This chapter reviews current computational models and proposes future directions for computer modeling in the field of epilepsy. We consider the potential therapeutic applications of modeling in the both the treatment and prevention of epilepsy. Additionally, we discuss the benefits of computer modeling for research. The models discussed include single cells with mutated ion channels, mean-field network and detailed network models. We conclude by suggesting some excellent resources for those interested in learning more about computer modeling in neuroscience and epilepsy.

COMPUTER MODELING TO PREVENT SEIZURES

Computational modeling is not just useful for clinical applications indirectly via research; it is already directly applicable to clinical practice. Aside from the well-known application of computer modeling to the discovery and development of pharmaceutical agents,^21–22 it has also been instrumental in designing therapies to prevent or reduce seizures, some of which have already been successfully used in human patients. For the purpose of this chapter, such therapies can be broadly classified into dynamic, which only exert their effects in response to seizures, and static, which exert their effects continuously (or continually, in some cases).

Static Therapies

In contrast to devices that detect and respond to seizures, there are also devices that deliver scheduled pulses, i.e., their activity is defined by a preset pattern (periodic pacing), independently of when the patient seizes. Such devices have also shown promising reduction in seizure frequency and do not require an extended calibration period as they do not need to detect seizures.²

Other therapies that exert their effects independently of the patient’s state include pharmacological treatments.^21–22 These agents affect subcellular mechanisms, such as ion channels, transporters, pumps, and receptors. Computational models that incorporate these subcellular mechanisms can help identify therapeutic targets and also show how their modulation may influence dynamics at the cellular and network levels.

Here, we will introduce a computational model used by Dyhrfjeld-Johnsen et al. (2008) to illustrate the effect of a channelopathy on cellular excitability. Channelopathies - pathological changes in the expression or function of ion channels - are of great interest in the field of epilepsy because they have been linked to both inherited and acquired epilepsies. For those inherited epilepsies whose mutations have been discovered, the mutations have been predominantly channelopathies.³²

One common channelopathy occurring in epileptic animal models affects the hyperpolarization-activated, cyclic nucleotide-gated (HCN) channel responsible for an inward, mixed-cation current (I_h). Most experimental paradigms report that seizures reduce I_h a reduction thought to increase hyperexcitability³³ because it would lessen the shunting effect associated with I_h. However, in an experimental febrile seizure model, the hyperexcitable dendrites of CA1 pyramidal cells show a marked increase in I_h.³⁸ Computer modeling provided an explanation for these seemingly contradictory results.

Using a computational model, Dyhrfjeld-Johnsen et al. (2008) altered the h-current and examined the effects on the excitability of three detailed pyramidal cell models (Figure 2).³⁸ The models indicated that an increased I_h can contribute to hyperexcitability (Figure 2A). Analysis of the mechanism by which I_h enhanced excitability showed that the upregulated I_h depolarized the dendritic resting membrane potential, shifting it closer to threshold. When cells with increased I_h were held at the control resting membrane potential, no increase in excitability was observed (Figure 2B). These results highlight the complex relationship between I_h and neuronal excitability; perhaps functional effects cannot be predicted by looking at only the direction of changes in I_h.

Figure 2

Altered h-current changes neuronal excitability. Both the modified control CA1 pyramidal neuron model and models with altered I_h are subjected to a 1000 ms depolarizing current injection, with the membrane potential allowed to vary from control resting (more...)

Knowing that the hyperexcitability seen in increased I_h is related to the more positive resting membrane potential, we can then propose possible therapeutic interventions. For example, a pharmacological agent that can counteract the more depolarized membrane potential³⁸ with minimal disturbance to physiological functions, perhaps mediated by the M-current,^38–40 should be sufficient to reduce the I_h-associated network hyperexcitability seen in the above-mentioned febrile seizure model.³⁸

COMPUTER MODELING TO PREVENT EPILEPTOGENESIS

Understanding how the healthy brain becomes capable of seizing requires knowledge of the detailed changes associated with epileptogenesis. These alterations include cell loss, changes in network connectivity, mutated ion channels, and altered gene expression profiles. Quite often, multiple changes occur together, obscuring each factor’s contribution to the seizure-prone brain. In this scenario, untangling the role of each factor may be far easier in computational models than experimental ones.

Head trauma is one model of epilepsy in which multiple changes are known to occur. These alterations affect, among other brain regions, the dentate gyrus, an area of the hippocampal formation sometimes thought to gate network activity in the healthy brain. Epileptogenic changes seen in the dentate gyrus after head trauma include mossy fiber sprouting and hilar cell loss. Mossy fiber sprouting, i.e., the development of new axonal branches by granule cells, accounts for recurrent excitation among granule cells, consequent to the establishment of reciprocal synaptic contacts that are not normally present in the healthy dentate gyrus. Hilar cell loss does not only affect inhibitory interneurons, but it also reduces the number of excitatory mossy cells. The effect of reducing the number of excitatory mossy cell synapses onto the granule cells is not well understood.

