|Alain Destexhe (2007), Scholarpedia, 2(2):1402.||doi:10.4249/scholarpedia.1402||revision #91799 [link to/cite this article]|
The term spike-and-wave refers to a pattern of the electroencephalogram (EEG) typically observed during epileptic seizures. In particular, one of the most common type of epileptic manifestations, the absence seizure (also called "petit mal"), displays a clear-cut oscillation consisting of generalized and bilaterally synchronous spike-and-wave EEG patterns recurring at a frequency of about 3 Hz in humans (see Figure 1). The mechanisms underlying the genesis of such spike-and-wave seizures is the subject of this article.
Experimental models of generalized spike-and-wave seizures
Absence seizures with spike-and-wave patterns typically occur during childhood in a small proportion of human subjects, and in many instances, this type of epilepsy disappears with adolescence. Very similar seizures have been observed in a number of animal models. Cats treated with penicillin (either parenteral, see Prince and Farrell, 1969, or directly applied to the brain) or with convulsant drugs such as bicuculline, can develop absence-type of epileptic seizures, characterized by very similar EEG patterns as in human absence (see below). Some genetically-selected strains of rats (such as the Wag-Rij or GAERS) also show spontaneous seizures with spike-and-wave patterns occurring at a faster frequency (around 5-10 Hz) compared to cats and humans. In these experimental models, the behavioral correlates (the "absence") and the responsiveness to medications are also very similar to human absence.
The main advantage of experimental models is that a number of electrophysiological and pharmacological investigations can be performed, with the aim of better understanding the disease and design better therapies. A large body of literature exists for the electrophysiological correlates of spike-and-wave seizures, and in particular the first intracellular recordings (Pollen, 1964) revealed that the "spike" component is invariably associated with neuronal firing, while the "wave" is associated with a hyperpolarization of neurons, suggesting an active role of inhibition. However, no neurons were observed to selectively fire during the "wave", which remained a mystery for many years.
In the last decades, experimental models led to tremendous progress towards identifying the brain structures involved in absence seizures, and their cellular correlates. A large body of experimental results point to critical role for the thalamus in absence seizure generation:
- Spike-and-wave seizures disappear following thalamic lesions or by inactivating the thalamus (Pellegrini et al., 1979; Avoli and Gloor, 1981; Vergnes and Marescaux, 1992).
- Cortical and thalamic cells fire prolonged discharges in phase with the "spike" component, while the "wave" is characterized by a silence in all cell types (Pollen, 1964; Steriade, 1974; Fisher and Prince, 1977b; Avoli et al., 1983; McLachlan et al., 1984; Buzsaki et al., 1988; Inoue et al., 1993; McCormick and Hashemiyoon, 1998; Seidenbecher et al., 1998; Staak and Pape, 2001).
- Spindle oscillations, which are generated by thalamic circuits (Steriade et al., 1993; 2003), can be gradually transformed into spike-and-wave discharges and all manipulations that promote or antagonize spindles have the same effect on spike-and-wave seizures (Kostopoulos et al., 1981a, 1981b; McLachlan et al., 1984).
- Knock-out mice lacking the gene for the T-type calcium current in thalamic relay cells display a resistance to absence seizures (Kim et al., 2001), which clearly demonstrates that the thalamus, and in particular the T-type current mediated bursting of thalamic cells, are involved in this type of seizure activity.
Although these experiments would suggest a thalamic site for the genesis of seizures, experimental models also show that the cortex plays a critical role:
- Thalamic injections of high doses of GABAA antagonists, such as penicillin (Ralston and Ajmone-Marsan, 1956; Gloor et al., 1977) or bicuculline (Steriade and Contreras, 1998) led to 3-4 Hz oscillations with no sign of spike-and-wave discharge.
- Injection of the same drugs to the cortex, with no change in the thalamus, resulted in seizure activity with spike-and-wave patterns (Fisher and Prince, 1977a; Gloor et al., 1977; Steriade and Contreras, 1998).
