Epilepsy has been defined as a chronic, complex neurological disorder associated with abnormal electrical activity in the brain, marked by sudden recurrent episodes of sensory/motor disturbance, changes in behavior, with or without loss of consciousness, and/or convulsions (Nunes et al. 2012). This excessive activity can be produced by hyperexcited neurons acting independently or involve abnormal interactions among many neurons (Hobbs et al. 2010). Epilepsy is one of the most common chronic neurological affections, with more than 50 million patients worldwide and approximate 2 million new cases each year. Epilepsy responds to treatment in about 70 % of cases. Not all cases of epilepsy are lifelong, a substantial number of people improve to the point that medication is no longer needed. One seizure does not signal epilepsy (up to 10 % of people worldwide have one seizure during their lifetimes) (Chang and Lowenstein 2003). Epilepsy has been defined since 2005 by two or more unprovoked seizures, >24 h apart (Fisher et al. 2005). The definition of epilepsy has been recently revised in order to consider the diagnosis even after occurrence of a single unprovoked seizure, providing that we can demonstrate an enduring predisposition for recurrence, similar to the general recurrence risk after two seizures (more than 60 %) over the next 10 years. For instance a patient can have a single unprovoked seizure after trauma, a stroke, or central nervous system infection. A patient with such brain disorders has a high risk of developing epilepsy after a single unprovoked seizure.

The tendency to respond to particular stimuli with seizures also meets the conceptual definition of epilepsy. Reflex epilepsies are also associated with an enduring abnormal predisposition to have recurrent seizures.

The document also mentions as a general agreement that epilepsy should no longer be considered a disorder but a disease, the term implying a more substantial, long lasting derangement of neuronal functionality (Fisher et al. 2014).

Diseases of central nervous system are often associated with altered brain dynamics (Expert et al. 2010). It has been hypothesized that the dynamical properties characterizing a critical state may be considered as an important marker of brain well-being in both health and disease (Plenz 2012). During epileptic seizures the distribution of phase-locking intervals (PLI) is providing additional evidence for the criticality hypothesis. Furthermore, deriving the distribution of PLI from electrocorticogram (ECoG) data as an indicator of critical brain dynamics has shown that the system deviates from scale-free behavior during seizures. All scales closely follow a power-law probability distribution during pre-ictal time intervals with the exponent between 22 and 23.5 (see Fig. 15.2). The apparent robustness of the power-law against exact conditions (different anatomical regions with varying number of channels) strengthens the hypothesis of the relevance of a critical state in human brain dynamics. While the PLI distribution followed a power-law in time intervals preceding the seizure onset, a deviation from power-law behavior was observed in intervals containing the seizure attack.

Figure 15.2 shows the distribution of PLI derived from a pre-ictal, an ictal and a postictal time interval. The probability to find longer PLI increased during attacks thereby destroying the scale-free property of the original distribution. After the seizure this distribution slowly relaxed back to a power-law. In Fig. 15.2 this relaxation is not yet complete in the postictal time interval as there is still some residual seizure dynamics in the ECoG recording.

Critical systems have been defined as systems that are close to a critical point, near the boundary of an order-disorder phase transition. At criticality, these systems can avoid being trapped in one of two extreme cases: a disordered state (when interactions are too weak and the system is dominated by noise) or a globally ordered state in which all elements are locked (when interactions are too strong and the system is completely static). A dualism is essential for a complex system, like the brain, to function: it must maintain some order to ensure coherent functioning (i.e., generate a reproducible behavior in response to a certain stimulus) while allowing for a certain degree of disorder to enable flexibility (i.e., adapt to varying external conditions). Such dualism is possible at criticality.

While many degrees of order/disorder are possible, the subtle balance between order and disorder at criticality manifests itself in certain general statistical properties: critical systems exhibit spatial and temporal correlations that are long range (i.e., on scales that are larger than those on which mutual interactions take effect) and follow power-law distributions. Recent research has shown that brain networks, by being in the critical state, optimize their response to inputs and maximize their information processing ability (Shew and Plentz 2013).

Haimovici and colleagues have presented a simple brain model that, if tuned to criticality, explains the broad range of experimental observations of human brain activity, in particular, reproducing key findings obtained with functional magnetic resonance imaging (fMRI) (Haimovici et al. 2013). fMRI research has been able to deliver an important observation: the human brain at rest exhibits a large-scale spatiotemporal organization into distinct functional networks—so-called resting state networks (RSN) (Fox and Raichle 2007). RSNs are areas of the resting brain—measured in subjects performing any cognitive, or motor tasks—in which fluctuations of neural activity are correlated, as revealed by the fact that BOLD signal fluctuations within the same network are synchronous. Each RSN can be related to a specific set of cortical areas associated with certain functions: cognitive, sensory (visual, auditory), and motor RSNs, for instance, have been identified (see Fig. 15.3).