It is quite challenging to separate these alterations in experimental models of epilepsy, but computer modeling provides a flexible way to study the changes in isolation. Santhakumar et al. (2005), Dyhrfjeld-Johnsen et al. (2007), and Morgan and Soltesz (2008) studied, in progressively more detail, the effects of structural changes in the dentate circuitry on hyperexcitability.^17–19 The first of these studies played a major role in demonstrating the promise of large-scale, data-driven models in epilepsy research as it detailed the construction of the dentate gyrus model, containing four biophysically realistic cell types, each connected via realistic synapses using connection probabilities derived from in vivo and in vitro experiments. Using the 500-cell model that was thus constructed, Santhakumar et al. (2005) were able to show that structural changes alone can predispose the dentate network to hyperexcitability.¹⁹

Dyhrfjeld-Johnsen et al. (2007) expanded the functional model of Santhakumar et al. (2005) to over 50,000 cells, a scale of 1:20 compared to the full-size rat dentate gyrus. Their experiments also used a complete 1:1 scale structural model of the dentate gyrus to determine the graph-theoretical characteristics of the dentate network. The results of the structural model showed that the dentate gyrus is a small-world network. In a small-world network, cells make many connections to their close neighbors, yet the number of cells along a path from a given cell to any distant cell remains quite small due to the presence of a few long distance connections. By combining the structural model results with those of the functional model at varying levels of dentate injury, Dyhrfjeld-Johnsen et al. (2007) showed that head injury causes substantial alterations to the small-world structure of the dentate gyrus, resulting in a hyperexcitability profile closely correlated with structural alterations.¹⁷

Because the specific pattern of new granule cell connections that occurs with mossy fiber sprouting is not known, Morgan and Soltesz (2008) studied the pathological alterations in the dentate gyrus circuitry in even more detail.¹⁸ They questioned whether the hyperexcitability of the sprouted network depends on the specific pattern of new connections.¹⁸ To answer the question, Morgan and Soltesz compared non-random patterns of connectivity to a control network in which the granule cells were connected together randomly (Figure 4A). In each case, the model had the same number of connections among granule cells, but the connections were distributed differently among the cells.

Figure 4

Reconnecting the granule cell network. In temporal lobe epilepsy, granule cells in the dentate gyrus sprout axon collaterals that synapse onto other granule cells, creating a recurrent excitatory circuit. A: In the control network, connections were modeled (more...)

They found that simply rewiring the granule cell network in certain ways could markedly increase excitability (Figure 5). In particular, if the connections were redistributed so that most granule cells had few granule cell connections, but some rare granule cells (“hubs”) had many connections (Figure 4B), network activity increased greatly. These highly connected cells made the dentate network significantly more excitable without changing the total excitatory drive of the network, demonstrating the potential importance of hub cells in seizures (compare Figure 5A and 5B). Experimental work has supported the presence of hub cells in the dentate gyrus after injury, thus beginning to validate the model’s prediction and pointing to the importance of understanding the microcircuit connectivity in seizure-prone networks.⁴¹ This work suggests that therapeutic efforts to prevent mossy fiber sprouting could reduce epileptogenesis in people who have experienced head trauma.

Figure 5

Highly interconnected granule cell hubs greatly augment network excitability. Both A and B represent raster plots of granule cell firing in a network with 50% of maximal granule cell-to-granule cell connections, where stimulation was delivered via the (more...)

Epileptogenic changes are not limited to neurons and their connections. Glia dysfunction has been implicated in epileptogenesis, and therefore deserves consideration as a possible therapeutic target.^42–44 Its significance arises especially because of the glial role in regulating the concentration of extracellular potassium, and because of the ability of glial cells to interfere with inhibition,⁴⁵ to release ATP,³⁹ and to affect glutamate concentration at nearby synapses.^{11, 44, 46} Cressman et al. (2009) investigated the role of ion concentrations and glia in epileptic networks using a model of a single cell¹¹ and a network.⁴⁴

In this work, they first examined the effects of intracellular and extracellular ion concentrations on neuronal excitability and seizure frequency with a mathematical model of a neuron and its extracellular space, including the glia surrounding it.¹¹ Using the model, they showed that this single cell was capable of producing abnormal bursts of action potentials, as may be seen during seizures. The model also illustrated how increased extracellular potassium could lead to depolarization block, during which the cell is depolarized but unable to spike. Some studies have implicated depolarization block in inhibitory interneurons during seizure-like events in brain slices, which could free excitatory cells to spike excessively in bursts.^{11, 47}

Then, to examine the role of glia directly, they extended the single cell model to a 200 cell network model consisting of pyramidal and inhibitory cells and accounting for glial function, ion pumps, and diffusion. Their model illustrated how glial dysfunction could cause neural networks to be less resilient to small perturbations such that a network exhibiting normal persistent activity associated with higher level functions could suddenly transition to seizure-like activity.⁴⁴ For example, they showed that the rearrangement of astrocytes associated with epileptogenesis leads to increased extracellular potassium concentration and a reduced ability to buffer the extracellular potassium, as well as increased strengths of excitatory synapses.⁴⁴ The behavior of their model was consistent with several experimental results,⁴⁴ and it underscores the potential of glia as therapeutic targets.