- The threshold for epileptogenesis was much lower in the cortex compared to the thalamus (Steriade and Contreras, 1998).
- Diffuse application of a dilute solution of penicillin to the cortex resulted in spike-and-wave seizures although the thalamus was intact (Gloor et al., 1977).
- An important proportion of thalamic neurons are steadily hyperpolarized and completely silent during cortical seizures with spike-and-wave patterns (Steriade and Contreras, 1995; Lytton et al., 1997; Pinault et al., 1998).
- A form of spike-and-wave activity can be observed in cortex following thalamic inactivation or thalamectomy (Marcus and Watson, 1966; Pellegrini et al., 1979; Steriade and Contreras, 1998).
Taken together, data on experimental models show that both thalamus and cortex are necessary to generate seizures. However, how to generate a coherent framework that accounts for all these sometimes contrasting data, constitutes a major challenge, and also a strong motivation for building computational models.
Computational models of generalized spike-and-wave seizures
Computational models have been used for decades to investigate mechanisms of epileptogenesis, and probably the largest part of this theoretical effort concerns focal seizures, or seizures involving the hippocampal formation and limbic structures. Focal seizures, like absence seizures, are related to natural oscillatory mechanisms present in the central nervous system. In the case of focal seizures, the pathological oscillation seems related to "fast" oscillation types in cortex and hippocampus (for a recent review, see Traub et al., 2005). The present review focuses on models of generalized spike-and-wave seizures, which are linked to a different type of oscillation (sleep spindles) and different brain structures, namely the cerebral cortex (intracortical spike-and-wave seizures) and the thalamus (thalamocortical spike-and-wave seizures), as detailed in the two sections that follow. Some of the predictions of the models have been tested experimentally, as also overviewed here.
Modeling the genesis of spike-and-wave EEG patterns
As a first step to model seizures, computational models were designed to model the genesis of spike-and-wave EEG patterns (Destexhe, 1998). One of the main motivation of such a model was to explain the observation that the "spike" is associated with firing of all cell types in cortex (including interneurons; see Steriade, 1974), while the "wave" is associated with hyperpolarization and neuronal silence (see above). In particular, this model explored the hypothesis that slow K+ currents, triggered by the firing of the cells during the "spike", underlies the hyperpolarization and the "wave". This hypothesis was tested in computational models of cortical pyramidal cells, bombarded by synaptic inputs according to the firing schemes observed in experimental models. The model consisted of a network of unconnected cells, from which extracellular field potentials were simulated by linear summation of all current sources (which were here synaptic) according to Coulomb's law.
This model successfully accounted for the following observations:
- With moderate discharges of excitatory and inhibitory neurons, the simulated field potentials consisted in negative deflections, consistent with the typical EEG patterns seen during spindle oscillations;
- With stronger discharges, the deflections became prominent and formed a negative "spike";
- Subsequent to the "spike", a positive "wave" could be generated, and consisted of hyperpolarizations due to K+ currents.
- The coexistence between "normal" (spindle-like) and "abnormal" (spike-and-wave) patterns required that the K+ currents were very nonlinearly dependent on the cellular discharges.
K+ current needed to be negligible for moderate discharges, but very powerful for strong discharges. This nonlinear dependency was explained in this model by the nonlinearity intrinsic to the transduction mechanism of GABAB receptor-mediated responses (Destexhe and Sejnowski, 1995).
Modeling the genesis of spike-and-wave oscillations in cortical circuits
As reviewed above, the simplest structure displaying spike-and-wave seizures is the cerebral cortex, as shown in the isolated cortex or athalamic preparations in cats (Marcus and Watson, 1966; Pellegrini et al., 1979; Steriade and Contreras, 1998). Computational models were designed to account for such intracortical seizure generation based on different mechanisms. One model (Destexhe et al., 2001) postulated that the oscillation arises from inhibition-rebound interactions internal to cortex. This model was based on the following ingredients:
- the presence of a small proportion of rebound-bursting neurons in cortex (called "LTS cells"; see de la Pena and Geijo-Barrientos, 1996).
