The duration of these epochs was most sensitive to changes in GABA A in cortex and the slope of the sigmoid transfer function for cortical INs. The model successfully demonstrated a control strategy to terminate seizures through both negative and positive current pulses. The phase space analysis in this study is an excellent example of the ease with which macroscopic models can be analyzed numerically. An excellent review of these population models is given in Lopes Da Silva, et al.
Recently, Kramer, et al. In this study the authors modeled the cortex as a system of fourteen differential equations — one each for mean excitatory and inhibitory membrane potentials of cortical populations, and twelve equations mimicking the dynamics of excitatory and inhibitory synaptic and external inputs from other layers. For certain parameter sets the average membrane potential of the excitatory cortical neurons bifurcates between steady state normal activity and limit cycle seizure-like activity as a function of the excitation in the system.
The authors explored three control strategies to eliminate the limit cycle in the average membrane potential of the excitatory cortical neurons: 1 linear controller, 2 differential controller, and 3 filter controller. All three controllers were successful in terminating the oscillations in the model; however, the filter controller was the most successful strategy since other controllers pushed the model to a depolarized state while eliminating the limit cycle.
The mean field models have certain advantages over the more detailed models described in the following section. These models are suitable for looking into transitions from interictal to ictal states, and for exploring EEG analysis from epilepsy patients as the macroelectrodes used for EEG recordings represent the average local field potential arising from neuronal populations similar to the lumped models.
Surgical treatments fail to stop seizures from occurring in a certain fraction of patients. Mean field models might be used for more precise identification of brain structures that belong to the seizure-triggering zone. Very often, epileptic activity spreads over quite extended regions and involves several structures cortical and sub-cortical.
Further, these models are easier to analyze numerically because relatively few variables and parameters are involved. The main disadvantage of these models is that they fail to suggest molecular and cellular mechanisms of epileptogenesis and thus are unable to model therapeutics targeting molecular pathways responsible for seizures. Detailed biophysical network models of epilepsy are used to investigate the role of biophysical and molecular properties of single neuron and neuronal networks in causing seizure-like patterns of activity.
For example, how can the shift in synaptic weights or change in conductance of certain ionic currents cause seizure-like brain storms? Firing patterns of individual neurons are mostly controlled by various ion channel conductances, synaptic inputs, and the nearby microenvironment of neurons. Thus these models look into the molecular bases of epilepsy and can suggest therapeutics based on their predictions.
Despite the limitations caused by the constraints of computational power and the uncertainty of many of the details of neuronal connections and their biophysical properties, these models are one of the most useful areas of computational epilepsy. The general framework for these models is to reproduce the experimentally observed properties of neuronal networks and then to investigate the effect of various factors on the behavior of the networks.
Such detailed neuronal models provide access to factors that are usually inaccessible through experimental means. The small-scale network models are useful for making predictions that could be generalized to larger networks.
Skinner, et al. They then used the same set of parameters in the larger network of several tens of neurons and observed that the large network followed the same pattern of activity as seen in the smaller network. They extracted various parameters, such as synaptic and input currents relevant for the epileptic behavior under consideration. In most models of pathological conditions such as seizures, a shift from dominant or balanced inhibition to dominant excitation in a neuronal network is considered to be responsible for the network transition from the preictal to ictal state Trevelyan et al.
In such conditions of imbalance between inhibition and excitation, moderate perturbations can drive a neuronal network from physiological to seizure-like activity. However, recent computational studies have questioned this idea Van Drongelen, et al.
A neocortical network consisting of neurons PCs and INs exhibited seizure-like behavior when the synaptic excitation was decreased Figure 2A. In order to transition to a seizure-like state the excitation to both excitatory cells and inhibitory cells needed to be reduced Figure 2B. Reducing each one alone was insufficient to cause the network to seizure-like behavior Figure 2D, E. One possible explanation for this behavior could be the reduced firing rate in INs in response to reduced excitation and hence reduced relative inhibition in the network.