COMPUTER MODELING TO ASSIST RESEARCHERS

Computer modeling and experimentation are complementary in research and the development of therapeutics. Each approach provides unique benefits and is improved by contributions of the other. Though definitive confirmation of scientific fact requires experimental results, modeling serves the field by enabling a flexibility and efficiency not always possible in experiments and can help researchers design more focused experiments.³⁹

One example of a scenario in which computer modeling allowed researchers to extend their experimental observations occurred during an electrophysiological study of hippocampal mossy cells (see also above) after head injury. These excitatory neurons, located in the dentate hilus, are among the most vulnerable neurons in the entire mammalian brain;⁴⁸ factors including strong excitatory inputs, a sustained response to excitatory input, and a high level of spontaneous activity render them particularly susceptible to excitotoxicity.⁴⁹ Significant mossy cell loss is observed in human epileptic tissue and in animal models after experimental head trauma.^50–52 However, several lines of evidence suggest that some mossy cells survive trauma^{49–50, 52} and that these surviving mossy cells may spread or amplify dentate network hyperexcitability.

Howard et al. (2007) used a rat fluid percussion injury model to study the changes in surviving mossy cells after head trauma, comparing their I-F (current v. spike frequency) and I-V (current v. membrane potential) curves before and after trauma.⁵³ Surprisingly, they found no significant difference. Yet on closer inspection, extensive, opposing alterations were found in various membrane currents and properties that together resulted in the unchanged I-F and I-V relationships observed in mossy cells after head trauma. The resting membrane potential was depolarized, the tetraethylammonium (TEA)-sensitive potassium current decreased, and the voltage-dependent sodium channel required more depolarized potentials to activate.

Howard et al. then used computer modeling to understand whether each one of these changes would affect the dentate network when considered separately. Notably, when modeled alone, each of these alterations dramatically affected network excitability (Figure 3), despite cancelling each other when occurring together. In this case, the computational model complemented the experimental observations by vividly demonstrating the importance of potentially homeostatic mechanisms⁵⁴ in regulating overall levels of neuronal activity in large networks.

Figure 3

Individual post-traumatic changes to intrinsic properties of mossy cells have robust effects on dentate gyrus network hyperexcitability. Dentate gyrus network activity in response to a single simulated perforant path stimulation at t = 5 ms is plotted (more...)

SUMMARY OF APPROACHES TO MODELING EPILEPSY

The models described above vary in their level of detail and scope (see Figure 1) and there are valid reasons for the different approaches. Researchers seeking an overall description of seizure dynamics would not necessarily want it to be in terms of the activity of thousands of neurons. For them a higher level approach, based on the assumption that the neural network can be characterized in aggregate terms, would be more appropriate. These aggregate, macroscopic models, such as the Lopour et al. model described above,¹⁴ are often called mean-field models (Figure 1A), indicating that their base components are entire populations of neurons similar enough to be grouped together and described in terms of average properties. Most such approaches are based on a computational model developed by Wilson and Cowan⁵⁵ that had two interconnected neuronal populations, one excitatory and one inhibitory. Though the cells are described as populations, using an average, rather than individually, the average properties are still informed by physiological data. The models often produce results in the form of EEG traces, directly comparable to patient data.

Such models may also make predictions about the role of a cell population in seizure dynamics, such as one model that split the inhibitory population into separate fast and slow components while maintaining a single excitatory population.¹³ The model was fit to real patient EEG data taken from pre-ictal, pre-onset, and ictal time periods, and it could produce realistic EEG waveforms. The model made several experimentally verifiable predictions about the role of excitatory and inhibitory populations in seizures, including – paradoxically – that slow inhibition increases prior to seizure onset, but contributes to overall excitation by inhibiting mainly the fast inhibition component.¹³

These macroscopic models have an advantage for describing seizure dynamics because they require relatively few computational resources. Their smaller computational requirements enable them to simulate the longer time periods required to model transitions into and out of the seizure state. Understanding what prompts the transition from non-epileptiform activity to the seizure state is crucial for seizure detection and intervention, and high level models are well suited to describe such system level dynamics.⁵⁶

In contrast, there are questions that call for much lower level, detailed computational models. For example, researchers interested in how a particular ion channel mutation affects network hyperexcitability would need a highly detailed, biologically realistic model that could incorporate well-characterized ion channel properties and output precise spike times for each cell in the network (Figure 1B). Such computational models are also useful for exploring the altered connectivity and cell loss seen in most models of epilepsy.¹⁹ The various models from the Soltesz lab described above are examples of large scale, highly detailed, biologically realistic network models.^{17–19, 38, 53}