- The presence of GABAB-mediated inhibition in cortex, and in particular its highly nonlinear stimulus-response dependency (Thomson and Destexhe, 1999). In such a model, when fast inhibition (GABAA-mediated) was antagonized (mimicking the action of bicuculline in the experiments), all neuron types produced prolonged discharges, which generated the "spike" in the EEG. These prolonged discharges activated (GABAB-mediated) K+ currents and hyperpolarization in pyramidal neurons, which stopped the discharges and generated a positive slow "wave" in the simulated EEG.
- At the offset of GABAB IPSPs, a fraction of pyramidal cells generated a rebound burst, entraining the entire network in prolonged discharges and restarting the oscillation cycle.
Another type of model of cortical seizures was based on a slightly different mechanism (Timofeev et al., 2002). This model included interconnected pyramidal neurons and interneurons and pyramidal cells had a hyperpolarization-activated (Ih) current, which could also produce rebound properties. The seizure was generated in this case by an elevated extracellular K+ concentration in a focus, leading to particularly strong rebound properties of Ih-containing pyramidal neurons, entraining the entire network in slow hypersynchronized oscillations.
Thus, computational models show that networks of excitatory and inhibitory neurons can generate forms of seizure activity. In both cases, the oscillation was due to mutual interactions between rebound properties and strong K+ currents, which can generate spike-and-wave patterns in the EEG. Note that this intracortical spike-and-wave oscillation is typically of low frequency (1-2 Hz), and the "spike" component is usually less pronounced compared to the typical absence patterns (see analysis in Destexhe et al., 2001). These two features were observed experimentally in athalamic cats (Marcus and Watson, 1966; Pellegrini et al., 1979; Steriade and Contreras, 1998; see also conclusions below).
Modeling the genesis of generalized spike-and-wave oscillations in thalamocortical circuits
As seen above, although cortical circuits can generate some form of spike-and-wave activity, this activity is likely to be different from the typical absence seizures. In particular, experiments (reviewed in Section 1) have shown that an intact thalamus is necessary. This paradoxical observation was investigated by computational models of the thalamocortical system (Destexhe, 1998, 1999). The structure of these models is schematized in Figure 3, it contained two thalamic cell types (TC and RE cells), and two types of cortical neurons (RS and FS cells - see Figure 4). TC and RE cells generated bursts of action potentials due to the presence of a T-type calcium current, while RS cells contained slow K+ currents responsible for the spike-frequency adaptation typical of these cells.
Such thalamocortical models explored the hypothesis that the 3 Hz oscillation arises from intact thalamic circuits under the action of an excessively strong cortical feedback. The model showed that, if one takes into account the nonlinear properties of GABAB receptors, then strong corticothalamic feedback can "switch" thalamic circuits into a slow oscillatory mode around 3 Hz. This strong feedback was consequent to an increased cortical excitability, and thus, such a system could generate spike-and-wave oscillations, and a progressive transformation from spindle to spike-and-wave activity as cortical excitability was increased (see Figure 4). The mechanism was that, due to increased cortical excitability, corticothalamic feedback becomes strong enough to activate prolonged discharges in thalamic neurons and evoke IPSPs in relay cells dominated by the GABAB component. This slow inhibition sets the frequency to about 3 Hz and the oscillation is generated by a thalamocortical loop in which the thalamus is intact (see details in Destexhe, 1998). Therefore, if the cortex is inactivated during spike-and-wave, this model predicts that the thalamus should resume generating spindle oscillations, as observed experimentally in cats treated with penicillin (Gloor et al., 1979). A form of "fast" spike-and-wave activity (5-10 Hz), similar to rats and mice, could also be simulated by the same model, based on a different balance between GABAA and GABAB receptors (Destexhe, 1999). The type of "fast" spike-and-wave absence seizures of the WagRij rat genetic model was also modeled based on coexisting attractor dynamics (Suffczynski et al., 2004).
