Quantifying uncertainty in perturbed brain networks: towards a decision support tool for epilepsy surgery

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Many natural and man-made systems can be described in terms of networks, in which a set of nodes is connected by edges to make a network structure. Examples include communication or transport networks, as well as networks in biological systems. Often, in real world applications, the nodes of these networks behave dynamically: their properties change over time. Understanding the ways in which network structure can lead to different dynamic behaviors is a fundamental unsolved problem in applied nonlinear dynamics. We also lack fundamental understanding of the ways in which perturbations to networks, for example the removal of particular nodes, leads to changes in network dynamics. Previous investigations into these problems have often focused on particular kinds of network behavior, such as the synchronisation of oscillations or more complex dynamics. However it is important to extend these studies to include dynamics that undergo sporadic switching between qualitatively different states. Such systems underpin the concept of "dynamic diseases" and therefore studies of perturbations to networks with these dynamics falls naturally into the EPSRC Healthcare Technologies theme. A pertinent example is epilepsy; a prevalent neurological disorder in which nodes in networks of the brain sporadically produce abnormal activity, causing a person to suffer a seizure. We can consider that the dynamics of brain networks in the epileptic brain undergo "state-switching" from periods of healthy functioning to periods in which abnormal activity in seizures occur. There is much we do not know about why seizures occur in networks, and in particular, we often do not know how to treat a particular person's epilepsy, so that seizures no longer occur. One of the least understood forms of treatment is surgery, in which nodes of brain networks are removed, with the hope that this will stop the occurrence of seizures. In order to better understand seizures and how surgery may abate them, I will study mathematical models of brain networks that can generate seizure-like state-switching dynamics. In these models, surgery can be simulated by removing nodes from the network and quantifying to what extent state-switching is reduced. In order to do this, I need to develop ways to choose, for a given network, which nodes should be removed in order to most effectively reduce the ability to switch from one state to another. In large networks, it soon becomes intractable to test the effect that the removal of every possible set of nodes has on its dynamics. I will therefore develop computational approaches to efficiently estimate the set of nodes that should be removed in order to limit the ability of a network to switch between states. Another critical problem is that there are many different mathematical models that can be used to generate state-switching dynamics, and these may yield different predictions for which nodes should be removed. In order to quantify this uncertainty in predictions, I will use the computational methods I develop to calculate predictions under different choices of models, and quantify to what extent predictions depend on the choice of model. To test the applicability of the developed methods and understanding to the real world clinical problem, I will apply my methods to a set of data derived from patients who have undergone epilepsy surgery. I will derive network representations of each persons brain from this data and then use my mathematical tools to predict which nodes should have been removed in order to render them seizure free. These predictions can be tested since we know which nodes were actually removed in the patients' surgery, and whether the removal of those nodes resulted in seizure freedom.