UC Berkeley

Epilepsy is a neural network disorder that manifests when certain elements (neuron types, sub-networks) malfunction or fail. Epileptiform activity, in turn, is characterized by the excessive synchronous firing of populations of neurons. In this dissertation, we present a mathematical model of the human cortex based on the activity of populations of neurons best captured at the meso-scale to study epileptic seizure dynamics. We then investigate further developments of the use of a spatially, temporally and cell type specific stimulation technique called optogenetics to trigger or to inhibit epileptiform activity in the cortical model.

Optogenetics involves the genetic modification of a host neuron to express light activated ion channels. To incorporate this method of stimulation into the meso-scale cortical model, we first develop a scale free mathematical model of optogenetic channel dynamics, which enables study of micro-scale level optogenetic activity at the meso-scale. We then integrate the optogenetic model into the meso-scale cortical model to study the combined dynamics of cortico-optogenetic activity in time and two spatial dimensions. Through this combined model, we explore the efficacy of optogenetic stimulation in an open loop configuration to inhibit epileptic seizures. Next, we close the loop using techniques of classical control theory, and investigate the controllability of seizures in two parameter spaces that correspond well with patient seizure data. By basing our control effort on measurements of cortical activity that are clinically relevant, we aim to provide a physiologically safe and efficient way of seizure inhibition. We also study the dynamics of the combined cortico-optogenetic model using bifurcation analysis. We then explore the use of optogenetic stimulation as an excitatory technique to drive seizure like activity in a normally functioning cortical model. All of this makes a strong case for the consideration of optogenetics as a highly specific cortical stimulation modality in seizure research.

Finally, we present preliminary results from work that describes the link between cortical metabolic demands and cortical activity. A quantitative definition of this link will aid in reconciling the different temporal scales of electrode measurements and imaging techniques like functional magnetic resonance imaging, while also providing a clearer picture of the role of glucose and oxygen metabolism in multiple states of cortical activity, such as normal sleep, awake, and seizure states.