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Epilepsies as dynamical diseases of brain systems basic models of the transition between normal and epileptic activity
Epilepsia, (2003)
Аннотация
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 steady-state" 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
here is photosensitive epilepsy. CONCLUSIONS: We present an overview
of these basic models, based on neurophysiologic recordings combined
with signal analysis and on simulations performed by using computational
models of neuronal networks. We pay especial attention to recent
model studies and to novel experimental results obtained while analyzing
EEG features preceding limbic seizures and during intermittent photic
stimulation that precedes the transition to paroxysmal epileptic
activity.
