# Models of Epilepsy

## Contents |

# Chronic_Models

## Electrical Induction

- Kindling
- Generally used as a model of Temporal Lobe Epilepsy
- Short electrical stimuli to limbic brain regions
- See a progressive increase in severity of seizures

## Chemical Induction

- Pilocarpine
- Cholinergic, muscarinic agonist

- Kainate
- Excitotoxic glutamate analogue

## Genetic Epilepsy

Most of these models are a representation of generalized epilepsy, instead of induced partial epilepsy (as is common in the induced models). These are commonly used to study mechanisms of epilepsy instead of epilepsy prevention.

- Mutant animals with reflex epilepsy
- Seizures elicited by sensory stimulation

- Mutants with spontaneous, recurring seizures
- Transgenic or knock-out mice
- Not as commonly used in drug studies

(Loscher, 2002)

## Acute Models

These are models of seizures, not epilepsy, as they do not reoccur randomly.

## Maximal Electroshock Seizures (MES)

This model has been used to identify drugs with affects against tonic-clonic seizures. It may also be used to test drugs against partial seizures. It's popularity stems from the fact that it is easy to induce. (Loscher, 2002).

## Pentylenetetrazole Seizure Test (PTZ)

This model has been used to identify drugs with affects against non-convulsive absence or myoclonic seizures (Loscher, 2002). Repeated injections can produce a type of chemical kindling. This method is a good measure of seizure susceptibility and screening of new drugs. At low doses, this treatment can induce absence-like seizures (Sarkisian, 2001). PTZ is a GABA antagonist.

Initially this chemical, which is a tetrazol derivative, produces myoclonic jerks, followed by sustained activity which may lead to a generalized tonic-clonic sizures. It is a chemical convulsant. This model can be used to identify proconvulsants as well as anticonvulsants. (Deyn, 1992)

## Hippocampal_Seizures

- Excitatory agonists
- NMDA
- Glutamate
- Kainic acid

- Inhibitory antagonists
- Bicuculline
- Can be applied focally and systemically. Induces acute simple focal seizures. It is believed to block GABAergic transmission as a competitive antagonist.

- Allylglycine

- Bicuculline
- Cholinergics
- Pilocarpine
- Anticholinesterases

- Other
- Tetanus toxin
- Fluorothyl

## To_Study_Extrahippocampal_Involvement

- Focal treatments

## Penicillin

A popular model to study simple partial seizures. Acute focal seizures develop after application. The model is popular for the study of spreading seizure activity. The suggested mechanism is a competition for GABA at the receptor. (Deyn, 1992)

# In_vitro_models

A number of different preparations can be used in vitro. These include whole brain, whole structure, brain slice, and dissociated cells, moving from the systems level down to the cellular level.

- GABAa receptor antagonists/modulators
- Bicuculline
- Picrotoxin
- low extracellular chloride

These act to disrupt the inhibition/excitation balance and create an epileptogenic focus. Interictal spikes occur within slices exposed to media containing any of these conditions (Sarkisian, 2001).

- K channel antagonists/modulators
- 4-aminopyridine
- Tetraethyl-amonium
- High extracellular K

- NMDA receptor modulators
- zinc
- Glycine
- Low extracellular magnesium

(Sharfman, 2002)

# Mathematical_Models

Computational models help elucidate extremely complex mechanisms involved in epilepsy. The disorder can involve multiple causes and include multiple levels, from a cellular level all the way up to a network level. Models can help to combine all of these factors and allow researchers to manipulate inputs they would not be able to experimentally. They provide a way of using experimental results to make further predictions not yet testable as well as providing a comparison to experimental work. Keep in mind that mathematical models of epilepsy do not necessarily come from models of seizures (Lytton, 2008).

Different scales, or dimensions, can be considered when modeling epilepsy. First, we have the spatial scale. The model can try to represent biological factors at the cellular level, such as ion channels, all the way up to different brain areas. There is also a temporal scale. Depending on which aspect of epilepsy you are modeling, you will have a very different time scale. Modeling interictal spikes occurs over milliseconds, seizures occur over seconds, drug treatments must be followed over months, while the progression of the disease can last years. We can also model transitions occurring in seizures, such as the development of increase synchrony, or the movement from the tonic to clonic phase. (Lytton, 2008).

