چكيده به لاتين
Nowadays, with technological advancements and increasing computing power, the demand for using mathematical models to describe various biological and natural phenomena has increased significantly. Biological Sciences and neuroscience, in particular, have been overlapped with mathematical sciences and have created common grounds in recent decades. The use of mathematical models to describe the function of brain in normal and abnormal conditions have become widespread and many models have been developed for this purpose. In fact, the studies on the causes of formation and methods of controlling and treating some diseases or disorders of the nervous system, such as epilepsy and epileptic seizures, is not limited to laboratories at present, and many scholars from a variety of disciplines are involved in this research. So far, several models have been developed to identify patterns appearing in the brain signals of patients with epilepsy. One can imagine the brain as a dynamic system that has various dynamical behaviors with different characteristics. One of these dynamics can be epileptic seizures, and in fact, the occurrence of epileptic seizures can be attributed to a particular dynamic phenomenon, such as bifurcation or bistability. For this reason, this thesis attempts to study the dynamics of this subject by mathematical models and in particular, neural mass models.
In this thesis, in the initial chapters, physiology and anatomy of the brain, epileptic disease, types, roots, characteristics of each type, and ways of controlling or treating it are reviewed. In Chapter 4, different types of modeling are described and several important models are reviewed and evaluated. In chapter 5, various types of dynamic mechanisms to explaining of seizures occurrence are discussed. In chapter 6, two important neural mass models (Jansen-Rit model and Suffczynski model) are analyzed dynamically and the existence of the previously described dynamic mechanisms are evaluated and various dynamics that each model is capable of producing are examined. It will be shown that the Suffczynski model has a very rich dynamics, and many of the mechanisms can be explained by this model. Finally, in chapter 7, conclusions are made and suggestions for future work are presented.
This thesis has several innovations, including the suggestion of a new mechanism (nonlinear resonance) to describe epileptic seizures. Also, in the sixth chapter, a primary new model has been presented which describe epileptic seizures and the model’s output is similar with some types of epileptic signals.
