The understanding of the origins of neurological disorders,such as Epilepsy, Alzheimer’s disease (AD), represents one of the most urgent and challenging areas of current scientific enquiry. In USA alone, $20\%$ of the general population fall into one of these categories, thus creating an enormous need for medical intervention. Neurological disorders lead to system-level deficits which can cause disruptions in structural connectivity, functional organization, and information processing across various brain regions. Characterizing these system-level deficits from neuronal dynamics perspective is crucial for developing targeted interventions aimed at restoring normal brain function. Fueled by the rapid advancement in neural recording technologies both at the single and population level, we develop a data driven framework to characterize the neuronal dynamics in neurological disorders that can advance our understanding, diagnosis, and treatment of neurological disorders, ultimately improving patient outcomes and quality of life.

In this thesis, we study one of the most prevalent and debilitating neurological disorders called Epilepsy: approximately 65 million people suffer from it globally. In patients with epilepsy, the normal signaling mechanism in the brain is disrupted by sudden and synchronized bursts of electrical pulses, leading to recurrent episodes of seizures. Epileptic seizures can be broadly classified into two types: generalized seizures which involve multiple cross-hemisphere epileptic foci and focal seizures where the epileptic focus is localized to a specific brain region. About one-third of patients with focal seizures, cannot be treated with anti-seizure medications and they need to undergo a resective surgery for the removal of Epileptogenic zone (EZ), which is the site of the cortex responsible for generating seizures. In the pre-surgical stage, the patient is placed under intracranial EEG (iEEG) monitoring in the hospital leading to iEEG recordings during actual seizures, referred to as ictal segments. Synchronous electrical signals recorded in the ictal segments have been modeled as network/collective dynamics involving all the channels leading to automated identifications of channels that drive the observed seizures. These channels are referred to as seizure onset zones (SOZs) as they constitute parts of the EZ active during observed seizures. Another correlate of this synchronous activity are short duration oscillatory field potential, known as High Frequency Oscillations (HFO), that are observed at the level of individual electrodes of iEEG. SOZ channels have distinctly higher rates of HFOs during the ictal segment, allowing neurologists to identify SOZs without any explicit network modeling. Once the SOZ has been identified then the surgeons resect the SOZ if possible. However, this approach has led to success in about only $60-70\%$ of the patients because there might be parts of EZ that did not participate in generating seizures during the limited observation window; such unobserved parts of EZ are known as potential seizure onset zones (PSOZs). The inability of SOZ to completely encapsulate EZ in many patients, along with the hardships and risks associated with lengthy hospitalization period -often lasting two weeks or more- has prompted the need to find accurate physiological biomarkers of EZ during the interictal period, i.e, the majority of the time when patients do not have seizures.

HFOs observed during ictal periods have also been observed to be present at higher rates in SOZ channels (determined from ictal periods) during interictal periods, leading to the hope that resection of channels with high interictal HFO rates would lead to seizure freedom. However, the presence of HFOs arising from cognitive processes (physiological HFOs) during interictal periods have diminished the predictive power of interictal HFO rate in the context of surgical outcome prediction. In the first part of the thesis, we develop a weakly supervised deep learning model to filter out the physiological HFOs and thus extract the pathological cluster of HFOs: epileptogenic HFOs (eHFO). In retrospective validation on a patient cohort of 15 patients, the eHFO cluster was found to be a better biomarker of EZ compared to Real HFO cluster (HFO cluster after filtering for artifacts) as it was able to correctly predict the post surgical outcomes of patients with an F1 score of $87\%$ in comparison to Real HFO cluster's $72\%$. However, when tested on a much larger patient cohort (159 patients), we found that a significant percentage of patients ($ \sim 25\%$) did not have enough HFO detections and as a result the eHFO resection ratio was not able to correctly predict the surgical outcomes of those patients. Therefore, there is a need to look beyond HFOs in the space of potential interictal biomarkers of EZ.

Recently, there is a growing interest in determining whether synchronization effects can be observed in the interictal period and their temporal dynamics can be leveraged to delineate EZ. The problem of studying such effects and using them for better surgical outcome prediction is still open and we address this in the second part of the thesis. In particular, we use Power-Phase coupling amongst channels to construct a sequence of directed weighted networks from interictal segments. We leverage the topological dynamics of the network, both local and global, to train a machine learning model to identify SOZ (ground truth obtained from ictal data) from purely interictal segments. The model identifies the SOZ with over $95\%$ accuracy. One of the hallmarks of the constructed networks is that they occasionally transition into a state of hyper-synchrony with SOZ and PSOZ nodes being the hub of these hyper-synchronous states. We hypothesize that these hyper-synchronous states are 'mini seizures' in the interictal phase and our machine learning model is able to identify them and use them for not only accurate SOZ identification but also identify PSOZ. The only way to validate whether our model has truly identified PSOZ and hence EZ is through surgical outcome prediction. In the third part of thesis, we construct a set of features from SOZ model prediction scores along with the constructed network flow dynamics to propose a network based biomarker of EZ. In retrospective validation on a patient cohort of 159 patients, the network based biomarker was able to correctly predict the post surgical outcomes of patients with an F1 score of $89\%$. Finally, we develop an integrated framework to exploit the interplay between the constructed network and pathological HFO cluster to propose a novel biomarker of EZ. At the heart of this framework is a regression model which predicts the pathological HFO rate using a mixture of local and global properties of the constructed network. The summary statistics of the $R^2$ of the regression model along with the previously computed features (SOZ model prediction scores and epileptic network flow dynamics) is proposed as a novel biomarker of EZ. In retrospective validation on a patient cohort of 159 patients, the novel biomarker was able to correctly predict the post surgical outcomes of patients with an F1 score of $98\%$. A closer inspection into the summary statistics of the regression model for non-seizure free patients reveals a cluster of pathological HFO whose rate cannot be explained by the constructed network thus revealing the presence of a brain region capable of generating seizures outside of the one sampled by iEEG.