## Macroscopic (Mean Field) Models

These models describe the mean spatiotemporal activity of two types of neurons: excitatory principle cells (PCs) and inhibitory interneurons (INs). It is based on the fact that well organized populations of neurons sum their extracellular currents when synapses are activated. This reflects in the EEG signal. They ignore the biophysical properties of each individual cell. When there are populations of neurons, two types of transfer functions are used. The first type is the linear pulse to wave transfer function, which is used to transform action potential density presynaptically to average inhibition or excitation at the postsynaptic population. The second is the nonlinear wave to pulse transform, which is used to transform the wave activity of a subpopulation to average firing rate of the subpopulation. More subpopulations can be added (other than simply PCs and INs) to make the network more complex.

These models are good for looking at transitions from interictal to ictal states. EEG data is recording average local field potentials, so they are also good at characterizing this data. They provide a more simplistic way to model seizures that focus on epileptic processes occurring in a large-scale system. Also, due to the limited number of parameters and variables, they are easier to analyze. Since they are more general, these models are unable to describe the cellular and molecular processes underlying epilepsy. To understand these types of mechanisms, a more complex model must be used.

(Ullah & Schiff, 2009)

## Biophysical Network Models

These models are used to look at the molecular mechanisms of a single neuron or neuronal network in processes underlying epilepsy. Parameters such as ionic currents, conductance, synaptic weights, microenvironments, and synaptic inputs are all considered when determining the firing pattern of a neuron. There are constraints in computational power and uncertainty about the value of certain parameters that go into these models. There can be many levels modeled, from a single neuron, to a network with millions of neurons. These more complex and detailed models aim to mimic experimentally observed characteristics of networks and provide access to factors inaccessible with experimental procedures. (Ullah & Schiff, 2009)

This is a more microscopic approach and can be further divided. It may look at neurons, in which the model focuses on membrane components, ion channels, and transmembrane currents. It can also look at networks of neurons, in which the model focuses on main cells, interneurons, astrocytes, synapses, and gap junctions. These models have made a significant impact in elucidating the role of interneurons in hyperexcitability. (Fabrice)

## Graphical Representations

These models take into account the topology of the network along with the functional aspects (which the previous two models use). The main focus is on how changes in network topology affect network stability. Such models have been used to study damage done to the dentate gyrus in temporal lobe epilepsy. In a study by Lytton et al. (1998), they found that mossy fiber sprouting combined with disinhibition is needed to produce seizure-like activity in models. They based the model on anatomical changes found in the dentate gyrus after seizure.

(Ullah & Schiff, 2009)

## Stochastic Models

This is a type of dynamic model, one which describes change, that involves fitting a data to a distribution. Synthetic data is created from model parameters, such as the parameters of a Gaussian distribution. This is a good approach when you have a highly complex system in which it is too difficult to model the individual underlying details. This type of model has been used to understand the prediction of seizure onset. It has been suggested that the occurrence follows a Poisson distribution. (Lytton, 2008).

Some specific examples of this model type are: Poisson models, Monte Carlo models, and Markov models.

## Poisson Model

This determines the probability of a given number of events occurring within a specified interval. The average rate of the events must be known, and each even must occur independently of the time since the last event. The equation is given by:

f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!},\,\! where \lambda = the expected number of events within the interval, where \lambda∈N k = the number of occurrences of the event, where k∈N f = the probability that \lambda will occur

Time intervals that are independently drawn can be generated using this model (Lytton, 2008).

### Monte Carlo Models

This model relies on repeated random sampling from distributions to compute results. These models can be good for when there is significant uncertainty in the inputs. Monte Carlo models tend to be used look at molecules and ions in the synapses. (Lytton, 2008).

### Markov Models

These models allow for the determination of a future state that is only dependent on the current state and not the past. A series of states can be used with transition probabilities between them. Markov models allowed for the inclusion of the state of a patient in predicting seizures. They are also used to model ion-channel transitions. (Lytton, 2008).

## Deterministic Models

These do not evolve randomly but instead are determined by initial conditions. Therefore, unlike stochastic models which generate probabilities, they lead to precise predictions. These models can lead to chaos. Differential equations are generally used to describe these systems, along with initial conditions and the evolution of state variables along a trajectory. The Hodgkin-Huxley model is an example of a deterministic model.

<a name="Lumped_Models" id="Lumped_Models"></a>#### Lumped Models

These are also called low-dimensional mean-field models, and simulate large groups of neurons (Lytton, 2008). Wilson and Cowan used a neural lump model with

## Nonlinear Systems

A nonlinear systems is any in which the input is not directly proportional to the input. Some characteristics are that they tend to heavily rely on the initial conditions and can lead to phenomena such as chaos. In a nonlinear system, small changes can produce big effects.

## References

Ghanim Ullah and Steven J. Schiff (2009), Scholarpedia, 4(7):1409. "Models of Epilepsy"