Normal brain rhythms and the transition to epileptic activity€¦ · Lopes da Silva F, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. Epilepsies as dynamical diseases of

School on Modelling, Automation and Control of

Physiological variables

at the Faculty of Science,

University of Porto

2 -3 May, 2007

Topics on Biomedical Systems Modelling:

Normal brain rhythms and the transition to

epileptic activity

Fernando Lopes da Silva

Center of Neuroscience

Swammerdam Institute for Life Sciences

University of Amsterdam

Normal brain rhythms and the

transition to epileptic activity

The case of the brain rhythm in the alpha (8 -12 Hz) frequency range appearing over the

somatosensory cortex:

the mu rhythm

One interesting

property of the

Alpha rhythm of

the somato-

sensory cortex

(Mu rhythm) is

that it is

modulated by

movements of

the hands:

It is attenuated,

desynchronized

alpha (ERD), by

moving the

hands, and it is

enhanced at rest

(synchronized

alpha or ERS)

Power changes in

the Apha (Mu

rhythm) and Beta

frequency ranges

ERD and ERS

Depending on

whether the hand or

the foot is moved,

the spatio-temporal

pattern differs;

the patterns of both

conditions appear

as mirror images.



Two questions put to the theoreticians or modelers:

1. How is the Alpha rhythmic activity generated?

2. How can the mirror images of the spatio-temporalpatterns of ERD/ERS associated with hand or

foot movements be accounted for?

Basic neuronal network responsible for

rhythmic activities in

thalamo-cortical circuits

Steriade 1999



Computational model of the thalamo-

cortical neuronal networks

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.

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)

Model

scheme

© SEIN, 2003

pyramidal cells

population

thalamocortical cells

population

interneuronal

population

thalamic RE cells

population

external inputs

burst generation

process

This result is an answer to question # 1:

How is the Alpha rhythmic activity generated?



But we have to consider also the second question:

2. How can the mirror images of the spatio-

temporal patterns of ERD/ERS associated with

hand or foot movements be accounted for?

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 cells

burst firing is provided

by IT calcium current

Thalamic

ReticularNucleus

Thalamo-corticalRelayNucleus

Excitation Inhibition

This result means that the mechanism of recurrent inhibition between

neighboring thalamo-cortical modules can account for the mirror images of the

spatio-temporal patterns of ERD/ERS elicited by hand or foot movements,

respectively.

ERD

ERS



• How can this transition to epileptic

activity take place?

How does the transition to “epileptic

activity” take place?

We have to examine how this occurs in

patients and in animal models

EEG and

Video

during an

epileptic

absence

(“petit

mal”)

! 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 model for absences seizures

(Gilles van Luijtelaar and Ton Coenen)

Spontaneousabsence:

Patient isrequested topress a buttonimmediately aftera technician didthe same.



• This is likely to be due to the fact that these neuronal

networks are complex non-linear systems:

• Such networks may display complex dynamics with

more than one stable state; in this case:

• These observations indicate that neuronal networks

can display qualitatively different dynamical states.

" A normal “on-going steady-state”, and

" An “oscillatory epileptiform, or paroxysmal state”.

This is what happens in epilepsy.

Ca 2+ T-channel

GABA

A & BComputer model

of a thalamo-

cortical network

capable of

displaying a

bifurcation

betweem two

states, (i) a

normal

oscillatory state,

and (ii) a

paroxystic

seizure state.

Simulation example

Simulated epoch

Power spectra

Spindle - rat

On-going state- model

Paroxysm - rat

Paroxysmal state - model

two stable statesThis is evidence for bi-stability: one network

Example

of a

bifurcation

between

two states:

“normal”

&

“seizure”

(absence

type),

both in

the model

and in

EEG real

signals.

Sensitivity of the Model to a set of parameters

Occurrence of transition to “epileptic

seizure” mode: parameter sensitivity

Phase portraits of the system under non

epileptic and epileptic conditions



" One prediction is that for this kind of seizures the

transition occurs randomly;

" A second prediction is that it should be possible to

stimulate the system in such a way that the transition

to the “seizure mode” may be aborted. This implies

that it should be possible to control the system’s

behavior.

What are the predictions of the model with respect to

the dynamics of absence seizures?



• The 1st prediction was tested by calculating

the distributions of durations and of intervals

inter-paroxysms.

Distribution of Durations

either of paroxysmal events or of inter-

paroxysmal events


Probability of termination in

unit time : p

Probability of survival of unit

time : 1- p

Process duration

Nu

mb

er o

f p

roce

sses

Exponential distribution

of process durations

P(t) = (1-p)(1-p)….(1-p)p

1 - p = e-! ! p = 1 - e-!

P(t) = (1 - e-!)e-!t

e-! " 1 - !

P(t) = !e-!t

Termination of a process

is random in time with

constant probability

simple 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

!e-!t

log

time

Prediction

Distributions of epochs duration - comparison of

simulated and rat (WAG/Rij) experimental data


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.

New hypothesis to be tested:

K+ accumulation occurs in the course of SWD in glial

cells affecting the excitability of neurons.

,

!" /1 xeCxy##

=

!" /1 xeCxy##

=



Real EEG signals

Neuronal networks

Models/Simulated EEGs Statistics/

Dynamics

Signal analysis

Statistics/

Dynamics



The second prediction is that it should be

possible to control the occurrence or the

evolution of a seizure by means of counter-

stimulation.

Indeed in bistable systems a limit cycle may

be annihilated by a perturbation applied at the

appropriate time.

Counter-stimulation is capable of annihilating the

transition to the paroxysmal oscillation

Negative

stimulus

Positive

stimulus


transition to epileptic activityCollaborators from the Institute of Epilepsy SEIN (“Meer en

Bosch”, Heemstede) and MEG Center (Free University,

Amsterdam):

Stiliyan Kalitzin,

Piotr Suffczynski

Jaime Parra.

Dimitri Velis.

Wouter Blanes.

Elan Ohayon

Fernando Lopes da Silva

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.

Suffczynski P, Lopes da Silva F, Parra J, Velis D, Kalitzin S. Epileptic transitions:

model predictions and experimental validation. J Clin Neurophysiol. 2005

Oct;22(5):288-99.

Suffczynski P, Kalitzin S, Lopes da Silva FH. Dynamics of non-convulsive

epileptic phenomena modeled by a bistable neuronal network. Neuroscience.

2004;126(2):467-84.

Lopes da Silva F, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN.

Epilepsies as dynamical diseases of brain systems: basic models of the transition

between normal and epileptic activity. Epilepsia. 2003;44 Suppl 12:72-83.

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.

Suffczynski P, Kalitzin S, Pfurtscheller G, Lopes da Silva FH. Computational

model of thalamo-cortical networks: dynamical control of alpha rhythms in

relation to focal attention. Int J Psychophysiol. 2001 Dec;43(1):25-40.

Thalamo-cortical networks possess bi-stability. In Phase-space:

the normal steady-state is within the separatrix ( ),

the complex oscillatory (paroxysmal) state is outside.

Phase-space

Documents

Normal brain rhythms and the transition to epileptic activity€¦ · Lopes da Silva F, Blanes W, Kalitzin SN, Parra J, Suffczynski P, Velis DN. Epilepsies as dynamical diseases of