Similarly to the intracortical models reviewed above, the mechanism of spike-and-wave oscillation depended on rebound mechanisms, but in this case the rebound was provided by thalamic neurons. This is in agreement with the resistance to seizure in mice lacking the T-type current responsible for rebound bursts in thalamic neurons (Kim et al., 2001). The thalamocortical model postulates that during the negative EEG "spike", the hyperexcitable cortex undergoes runaway excitation and entrains a prolonged firing of all cell types (including thalamic cells); after a few tens of milliseconds, the GABAB-mediated inhibition (as well as intrinsic currents) evoked strong K+ currents in excitatory cells, stopping the synchronous discharges, while generating a positive "wave" in the EEG. At the offset of these strong K+ currents, thalamic cells produce synchronized rebound bursts, which entrain the whole circuit into the next cycle.
Testing the predictions of the models
The thalamocortical model of spike and wave seizures reviewed above accounts for a large body of experimental data on cat and rat experimental models, and rested on two main predictions. The first prediction was that GABAB responses needed to be highly nonlinear and that this nonlinearity should arise from mechanisms intrinsic to the synapse (Destexhe and Sejnowski, 1995). This prediction was tested experimentally using dual recordings in thalamic slices (Kim et al., 1997) and in cortical slices (Thomson and Destexhe, 1999). In both structures, single-axon connections between inhibitory and excitatory neurons demonstrated the presence of GABAB receptors (only in a subset of connections in cerebral cortex). It was shown that no detectable GABAB responses are observed if the presynaptic neuron fires isolated spikes, but strong GABAB IPSPs are evoked for prolonged discharges patterns (at least 3 spikes at 100 Hz), as predicted.
A second main prediction was that physiologically intact thalamic circuits, which normally oscillate around 10 Hz, can be switched to a slower oscillatory mode around 3 Hz by the action of corticothalamic feedback. This switching should be dependent on GABAB receptors. These predictions were tested in thalamic slices following electrical stimulation of corticothalamic fibers (Bal et al., 2000; Blumenfeld and McCormick, 2000). These experiments showed that it is indeed possible to switch normal thalamic circuits to 3 Hz (see Fig. 5), and that this switching depends on GABAB receptors, exactly as predicted by the model.
It was found recently that the antiepileptic drug vigabatrin strongly affects spike-and-wave discharges in rats (Bouwman et al., 2003). This drug increases GABA concentrations by inhibiting GABA transaminase, one of the major enzymes implicated in GABA degradation. In particular, Bouwman et al. (2003) demonstrated that vigabatrin decreases the frequency of spike-and-wave discharges (from 7.5 Hz to 5.6 Hz), as well as prolongs the duration of seizures (from 1.04 sec to 1.52 sec). This effect occurs presumably through boosting of both GABAA and GABAB responses, and is in agreement with predictions of the model (see Fig. 3 in Destexhe, 1999).
Finally, it was shown that in the Wag-Rij rat genetic model of absence epilepsy, the seizure seems to start in a focus located in somatosensory cortex (Meeren et al., 2002). This observation is not necessarily inconsistent with the present thalamocortical model. It is conceivable that a given cortical area may have higher excitability, and starts the seizure within the loop defined with its associated thalamic nucleus, and later spreads to the whole thalamocortical system, even if some areas are not hyperexcitable (or less hyperexcitable). These points should be considered in future models.
In conclusion, computational models have contributed the following points to the understanding of spike-and-wave seizures:
- The typical "spike" and "wave" pattern of the EEG is known to be related to "firing" and "silence", respectively. Computational models can reproduce these characteristic features based on the fact that the high level of firing during the "spike" produces a subsequent hyperpolarization mediated by slow K+ currents during the "wave" (a mixture of GABAB synaptic currents and intrinsic K+ conductances). The fact that no positive wave is observed for moderate discharges (such as during spindle oscillations) can be explained by the nonlinearity of GABAB currents.
