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  • Review Article
  • Published:

Computer modelling of epilepsy

Nature Reviews Neuroscience volume 9, pages 626–637 (2008)Cite this article

Key Points

  • Computer modelling of epilepsy is a branch of systems biology, a science that aims to combine the discoveries made by reductionist approaches into systems in order to understand how primary pathologies and secondary reactions interact to produce disease. Epilepsy, a dynamical disease of the brain, is well suited to study from the perspective of dynamical systems.

  • Epilepsy is a complex set of syndromes with the commonality of recurrent seizures. Not only do the many individual epilepsy syndromes have different causes, but most epilepsies develop owing to the interaction of many causes at molecular, cellular, network and developmental levels, defying efforts to define simple cause-and-effect relations and suggesting the need for computer modelling.

  • Knowledge discovery and data mining provides the substrate and support for dynamical modelling and allows the findings to be applied back to the research and clinical settings. The various dynamical modelling techniques that are used include stochastic models, low-dimensional (lumped) deterministic models and detailed neuronal network models.

  • Computer models are applied across the range of epilepsy phenomenology, from the molecular to the clinical. At the patient level, Markov models have been used to assess patterns of remission and relapse in pediatric epilepsy. At the molecular level, deterministic models can predict alterations in cellular activity with ion-channel mutations.

  • Many seizure models simulate activity at the network level. Some of these are lumped models, which use mean-field approximations to reduce the activity of many neurons to simple oscillators that are then coupled to produce complex activity patterns. Other models incorporate the details of neural activity and synaptic interactions, in order to reach down to the molecular level at which drug effects take place.

  • Uncommonly among areas of neuroscience research, computer modelling is immediately accessible through downloads of established models. An intrinsically collaborative activity, the future of the endeavour lies in the cooperative efforts of clinicians, experimentalists and modellers.

Abstract

Epilepsy is a complex set of disorders that can involve many areas of the cortex, as well as underlying deep-brain systems. The myriad manifestations of seizures, which can be as varied as déjà vu and olfactory hallucination, can therefore give researchers insights into regional functions and relations. Epilepsy is also complex genetically and pathophysiologically: it involves microscopic (on the scale of ion channels and synaptic proteins), macroscopic (on the scale of brain trauma and rewiring) and intermediate changes in a complex interplay of causality. It has long been recognized that computer modelling will be required to disentangle causality, to better understand seizure spread and to understand and eventually predict treatment efficacy. Over the past few years, substantial progress has been made in modelling epilepsy at levels ranging from the molecular to the socioeconomic. We review these efforts and connect them to the medical goals of understanding and treating the disorder.

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Figure 1: The river of epilepsy.
Figure 2: Markov model of childhood-epilepsy outcome in 602 children.
Figure 3: A lumped model of absence epilepsy.
Figure 4: A lumped model of MTLE.
Figure 5: Reduction of excitatory strength leads to seizure in a detailed neocortical model.

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Acknowledgements

I would like to thank S. Neymotin, J. Reggia, P. Rutecki, P. Suffczynski, W. van Drongelen and three anonymous reviewers for many helpful suggestions, and the National Institute of Health for 20 years of support.

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  1. Departments of Physiology, Pharmacology, Biomedical Engineering and Neurology, State University of New York Downstate Medical Center, Brooklyn, New York, USA

    William W. Lytton

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DATABASES

ModelDB 

Hodgkin–Huxley equations

model applied to MTLE

model of absence epilepsy

Wilson and Cowan's 1972 model

FURTHER INFORMATION

William W. Lytton's homepage

From Computer to Brain

Genesis

Matlab

Neuron

Octave

Task force on epilepsy classification and terminology

XppAuT

Glossary

Generalized seizure

A seizure that seems to start simultaneously across cortical sites.

Focal seizure

A seizure that starts at a particular location in the brain.

Secondary generalization

A process whereby an initially focal seizure spreads to involve the entire brain.

Dynamical model

A computer or physical model that reproduces change in an experimentally observable feature. In the case of dynamical models of motion, these changes would be in position and velocity.

Tonic–clonic

A common pattern of convulsion that involves a phase of contraction of the extensor muscles (the tonic) followed by a phase of alternating flexor–extensor contractions (the clonic phase).

Seizure semiology

The detailed study of the progress of a seizure.

Scale model

A small physical model of an object, with correct proportions.

Verbal model

An informal descriptive explanation of an object or phenomenon.

Systems biology

The analysis of element interactions in biological systems. Owing to the complexity of these systems, the computer is often used as a tool for analysis and simulation. Objects of study include metabolic and expression pathways but extend up to the study of macroscopic systems. The goal is to insert the results of reductionist study back into the systems from which they were extracted.

Parameter

In a computer model, parameters are the constant values in the set of equations that describe the model. These values are set by the user and determine the behaviour of the model.

Stochastic model

A computer model that attempts to replicate phenomenology by drawing exemplars (which might be locations or time intervals) from a probability distribution. The prototypical example is the model of Brownian motion.

Poisson model

A stochastic model that generates time intervals that are independently drawn from a Poisson distribution. The Poisson distribution is the limiting case of the binomial distribution for large 'n' (number of events) and small 'p' (probability of event occurrence).

Monte Carlo model

A stochastic model that uses repeated random sampling from one or more distributions.

Markov model

A stochastic model that uses a series of connected states with transition probabilities between them.

Discretization

A process whereby continuous time is divided into timesteps, or whereby continuous space is divided into segments or compartments, in order to simulate continuous reality in the discontinuous words of computer memory.

Finite-difference approximation

A process whereby the infinitesimal changes of continuous curves (in time or space) are approximated with a finite change that is based on the curve's values at a discrete timestep or spatial interval.

State variable

In a dynamical model, state variables are the values that change with time.

Trajectory

In a dynamical model, the trajectory is the path that is followed by the n state variables through the n-dimensional state space. This is a higher-dimensional generalization of the notion of trajectory as a term that is commonly used to describe motion. However, trajectories in models of motion include velocities as well as locations.

Attractor

The set of stable trajectories of a dynamical system in state-space. If a trajectory is perturbed away from an attractor it will tend to move back to it.

Mean-field approximation

An approximation that is used when large numbers of elements (for example, neurons) make it impracticable to model the influence of each element individually. Instead, the effect of a large ensemble of elements is estimated as a field, the influence of which is widely felt.

Lumped model

A model that approximates the activity of a large ensemble of neurons using a single-state variable that typically represents the proportion of neurons that are active at a given time.

Cortical minicolumn

A group of cortical cells that interact with each other more than they interact with neurons in neighbouring columns. Although columnar structure was originally identified physiologically as groups of neurons with shared properties, it has since been sought anatomically and variously identified as groups of 100–200 neurons (∼30 μm across).

State space

The dimensionality of a dynamic system. The current state of the system can be described as a point in state-space. Also called phase space.

Parameter space

The m-dimensional space in which the parameters of a system can be defined as a single point.

Ictogenesis

The generation of a seizure (the ictus) by dynamical, cellular and synaptic processes.

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Lytton, W. Computer modelling of epilepsy. Nat Rev Neurosci 9, 626–637 (2008). https://doi.org/10.1038/nrn2416

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