Abstract

Computational modeling studies and explains neuronal behaviors by modeling their underlying dynamics. Specifically, Neural Mass Model (NMM) is a part of computational modeling that refers to populations (masses) of neurons inside the brain. NMMs have a variety of applications, e.g., characterization of the neurobiological process and artificial brain. NMMs are well investigated, and the available NMMs in the literature proposed two populations of neurons in communication with each other, namely, the population of pyramidal cells and the population of intra-neurons. Recent advanced technologies that facilitate spatiotemporal resolution neuroimaging data have contributed to develop more realistic NMMs. NMM's underlying behavioral dynamics must be appropriately analyzed to understand the brain's functional and structural relationship. In this thesis, first, we develop a novel method capable of detecting the model's underlying behavioral dynamics over high dimensional parameter space. This novel idea attempts to overcome the disadvantages of the bifurcation analysis over high-dimensional space. Moreover, physiologically interesting and non-interesting dynamics are localized over high-dimensional parameter space using the proposed approach. In order to validate the presented algorithm, we use the accuracy and F1-score as our metric. Second, we develop a method that localizes epileptic changes of electroencephalogram (EEG) signal over time as an application of NMMs in the real EEG data. It is studied in the state of the art that the gradual changes over the EEG signals can be interpreted as instability over the parameters of the NMMs. Furthermore, the progressive evolution of EEG's activity in pathological cases (e.g., epileptic seizures) is supposed to be characterized by a transition of the dynamics of the NMMs. The proposed algorithm is capable of detecting transitions of dynamics over simulated multi-dynamical signals. In addition, this method is capable of detecting the dynamic results in the best fitting time series with respect to frequency.