Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition
F.Wendling,1F.Bartolomei,2J.J.Bellanger1and P.Chauvel2
1Laboratoire Traitement du Signal et de L'Image,INSERM,UniversiteÂde Rennes1,Campus de Beaulieu,35042Rennes Cedex, France
2Laboratoire de Neurophysiologie et Neuropsychologie,INSERM,UniversiteÂde la MeÂditerraneÂe,13385Marille Cedex5, France
Abstract
This paper focus on high-frequency(gamma band)EEG activity,the most characteristic electrophysiological pattern in focal izures of human epilepsy.It starts with recent hypothes about:(i)the behaviour of inhibitory interneurons in hippocampal or neocortical networks in the generation of gamma frequency oscillations;(ii)the nonuniform alteration of GABAergic inhibition in experimental epilepsy(reduced dendritic inhibition and incread somatic inhibition);and(iii)the possible depression of GABA A,fast circuit activity by GABA A,slow inhibitory postsynaptic currents.In particular,the hypothes are introduced in a new computational macroscopic model of
EEG activity that includes a physiologically relevant fast inhibitory feedback loop.Results show that strikingly realistic activity is produced by the model when compared to real EEG signals recorded with intracerebral electrodes.They show that,in the model,the transition from interictal to fast ictal activity is explained by the impairment of dendritic inhibition.
Keywords:dis-inhibition,gamma band activity,interneuronal circuits,intracerebral EEG
Introduction
High-frequency EEG waves originating from one or veral brain regions are the most characteristic electrophysiological pattern in focal izures of human epilepsy.Paradoxically,very few works are dedicated to their analysis compared to phasic interictal events.Low-voltage rapid discharges are often obrved at izure ont during presurgical evaluation of refractory partial epilepsies when intracer-ebral electrodes(depth-EEG)are ud to record EEG signals.Low-amplitude waves with maximum frequencies belonging to the gamma band(20±100Hz and beyond)(Bragin et al.,1999)have been reported in clinical studies(Allen et al.,1992).The regions they originate from are generally considered to be highly epileptogenic, and anatomically de®ne a particular zone,referred to as the `epileptogenic zone'Understanding of the epileptogenic zone network organization can lead
to limited surgical rection aimed at suppressing izures.Although fast EEG waves can now be well characterized from a signal-processing standpoint,underlying cellular mechanisms still remain to be understood.Here,potential clinical bene®ts are obvious:the understanding of neurophysiological and neurobiological factors implied in the generation of ictal fast waves could lead to the development of new therapeutic procedures aimed at neutralizing epileptogenic networks responsible for the initiation of izures.
Modelling may be a way to progress in this understanding. Recently,studies bad on experimental and/or computational models provided new insight in the understanding of neuronal mechanisms involved in rapid EEG activity.
On the one hand,there was evidence that oscillations of gamma frequency are linked to the behaviour of inhibitory interneurons in hippocampal or neocortical networks(`inhibition-bad rhythms') (Jefferys et al.,1996;Whittington et al.,2000).On the other hand, results showed that two types of GABA A inhibitory postsynaptic currents(IPSCs)may play a crucial role in the formation of nested theta/gamma rhythms in hippocampal pyramidal cells(White et al., 2000).
In the®eld of epilepsy,the role of inhibition and the relationship between the inhibition/excitation bala
nce and epileptogenesis have been largely investigated in experimental studies(Dichter,1997). New advances now demonstrate that GABAergic inhibition that controls neuronal excitability is not uniformly altered in experimental temporal lobe epilepsy models;if dendritic inhibition is reduced, somatic inhibition is,in contrast,incread as a result of the hyperactivity of somatic projecting interneurons(Cossart et al., 2001).
In order to relate the aforementioned recent results to rapid activity (gamma band)obrved in EEG izure signals,we started from an existing macroscopic neurophysiologically relevant model of the EEG(neuronal population model)that differs from detailed micro-scopic models of interconnected individual neurons(Traub et al., 1997).The concepts upon which this model is bad were initially developed by Freeman1978)in their works dealing with perceptual processing in the olfactory system and,in the same time,by Lopes da Silva et al.,(1974,1976)in their study of the underlying mechanisms of alpha rhythm generation.In a previous study(Wendling et al., 2000),we showed that population models may explain veral
Correspondence:Dr F.Wendling,as above.
