General anesthesia (GA) is an important medical procedure that induces unconsciousness to patients during surgery. Consciousness is a salient feature of the brain, whose neurophysiological features are difficult to be distinguished from unconsciousness. Though it can be defined as an event arising due to interactions in the nervous system, it entirely is not a reliable mechanism. Thus, tracking changes in the brain waves caused by GA is a challenging problem in neuroscience. The exact mechanism to quantify the state of the brain and to distinguish between conscious and unconscious brain is still difficult. Specific features to characterize the state of the brain from the patterns of the brain signal is challenging. Present-day depth of anesthesia monitors index values does not quantify the state of the brain.

An alternative approach is to use dynamical systems theory to assess the underlying dynamics of the brain with imaging technology (e.g., electroencephalographic and electrocorticographic data). Previous results from the literature suggest that stability can play a role in the characterization of unconsciousness. This thesis proposes a detailed study that focus on dynamical systems properties that go beyond stability. In particular, the proposed methodology aims to assess which regions of the brain intervene in the process of consciousness and unconsciousness, as well as quantify how often they interact with each other. Specifically, the approach seeks to leverage the eigenstructure of the underlying approximation of the neural activity captured from intracranial electrocorticographic data.

Our results show that it is possible to differentiate between anesthetic stages of the brain using eigendecomposition. This was possible through a framework that provides a regularised way to sparsify the state estimates of electrocorticographic (ECoG) signal to get a model for analysis of changes in the brain waves affected by GA. Later to look at the eigenvalues and eigenvectors, which gives the frequency of oscillation and direction between different regions of the brain, respectively. It was also observed that the pattern in the evolution of eigenvalues during different anesthetic stages could be able to interpret if the subject was under anesthesia or not.