Furthermore, the burst-firing PCs were found to be critical for observing various behaviors in the network. Without these burst-firing cells the irregular and regular spiking increased synchrony are both lost Figure 2C. These findings are supported by experimental observations where brain tissue makes a transition to seizures when a small amount of CNQX AMPA receptor blocker is added to it. They also showed that Riluzole persistent sodium current blocker reduced the network burst frequency Van Drongelen, et al.
The unexpected result of this study is one example emphasizing the value of computational modeling in epilepsy, as intuition in absence of modeling would have suggested that increased excitation alone would cause seizures. Destexhe and colleagues have done extensive work to explain absence seizures by developing detailed models of thalamocortical networks. A major finding of these efforts is the role played by the interplay between thalamocortical regions in generating absence seizures. This study also showed that the suppression of GABA B could cause the network to transition from controlled spindle oscillations to low frequency Hz hyper-synchronized oscillations.
The study however suggests that the low frequency hyper-synchronized oscillations are not sufficient to explain seizures. The typical spike-and-wave patterns of absence seizures require an interplay between both thalamus and cortex. Although seizures could be generated intracortically, the thalamus seems to be necessary for absence seizures.
Spike-and-wave seizures disappear following the inactivation of the thalamus. They expanded their thalamus model to a thalamocortical network model to investigate the role played by these two regions in absence seizures. Blocking GABA A in thalamus switched the spindle oscillations to low frequency oscillations Hz , and spike-and-wave seizures could not be observed.
The findings of the model were experimentally confirmed by Bal, et al. They observed strong synchronization in TC cells and an enhancement of burst discharges in RE, which is in agreement with the prediction that a strong GABA B response is responsible for the slow oscillations in intact thalamus.
In various seizure models, very fast oscillations having frequencies greater than 70Hz have been observed, immediately before spontaneous seizures both in vivo and in vitro see for example Traub, et al. Such oscillations occur in close proximity to the seizure onset sites, and might be a functional indicator of the location of the epileptic focus.
Roger Traub and colleagues have performed detailed network modeling in conjunction with experimental studies to understand the mechanism of very fast oscillations and their transition to seizures Traub, et al. Understanding these very fast oscillations is extremely important as this could provide clues to factors that initiate seizures and possible therapeutic targets. Based on their observations, they drew the hypothesis that the electrical coupling between the axons of PCs through gap junctions is necessary for very fast oscillations, although the kinetics of potassium channels and recurrent excitation may also play a role.
Most recently, experimental evidence from Trevelyan ; unpublished data, suggests that high frequency inhibitory activity may contribute to such high frequency field oscillations. Computational modeling tied to experiments will work together in the coming years to sort out the role and origins of high frequency oscillations in seizures.
Homeostatic scaling is a synaptic plasticity mechanism that scales up or down the excitation in a single neuron, or entire network, to tune its excitability to certain target values see Marder and Prinz, ; Turrigiano, for review. For example, if the frequency of a network drops below a certain target frequency the network raises its excitability to achieve this target frequency. Homeostasis thus maintains a balanced excitatory-inhibitory environment in the brain.
However, there is theoretical evidence that homeostatic plasticity could be a possible mechanism for post-traumatic epileptogenesis. Within few hours of head injury many patients with deep intracranial wounds display clinical seizures. Houweling, et al.
They constructed a network model that mimics traumatic-induced deafferentiation by reducing the excitatory inputs. Homeostatic plasticity was taken into account by making the synaptic strengths variable as a function of average firing rate of the network. The deafferentiated network has reduced excitability and thus reduced firing rate in PCs. They found that increased homeostasis could cause epileptic type bursts in PCs.
The burst rate, spikes per burst, and velocity of bursts increases with increasing homeostasis. Following the strategy in Houweling, et al. The authors constructed a cortical network model to show that homeostatic plasticity in networks with deafferentation beyond a certain degree could cause pathological periodic discharges with similar patterns as seen in pathological conditions. As above, deafferentation after trauma was modeled as a reduction in the excitatory inputs in the network.
