Emergent Phenomena From Dynamic Network Models: Mathematical Analysis of EEG From People With IGE

In this thesis mathematical techniques and models are applied to electroencephalographic (EEG) recordings to study mechanisms of idiopathic generalised epilepsy (IGE). First, we compare network structures derived from resting-state EEG from people with IGE, their unaffected relatives, and healthy controls. Next, these static networks are combined with a dynamical model describing the ac- tivity of a cortical region as a population of phase-oscillators. We then examine the potential of the differences found in the static networks and the emergent properties of the dynamic network as individual biomarkers of IGE. The emphasis of this approach is on discerning the potential of these markers at the level of an indi- vidual subject rather than their ability to identify differences at a group level. Finally, we extend a dynamic model of seizure onset to investigate how epileptiform discharges vary over the course of the day in ambulatory EEG recordings from people with IGE. By per- turbing the dynamics describing the excitability of the system, we demonstrate the model can reproduce discharge distributions on an individual level which are shown to express a circadian tone. The emphasis of the model approach is on understanding how changes in excitability within brain regions, modulated by sleep, metabolism, endocrine axes, or anti-epileptic drugs (AEDs), can drive the emer- gence of epileptiform activity in large-scale brain networks. Our results demonstrate that studying EEG recordings from peo- ple with IGE can lead to new mechanistic insight on the idiopathic nature of IGE, and may eventually lead to clinical applications. We show that biomarkers derived from dynamic network models perform significantly better as classifiers than biomarkers based on static network properties. Hence, our results provide additional ev- idence that the interplay between the dynamics of specific brain re- gions, and the network topology governing the interactions between these regions, is crucial in the generation of emergent epileptiform activity. Pathological activity may emerge due to abnormalities in either of those factors, or a combination of both, and hence it is essential to develop new techniques to characterise this interplay theoretically and to validate predictions experimentally

Neural Field Models: A mathematical overview and unifying framework

Rhythmic electrical activity in the brain emerges from regular non-trivial interactions between millions of neurons. Neurons are intricate cellular structures that transmit excitatory (or inhibitory) signals to other neurons, often non-locally, depending on the graded input from other neurons. Often this requires extensive detail to model mathematically, which poses several issues in modelling large systems beyond clusters of neurons, such as the whole brain. Approaching large populations of neurons with interconnected constituent single-neuron models results in an accumulation of exponentially many complexities, rendering a realistic simulation that does not permit mathematical tractability and obfuscates the primary interactions required for emergent electrodynamical patterns in brain rhythms. A statistical mechanics approach with non-local interactions may circumvent these issues while maintaining mathematically tractability. Neural field theory is a population-level approach to modelling large sections of neural tissue based on these principles. Herein we provide a review of key stages of the history and development of neural field theory and contemporary uses of this branch of mathematical neuroscience. We elucidate a mathematical framework in which neural field models can be derived, highlighting the many significant inherited assumptions that exist in the current literature, so that their validity may be considered in light of further developments in both mathematical and experimental neuroscience.Comment: 55 pages, 10 figures, 2 table

Classification of human chronotype based on fMRI network-based statistics

Chronotype—the relationship between the internal circadian physiology of an individual and the external 24-h light-dark cycle—is increasingly implicated in mental health and cognition. Individuals presenting with a late chronotype have an increased likelihood of developing depression, and can display reduced cognitive performance during the societal 9–5 day. However, the interplay between physiological rhythms and the brain networks that underpin cognition and mental health is not well-understood. To address this issue, we use rs-fMRI collected from 16 people with an early chronotype and 22 people with a late chronotype over three scanning sessions. We develop a classification framework utilizing the Network Based-Statistic methodology, to understand if differentiable information about chronotype is embedded in functional brain networks and how this changes throughout the day. We find evidence of subnetworks throughout the day that differ between extreme chronotypes such that high accuracy can occur, describe rigorous threshold criteria for achieving 97.3% accuracy in the Evening and investigate how the same conditions hinder accuracy for other scanning sessions. Revealing differences in functional brain networks based on extreme chronotype suggests future avenues of research that may ultimately better characterize the relationship between internal physiology, external perturbations, brain networks, and disease

Revealing a brain network endophenotype in families with idiopathic generalised epilepsy

Idiopathic generalised epilepsy (IGE) has a genetic basis. The mechanism of seizure expression is not fully known, but is assumed to involve large-scale brain networks. We hypothesised that abnormal brain network properties would be detected using EEG in patients with IGE, and would be manifest as a familial endophenotype in their unaffected first-degree relatives. We studied 117 participants: 35 patients with IGE, 42 unaffected first-degree relatives, and 40 normal controls, using scalp EEG. Graph theory was used to describe brain network topology in five frequency bands for each subject. Frequency bands were chosen based on a published Spectral Factor Analysis study which demonstrated these bands to be optimally robust and independent. Groups were compared, using Bonferroni correction to account for nonindependent measures and multiple groups. Degree distribution variance was greater in patients and relatives than controls in the 6-9 Hz band (p = 0.0005, p = 0.0009 respectively). Mean degree was greater in patients than healthy controls in the 6-9 Hz band (p = 0.0064). Clustering coefficient was higher in patients and relatives than controls in the 6-9 Hz band (p = 0.0025, p = 0.0013). Characteristic path length did not differ between groups. No differences were found between patients and unaffected relatives. These findings suggest brain network topology differs between patients with IGE and normal controls, and that some of these network measures show similar deviations in patients and in unaffected relatives who do not have epilepsy. This suggests brain network topology may be an inherited endophenotype of IGE, present in unaffected relatives who do not have epilepsy, as well as in affected patients. We propose that abnormal brain network topology may be an endophenotype of IGE, though not in itself sufficient to cause epilepsy

Multilevel Computational Modelling in Epilepsy: Classical Studies and Recent Advances

Springer Series in Computational NeuroscienceIn this chapter we present a review of computational models for study- ing the dynamic mechanisms that describe the function of the human brain, with a specific focus on epilepsy. Epilepsy is a neurological disorder characterised by an in- creased likelihood of recurrent seizures, which in turn are characterised by transient, pathological episodes of hypersynchronised neural activity resulting in a variety of behavioural symptoms. Our chapter introduces some of the key concepts of epilepsy from a clinical perspective, before describing some of the classical approaches to modelling brain activity across multiple levels of description. We then focus on how these models have been used to explain and predict experimental and clinical phe- nomena within the field of epilepsy research. Here we focus on techniques that seek to integrate computational modelling with experimental and clinical measures, as we believe this “systems approach” to epilepsy research is from where the most significant new advances, particularly with regards model validation, will occur. We highlight some of the key studies, as well as emphasising more recent breakthroughs to provide a useful entry point into this rapidly expanding field of research.Medical Research CouncilEpilepsy Research U