Email:fabrice.wendling@univ-rennes1.fr
Received18October2001,revid27February2002,accepted15March
2002
doi:10.1046/j.1460-9568.2002.01985.x
European Journal of Neuroscience,Vol.15,pp.1499±1508,2002ãFederation of European Neuroscience Societies
rhythms obrved in depth-EEG epileptic signals.Particularly,we demonstrated that realistic epileptiform activity can be simulated when model parameters are altered according to current hypothes about epileptogenesis (balance between excitation and inhibition,excitatory couplings between distant neural populations).However,we also noticed that fast EEG activity cannot be produced when only a slow dendritic inhibitory loop is reprented in the model.In the prent article,we report an extension of the model that now takes into account recent hypothes about:(i)the respective role of dendritic-projecting and somatic-projecting interneurons and (ii)the possible inhibition-related functional reorganizations that take place in the epileptic tissue.The model is described in the next ction and explored in the methods in terms of its three main parameters,namely dendritic excitation,dendritic inhibition and somatic inhibition provided by interne
urons to pyramidal cells.Necessary conditions to obtain transitions between typical periods of epileptic activity,including low-voltage rapid discharges,are established.Under the conditions,very realistic signals are produced by the model.They are compared with real epileptic signals recorded in vivo in the human
brain
F I
vistarG .1.From the hippocampal neuronal population organization to the neuronal population model.(a)Structurally,the neuronal population is considered to be compod of four neuronal subts:pyramidal cells,excitatory interneurons,dendritic-projecting interneurons with slow synaptic kinetics (GABA A,slow )and somatic-projecting interneurons (grey rectangle)with faster synaptic kinetics (GABA A,fast ).Subt of pyramidal cells project to and receive feedback from subts of interneurons.As described in (Banks et al .,2000),dendritic interneurons project to somatic ones.(b)The model accounts for the neuronal population organization.In each subt,the average pul density of afferent action potentials is changed into an average inhibitory or excitatory postsynaptic membrane potential using a linear dynamic transfer function of impul respon h e (t ),h i (t ),or h g (t ),while this potential is converted into an average pul density of potentials ®red by the neurons using a static nonlinear function [asymmetric sigmoid curve,S (v )].The subt of somatic-projecting interneurons (grey rectangle)receive input from both subts of pyramidal and dendritic interneurons.(c)the model output reprents the summated average postsynaptic potentials on pyramidal cells.It re¯ects an EEG signal.
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Bartolomei et al.,2000using intracerebral multiple lead electrodes (stereoelectroencephalography or SEEG,a diagnostic procedure ud in the presurgical evaluation of patients suffering from refractory partial epilepsy).The results are then discusd with a special emphasis on the possible impairment of dendritic inhibition in the transition between interictal to ictal activity,as predicted by the model.
how old
The model
Different modelling strategies have been propod to relate macro-scopic EEG phenomena with oscillations in neuronal populations.In the paper of Whittington et al.(2000),two complementary approaches are prented.In the®rst one,referred to as`detailed', single neurons are accurately modelled for their structural components(dendrites,soma and axon)and functional properties (voltage-dependent channels with kinetics derived from experimental voltage-clamp studies).Then,networks are built from the intercon-nection of a large enough veral thousands)of neurons and different types of interneurons.In the networks,the EEG activity that cor
responds to summated postsynaptic potentials that can develop on different parts of pyramidal cell membranes can be spatially and temporally studied for various parameters such as the types of neurons introduced in the network,network size,connect-ivity patterns or conduction delays.In the cond one,referred to as `reduced',a small number of neurons is ud to better understand a particular dynamic behaviour,such as synchronization in networks of interneurons(White et al.,1998).
