin, J. Parra, D. Velis, F. Lopes da Silva, Enhancement of phase clustering in the EEG/MEG gamma frequency band anticipates transition to paroxysmal epileptiform activity in epileptic patients with known visual sensitivity, IEEE-TBME, v.49, 11 p 1279-1286, 2002