- Several models have reproduced the conditions for the genesis of such pathological patterns. A form of spike-and-wave can be generated intracortically, through mutual inhibition-rebound interactions. In this case, the spike-and-wave oscillation is slow (around 1.5-2 Hz), and the "spike" component is relatively modest (see Figure). It can also be generated by the thalamocortical system, in which case the oscillation is around 2-4 Hz and the spike component is more pronounced, as observed experimentally.
- Models have explored a mechanism for spike-and-wave oscillation which depends on one key element: the thalamus can be switched to a slow 3 Hz oscillation by excessively strong corticothalamic feedback. Such a switch also depends on the nonlinearity of GABAB currents. This switching mechanism was identified experimentally and forms the basis of a "corticothalamic" scheme, in which the pathological oscillation is generated by an increased cortical excitability acting on a physiologically intact thalamus. Whether this increased cortical excitability is diffuse or focal, should be investigated by future models and experiments.
A detailed overview of models of absence seizures, and how they relate to the oscillatory mechanisms during sleep, has been given in Destexhe and Sejnowski (2001).
- Avoli M, Gloor P (1982) Role of the thalamus in generalized penicillin epilepsy: observations on decorticated cats. Exp. Neurol. 77, 386-402.
- Avoli M, Gloor P, Kostopoulos G, Gotman J (1983) An analysis of penicillin-induced generalized spike and wave discharges using simultaneous recordings of cortical and thalamic single neurons. J. Neurophysiol. 50, 819-837.
- Bal, T., Debay, D. and Destexhe, A. (2000) Cortical feedback controls the frequency and synchrony of oscillations in the visual thalamus. J. Neurosci. 20, 7478-7488.
- Blumenfeld, H. and McCormick, D.A. (2000) Corticothalamic inputs control the pattern of activity generated in thalamocortical networks. J. Neurosci. 20, 5153-5162.
- Bouwman BM, van den Broek PL, van Luijtelaar G and van Rijn CM. (2003) The effects of vigabatrin on type II spike wave discharges in rats. Neurosci. Lett. 338, 177-180.
- Buzsaki G, Bickford RG, Ponomareff G, Thal LJ, Mandel R, Gage FH (1988) Nucleus basalis and thalamic control of neocortical activity in the freely moving rat. J. Neurosci. 8, 4007-4026.
- de la Pena E, Geijo-Barrientos E. (1996) Laminar organization, morphology and physiological properties of pyramidal neurons that have the low-threshold calcium current in the guinea-pig frontal cortex. J. Neurosci. 16, 5301-5311.
- Destexhe A (1992) Nonlinear Dynamics of the Rhythmical Activity of the Brain (in French), Doctoral Dissertation, Free University of Brussels, Belgium.
- Destexhe A (1998) Spike-and-wave oscillations based on the properties of GABAB receptors. J. Neurosci. 18, 9099-9111.
- Destexhe A (1999) Can GABAA conductances explain the fast oscillation frequency of absence seizures in rodents ? Eur. J. Neurosci. 11, 2175-2181.
- Destexhe A, Sejnowski TJ (1995) G-protein activation kinetics and spill-over of GABA may account for differences between inhibitory responses in the hippocampus and thalamus. Proc. Natl. Acad. Sci. USA 92, 9515-9519.
- Destexhe A, Sejnowski TJ (2001) Thalamocortical Assemblies, Oxford University Press, Oxford UK.
- Destexhe, A. Contreras, D. and Steriade, M. (2001) LTS cells in cerebral cortex and their role in generating spike-and-wave oscillations. Neurocomputing 38, 555-563.
