Modelling Transition From Normal To Epileptic Eeg Signals: A Neuron-Astrocyte Mass Action Approach

Abstract

Epileptic seizures occur intermittently as a result of complex dynamical interactions among many regions of the brain. The sudden and apparently unpredictable nature of refractory seizures is one of the most disabling aspects of the disease. Therefore, there is need for interdisciplinary research efforts directed at better understanding of the mechanisms involved in the emergence of epileptic seizures. Our research objective in this field is the use of applied methods from deterministic and nondeterministic dynamical systems modeling to study epilepsy. Dynamical systems refer to systems whose state variables evolve in time. By the assumption of deterministic system,the physiological system (the brain) can be treated as low dimensional without any random components. Nondeterministic assumption on the other hand allows randomness in some input components. We developed at the macroscopic level physiologically based mathematical models of parts of the brain believed to be eliciting the abnormal signals observed during Generalized Absence Epilepsy (GAE) and Temporal Lobe Epilepsy (TLE). In developing our models, we considered the activities of nerve cells, the surrounding astrocyte cells and the dynamics of extracellular neurotransmitters and conducted parameter sensitivity studies on our models. The models were then validated using Electroencephalogram (EEG) data of epileptic patients. The important conclusion from our findings is that the transition from normal to epileptic brain activity is critically dependent on small variations in few system parameters and/or the balance between a small number of system parameters, be it neural or astrocytes activity dependent.

Keywords

• dynamical systems
• temporal lobe epilepsy
• neuron-astrocyte mass action model