Besides the modelling techniques lying at the cellular and network levels,another approach lying at a higher level of he population level,was propod in the early 70s.It starts from the fact that neurons form populations and that the EEG is a re¯ection of enmble dynamics arising from intercon-nected populations of pyramidal cells and interneurons.This approach was initially propod by Freeman(1978)and coworkers who made substantial progress in the understanding of perceptual processing in the olfactory system.Their studies,spanning the three last decades,are bad on experimental data and on computational models in which the dynamics of each neural enmble are reprented by a2nd order ordinary differential equation having a static nonlinearity identi®ed as a asymmetric sigmoid curve (Eeckman&Freeman,1991).They led to a model of the olfactory area able to produce EEG signals that approximate experimentally recorded EEGs quite accurately.Similar ideas developed at the same time by Lopes Da Silva et al.(1974)led to the develo
pment of a lumped-parameter population model able to explain the alpha rhythm of the EEG(Stam et al.,1999).
我叫金三顺插曲The EEG model upon which we have ud follows the same approach but in a different context,namely the physiological interpretation of EEG signals recorded with intracerebral electrodes in epileptic patients according to the stereoelectroencephalographic method(Talairach&Bancaud,1973).
In its earlier form,the model reprented a cluster of neurons containing three interacting subts.The®rst subt was compod of the main pyramidal cells in the hippocampus or neocortex). It received a feedback from two other subts compod of local interneurons,either excitatory or inhibitory.Model parameters were altered according to current hypothes about epileptogenesis. Speci®cally,the in¯uence of the balance between excitatory and inhibitory synaptic gains was analyd and conditions for realistic epileptiform activity,such as sustained discharges of spikes±a typical ictal pattern,to occur were found.It was also obrved that the model was not able to reprent fast EEG activity such as low-voltage rapid discharges often obrved in depth-EEG signals at izure ont.This fact was easily explained by the values of average synaptic time constants ud in transfer functions of feedback loops in the model that act as low-pass®lters and w
hich are not compatible with experimentally obrved frequencies(20±80Hz).
In this new model version,a fourth subt is added in order to reprent a cond class of inhibitory interneurons with faster kinetics than tho already included.This modi®cation is bad on biblio-graphical material.In the hippocampus,a ries of studies bad on a variety of techniques(Miles et al.,1996)demonstrate that there are two types of GABA A synaptic respons in CA1pyramidal neurons: a fast one near the soma and a slow one in the dendrites.The®rst one (GABA A,fast)is a rapidly activated and decaying IPSC mediated by somatic synaps and the cond one(GABA A,slow)is a slowly rising and decaying IPSC mediated by dendritic synaps.More recent works(White et al.,2000)suggest that two parate class of interneurons(for simplicity called`GABA A,fast interneurons'and `GABA A,slow interneurons'in the following)give ri to the two IPSCs and show that the class of GABA A,fast interneurons mainly contribute to hippocampal gamma rhythms.Moreover,as suggested by Banks et al.(2000),both class interact;GABA A,slow cells inhibit not only pyramidal cells but also GABA A,fast interneurons.
The model was re-designed in order to reprent this functional organization of interacting subts of principal cells and interneurons; it is summarized in Fig.1a.
First,we added a new inhibitory feedback loop to the previous model in order to reprent a subt of interneurons providing somatic inhibition to pyramidal cells(GABA A,fast interneurons).Like the two other class of interneurons(excitatory and slow inhibitory), the interneurons receive excitatory input from pyramidal cells. However,they also receive afferent inhibitory input from GABA A,slow interneurons.
As,shown in Fig.1b,the model consists of four subts of neurons,namely the main pyramidal cells),the excitatory interneurons,the slow dendritic-projecting inhibitory interneurons and the fast somatic-projecting inhibitory interneurons.The in¯uence from neighbouring areas is reprented by an excitatory input p(t) (modelled by Gaussian white noi)that globally describes the average density of afferent action potentials.The model output corresponds to the postsynaptic activity of the®rst subt(summated postsynaptic potentials in activated pyramidal cells).It is interpreted as an EEG signal(Fig.1c).
