An innovative mathematical architecture for modelling neuronal electrical activity is presented, called the cognitive rhythm generator (CRG), wherein the proposed architecture is a hybrid model comprised of three interconnected stages, namely: (1) a bank of neuronal modes; (2) a ring device (limit-cycle oscillator); and (3) a static output nonlinearity (mapper). Coupled CRG networks are employed to emulate and elucidate the dynamics of biological neural networks, including the recurrent networks in the hippocampus. Several species of ring devices are described and investigated, including the clock, labile clock, hourglass and multistable ring systems, and their applications to neuronal modelling explored. Complexity measures such as the maximum Lyapunov exponent, correlation dimension and detrended fluctuation analysis are applied to compare model and biological records and validate the CRG methodology. The basis of neural coding is also examined in mathematical detail, with particular regard to its description by Volterra-Wiener kernel formalism, from which the neuronal modes are derived. Applications to theta-gamma coding are discussed. Further on in the thesis, a CRG epileptiform network model of spontaneous seizure-like events (SLEs) is developed and used as a platform to test neuromodulation approaches for seizure abatement. (Neuromodulation mentioned here refers to methods involving electrical stimulation of neural tissue for therapeutic benefit). Spontaneous SLE transitions in the epileptiform network are shown to be related to the mechanism of intermittency, as determined by examining the state space dynamics of the model. The onset of SLEs is associated with increased network excitability and decreased stability, consistent with experimental results from the low-magnesium/high-potassium in vitro model of epilepsy. Lastly, a novel strategy for therapeutic neuromodulation is presented wherein a coupled CRG network (called the “therapeutic network”) is interfaced with the epileptiform network model, forming a closed loop for responsive, biomimetic neuromodulation of the epileptiform network. Relevance to clinical applications and future work is discussed.

An innovative mathematical architecture for modelling neuronal electrical activity is presented, called the cognitive rhythm generator (CRG), wherein the proposed architecture is a hybrid model comprised of three interconnected stages, namely: (1) a bank of neuronal modes; (2) a ring device (limit-cycle oscillator); and (3) a static output nonlinearity (mapper). Coupled CRG networks are employed to emulate and elucidate the dynamics of biological neural networks, including the recurrent networks in the hippocampus. Several species of ring devices are described and investigated, including the clock, labile clock, hourglass and multistable ring systems, and their applications to neuronal modelling explored. Complexity measures such as the maximum Lyapunov exponent, correlation dimension and detrended fluctuation analysis are applied to compare model and biological records and validate the CRG methodology. The basis of neural coding is also examined in mathematical detail, with particular regard to its description by Volterra-Wiener kernel formalism, from which the neuronal modes are derived. Applications to theta-gamma coding are discussed. Further on in the thesis, a CRG epileptiform network model of spontaneous seizure-like events (SLEs) is developed and used as a platform to test neuromodulation approaches for seizure abatement. (Neuromodulation mentioned here refers to methods involving electrical stimulation of neural tissue for therapeutic benefit). Spontaneous SLE transitions in the epileptiform network are shown to be related to the mechanism of intermittency, as determined by examining the state space dynamics of the model. The onset of SLEs is associated with increased network excitability and decreased stability, consistent with experimental results from the low-magnesium/high-potassium in vitro model of epilepsy. Lastly, a novel strategy for therapeutic neuromodulation is presented wherein a coupled CRG network (called the “therapeutic network”) is interfaced with the epileptiform network model, forming a closed loop for responsive, biomimetic neuromodulation of the epileptiform network. Relevance to clinical applications and future work is discussed.

Eine wichtige Folge des Status epilepticus ist die Entwicklung einer chronischen Epilepsie. Die genauen Mechanismen und die Kinetik der Epileptogenese sind weitestgehend unklar. Ziel der vorliegenden Arbeit war ein besseres Verständnis des Prozesses durch die In-vitro-Analyse von Lokalisation und Kinetik funktioneller Folgen des Status epilepticus in vivo. In kombinierten Hippokampus-entorhinaler Kortex Hirnschnittpräparaten von Wistar-Ratten nach elektrisch induziertem selbsterhaltendem Status epilepticus (self-sustaining status epilepticus, SSSE) wurden im Niedrig-Magnesium-Modell anfallsartige Ereignisse (AE) ausgelöst und untersucht. Die In-vitro-Analyse der AE wurde eine, vier und acht Wochen nach SSSE durchgeführt. Um das räumliche Verhalten der epileptischen Aktivität beurteilen zu können, wurde die Messung des extrazellulären Feldpotenzials mit der Analyse intrinsischer optischer Signale kombiniert. Im Verlauf nach SSSE kam es zu einer Latenzverkürzung bis zum Auftreten epileptischer Aktivität und zu einer Zunahme der AE-Frequenz. Vier und acht Wochen nach SSSE stieg der Anteil der AE mit großflächigem Ursprung signifikant an. Im Verlauf nach SSSE wurden außerdem zunehmend diskontinuierliche Ausbreitungsmuster der Anfallsaktivität beobachtet. Acht Wochen nach SSSE zeigten 50% der Präparate zudem eine zeitlich und räumlich von den AE unabhängige, hochfrequente Aktivität im Gyrus dentatus. Zusammenfassend wurden eine Latenzverkürzung und eine Zunahme der AE-Frequenz als Hinweise für eine gesteigerte Exzitabilität des Hirngewebes nach SSSE gesehen. Neben dem großflächigen Ursprung deutet auch die Zunahme diskontinuierlicher Ausbreitungsmuster auf eine gesteigerte Synchronizität des neuronalen Netzwerkes nach SSSE hin. Die autonome Aktivität im Gyrus dentatus spricht dafür, dass die in vorangegangenen Studien beschriebenen strukturellen Änderungen in dieser Region mit einer veränderten Funktionalität einhergehen. / The development of chronic epilepsy is a serious consequence of Status epilepticus. Little is known about the mechanisms and kinetic of the epileptogenic process. The aim of this md-thesis was the analysis of localisation and kinetic of functional deficits in vitro after Status epilepticus in vivo. Using the Low-Magnesium-Model, seizure-like events (SLE) were induced in combined hippocampal-entorhinal cortex slices of wistar rats after electrically induced self-sustaining Status epilepticus (SSSE). One, four and eight weeks after SSSE the in-vitro-analysis of SLE was performed. In order to determine onset and spread-pattern of epileptic activity, the measurement of the extracellular field-potential was combined with the imaging of intrinsic optical signals (IOS). In the time course after SSSE there was a reduction of the latency to onset of seizure activity and an increase of the SLE-frequency. Four and eight weeks after SSSE a significant increase of SLE with regional onset was found. In Addition, there was an increase of non-contiguous propagation of seizure activity. Eight weeks after SSSE 50% of the brain-slices showed autonomous high-frequent activity in the dentate gyrus. In conclusion a reduction of the latency to onset of seizure activity and an increase of the SLE-frequency were found. These changes are indicators of increased excitability after SSSE. Other than the regional onset, the non-contiguous spread-pattern also indicates increased synchronicity of the neuronal network after SSSE. The autonomous activity in the dentate Gyrus shows, that the previously described structural changes in this region lead to functional deficits.