Even within network models that include multiple, distinct cells, there are a wide variety of approaches. Neurons can be modeled at various levels of detail, ranging from morphologically detailed models with over a thousand compartments or morphologically simplified cells with detailed subcellular mechanisms (Figure 1D) to integrate-and-fire neurons (Figure 1C) and even simpler representations.³⁴ The level of sophistication at which a neuron should be modeled depends on the complexity of the computation it is expected to perform. While integrate-and-fire neurons may be sufficient to produce expected spiking patterns in some cases,¹⁹ specific distributions of ion channels and synapses along dendrites may be necessary to model more complicated functions performed by neurons, such as coincidence detection.³⁴ The Cressman et al. models described above^{11, 44} employed mathematical neurons with subcellular and extracellular mechanisms described by a few equations. This level of detail was sufficient to answer the questions they posed in the model, and enabled them to run the longer simulations necessary to characterize the dynamics in the ion concentrations. To model the astrocytic rearrangement more concretely, as they propose for future work, a more detailed model that incorporated 3D cell positions would probably be necessary.⁴⁴

As mentioned in passing above, computer modeling is limited by time and resource availability. If a model contains very detailed components (such as numerous ion channel types or detailed cell morphology), it may be necessary to remove complexity from another area of the model, either the scope (number of cells) or the length of simulation time (whether the model simulates activity occurring over a few milliseconds or several days). For this reason, often the more detailed a model is, the smaller its scope and simulation time.

Because of the above limits, computational models used in epilepsy generally describe only part of the disorder,²⁰ such as aggregate electrical dynamics during seizures¹³ or altered neural connectivity found in the affected areas of the epileptic brain.¹⁹ While partial models can provide much insight, there is significantly more explanatory power in a model that answers questions covering multiple levels simultaneously, such as: “how do the altered firing patterns of cell type ‘A’ influence the EEG signal after seizure onset?”

THE FUTURE OF COMPUTER MODELING OF EPILEPSY

Given the rapid rate at which technology is developed, it is easy to imagine that computers will soon be fast enough to support a detailed, biologically realistic model of the entire human brain that could answer questions such as the one above.⁵ Today modelers must pick between modeling seizure dynamics and transitions (which require lengthy simulation times) or detailed biological structures and mechanisms; in the future it will be possible to do both at once. Such a powerful model would represent a significant tool for understanding overall seizure and transition dynamics in terms of network and cell-level activity, an area of epilepsy research that needs significant development.⁴⁷

Already, advances in neural simulation tools allow them to run simulations in parallel (on multiple computers at once) in a fraction of the time it would take to run the same simulation on a single processor. These parallel models can support far more neurons and detail so that, for example, network models focusing on altered connectivity in epilepsy can be scaled up to full size to enable more realistic neural connectivity. Additionally, detailed network models of particular brain regions could be made bilateral. Both computational models and in vitro experiments generally approach epilepsy “unilaterally,” without regard to which side of the brain is being observed or any effects of the contralateral hemisphere. However, the two sides of the brain vary remarkably in ways relevant to epilepsy. For example, there is known to be significant asymmetry between the bilateral connections of the hippocampal formation.⁵⁷ Bilateral models could address the effects of contralateral connections and asymmetry⁵⁷ on seizures and seizure generalization.

The computational models all described so far have been simulations, in which software is configured to produce the model. However, as we create models with increasing numbers of cells, it is worth noting that a model of the whole human brain would be quite resource-intensive. For example, the Blue Brain project mentioned above uses 8,192 processors to model 10,000 highly detailed, multi-compartmental neurons with 100 million synapses.^{5, 58} A model of the whole human brain would need to include 100 billion neurons and 10 quadrillion synapses, an expensive endeavor that is projected to require millions of processors and roughly 100 megawatts of power.⁵⁸

To overcome these limitations, another approach toward modeling has been developed. Rather than configure software, some modelers are configuring hardware to emulate neural networks, such as the recent Neurogrid project.⁵⁸ The resulting neuromorphic chips can be combined to produce a device capable of emulating a million neurons and six billion synapses in real time. Though these neurons are less detailed than those on the Blue Brain computer, they still contain multiple compartments and realistic ion channels. Highly detailed neurons can be modeled as well if the overall number of neurons is decreased; models with hundreds of compartments and any number of distinct ion channel types are not unfeasible.⁵⁸

One of the main arguments against hardware modeling is its lack of flexibility. However, significant improvements have been made against this limitation. The current Neurogrid device can support 16 different cell types, with each type having its own combination of ion channels.⁵⁸ The connections between cells are programmed using random access memory (RAM) and can be changed on demand. The results of the neuromorphic simulations can be viewed on an interactive display in real time at various levels, from the spike patterns of a single cell to the activity of a whole cortical layer. The applications of such a tool to epilepsy research are apparent: the ability to quickly model such a large number of neurons over a large simulation time is just what we need to characterize seizure dynamics in terms of cell and ion channel activity.