What Haimovici and colleagues found is that such a model can lead to activity clusters similar to those found for RSN activity (Haimovici et al. 2013). But for the model to match the experimental data, the activation threshold had to be set exactly at the level at which their model becomes critical, as illustrated in Fig. 15.3. At criticality, their model predicts a number of statistical properties that are consistent with experiments: the brain forms activity clusters whose size follows a power law with slope of −3/2, the hallmark of neuronal avalanches (Beggs and Plenz 2003), corresponding to a peak in the size of the second-largest cluster, as found in percolation models (Margolina et al. 1982); the correlation length (the distance at which two points in the system behave independently) and its fluctuations diverge and match those seen in human brain data.

The human neocortex consists of a large number of minicolumns in parallel vertical arrays (Mountcastle 1957, 1997; Buxhoeveden and Casanova 2002; Casanova et al. 2007; Shepherd and Grillner 2010). Minicolumns are the first step in a nested series of nodes or echelons of increasing complexity (Mountcastle 1997; Szentagothai 1975). Within minicolumns, cortical neurons are aggregated into five horizontal layers (or laminae), namely two supra-granular, one granular and two infra-granular layers. Other levels of modular organization include multiple minicolumns, macrocolumns, and large-scale networks of macrocolumns that are interconnected with the entire brain (Buxhoeveden and Casanova 2002; Opris and Casanova 2014).

In contrast to the sparse but organized connectivity between the modules of control subjects, brain connectivity of epileptic patients shows a configuration where nodes in a functional module are more connected to different functional modules. Recently, Vaessen et al. (2014) examined connectivity of whole brains of children with frontal lobe epilepsy (FLE) and compared their structural and functional connectivity with the same in healthy controls. Their measurements of the functional connectivity was derived from the dynamic fluctuations of the fMRI, while the structural connectivity was determined from fiber tractograms of diffusion weighted MRI. The whole brain network patterns of connectivity were characterized with graph theoretical metrics and further decomposed into modules. Then, the graph metrics with the extracted connectivity within and between modules were related to cognitive performance.

As shown in Fig. 15.4a, the modularity algorithm extracted four modules from the averaged functional connectivity matrix over all subjects. Spatial organization of module #1 was considered the “default mode network” with network nodes distributed in the frontal, temporal and parietal lobes (Vaessen et al. 2014). Module #2 was distributed over the frontal and subcortical regions. Module #3 was localized in the occipital lobe. Module #4 nodes were distributed over frontal, temporal and occipital regions. All four modules seemed to be symmetric to the inter-hemispheric fissure. As shown in Figs. 15.4a, b when the structural connections were organized according to the modularity index of the frontal cortex, the structural modularity revealed bilateral structural sub networks. For the structural connectivity matrix the modularity algorithm determined only two modules, which were highly symmetric over the two hemispheres. After functional connections were organized according to these structural connectivity modules, the sub organization vanished (Fig. 15.4c, d). An interactive view of functional connectivity and structural connectivity was displayed as between-module, within-module averaged over all modules and individual within-module connections (Fig. 15.4e, f). It was further shown that functional “disturbances” of epileptic children were related to increased clustering and stronger modularity compared to healthy controls, which was accompanied by stronger within- and weaker between-module functional connectivity. While structural modularity increased with stronger cognitive impairment, it was concluded that decreased coupling between large-scale functional network modules may represent a hallmark for impaired cognition in childhood FLE.

High-frequency oscillations (HFO) in the 80(100)–500 Hz range are considered an important biomarker of cortical epileptogenicity. Although HFO may be present in non-epilepogenic brain structures, it has been shown that the ripple (<250 Hz) and particularly fast ripples (>250 Hz) subbands have are highly specific to the seizure onset zone (Zijlmans et al. 2012). Using dense 2D microelectrode arrays (MEA) having a spacing of 0.4 mm between electrodes, Schevon and colleagues have shown that about ~90 % of the recorded HFOs were limited to a single channel (Schevon et al. 2009). This is consistent with the idea that most of the spontaneous HFO events are confined within a minicolumn, and spreading the activity requires a recruitment process of several minicolumns, possibly through an avalanche process following a power-law, as suggested by several other studies using intracranial recordings (Worrell et al. 2002; Wu et al. 2014).