- Fisher, R.S., Prince, D.A. (1977a) Spike-wave rhythms in cat cortex induced by parenteral penicillin. I. Electroencephalographic features. Electroencephalogr. Clin. Neurophysiol. 42, 608-624.
- Fisher, R.S., Prince, D.A. (1977b) Spike-wave rhythms in cat cortex induced by parenteral penicillin. II. Cellular features. Electroencephalogr. Clin. Neurophysiol. 42, 625-639.
- Gloor P, Pellegrini A, Kostopoulos GK (1979) Effects of changes in cortical excitability upon the epileptic bursts in generalized penicillin epilepsy of the cat. Electroencephalogr. Clin. Neurophysiol. 46, 274-289.
- Gloor P, Quesney LF, Zumstein H (1977) Pathophysiology of generalized penicillin epilepsy in the cat: the role of cortical and subcortical structures. II. Topical application of penicillin to the cerebral cortex and subcortical structures. Electroencephalogr. Clin. Neurophysiol. 43, 79-94.
- Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500-544.
- Inoue M, Duysens J, Vossen JMH, Coenen AML (1993) Thalamic multiple-unit activity underlying spike-wave discharges in anesthetized rats. Brain Res. 612, 35-40.
- Kim U, Sanchez-Vives MV, McCormick DA (1997) Functional dynamics of GABAergic inhibition in the thalamus. Science 278, 130-134.
- Kim D, Song U, Keum S, Lee T, Jeong M-J, Kim S-S, McEnery MW and Shin HS. (2001) Lack of the burst firing of thalamocortical relay neurons and resistance to absence seizures in mice lacking the alpha-1G T-type Ca2+ channels. Neuron 31, 35-45.
- Kostopoulos G, Avoli M, Gloor P (1983) Participation of cortical recurrent inhibition in the genesis of spike and wave discharges in feline generalized epilepsy. Brain Res. 267, 101-112.
- Kostopoulos G, Gloor P, Pellegrini A, Gotman J. (1981a) A study of the transition from spindles to spike and wave discharge in feline generalized penicillin epilepsy: microphysiological features. Exp. Neurol. 73, 55-77.
- Lytton WW, Contreras D, Destexhe A and Steriade M (1997) Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. J. Neurophysiol. 77, 1679-1696.
- Marcus EM, Watson CW (1966) Bilateral synchronous spike wave electrographic patterns in the cat: interaction of bilateral cortical foci in the intact, the bilateral cortical-callosal and adiencephalic preparations. Arch. Neurol. 14, 601-610, 1966.
- McCormick DA and Hashemiyoon R. (1998) Thalamocortical neurons actively participate in the generation of spike-and-wave seizures in rodents. Soc. Neurosci. Abstracts 24, 129.
- McLachlan RS, Avoli M, Gloor P (1984) Transition from spindles to generalized spike and wave discharges in the cat: simultaneous single-cell recordings in the cortex and thalamus. Exp. Neurol. 85, 413-425.
- Meeren HK, Pijn JP, Van Luijtelaar EL, Coenen AM and Lopes da Silva FH. (2002) Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. J. Neurosci. 22, 1480-1495.
- Pellegrini A, Musgrave J, Gloor P (1979) Role of afferent input of subcortical origin in the genesis of bilaterally synchronous epileptic discharges of feline generalized epilepsy. Exp. Neurol. 64, 155- 173.
- Pinault, D., Leresche, N., Charpier, S., Deniau, J.M., Marescaux, C., Vergnes, M. and Crunelli, V. (1998) Intracellular recordings in thalamic neurones during spontaneous spike and wave discharges in rats with absence epilepsy. J. Physiol., 509, 449-456.
- Pollen DA (1964) Intracellular studies of cortical neurons during thalamic induced wave and spike. Electroencephalogr. Clin. Neurophysiol. 17, 398-404.
- Prince, D.A. and Farrell, D. (1969) "Centrencephalic" spike-wave discharges following parenteral penicillin injection in the cat. Neurology 19: 309-310.