Homeostatic plasticity, while trying to maintain the target frequency, by enhancing the excitatory inputs and reducing inhibition could cause periodic discharges in the network. The study found a negligible role of inhibitory down regulation in generating these discharges — they were mostly regulated by excitation. To get to the target frequency, the intact cells increased their frequency beyond the post-deafferented state, while the deafferented cells increased their firing rate in order to recover the mean target firing rate.
They showed that the transition to pathological conditions due to homeostatic plasticity is a nonlinear phenomenon. The functional models described above consider the synaptic interactions among various neuronal types to be the primary determining factor of the functional state of neuronal networks. Seizure-like behavior, for example, is typically modeled as the transition from dominant inhibition to dominant excitation.
New models of pharmacoresistant epilepsy, for example, the 6 Hz psychomotor seizure test, lamotrigine-resistant amygdala-kindled rat, and the intrahippocampal kainic acid mouse model of temporal lobe epilepsy are now frequently used for drug discovery. CHAPTER 7 - Thalamic, Thalamocortical, and Corticocortical Models of Epilepsy with an Emphasis on Absence Seizures. THOMAS BUDDE, HANS-CHRISTIAN.
These kinds of models ignore the role played by the topology of the network. Graphical representation models take into consideration the topological details of the network along with functional details. The main focus of graphical representation models in epilepsy has been the effect of changes in network topology on the stability of networks. In the surgically removed hippocampus from patients with temporal lobe epilepsy TLE , major changes in the anatomy of dentate gyrus were observed Babb, et al.
These changes include cell death and formation of new synaptic connections as axons sprout. To investigate the role of anatomical changes in causing spontaneous seizures, Lytton and coworkers developed a network model of the dentate gyrus Lytton, et al. The model consisted of granule cells the principal excitatory cells located in the granule layer , inhibitory aspiny interneurons, and excitatory mossy cells that reside largely within the hilus.
They further supposed that the cells that die mostly include mossy cells and aspiny interneurons.
The axons of granule cells sprout mossy fiber sprouting 1 into areas denervated by the cell loss and mostly form synapses to other granule cells. This study found that mossy fibers sprouting along with disinhibition is necessary to produce repeated firing in the granule cells characteristic of seizures.
Other excellent examples of graphical representation models are those studied in Santhakumar et al. These network models are based on the dentate gyrus model of MTLE and consists of eight cell types: granule cells excitatory , mossy cells excitatory , basket cells inhibitory , hilar interneurons with axonal projections to the perforant-path termination zone, axo-axonic cells inhibitory , hilar interneurons with axonal projections to commissural-associational pathway termination zone, interneuron selective cells, and molecular layer interneurons with axonal projections to the perforant-path termination zone.
This result indicates that once the degree of mossy fiber sprouting is above a certain limit the network can sustain seizure-like activity regardless of the number of hilus cells present. Furthermore, mossy cell loss is neither necessary nor sufficient to increase excitability, since deletion of mossy cells consistently resulted in decreased excitability in model networks and impeded the propagation of network hyperexcitability.
Behavioral characterization and scoring of seizures in rodents Lighthall JW Controlled cortical impact: a new experimental brain injury model. For example, how can the shift in synaptic weights or change in conductance of certain ionic currents cause seizure-like brain storms? Note the presence of the outlier with high cognitive performance and high anxiety level. Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data.
This behavior is in contrast to previous assumptions where the reduction in mossy cells was considered to cause increased excitability, since mossy cells excite basket cells that in turn inhibit granule cells. Following Santhakumar et al. No change in the path length with only sprouting no hilus cell loss indicates that the hilus cell loss mainly mossy cells plays a major role in changing the path length of the network.
On the other hand, the clustering coefficient in the case where only sprouting is considered follows a very similar course to the case where both sprouting and hilus cell loss is considered, indicating that sprouting is the main determinant of the changes in clustering coefficient. The decrease in hyperexcitability started at the same point where the network topology converted from small world network to normal network. This biphasic behavior in the hyperexcitability cannot be explained by only sprouting as the hyperexcitability increased monotonically up to maximum level with increasing sprouting.