Gerold Baier

Maximum hyperchaos in generalized Hénon maps

Abstract An N -dimensional diffeomorphism containing a single quadratic term is presented which generalizes the Henon map. It generates chaos with N - 1 directions of stretching and folding.

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model.

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Self-organised transients in a neural mass model of epileptogenic tissue dynamics

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy.

Event-based sonification of EEG rhythms in real time

OBJECTIVE To introduce a sound synthesis tool for human EEG rhythms that is applicable in real time. METHODS We design an event-based sonification which suppresses irregular background and highlights normal and pathologic rhythmic activity. RESULTS We generated sound examples with rhythms from well-known epileptic disorders and find stereotyped rhythmic auditory objects in single channel and stereo display from generalized spike-wave runs. For interictal activity, we were able to separate focal rhythms from background activity and thus enable the listener to perceive its frequency, duration, and intensity while monitoring. CONCLUSIONS The proposed event-based sonification allows quick detection and identification of different types of rhythmic EEE events in real time and can thus be used to complement visual displays in monitoring and EEG feedback tasks. SIGNIFICANCE The significance of the work lies in the fact that it can be implemented for on-line monitoring of clinical EEG and for EEG feedback applications where continuous screen watching can be substituted or improved by the auditory information stream.

The cycling hair follicle as an ideal systems biology research model

Please cite this paper as: The cycling hair follicle as an ideal systems biology research model. Experimental Dermatology 2010; 19: 707–713.

A spatially extended model for macroscopic spike-wave discharges

Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model.

A Computational Study of Stimulus Driven Epileptic Seizure Abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

The importance of modeling epileptic seizure dynamics as spatio-temporal patterns

The occurrence of seizures is the common feature across the spectrum of epileptic disorders. We describe how the use of mechanistic neural population models leads to novel insight into the dynamic mechanisms underlying two important types of epileptic seizures. We specifically stress the need for a spatio-temporal description of the rhythms to deal with the complexity of the pathophenotype. Adapted to functional and structural patient data, the macroscopic models may allow a patient-specific description of seizures and prediction of treatment outcome.

A meeting of two chronobiological systems: Circadian proteins period1 and bmal1 modulate the human hair cycle clock

The hair follicle (HF) is a continuously remodeled mini organ that cycles between growth (anagen), regression (catagen), and relative quiescence (telogen). As the anagen-to-catagen transformation of microdissected human scalp HFs can be observed in organ culture, it permits the study of the unknown controls of autonomous, rhythmic tissue remodeling of the HF, which intersects developmental, chronobiological, and growth-regulatory mechanisms. The hypothesis that the peripheral clock system is involved in hair cycle control, i.e., the anagen-to-catagen transformation, was tested. Here we show that in the absence of central clock influences, isolated, organ-cultured human HFs show circadian changes in the gene and protein expression of core clock genes (CLOCK, BMAL1, and Period1) and clock-controlled genes (c-Myc, NR1D1, and CDKN1A), with Period1 expression being hair cycle dependent. Knockdown of either BMAL1 or Period1 in human anagen HFs significantly prolonged anagen. This provides evidence that peripheral core clock genes modulate human HF cycling and are an integral component of the human hair cycle clock. Specifically, our study identifies BMAL1 and Period1 as potential therapeutic targets for modulating human hair growth.

Towards a large-scale model of patient-specific epileptic spike-wave discharges

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.