Piotr Suffczynski

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

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).

Dynamics of the human alpha rhythm: evidence for non-linearity?

OBJECT For a better understanding of the physiological mechanisms responsible for alpha rhythms it is important to know whether non-linear processes play a role in their generation. We used non-linear forecasting in combination with surrogate data testing to investigate the prevalence and nature of alpha rhythm non-linearity, based on EEG recordings from humans. We interpreted these findings using computer simulations of the alpha rhythm model of Lopes da Silva et al. (1974). METHODS EEGs were recorded at 02 and O1 in 60 healthy subjects (30 males; 30 females; age: 49.28 years; range 11-84) during a resting eyes-closed state. Four artefact-free epochs (2.5 s; sample frequency 200 Hz) from each subject were tested for non-linearity using a non-linear prediction statistic and phase-randomized surrogate data. A similar type of analysis was done on the output of the alpha model for different values of input. RESULTS In the 480 (60 subjects, 2 derivations, 4 blocks) epochs studied, the null hypothesis that the alpha rhythms can result from linearly filtered noise, could be rejected in 6 cases (1.25%). The alpha model showed a bifurcation from a point attractor to a limit cycle at an input pulse density of 615 pps. Non-linearity could only be detected in the model output close to and beyond this bifurcation point. The sources of the non-linearity are the sigmoidal relationships between average membrane potential and output pulse density of the various cells of the neuronal populations. CONCLUSION The alpha rhythm is a heterogeneous entity dynamically: 98.75% of the epochs (type I alpha) cannot be distinguished from filtered noise. Apparently, during these epochs the activity of the brain has such a high complexity that it cannot be distinguished from a random process. In 1.25% of the epochs (type II alpha) non-linearity was found which may be explained by dynamics in the vicinity of a bifurcation to a limit cycle. There is thus experimental evidence from the point of view of dynamics for the existence of the two types of alpha rhythm and the bifurcation predicted by the model.

Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network

It is currently believed that the mechanisms underlying spindle oscillations are related to those that generate spike and wave (SW) discharges. The mechanisms of transition between these two types of activity, however, are not well understood. In order to provide more insight into the dynamics of the neuronal networks leading to seizure generation in a rat experimental model of absence epilepsy we developed a computational model of thalamo-cortical circuits based on relevant (patho)physiological data. The model is constructed at the macroscopic level since this approach allows to investigate dynamical properties of the system and the role played by different mechanisms in the process of seizure generation, both at short and long time scales. The main results are the following: (i) SW discharges represent dynamical bifurcations that occur in a bistable neuronal network; (ii) the durations of paroxysmal and normal epochs have exponential distributions, indicating that transitions between these two stable states occur randomly over time with constant probabilities; (iii) the probabilistic nature of the onset of paroxysmal activity implies that it is not possible to predict its occurrence; (iv) the bistable nature of the dynamical system allows that an ictal state may be aborted by a single counter-stimulus.

Dynamical diseases of brain systems: different routes to epileptic seizures

In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the systems attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the systems parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the systems response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed.

Dynamics of epileptic phenomena determined from statistics of ictal transitions

In this paper, we investigate the dynamical scenarios of transitions between normal and paroxysmal state in epilepsy. We assume that some epileptic neural network are bistable i.e., they feature two operational states, ictal and interictal that co-exist. The transitions between these two states may occur according to a Poisson process, a random walk process or as a result of deterministic time-dependent mechanisms. We analyze data from animal models of absence epilepsy, human epilepsies and in vitro models. The distributions of durations of ictal and interictal epochs are fitted with a gamma distribution. On the basis of qualitative features of the fits, we identify the dynamical processes that may have generated the underlying data. The analysis showed that the following hold. 1) The dynamics of ictal epochs differ from those of interictal states. 2) Seizure initiation can be accounted for by a random walk process while seizure termination is often mediated by deterministic mechanisms. 3) In certain cases, the transitions between ictal and interictal states can be modeled by a Poisson process operating in a bistable network. These results imply that exact prediction of seizure occurrence is not possible but termination of an ictal state by appropriate counter stimulation might be feasible.

Electrical brain-stimulation paradigm for estimating the seizure onset site and the time to ictal transition in temporal lobe epilepsy

OBJECTIVE To explore and validate a novel stimulation and analysis paradigm proposed to monitor spatial distribution and temporal changes of the excitability state in patients with temporal lobe epilepsy (TLE). METHODS We use intermittent pulse stimulation in the frequency range 10-20Hz. A quantitative measure of spectral phase de-modulation, the relative phase clustering index (rPCI) was applied to the evoked EEG signals, measured from electrodes implanted in the hippocampal formation. RESULTS We found that in the interictal periods, high values of rPCI recorded from specific sites were correlated with the most probable seizure onset sites (SOS). Furthermore we found that high values of rPCI from certain locations correlated with shorter time intervals to the next seizure. CONCLUSIONS Our clinical findings indicate that although the precise moment of ictal transitions is in general unpredictable, it may be possible to estimate the probability of occurrence of some epileptic seizures. SIGNIFICANCE The use of the rPCI for probabilistic forecasting of upcoming epileptic seizures is warranted. rPCI measurements may be used to guide interventions with the aim of modifying local tissue excitability that ultimately might prevent ictal transitions.

