Epilepsies as Dynamical Diseases of Brain Systems: Basic Models of the Transition Between Normal and Epileptic Activity

Abstract

Summary:Purpose: The occurrence of abnormal dynamics in a physiological system can become manifest as a sudden qualitative change in the behavior of characteristic physiologic variables. We assume that this is what happens in the brain with regard to epilepsy. We consider that neuronal networks involved in epilepsy possess multistable dynamics (i.e., they may display several dynamic states). To illustrate this concept, we may assume, for simplicity, that at least two states are possible: an interictal one characterized by a normal, apparently random, steady-state of ongoing activity, and another one that is characterized by the paroxysmal occurrence of a synchronous oscillations (seizure).Methods: By using the terminology of the mathematics of nonlinear systems, we can say that such a bistable system has two attractors, to which the trajectories describing the system's output converge, depending on initial conditions and on the system's parameters. In phase-space, the basins of attraction corresponding to the two states are separated by what is called a "separatrix." We propose, schematically, that the transition between the normal ongoing and the seizure activity can take place according to three basic models:Model I: In certain epileptic brains (e.g., in absence seizures of idiopathic primary generalized epilepsies), the distance between "normal steady-state" and "paroxysmal" attractors is very small in contrast to that of a normal brain (possibly due to genetic and/or developmental factors). In the former, discrete random fluctuations of some variables can be sufficient for the occurrence of a transition to the paroxysmal state. In this case, such seizures are not predictable.Model II and model III: In other kinds of epileptic brains (e.g., limbic cortex epilepsies), the distance between "normal steadystate" and "paroxysmal" attractors is, in general, rather large, such that random fluctuations, of themselves, are commonly not capable of triggering a seizure. However, in these brains, neuronal networks have abnormal features characterized by unstable parameters that are very vulnerable to the influence of endogenous (model II) and/or exogenous (model III) factors. In these cases, these critical parameters may gradually change with time, in such a way that the attractor can deform either gradually or suddenly, with the consequence that the distance between the basin of attraction of the normal state and the separatrix tends to zero. This can lead, eventually, to a transition to a seizure.Results: The changes of the system's dynamics preceding a seizure in these models either may be detectable in the EEG and thus the route to the seizure may be predictable, or may be unobservable by using only measurements of the dynamical state. It is thinkable, however, that in some cases, changes in the excitability state of the underlying networks may be uncovered by using appropriate stimuli configurations before changes in the dynamics of the ongoing EEG activity are evident. A typical example of model III that we discuss...

The Impact of EEG/MEG Signal Processing and Modeling in the Diagnostic and Management of Epilepsy

“…Whether or not this relationship may be relevant, it is certain that concepts derived from nonlinear dynamical theory have entered the field of what we may call quantitative epileptology to characterize the dynamical behavior of neuronal networks in the epileptic brain [69]. [70], [71]. As stated by Lytton [74] in his recent review on "Computer modeling in epilepsy," it has long been recognized that computer modeling will be required to "disentangle causality, to better understand seizure spread, and to understand and eventually predict treatment efficacy."…”

Potentially Pathological Alpha-Pattern as a Variant of Vigilance EEG in Drug-Resistant Epilepsy

“…Проведенные на настоящий момент исследования особенностей альфа-активности у пациентов с эпи-лепсией выявили только снижение вариабельно-сти частоты основного ритма в этой группе паци-ентов [15]. Однако, несмотря на очевидную роль таламо-кортикального взаимодействия в распро-странении разрядной активности при эпилепсии в экспериментальных и математических моделях [2, 9,20], патофизиологические аспекты его иссле-дованы недостаточно для выявления однозначных взаимосвязей [21]. Особенности и эволюция аль-фа-ритма в норме и при неэпилептической пато-логии постоянно и активно изучаются, в том числе с применением все более новых и сложных методов математической обработки [10,19,22].…”

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

“…From a theoretical point of view, Lopes da Silva [42,43] proposed two different scenarios about how a seizure could evolve. In the first scenario, a seizure can occur with a sudden and abrupt transition in brain activity dynamics, in which case it would not be preceded by detectable dynamical changes in the eeg.…”

“…Theoretical and computational models have advanced the understanding of brain dynamics by providing a framework in which to compare the experimentally observed eeg patterns. Lopes da Silva et al [42] redefined epilepsy as a dynamical disease of the brain. Most of the methodologies described previously in this appendix assume the existence of a type of preictal state.…”