Inferring signaling structures in the brain via directed information [electronic resource]
Keywords: Electrical Engineering.

This thesis examines the information-theoretic tool of directed information as a mechanism to improve our understanding of the brain. As increasing amounts of neural data is experimentally obtained, there is a growing need to understand the underlying mechanisms in the brain that generate it. In our work we propose the tool of directed information to infer signaling structures in the brain. Specifically, we apply this tool to two important inference problems: inferring neuronal connections from spike trains, and inferring seizure foci from electrocorticograms. A spike train is a time series that represents the signal a neuron sends to neurons to which it is connected. Since we are looking at inferring neuronal connections, we need to choose a model for neuronal computation, trading off accuracy for simplicity. The leaky integrate-and-fire (LIF) model is a commonly used model that captures more realistic dynamics than simpler integrate-and-fire models, and is easier to analyze than compartmental models. The LIF model is an analog model that must be discretized to analyze the directed information. We derive a discrete model of the LIF to calculate the spike train dynamics of an LIF neuron. We then use these dynamics to calculate the directed information between two neurons, which can then be used to validate estimators of directed information. In general, if two neurons are connected, then by estimating the directed information we can determine that these neurons are connected. If two neurons are not connected, however, there are situations in which their directed information causes us to incorrectly infer that a connection exists between them, typically due to the influence of a third, unobserved neuron. We propose a method to mitigate such false inferences by leveraging information the neurobiologist may have about the propagation structure. We verify the effectiveness of this method to reduce false positives by compartmental model simulations in NEURON. The second type of inference problem covered in this thesis relates to the medical treatment of epilepsy patients. About a third of all people with epilepsy have seizures that cannot be controlled with medication, leading to a need for surgical intervention. A particular class of seizures are known as focal seizures, in which the seizures are initiated in a particular region of the brain, known as the seizure focus, by neurons that have highly correlated activity. This synchronous activity then causes increased synchronous activity in adjacent regions, and thereby continues to spread across the brain. The goal of the surgery in patients with focal seizures is to locate and remove the piece of brain containing the focus. This neural activity can be measured by placing electrodes on the brain, and recording a signal known as an electrocorticogram (ECoG). ECoG measures the aggregated spiking activity of thousands of nearby neurons, and thus signals recorded from these electrodes often appear random. However, when the patient experiences a seizure, correlations emerge across these electrodes, due to the spreading of the increased activity in the neurons contained in the focus. Based on this insight, we use directed information, a measure of directed correlation, to determine how this increased neural activity spreads out from the focus as measured in the electrodes. We then fit a maximum spanning tree on the graph of pairwise directed information to determine the location the focus of the seizure. To evaluate our technique, we apply it to ECoG data obtained for three human patients and show its accuracy in localizing the seizure foci.