COMPUTER MODELING RESOURCES

Computer modeling is a useful research tool available to almost everyone. The monetary investment in computer modeling can be small, requiring resources available to anyone with a computer and internet access or, for more intensive modeling, resources readily accessible at research institutions or through multipurpose shared resources such as the National Science Foundation’s TeraGrid.⁵⁹

Researchers and clinicians interested in computer modeling are urged to explore the many computational models freely available online at the ModelDB website.⁶⁰ In most cases, the software used to create such models are also freely available online (e.g. the neural simulators NEURON⁶¹ and GENESIS⁶²) or through network licenses at academic institutions (MATLAB⁶³). The time required to learn these programs is comparable to the time required to learn various experimental techniques and results can be obtained quickly. Importantly, the researcher has far more control over the factors important to obtaining results from models than is possible with experiments.

The large scale, detailed, biologically realistic models referenced above employed NEURON, but many successful models have employed GENESIS as well. For example, van Drongelen et al. (2007) produced a detailed, 656 cell neocortical network with GENESIS.⁶⁴ The model included two types of pyramidal cells, basket cells, and chandelier cells, with small world connectivity. The cells contained realistic ion channels and gap junctions. They used this model to explore the effect of synapse weights on the ability of the cortical network to form and sustain seizure-like oscillations and to observe the activity displayed by subpopulations of neurons during these oscillations. Surprisingly, among other results, they found that a weakening of excitatory connections in the neocortex may enable the propagation of seizure-like activity and concluded that strong excitatory connections are not always necessary for a network to produce seizures.⁶⁴

Both NEURON and GENESIS can be run in parallel, which allows for a near linear speed increase in modeling time; to run a model for the same simulation on two processors will take roughly half the time taken to run the model on one processor. The authors recently ran a 1000 ms simulation of over one million detailed cells in under 2 hours, using parallel NEURON on 608 processors.⁶⁵ MATLAB can be run in parallel as well, using its Parallel Computing Toolbox.

All three of these software programs have extensive online documentation, tutorials, and user forums supported by the software developers. Both NEURON and MATLAB regularly hold in-person workshops as well. While both NEURON and GENESIS have graphical user interfaces (GUIs), these GUIs are generally most useful when building single cell models. For network models, there is a simulation software-independent tool called NeuroConstruct, which provides an interface to NEURON, GENESIS, and other programs for those who prefer not to work with code directly.⁶⁶

In addition to software-specific resources, there are some excellent books on computational neuroscience in general⁶⁷ and computational modeling of epilepsy in particular,⁹ useful for the potential modeler or anyone wanting a deeper understanding of computer modeling in neuroscience and epilepsy.

CONCLUSION

A detailed model of the entire human brain, which could be accessed at any level of detail and be personalized for individualized patient treatment analysis no longer looks quite so outlandish. Likewise, it appears that an implantable seizure detection and intervention device will be available as a standard treatment option before long. Such exciting advancements made possible through computer modeling should inspire researchers and clinicians to be even more creative in their approaches to epilepsy therapies. We look forward to the advances the next decade will bring in computer modeling of epilepsy.

References

1.

World Health Organization. Epilepsy, Epilepsy Fact Sheet. [Accessed August, 2010]. http://www​.who.int/mediacentre​/factsheets/fs999/en/index​.html .

2.

Jobst BC, Darcey TM, Thadani VM, Roberts DW. Brain stimulation for the treatment of epilepsy. Epilepsia. 2010;51:88–92. [PubMed: 20618409]

3.

Glasscock E, Qian J, Yoo JW, Noebels JL. Masking epilepsy by combining two epilepsy genes. Nat Neurosci. 2007;10(12):1554–1558. [PubMed: 17982453]

4.

Hines M, Markram H, Schürmann F. Fully implicit parallel simulation of single neurons. Journal of Computational Neuroscience. 2008;25(3):439–448. [PMC free article: PMC2760991] [PubMed: 18379867]

5.

Markram H. The Blue Brain Project. Nat Rev Neurosci. 2006;7(2):153–160. [PubMed: 16429124]

6.

Rolls ET, Loh M, Deco G, Winterer G. Computational models of schizophrenia and dopamine modulation in the prefrontal cortex. Nat Rev Neurosci. 2008;9(9):696–709. [PubMed: 18714326]

7.

Moustafa AA, Gluck MA. A Neurocomputational Model of Dopamine and Prefrontal–Striatal Interactions during Multicue Category Learning by Parkinson’s Patients. Journal of Cognitive Neuroscience. 0(0):1–17. [PubMed: 20044893]

8.

