Jesús Pastor, Rafael García de Sola and Guillermo J. Ortega
Instituto de Investigación Sanitaria Hospital de la Princesa, Madrid
Ranging from its most basic mechanisms to the clinical symptoms, epilepsy is tightly associated with the word “synchronization”. In fact, synchronization phenomena underlying epilepsy are described in several mechanisms at different temporal and spatial scales. At the lowest spatial scale, hippocampal and neocortical interictal spikes appear as the result of synchronized activity of pyramidal cells. At a larger spatial scale, epileptic seizures are usually described as a state of «hypersynchrony» encompassing extended cortical areas. Synchronization and epilepsy are so associated one to each other that lack of synchronization, or desynchronization, has been highlighted in recent years as a key aspect of the underlying dynamic in this pathology. The word synchronization comes from two Greek words, chronos and same, which means «sharing the same time»; therefore, a synchronized event is always composed by the temporal coincidence of two or more actions. However, it is usually understood the existence of an underlying mechanism that cause the synchronization itself. In this sense, synchronization is assumed differently from chance, because no deterministic causal effect exists in the last one. On the other hand, the use of the word synchronization is generally associated with a mechanism, known or not, that makes possible the temporal coincidence. In the above sense, and from the very beginning of epilepsy research, the word synchronization is found in many aspects of this pathology. Every time we found the word synchronization in epilepsy, one is tempted to think in a pathological substrate that would make it possible. However, it seems that synchronization in epilepsy has suffered from bifurcating routes since the beginnings of the quantitative descriptions of epileptic phenomena. The very clever and insightful descriptions made by the epilepsy researches in the late 40’s and 50’s (Penfield & Jasper, 1954) were plagued by the words synchronization and hypersynchronization, and today they are still used almost in the same fashion that were originally used. However, since the first description of the synchronization phenomena by Christian Huygens in 1673 to now- days, there has been a profound revision and enlargement of the concept of synchronization especially in the last years (Pikovsky et al., 2001). Chaos theory, complex networks methodologies and nonlinear time series analysis have dug into the traditional concept of synchronization with the net result of a completely new proposal of what synchronization actually is. Today, in fact, there is no more a single synchronization phenomena, but instead, the traditional term has been split in several, more specific terms to characterize the numerous forms of the underlying mechanism but also, of the different kind of synchronized objects. It seems that the new understanding we have today of synchronization is far from being adopted by the epileptologists, especially by the physician community. New terms as lag or full synchronization are rarely seen in clinical works, which is rather frustrating, because synchronization research in the last years has opened up new and powerful techniques, which would very useful in the improvement of diagnostic or therapeutic techniques.
This chapter is intended to review some of the new advances in synchronization in general and specifically in epilepsy research. A very brief mathematical introduction will be presented in order to fully understand the whole range of synchronization concepts presented in the chapter, either in the theoretical or empirical fields. Our aim thus is to show only the most basic methods and applications of synchronization and epilepsy.
Contemporary concepts of synchronization
In general terms, synchronization between two systems is defined as the adjustment of their internal rhythms due to an existing (weak) interaction between them (Pikovsky et al., 2001). Therefore, the following ingredients are essential for synchronization:
a. There must exist two or more self-sustained oscillators, i.e., systems capable of generating their own rhythms,
b. The systems adjust their own rhythms due to a (weak) interaction between them, and
c. The adjustment of rhythms occurs in a certain range of systems’ mismatch; in particular, if the frequency of one oscillator is slowly varied, the second system follows
The presence of self-sustained oscillators is needed for synchronization. This requirement is fundamental at the time of differentiating actual synchronization from other phenomena, for instance resonance. Self-sustained oscillators typically are represented mathematically by nonlinear differential equations, as for example Van der Pol oscillator. This kind of oscillator is able to oscillate with its own rhythm without external driving. Moreover, self-sustained oscillators can adjust their frequency, which is the key concept in synchronization. Two isolated different self-sustained oscillators, with different intrinsic frequencies can oscillate at the same frequency when they interact with each other. Note that synchronization refers to a dynamical process instead of a stationary state. Synchronization is a process by which two or more systems adjust their rhythms in the course of time. This means that the interaction allows (generally small) variations of the intrinsic rhythms, but always try to reach the common frequency. One aspect of the formal synchronization definition worth of mentioning is point b), which states that the rhythms are adjusted by a weak interaction. Although this is the very general concept, adjustment of rhythms through the weak interaction allows differentiating activity raised due to a true synchronization between two or more systems from, the activity derived from a compound system in which several subsystems are tightly connected. Note lastly that the synchronization definition used encompass the case of a unidirectional synchronization known as synchronization by driving. We will review below basically the most important concepts of oscillators and synchronization.
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