Time Distributions Of Paroxysmal Events

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Here we discuss how our model results compare with experimental findings on rat models of absence epilepsy. The proposed scenario of transitions occurring randomly in time in a bistable network (points 1, 2) cannot be verified in a real system on the basis of single event analysis. However, the distribution of event duration over a long time of observation can offer a way for testing the model predictions. Therefore, it is interesting to compare model data with those obtained experimentally. The histograms of duration of experimental ictal and in-between ictal activity in WAG/Rij rats after administration of vigabatrin have exponential shape (see Figure 25.4, lower panel) providing an example of the real system in which seizure initiation and termination are random processes with constant probabilities over time. Other examples from various epileptic systems, including human experimental data, can by found in Suffczynski et al. (2005, 2006). In a number of cases, the null hypothesis of bistable system with fixed probability of transitions could not be rejected. However, we also found evidence for modulation of transition probabilities by specific neuronal processes that were not included in the present model.


Parameter analysis of the model network revealed that seizure duration is most sensitive to:

1. cortical GABAa inhibition (see Figure 25.5A)

2. to the slope of the sigmoid transfer function of cortical interneurons (see Figure 25.5B)

3. to changes of the Ca2+ currents, particularly in RE neurons (see Figure 25.5C).

We examine next a number of experimental findings that are in line with these three predictions of the model. Concerning the former, this is consistent with many experimental data obtained in animal models of absence epilepsy.

1. Investigations of the primary abnormalities underlying non-convulsive generalized seizures in GAERS rats revealed, among others, an impairment of GABA-mediated transmission in the neocortex (Avanzini et al., 1996). Similarly, the cortical hyperexcitability in WAG/Rij rats was demonstrated to be due to a decrease in GABA-mediated inhibition (Luhmann et al., 1995). Injection of GABAa antagonists such as penicillin or bicuculline to the cortex produced SWD discharges in cats (Gloor et al., 1990; Steriade and Contreras, 1998). Powerful control of cortical excitability by intracortical GABAA inhibition was also demonstrated in vivo and in a modeling study by Contreras et al. (1997).

2. The critical dependence of paroxysmal activity on the slope of the sigmoid transfer function of cortical interneurons does not have a straightforward interpretation. We may state that an increase of the slope of the sigmoid transfer function is directly related to narrowing the distribution of firing thresholds in a population and thus it represents an increased synchrony in that population. We hypothesize that the slope parameter may mimic the strength of gap-junctional connections within a population of interneurons. Therefore, it may be of interest to note that (a) it was proposed by Velazquez and Carlen (2000) that hyperventilation, which reduces blood CO2 levels and causes alkalosis, may rapidly enhance gap-junctional communication and neural synchrony and (b) anatomical data indicate that gap junctions in the neocortex are specifically formed among inhibitory cells (Galarreta and Hestrin, 2001). In the light of these two statements, our modeling results showing that an increase of a parameter characterizing synchrony within interneuronal population has a powerful effect on paroxysmal activity may be related to the effect of hyperventilation, which is a well-known method of absence seizure activation in human patients.

3. A decrease of a calcium current in the RE population (i.e. a decrease of parameter GRE) was found to decrease seizure duration and increase intervals between seizures (see Figure 25.5C). Our model results are compatible with the experimental findings in epileptic GEARS rats. Tsakiridou et al. (1995) has demonstrated that in these epileptic animals the low-threshold (IT) calcium conductance in the reticular nucleus neurons is elevated in comparison to non-epileptic controls. In the same strain of epileptic rats, a pharmacological reduction of a burst firing in reticular nucleus, attributed to a decrease of the IT calcium current and consequent decrease of calcium dependent potassium current, resulted in a decrement of paroxysmal discharge duration, measured over fixed time (Avanzini et al., 1992). Thomas and Grisar (2000) put forward an interesting hypothesis that increased synchrony of the thalamic network due to an increase of IT current conductance in the RE neurons may be related rather to phase-shift in the activity of the TC and RE neurons than to increase of the amplitude of LTS in RE cells, since the latter was unaffected by IT conductance changes. We also found in our model that an increase of IT current in the RE population changes the phase relation between TC and RE neurons, increasing the network synchrony as indicated by the enhancement of the peak in the power spectrum of the thalamic signals.


The model allowed also to investigate the mechanism by which antiepileptic drugs may affect the threshold for seizure occurrence. The most selective anti-absence drug, ethosuximide, is believed to exert its antiepileptic effect by antagonizing the burst firing in the TC neurons either by decreasing the IT current (Coulter et al., 1989, 1990, 1991) or, as a more recent study suggests, by acting on the non-inactivating Na+ current and on a Ca2+-activated K+ current (Leresche et al., 1998). In our model, a reduction of the amplitudes of LTS generated in the TC population (reflected on parameter GTC) results in a decrease of paroxysm duration and an increase of in-between seizure interval (see Figure 25.5D). The effect of benzodiazepines, such as clonazepam, is related to specific cellular targets within the thalamic networks. Indeed, the RE and TC neurons do not have the same kind of GABAA receptors; those of the former have molecular subunits with binding sites for benzodiazepines, in contrast to the latter. Thus, these anti-absence drugs are believed to enhance GABAA-mediated inhibition within the reticular nucleus (Huguenard and Prince, 1994) but not in TC cells and, in this way, to suppress GABA-mediated inhibition of RE to TC neurons and thus prevent absence seizures. This hypothesis is confirmed by our model since an increase of inhibitory strength between RE cells (reflected on parameter Q) decreases RE output and antagonizes paroxysmal activity (see Figure 25.5E), while an increase of GABAA-mediated inhibition in TC neurons has the opposite effect (not shown).

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