Computational modelling of epileptic seizure dynamics and control

Epilepsy is a neurological condition affecting about 50 million people worldwide. It is a condition of the nervous system in which neuronal populations alternate between periods of normal ongoing electrical activity and periods of paroxysmal activity. Computational models provide a powerful framework both for simulating dynamics of neuronal networks involved in epileptic seizures and for testing new treatment options. The aims of this thesis are to better understand the mechanisms involved in the dynamics of epileptic seizures and to devise stimulation paradigms that may be applied to control epileptic seizures, both by studying and applying computational models. Computational models can be used as descriptive tools, where observed phenomena are captured in a model. In Chapter 2 of the thesis activity-dependent channels are introduced in a realistic neuronal model, eliciting both steady state and limit cycle behaviour. The effect on the distribution of ictal and inter-ictal length is shown. In Chapter 3 we use a model at another level of abstraction. A model of coupled oscillators-rotators shows a variety of different dynamic behaviour patterns. It is interesting that, although the system may change states, the total activity of the system does not necessarily change. A correspondence between the realistic model and the analytical model is studied in Chapter 4. We show that within the given parameter space and studying the system at the level of general system dynamics, we infer that the analytical model will behave in a similar fashion as the realistic neuronal model. Neuronal models can also be used as prescriptive tools. In Chapter 5 we propose a reactive control paradigm of epileptic seizures. A control module applies counter stimuli to abort seizures. It is shown that the proposed method is able to control the system, while delivering a minimum amount of energy to the system. It will be favourable to detect a seizure before it actually manifests itself and prevent it from initiating. In Chapter 6 we propose a method to apply stimulation when detecting a baseline shift before the seizure, caused by the decrease of inhibition. It is shown that when applying stimulation with a proper polarity and ratio between cell populations, the moment of the first seizure can be postponed. Observed physiological phenomena can be connected to each other based purely on clinical evidence, without understanding the dynamics of the underlying mechanism. Computational models can be used to provide insight into those unknown mechanisms. In Chapter 7, we aim to connect two phenomena, namely high frequency oscillations (HFOs) and epileptic seizures. We present a possible underlying mechanism that gives rise to both phenomena. This study shows that microscopic features, like gap-junction dynamics, may be connected to macroscopic phenomena like HFOs and seizures by across-scale computational models. In conclusion we have improved the insight into dynamic mechanisms underlying epilepsy, using computational models. In the course of the thesis, computational modelling moved from a descriptive tool capturing observed epileptic phenomena, via a predictive tool, proposing different stimulation paradigms, to a prospective tool, that may be able to explain and predict epileptic phenomena.