Reinkensmeyer DJ, Iobbi MG, Kahn LE, Kamper DG, Takahashi CD. Modeling Reaching Impairment After Stroke Using a Population Vector Model of Movement Control That Incorporates Neural Firing-Rate Variability. Neural Computation. 2003;15(11):2619–2642. [PubMed: 14577856]

9.

Soltesz I, Staley KJ. Computational Neuroscience in Epilepsy. New York: Elsevier; 2008.

10.

Poirazi P, Brannon T, Mel BW. Arithmetic of Subthreshold Synaptic Summation in a Model CA1 Pyramidal Cell. Neuron. 2003;37(6):977–987. [PubMed: 12670426]

11.

Cressman J, Ullah G, Ziburkus J, Schiff S, Barreto E. The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics. Journal of Computational Neuroscience. 2009;26(2):159–170. [PMC free article: PMC2704057] [PubMed: 19169801]

12.

Poolos NP, Migliore M, Johnston D. Pharmacological upregulation of h-channels reduces the excitability of pyramidal neuron dendrites. Nat Neurosci. 2002;5(8):767–774. [PubMed: 12118259]

13.

Wendling F, Hernandez A, Bellanger J-J, Chauvel P, Bartolomei F. Interictal to Ictal Transition in Human Temporal Lobe Epilepsy: Insights From a Computational Model of Intracerebral EEG. Journal of Clinical Neurophysiology. 2005;22(5):343–356. [PMC free article: PMC2443706] [PubMed: 16357638]

14.

Lopour B, Szeri A. A model of feedback control for the charge-balanced suppression of epileptic seizures. Journal of Computational Neuroscience. 2010;28(3):375–387. [PMC free article: PMC2880706] [PubMed: 20135212]

15.

Brunel N. Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons. Journal of Physiology-Paris. 2000;94(5–6):445–463. [PubMed: 11165912]

16.

Brunel N, Wang XJ. What Determines the Frequency of Fast Network Oscillations With Irregular Neural Discharges? I. Synaptic Dynamics and Excitation-Inhibition Balance. J Neurophysiol. 2003 July 1;90(1):415–430. [PubMed: 12611969]

17.

Dyhrfjeld-Johnsen J, Santhakumar V, Morgan RJ, Huerta R, Tsimring L, Soltesz I. Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. J Neurophysiol. Feb 2007;97(2):1566–1587. [PubMed: 17093119]

18.

Morgan RJ, Soltesz I. Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures. Proc Natl Acad Sci U S A. 2008 Apr 22;105(16):6179–6184. [PMC free article: PMC2299224] [PubMed: 18375756]

19.

Santhakumar V, Aradi I, Soltesz I. Role of mossy fiber sprouting and mossy cell loss in hyperexcitability: a network model of the dentate gyrus incorporating cell types and axonal topography. J Neurophysiol. 2005 Jan;93(1):437–453. [PubMed: 15342722]

20.

Lytton WW. Computer modelling of epilepsy. Nat Rev Neurosci. 2008;9(8):626–637. [PMC free article: PMC2739976] [PubMed: 18594562]

21.

Weaver DF. Principles and Practice of Computer-Aided Drug Design as Applied to the Discovery of Antiepileptic Agents. In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 515–529.

22.

Jorgensen WL. The Many Roles of Computation in Drug Discovery. Science. 2004 March 19;303(5665):1813–1818. [PubMed: 15031495]

23.

NeuroPace. NeuroPace Submits PMA Application for FDA Approval of Novel Investigational Device for Epilepsy. 2010. [Accessed August, 2010]. http://www​.neuropace​.com/about/news/20100708.html .

24.

Echauz J, Wong S, Smart O, Gardner A, Worrell G, Litt B. Computation Applied to Clinical Epilepsy and Antiepileptic Devices. In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 530–558.

25.

Stephens ML, Spencer DD, Cavus I, et al. Microelectrode-based Epilepsy Therapy: A Hybrid Neural Prosthesis Incorporating Seizure Prediction and Intervention with Biomimetic Maintenance of Normal Hippocampal Function. In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 559–586.

26.

Jouny CC, Bergey GK. Dynamics of Epileptic Seizures during Evolution and Propagation. In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 457–470.

27.

Lehnertz K, Mormann F, Osterhage H, et al. State-of-the-Art of Seizure Prediction. Journal of Clinical Neurophysiology. 2007;24(2):147–153. 110.1097/WNP.1090b1013e3180336f3180316. [PubMed: 17414970]

28.

Lai Y-C, Osorio I, Frei MG, Harrison MAF. Are Correlation Dimension and Lyapunov Exponents Useful Tools for Prediction of Epileptic Seizures? In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 471–495.

29.

Afra P, Jouny CC, Bergey GK. Duration of complex partial seizures: An intracranial EEG study. Epilepsia. 2008;49(4):677–684. [PubMed: 18028402]

30.

Sun FT, Morrell MJ, Wharen RE Jr. Responsive Cortical Stimulation for the Treatment of Epilepsy. Neurotherapeutics. 2008;5(1):68–74. [PMC free article: PMC5084128] [PubMed: 18164485]

31.

