Epilepsy as diseases of the dynamics of neuronal networks: models and predictions Fernando Lopes da...

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.

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


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


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?


• 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


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


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


But ….

Does it hold in all similar cases?

Not exactly….

Gamma distribution of SWDs duration of GAER rats


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


• 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).


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.


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


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


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.


• 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.


• 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


• 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.


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


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.


The relative phase clustering index (rPCI) is computed for all signals and all stimulated epochs


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).


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%.


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?

http://www.cs.princeton.edu/gfx/proj/sugcon/models/brain.png

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?


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


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.



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.


• 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.


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.


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


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.


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


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

Epilepsy as diseases of the dynamics of neuronal networks: models and predictions Fernando Lopes da...

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