Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To understand the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity.Comment: http://journal.frontiersin.org/article/10.3389/fncom.2017.00025/ful

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

Spatio-temporal modelling and analysis of epileptiform EEG

In this thesis we investigate the mechanisms underlying the generation of abnormal EEG rhythms in epilepsy, which is a crucial step towards better treatment of this disorder in the future. To this end, macroscopic scale mathematical models of the interactions between neuronal populations are examined. In particular, the role of interactions between neural masses that are spatially distributed in cortical networks are explored. In addition, two other important aspects of the modelling process are addressed, namely the conversion of macroscopic model variables into EEG output and the comparison of multivariate, spatio-temporal data. For the latter, we adopt a vectorisation of the correlation matrix of windowed data and subsequent comparison of data by vector distance measures. Our modelling studies indicate that excitatory connectivity between neural masses facilitates self-organised dynamics. In particular, we report for the first time the production of complex rhythmic transients and the generation of intermittent periods of 'abnormal' rhythmic activity in two different models of epileptogenic tissue. These models therefore provide novel accounts of the spontaneous, intermittent transition between normal and pathological rhythms in primarily generalised epilepsies and the evocation of complex, self-terminating, spatio-temporal dynamics by brief stimulation in focal epilepsies. Two key properties of these models are excitability at the macroscopic level and the presence of spatial heterogeneities. The identification of neural mass excitability as an important processes in spatially extended brain networks is a step towards uncovering the multi-scale nature of the pathological mechanisms of epilepsy. A direct consequence of this work is therefore that novel experimental investigations are proposed, which in itself is a validation of our modelling approach. In addition, new considerations regarding the nature of dynamical systems as applied to problems of transitions between rhythmic states are proposed and will prompt future investigations of complex transients in spatio-temporal excitable systems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The Nonlinear Dynamic Conversion of Analog Signals into Excitation Patterns

Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations in the model system. Using a set of tuned excitable systems, it is possible to characterize signals by their spectral composition of excitation pattern. As an example we analyze an epileptic spike-and-wave time series.Comment: 14 pages, 5 figure

Interpreting EEG by voice: Vocal EEG Sonification

Hermann T, Baier G. Interpreting EEG by voice: Vocal EEG Sonification. In: Rinnot M, ed. Proceedings of the 1st Sketching Sonic Interaction Design Workshop. Holon, Israel: COST IC0601 SID and HIT; 2009.Vocal EEG sonifications are presented as a method for complex time series sonification that is particularly tailored to address both humans' articulatory and auditory competences in order to improve the understanding and communication of the underlying data. In Vocal EEG sonification, the EEG data is represented in real-time by synthesized sound in a systematic, reproducible, task-centered way using an articulatory sound synthesizer capable of creating vowel transitions. Patterns such as 'EEG at rest', epileptic EEG, sleep EEG, etc. are thereby turned into characteristically different sonic gestalts that human listeners can discern from listening to the 'data babble'. In this paper, we emphasize the aspect of designing sonification particularly for the purpose of enhancing communication about sonic patterns, and we conduct a preliminary study about the human skill to use the own vocal tract to mimic or imitate patterns heard in the sonification. Our study will show to what degree humans are capable to recognize signal types correctly, both from the original sonifications and from vocal imitations performed by trained sonification users and naive users without extended previous experience in sonification

A systems biology approach to the human hair cycle

The hair cycle represents a dynamic process during which a complex mini- organ, the hair follicle, rhythmically regresses and regenerates. The control mechanism that governs the hair cycle ('hair cycle clock') is thought to be an autonomous oscillator system, however, its exact nature is not known. This thesis aims to understand the human hair cycle as a systems biology problem using theoretical and experimental techniques in three distinct study approaches. Using mathematical modelling, a simple two-compartment model of the human hair cycle was developed. The model concentrates on the growth control of matrix keratinocytes, a key cell population responsible for hair growth, and bi-directional communication between these cells and the inductive fibroblasts of the dermal papilla. A bistable switch and feedback inhibition produces key characteristics of human hair cycle dynamics. This study represents the first mathematically formulated theory of the 'hair cycle clock'.A second chronobiological approach was adopted to explore the molecular control of the human hair follicle by a peripheral clock mechanism. The hypothesis was tested that selected circadian clock genes regulate the human hair cycle, namely the clinically crucial follicle transformation from organ growth (anagen) to organ regression (catagen). This revealed that intra- follicular expression of core clock and clock-controlled genes display a circadian rhythm and is hair cycle-dependent. Knock-down of Period1 and Clock promotes anagen maintenance, hair matrix keratinocyte proliferation and stimulates hair follicle pigmentation. This provides the first evidence that peripheral Period1 and Clock gene activity is a component of the human 'hair cycle clock' mechanism. Lastly, an unbiased gene expression profiling approach was adopted to establish important genes and signalling pathways that regulate the human hair cycle. This revealed that similar genes and pathways previously shown to control the murine hair cycle in vivo, such as Sgk3, Msx2 and the BMP pathway, are also differentially regulated during the anagen-catagen transformation of human hair follicles. In summary, by using a three-pronged systems biology approach, the thesis has shed new light on the control of human hair follicle cycling and has generated clinically relevant information: a) The hair cycle model may predict how hair cycle modulatory agents alter human hair growth. b) Period1 and Clock are new therapeutic targets for human hair growth manipulation. c) Gene expression profiling points to additional key players in human hair cycle control with potential for future therapeutic targets.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Polyrhythmic Organization of Coupled Nonlinear Oscillators

Baier G, Hermann T, Müller M. Polyrhythmic Organization of Coupled Nonlinear Oscillators. In: School of Computing and Mathematical Sciences (Greenwich). Department of Information Systems and Multimedia, ed. IV' 05: Proceedings of the Ninth International Conference on Information Visualisation (IV'05). Los Alamitos, CA, USA: IEEE Computer Society; 2005: 5-10.We study the rhythmic organization of coupled nonlinear oscillators. If oscillators with non-identical internal frequency are coupled, they generate a great variety of periodic and chaotic rhythmic patterns. Sonification of these patterns suggests their characterization in terms of polyrhythms: each oscillatory unit subdivides "measures" of equal or varying length differently. For the case of two coupled oscillators, the organization of these polyrhythms is exemplified as a function of the internal frequency ratio and the coupling strength. Some sonification strategies are presented which aid to detect complex rhythmic relationships between oscillators. The results may be of importance for the analysis of complex multivariate time series like human EEG