Treatment effects in epilepsy: a mathematical framework for understanding response over time.

Epilepsy is a neurological disorder characterized by recurrent seizures, affecting over 65 million people worldwide. Treatment typically commences with the use of anti-seizure medications, including both mono- and poly-therapy. Should these fail, more invasive therapies such as surgery, electrical stimulation and focal drug delivery are often considered in an attempt to render the person seizure free. Although a significant portion ultimately benefit from these treatment options, treatment responses often fluctuate over time. The physiological mechanisms underlying these temporal variations are poorly understood, making prognosis a significant challenge when treating epilepsy. Here we use a dynamic network model of seizure transition to understand how seizure propensity may vary over time as a consequence of changes in excitability. Through computer simulations, we explore the relationship between the impact of treatment on dynamic network properties and their vulnerability over time that permit a return to states of high seizure propensity. For small networks we show vulnerability can be fully characterised by the size of the first transitive component (FTC). For larger networks, we find measures of network efficiency, incoherence and heterogeneity (degree variance) correlate with robustness of networks to increasing excitability. These results provide a set of potential prognostic markers for therapeutic interventions in epilepsy. Such markers could be used to support the development of personalized treatment strategies, ultimately contributing to understanding of long-term seizure freedom.

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.

Epilepsy surgery: Evaluating robustness using dynamic network models.

Epilepsy is one of the most common neurological conditions affecting over 65 million people worldwide. Over one third of people with epilepsy are considered refractory: they do not respond to drug treatments. For this significant cohort of people, surgery is a potentially transformative treatment. However, only a small minority of people with refractory epilepsy are considered suitable for surgery, and long-term seizure freedom is only achieved in half the cases. Recently, several computational approaches have been proposed to support presurgical planning. Typically, these approaches use a dynamic network model to explore the potential impact of surgical resection in silico. The network component of the model is informed by clinical imaging data and is considered static thereafter. This assumption critically overlooks the plasticity of the brain and, therefore, how continued evolution of the brain network post-surgery may impact upon the success of a resection in the longer term. In this work, we use a simplified dynamic network model, which describes transitions to seizures, to systematically explore how the network structure influences seizure propensity, both before and after virtual resections. We illustrate key results in small networks, before extending our findings to larger networks. We demonstrate how the evolution of brain networks post resection can result in a return to increased seizure propensity. Our results effectively determine the robustness of a given resection to possible network reconfigurations and so provide a potential strategy for optimizing long-term seizure freedom.

Chytrid fungi distribution and co-occurrence with diatoms correlate with sea ice melt in the Arctic Ocean.

Global warming is rapidly altering physicochemical attributes of Arctic waters. These changes are predicted to alter microbial networks, potentially perturbing wider community functions including parasite infections and saprotrophic recycling of biogeochemical compounds. Specifically, the interaction between autotrophic phytoplankton and heterotrophic fungi e.g. chytrids (fungi with swimming tails) requires further analysis. Here, we investigate the diversity and distribution patterns of fungi in relation to abiotic variables during one record sea ice minimum in 2012 and explore co-occurrence of chytrids with diatoms, key primary producers in these changing environments. We show that chytrid fungi are primarily encountered at sites influenced by sea ice melt. Furthermore, chytrid representation positively correlates with sea ice-associated diatoms such as Fragilariopsis or Nitzschia. Our findings identify a potential future scenario where chytrid representation within these communities increases as a consequence of ice retreat, further altering community structure through perturbation of parasitic or saprotrophic interaction networks.

The Role of Excitability and Network Structure in the Emergence of Focal and Generalized Seizures.

Epileptic seizures are generally classified as either focal or generalized. It had been traditionally assumed that focal seizures imply localized brain abnormalities, whereas generalized seizures involve widespread brain pathologies. However, recent evidence suggests that large-scale brain networks are involved in the generation of focal seizures, and generalized seizures can originate in localized brain regions. Herein we study how network structure and tissue heterogeneities underpin the emergence of focal and widespread seizure dynamics. Mathematical modeling of seizure emergence in brain networks enables the clarification of the characteristics responsible for focal and generalized seizures. We consider neural mass network dynamics of seizure generation in exemplar synthetic networks and we measure the variance in ictogenicity across the network. Ictogenicity is defined as the involvement of network nodes in seizure activity, and its variance is used to quantify whether seizure patterns are focal or widespread across the network. We address both the influence of network structure and different excitability distributions across the network on the ictogenic variance. We find that this variance depends on both network structure and excitability distribution. High variance, i.e., localized seizure activity, is observed in networks highly heterogeneous with regard to the distribution of connections or excitabilities. However, networks that are both heterogeneous in their structure and excitability can underlie the emergence of generalized seizures, depending on the interplay between structure and excitability. Thus, our results imply that the emergence of focal and generalized seizures is underpinned by an interplay between network structure and excitability distribution.

Computational modelling in source space from scalp EEG to inform presurgical evaluation of epilepsy.

OBJECTIVE: The effectiveness of intracranial electroencephalography (iEEG) to inform epilepsy surgery depends on where iEEG electrodes are implanted. This decision is informed by noninvasive recording modalities such as scalp EEG. Herein we propose a framework to interrogate scalp EEG and determine epilepsy lateralization to aid in electrode implantation. METHODS: We use eLORETA to map source activities from seizure epochs recorded from scalp EEG and consider 15 regions of interest (ROIs). Functional networks are then constructed using the phase-locking value and studied using a mathematical model. By removing different ROIs from the network and simulating their impact on the network's ability to generate seizures in silico, the framework provides predictions of epilepsy lateralization. We consider 15 individuals from the EPILEPSIAE database and study a total of 62 seizures. Results were assessed by taking into account actual intracranial implantations and surgical outcome. RESULTS: The framework provided potentially useful information regarding epilepsy lateralization in 12 out of the 15 individuals (p=0.02, binomial test). CONCLUSIONS: Our results show promise for the use of this framework to better interrogate scalp EEG to determine epilepsy lateralization. SIGNIFICANCE: The framework may aid clinicians in the decision process to define where to implant electrodes for intracranial monitoring.

The role that choice of model plays in predictions for epilepsy surgery.

Mathematical modelling has been widely used to predict the effects of perturbations to brain networks. An important example is epilepsy surgery, where the perturbation in question is the removal of brain tissue in order to render the patient free of seizures. Different dynamical models have been proposed to represent transitions to ictal states in this context. However, our choice of which mathematical model to use to address this question relies on making assumptions regarding the mechanism that defines the transition from background to the seizure state. Since these mechanisms are unknown, it is important to understand how predictions from alternative dynamical descriptions compare. Herein we evaluate to what extent three different dynamical models provide consistent predictions for the effect of removing nodes from networks. We show that for small, directed, connected networks the three considered models provide consistent predictions. For larger networks, predictions are shown to be less consistent. However consistency is higher in networks that have sufficiently large differences in ictogenicity between nodes. We further demonstrate that heterogeneity in ictogenicity across nodes correlates with variability in the number of connections for each node.