- Ralston B, Ajmone-Marsan C (1956) Thalamic control of certain normal and abnormal cortical rhythms. Electroencephalogr. Clin. Neurophysiol. 8, 559-582.
- Seidenbecher T, Staak R, Pape, HC (1998) Relations between cortical and thalamic cellular activities during absence seizures in rats. Eur. J. Neurosci. 10, 1103-1112.
- Staak R and Pape HC. (2001) Contribution of GABA(A) and GABA(B) receptors to thalamic neuronal activity during spontaneous absence seizures in rats. J. Neurosci. 21, 1378-1384.
- Steriade M (1974) Interneuronal epileptic discharges related to spike-and-wave cortical seizures in behaving monkeys. Electroencephalogr. Clin. Neurophysiol. 37, 247-263.
- Steriade, M. (2003) Neuronal Substrates of Sleep and Epilepsy. Cambridge University Press, Cambridge, UK.
- Steriade M, Contreras D (1998) Spike-wave complexes and fast components of cortically generated seizures. I. Role of neocortex and thalamus. J. Neurophysiol. 80, 1439-1455.
- Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262, 679-685.
- Suffczynski P, Kalitzin S, Lopes Da Silva FH. (2004) Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126, 467-484.
- Thomson AM, Destexhe, A (1999) Dual intracellular recordings and computational models of slow IPSPs in rat neocortical and hippocampal slices. Neuroscience 92, 1193-1215.
- Timofeev I, Bazhenov M, Sejnowski TJ and Steriade M. (2002) Cortical hyperpolarization-activated depolarizing current takes part in the generation of focal paroxysmal activities. Proc. Natl. Acad. Sci. USA 99, 9533-9537.
- Traub RD, Contreras D, Whittington MA. (2005) Combined experimental/simulation studies of cellular and network mechanisms of epileptogenesis in vitro and in vivo. J. Clin. Neurophysiol. 22, 330-342.
- Vergnes M, Marescaux C (1992) Cortical and thalamic lesions in rats with genetic absence epilepsy. J. Neural Transmission 35 (Suppl.), 71-83.
- John W. Milnor (2006) Attractor. Scholarpedia, 1(11):1815.
- Valentino Braitenberg (2007) Brain. Scholarpedia, 2(11):2918.
- Eugene M. Izhikevich (2006) Bursting. Scholarpedia, 1(3):1300.
- James Meiss (2007) Dynamical systems. Scholarpedia, 2(2):1629.
- Paul L. Nunez and Ramesh Srinivasan (2007) Electroencephalogram. Scholarpedia, 2(2):1348.
- Roger D. Traub (2006) Fast oscillations. Scholarpedia, 1(12):1764.
- Eugene Roberts (2007) Gamma-aminobutyric acid. Scholarpedia, 2(10):3356.
- Richard H. Granger and Robert A. Hearn (2007) Models of thalamocortical system. Scholarpedia, 2(11):1796.
- Peter Jonas and Gyorgy Buzsaki (2007) Neural inhibition. Scholarpedia, 2(9):3286.
- Jeff Moehlis, Kresimir Josic, Eric T. Shea-Brown (2006) Periodic orbit. Scholarpedia, 1(7):1358.
- Arkady Pikovsky and Michael Rosenblum (2007) Synchronization. Scholarpedia, 2(12):1459.
- Maxim Bazhenov and Igor Timofeev (2006) Thalamocortical oscillations. Scholarpedia, 1(6):1319.
- S. Murray Sherman (2006) Thalamus. Scholarpedia, 1(9):1583.
- Childhood absence epilepsy (Wikipedia)
- Absence seizure (Wikipedia)
- Absence seizures (Epilepsy.com)
- Destexhe's Computational Neuroscience web-page
Cortex, Electroencephalogram, Epilepsy, Fast Oscillations, Hippocampus, Thalamocortical Circuit, Thalamocortical Oscillations, Thalamus