Each subt is characterized by:(i)a2nd order linear transfer function that transforms the average presynaptic pul density of afferent action potentials(the input)into an average postsynaptic membrane potential(the output),either excitatory,slow inhibitory or fast inhibitory with respective impul respon h e(t),h i(t)or h g(t), and(ii)a static nonlinear function±an asymmetric sigmoid functi
on S(v)=2e0/[1+e r(v0±v)]±that relates the average postsynaptic potential of a given subt to an average pul density of potentials ®red by the neurons.
Interactions between main cells and interneurons are summarized in the model by ven connectivity constants C1to C7which account for the average number of synaptic contacts.
Excitatory,slow inhibitory and fast inhibitory average postsynaptic membrane potentials are obtained from impul respons given by h e(t)=A a.e±at,h i(t)=B b.e±bt and h g(t)=G g.e±gt,respectively, with t b0,where A,B and G reprent the synaptic gains.They are shown in Fig.2.Model parameter values are given in Table1.The inhibitory feedback loop from the subt of fast somatic-projecting Epileptic activity explained by dendritic dis-inhibition1501
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inhibitory interneurons us a faster impul respon h g (t )(i.e.producing faster IPSP)than h i (t ).Here,the key parameter is the average somatic time delay 1/g which is chon 10times lower than the average dendritic time constant 1/b ,to be consistent with data provided in the book of Traub et al .(1999).Starting from the fact that each linear transfer function h e (t ),h i (t )and h g (t )introduces a p
留学美国法学申请要求air of ®rst order ordinary differential equations of the form:z Ç1(t )=z 2(t )and z Ç2(t )=Wgx (t )±2wz 2(t )±w 2z 1(t ),where W =A,W =B or W =G and w =a,w =b or w =g ,depending on the excitatory,slow inhibitory or fast inhibitory ca,and where x (t )and z 1(t )are the respective input and output signals of the linear transfert functions,the following t of 10differential equations that govern the population model can be easily established:y Ç0(t )=y 5(t )y Ç5(t )=AaS [y 1(t )±y 2(t )±y 3(t )]±2ay 5(t )±a 2y 0(t )y Ç1(t )=y 6(t )y
Ç6(t )=Aa {p (t )±C 2S [C 1y 0(t )]}±2ay 6(t )±a 2y 1(t )y
Ç2(t )=y 7(t )y
Ç7(t )=BbC 4S [C 3y 0(t )]±2by 7(t )±b 2y 2(t )y
Ç3(t )=y 8(t )yprevious是什么意思
Ç8(t)=GgC 7S[C 5y 0(t)±C 6y 4(t)]±2gy 8(t )±g 2y 3(t )y
Ç4(t )=y 9(t )y
Ç9(t )=BbS [C 3y 0(t )]±2by 9(t)±b 2y 4(t).This t of equations is solved by classical numerical integration methods (Runge-Kutta,for example;Press et al .,1993).Methods
蓝馨As already mentioned,the model output reprents an EEG signal.Six different types of EEG activity (numbered from 1to 6,for simplicity)are produced by the model.They are shown in Fig.3.From visual inspection,one can notice that they cloly remble real depth-EEG activity recorded interictally or ictally.Type 1and type 2,respectively,refer to normal background activity and sporadic spikes as obrved in real signals during interictal periods.Type 3and type 4,respectively,refer to sustained spikes activity and slow rhythmic activity.Both may be encountered at izure ont or during izures.Type 5refers to low-amplitude rapid discharges usually appearing at the beginning of ictal periods.Finally,type 6refers to slow quasi-sinusoidal activity.It rembles real ictal activity that often follows rapid ictal activity in time.The different types of activity depend on the three main parameter of the model,namely A ,B and G that,respectively,correspond to excitatory,slow inhibitory and fast inhibitory synaptic gains in feedback loops from interneurons to pyramidal cells and in the control of fast inhibitory interneurons by slow ones.Therefore,we studied the model for the three parameters using a systematic procedure.In particular,for different values of A (excitation),the (B ,G )plane (slow inhibition,fast inhibition)was explored by varying B and G around standard values (e Table 1).A procedure allowing the type of activity produced by the model to be automatically recognized for each point in the (B,G )plane was elaborated.It is bad on spectral features of simulated signals that are speci®c to each class of activity.Then,in order to globally reprent the mo