Some Insights Into Computational Models of (Patho)physiological Brain Activity

The amount of experimental data concerning physiology and anatomy of the nervous system is growing very fast, challenging our capacity to make comprehensive syntheses of the plethora of data available. Computer models of neuronal networks provide useful tools to construct such syntheses. They can be used to interpret experimental data, generate experimentally testable predictions, and formulate new hypotheses regarding the function of the neural systems. Models can also act as a bridge between different levels of neuronal organization. The ultimate aim of computational neuroscience is to provide a link between behavior and underlying neural mechanisms. Depending on the specific aim of the model, there are different levels of neuronal organization at which the model can be set. Models are constructed at the microscopic (molecular and cellular), macroscopic level (local populations or systems), or dynamical systems level. Apart from purely computational models, hybrid networks are being developed in which biological neurons are connected in vitro to computer simulated neurons. Also, neuromorphic systems are recently being created using silicon chips that mimic computational operations in the brain. This paper reviews various computational models of the brain and insights obtained through their simulations.

On the Quantification of SSVEP Frequency Responses in Human EEG in Realistic BCI Conditions

This article concerns one of the most important problems of brain-computer interfaces (BCI) based on Steady State Visual Evoked Potentials (SSVEP), that is the selection of the a-priori most suitable frequencies for stimulation. Previous works related to this problem were done either with measuring systems that have little in common with actual BCI systems (e.g., single flashing LED) or were presented on a small number of subjects, or the tested frequency range did not cover a broad spectrum. Their results indicate a strong SSVEP response around 10 Hz, in the range 13–25 Hz, and at high frequencies in the band of 40–60 Hz. In the case of BCI interfaces, stimulation with frequencies from various ranges are used. The frequencies are often adapted for each user separately. The selection of these frequencies, however, was not yet justified in quantitative group-level study with proper statistical account for inter-subject variability. The aim of this study is to determine the SSVEP response curve, that is, the magnitude of the evoked signal as a function of frequency. The SSVEP response was induced in conditions as close as possible to the actual BCI system, using a wide range of frequencies (5–30 Hz, in step of 1 Hz). The data were obtained for 10 subjects. SSVEP curves for individual subjects and the population curve was determined. Statistical analysis were conducted both on the level of individual subjects and for the group. The main result of the study is the identification of the optimal range of frequencies, which is 12–18 Hz, for the registration of SSVEP phenomena. The applied criterion of optimality was: to find the largest contiguous range of frequencies yielding the strong and constant-level SSVEP response.

The effects of vigabatrin on spike and wave discharges in WAG/Rij rats.

The effects of vigabatrin, which increases GABA concentrations by inhibiting GABA transaminase, on spike and wave discharges (SWDs) in the electroencephalogram of WAG/Rij rats were studied. Vigabatrin increased the incidence and duration of the SWDs, suggesting a quantitative GABA(A)ergic involvement in the mechanism(s) underlying the starting and stopping of an ongoing SWD. Also, vigabatrin decreased the SWD peak frequency, suggesting an important role of GABA(B) in the mechanism(s) underlying the peak frequency of the SWDs. Vigabatrin gradually changed the course of the hazard rates of the SWD durations, suggesting a qualitative GABAergic role in the mechanism(s) underlying the stopping of an ongoing SWD.

Magnetic source imaging in fixation-off sensitivity: relationship with alpha rhythm.

A patient in whom a variety of abnormal EEG findings can be elicited by elimination of central vision and fixation demonstrates fixation-off sensitivity. The underlying mechanisms of fixation-off sensitivity and its relationship with alpha rhythm remain unclear. To obtain a better understanding of this issue, we used a whole-head magnetoencephalograph to study an epileptic child with fixation-off sensitivity resulting in a 3-Hz, large-amplitude oscillation (300 microV) over the occipital regions on the EEG. Magnetic source localization revealed alpha activity around the calcarine fissure and surrounding parieto-occipital areas. Magnetic sources of abnormalities relating to fixation-off sensitivity, however, usually were located deeper in the brain, suggesting more extensively distributed sources, with involvement of the cingulate gyrus and the basomesial occipitotemporal region. Distributions of the sources of both types of activities show independent clusters but also an appreciable domain of overlap. Our findings indicate that abnormalities related to fixation-off sensitivity can emerge in thalamocortical networks, with larger and more anterior cortical distribution than those that generate alpha rhythm. Transition in the type of oscillation appears not only to depend on a change in cellular dynamics but also to be reflected in a different spatial distribution of the underlying neuronal networks.