NeuroPace. Clinical Trials. 2010. [Accessed August, 2010]. http://www​.neuropace​.com/trials/overview.html .

32.

Steinlein OK. Genetic mechanisms that underlie epilepsy. Nat Rev Neurosci. 2004;5(5):400–408. [PubMed: 15100722]

33.

Jung S, Jones TD, Lugo JN Jr, et al. Progressive Dendritic HCN Channelopathy during Epileptogenesis in the Rat Pilocarpine Model of Epilepsy. J Neurosci. 2007 November 21;27(47):13012–13021. [PMC free article: PMC3087381] [PubMed: 18032674]

34.

Marcelin B, Chauvière L, Becker A, Migliore M, Esclapez M, Bernard C. h channel-dependent deficit of theta oscillation resonance and phase shift in temporal lobe epilepsy. Neurobiology of Disease. 2009;33(3):436–447. [PubMed: 19135151]

35.

Shah MM, Anderson AE, Leung V, Lin X, Johnston D. Seizure-Induced Plasticity of h Channels in Entorhinal Cortical Layer III Pyramidal Neurons. Neuron. 2004;44(3):495–508. [PMC free article: PMC2386958] [PubMed: 15504329]

36.

Shin M, Brager D, Jaramillo TC, Johnston D, Chetkovich DM. Mislocalization of h channel subunits underlies h channelopathy in temporal lobe epilepsy. Neurobiology of Disease. 2008;32(1):26–36. [PMC free article: PMC2626192] [PubMed: 18657617]

37.

Zhang K, Peng B-w, Sanchez RM. Decreased I_H in Hippocampal Area CA1 Pyramidal Neurons after Perinatal Seizure-inducing Hypoxia. Epilepsia. 2006;47(6):1023–1028. [PubMed: 16822248]

38.

Dyhrfjeld-Johnsen J, Morgan RJ, Foldy C, Soltesz I. Upregulated H-Current in Hyperexcitable CA1 Dendrites after Febrile Seizures. Front Cell Neurosci. 2008;2:2. [PMC free article: PMC2525926] [PubMed: 18946517]

39.

Ascoli GA, Gasparini S, Medinilla V, Migliore M. Local Control of Postinhibitory Rebound Spiking in CA1 Pyramidal Neuron Dendrites. J Neurosci. 2010 May 5;30(18):6434–6442. [PMC free article: PMC3319664] [PubMed: 20445069]

40.

George MS, Abbott LF, Siegelbaum SA. HCN hyperpolarization-activated cation channels inhibit EPSPs by interactions with M-type K+ channels. Nat Neurosci. 2009;12(5):577–584. [PMC free article: PMC2674138] [PubMed: 19363490]

41.

Walter C, Murphy BL, Pun RYK, Spieles-Engemann AL, Danzer SC. Pilocarpine-Induced Seizures Cause Selective Time-Dependent Changes to Adult-Generated Hippocampal Dentate Granule Cells. J Neurosci. 2007 July 11;27(28):7541–7552. [PMC free article: PMC6672603] [PubMed: 17626215]

42.

Schwarcz R. Early glial dysfunction in epilepsy. Epilepsia. 2008;49:1–2. [PubMed: 18226166]

43.

Barres BA. The Mystery and Magic of Glia: A Perspective on. Their Roles in Health and Disease. 2008;60(3):430–440. [PubMed: 18995817]

44.

Ullah G, Cressman J Jr, Barreto E, Schiff S. The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: II. Network and glial dynamics. Journal of Computational Neuroscience. 2009;26(2):171–183. [PMC free article: PMC2951284] [PubMed: 19083088]

45.

Ortinski PI, Dong J, Mungenast A, et al. Selective induction of astrocytic gliosis generates deficits in neuronal inhibition. Nat Neurosci. 2010;13(5):584–591. [PMC free article: PMC3225960] [PubMed: 20418874]

46.

Somjen G, Kager H, Wadman W. Computer simulations of neuron-glia interactions mediated by ion flux. Journal of Computational Neuroscience. 2008;25(2):349–365. [PubMed: 18297383]

47.

Schiff SJ, Cressman JR, Barreto E, Ziburkus J. Towards a Dynamics of Seizure Mechanics. In: Soltesz I, Staley K, editors. Computational Neuroscience in Epilepsy. San Diego: Academic Press; 2008. pp. 496–512.

48.

Sloviter RS, Zappone CA, Harvey BD, Bumanglag AV, Bender RA, Frotscher M. ldquoDormant basket cellrdquo hypothesis revisited: Relative vulnerabilities of dentate gyrus mossy cells and inhibitory interneurons after hippocampal status epilepticus in the rat. The Journal of Comparative Neurology. 2003;459(1):44–76. [PubMed: 12629666]

49.