del behaviour as a function of A,B and G ,a coloured diagram,referred to as an `activity map'was elaborated.This map corresponds to the (B,G )plane exploration performed for a given value of A and in which a speci®c colour is ud to encode the type of activity (from 1to 6).This type is returned by the recognition procedure that automatically associates the signal simulated with a (B ,G )value to one of the 6possible class of activity (Fig.3a).Becau A was varied from 3to 7with a resolution of 0.5mV,B was varied from 0to 50mV with a resolution of 1mV and G was varied from 0to 30mV with a resolution of 1mV,about 13500simulations were performed.Each simulation produces an EEG gment of 20s sampled at 200Hz obtained by numerically integrating the t of equations prented in ction 2.As far as the Gaussian input noi is concerned,mean and variance were adjusted to obtain a rate ranging from 30to 150puls per cond,for which the model produces a signal similar to the normal background activity when other parameters are t to standard values (Table 1).Finally,simulated periods of epileptic activity,as well as simulated transitions between them,are compared with real depth-EEG signals recorded in human hippocampus using intracerebral electrodes.Recordings were performed on a 128channel BMSI acquisition system (Nicolet-BMSI,Madison,Wisconsin,USA).Signals are sampled at 200Hz on a bandpass ranging from 0.16Hz to 100Hz.Results Figure 4shows activity maps obtained for different values of A (excitation).Before analysing results in detail,general comments can be made from visual inspection
davosof the maps.First,one may notice that regions in the (B ,G )plane corresponding to the different types of activity produced by the model are relatively homogenous.Second,the region in red colour corresponding to rapid activity (type 5)starts to appear for incread values of A (excitation)when values of
part of meB
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教师节演讲稿G .2.Average postsynaptic membrane potentials:excitatory,slow inhibitory and fast inhibitory,respectively,obtained from impul respons given by h e (t )=A a .e ±at ,h i (t )=B b .e ±bt and h g (t )=G g .e ±gt ,t b 0(e Table 1for parameter values).1502 F.Wendling et al .
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(slow dendritic inhibition)decrea and values of G (fast dendritic inhibition)stay constant.Third,slow quasi-sinusoidal activity (type 6)reprented by the white region in the (B ,G )plane appears for lower values of G .Finally,one can also e that the surface of the T ABLE 1.Model parameters,interpretation and values ud to produce EEG signals
Parameter
Interpretation Standard value*A Average excitatory synaptic gain 3.25mV B Average slow inhibitory synaptic gain 22mV G Average fast inhibitory synaptic gain 10mV l/a Dendritic average time constan
t in the feedback excitatory loop a =100s ±1l/b Dendritic average time constant in the slow feedback inhibitory loop b =50s ±11/g Somatic average time constant in the fast feedback inhibitory loop g =500s ±1C l ,C 2
Average number of synaptic contacts in the excitatory feedback loop C 1=C ,C 2=0.8C (with C =135)C 3,C 4Average number of synaptic contacts in the slow feedback inhibitory loop C 3=C 4=0.25C C 5,C 6Average number of synaptic contacts in the fast feedback inhibitory loop C 5=0.3C ,C 6=0.1C C 7Average number of synaptic contacts between slow and fast inhibitory interneurons C 7=0.8C v 0,e 0,r Parameters of the nonlinear asymetric sigmoid function v 0=6mV (transforming the average membrane potential into an e 0=2.5s ±1r =0.56mV ±1average density of action potentials)*Standard values were established in Jann &Rit
(1995).
F I
G .3.(a)The different types of activity produced by the model and comparison with (b)real depth-EEG signals recorded in human hippocampus (during SEEG exploration and using intracerebral multiple lead depth-electrodes).In activity maps of Fig.4,each type of activity is coded by the colour indicated in brackets.
berthEpileptic activity explained by dendritic dis-inhibition
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