Ratzliff AH, Santhakumar V, Howard A, Soltesz I. Mossy cells in epilepsy: rigor mortis or vigor mortis. Trends Neurosci. Mar 2002;25(3):140–144. [PubMed: 11852145]

50.

Blumcke I, Suter B, Behle K, et al. Loss of hilar mossy cells in Ammon’s horn sclerosis. Epilepsia. 2000;41(Suppl 6):S174–180. [PubMed: 10999540]

51.

Lowenstein D, Thomas M, Smith D, McIntosh T. Selective vulnerability of dentate hilar neurons following traumatic brain injury: a potential mechanistic link between head trauma and disorders of the hippocampus. J Neurosci. 1992 December 1;12(12):4846–4853. [PMC free article: PMC6575779] [PubMed: 1464770]

52.

Toth Z, Hollrigel GS, Gorcs T, Soltesz I. Instantaneous Perturbation of Dentate Interneuronal Networks by a Pressure Wave-Transient Delivered to the Neocortex. J Neurosci. 1997 November 1;17(21):8106–8117. [PMC free article: PMC6573747] [PubMed: 9334386]

53.

Howard AL, Neu A, Morgan RJ, Echegoyen JC, Soltesz I. Opposing modifications in intrinsic currents and synaptic inputs in post-traumatic mossy cells: evidence for single-cell homeostasis in a hyperexcitable network. J Neurophysiol. 2007 Mar;97(3):2394–2409. [PubMed: 16943315]

54.

Turrigiano G. Homeostatic signaling: the positive side of negative feedback. Current Opinion in Neurobiology. 2007;17(3):318–324. [PubMed: 17451937]

55.

Wilson HR, Cowan JD. Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophysical Journal. 1972;12(1):1–24. [PMC free article: PMC1484078] [PubMed: 4332108]

56.

Suffczynski P, Kalitzin S, Lopes Da, Silva FH. Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience. 2004;126(2):467–484. [PubMed: 15207365]

57.

Shinohara Y, Hirase H, Watanabe M, Itakura M, Takahashi M, Shigemoto R. Left-right asymmetry of the hippocampal synapses with differential subunit allocation of glutamate receptors. Proceedings of the National Academy of Sciences. 2008 December 9;105(49):19498–19503. [PMC free article: PMC2593619] [PubMed: 19052236]

58.

Silver R, Boahen K, Grillner S, Kopell N, Olsen KL. Neurotech for Neuroscience: Unifying Concepts, Organizing Principles, and Emerging Tools. J Neurosci. 2007 October 31;27(44):11807–11819. [PMC free article: PMC3275424] [PubMed: 17978017]

59.

Beckman PH. Building the TeraGrid. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2005 August 15;363(1833):1715–1728. [PubMed: 16099743]

60.

Hines M, Morse T, Migliore M, Carnevale NT, Shepherd GM. ModelDB: A Database to Support Computational Neuroscience. Journal of Computational Neuroscience. 2004;17:7–11. [PMC free article: PMC3732827] [PubMed: 15218350]

61.

Carnevale NT, Hines ML. The NEURON Book. Cambridge University Press; 2006.

62.

Bower JM, Beeman D. The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System. 2nd ed. New York: Springer-Verlag; 1998.

63.

Wallisch P, Lusignan M, Benayoun M, Baker T, Dickey A, Hatsopoulos N. Matlab for Neuroscientists: An Introduction to Scientific Computing in Matlab. Academic Press; 2008.

64.

van Drongelen W, Lee HC, Stevens RL, Hereld M. Propagation of Seizure-like Activity in a Model of Neocortex. [Review] Journal of Clinical Neurophysiology. 2007 April;24(2):182–188. [PubMed: 17414974]

65.

Case MJ, Schneider CJ, Soltesz I. Parallel Computing Enables Full-Scale Modeling of the Rat Dentate Gyrus. Poster presented at: Joint Symposium on Neural Computation; Los Angeles: University of California; 2010.

66.

Gleeson P, Steuber V, Silver RA. neuroConstruct: A Tool for Modeling Networks of Neurons in 3D Space. Neuron. 2007;54(2):219–235. [PMC free article: PMC1885959] [PubMed: 17442244]

67.

Trappenberg T. Fundamentals of Computational Neuroscience. 2nd ed. New York: Oxford University Press; 2009.

68.

Golding NL, Kath WL, Spruston N. Dichotomy of Action-Potential Backpropagation in CA1 Pyramidal Neuron Dendrites. J Neurophysiol. 2001 December 1;86(6):2998–3010. [PubMed: 11731556]

69.

Dyhrfjeld-Johnsen J, Morgan RJ, Soltesz I. Double Trouble? Potential for Hyperexcitability Following Both Channelopathic up- and Downregulation of I(h) in Epilepsy. Front Neurosci. 2009 May;3(1):25–33. [PMC free article: PMC2695388] [PubMed: 19753094]

*

both authors contributed equally to this work