| The basal ganglia (BG) are a system of reentrant loops that process and shape information from throughout the neocortex as well as extracortical structures. The BG are uniquely positioned to regulate information flow among multiple brain structures. Due to the recurrent parallel loops that innervate the BG, it has been notoriously difficult to track behaviorally relevant information in this system. To elucidate the functional significance of the BG in generating behavioral output I adopt a multidisciplinary approach drawing upon techniques from connectivity analysis and mathematical modeling.;In chapters 2 and 3 I analyze local field potentials (LFPs) recorded in the primary motor cortex (M1) and dorsal striatum (dStr) of behaving and anesthetized rats. M1 heavily innervates dStr and is reciprocally influenced by the striatal systems it drives. In chapter 2, I address the issue of directed influence using Granger Causality (GC), a causality metric based on autoregressive modeling. In chapter 3, I further explore the dynamic connectivity between M1 and dStr using cross-frequency coupling (CFC). CFC occurs when a system exhibits entrainment between two or more orthogonal frequency bands. There are multiple types of entrainment a signal might exhibit such as amplitude to amplitude coupling or phase to amplitude coupling. The later is ubiquitous in neural systems and has been observed in data gathered both from animals and humans. For example, suppose that the amplitude of a signal's gamma component is maximized when the theta component is at one of its minima. In this case, we say that there exists phase to amplitude CFC with the gamma component entrained to the theta component.;In chapter 4, I develop a mathematical model that provides a novel framework in which to interpret experimental results. I model the BG using a nonlinear oscillator with different terms corresponding to the direct and indirect pathways. The oscillator is coupled to its own forcing function to model the reentrant dynamics of the BG. The key features of this model are 1) an inverting rather than strictly inhibitory gain arising from activity in the indirect pathway 2) explicit dependence of the direct and indirect pathways on one another given recent evidence suggesting that there is axonal collateralization from the same striatal neurons to nuclei of both pathways, 3) the direct pathway, when active, greatly increases the rate of change of the oscillator reflecting the fact that information routed through the direct pathway exerts a more rapid influence on cortical sites than information routed through the indirect pathway.;I discuss these results, their implications for neural systems, and the limitations of the analyses presented here. I describe possible avenues of research to build upon and clarify our results. The reciprocal dynamics of the BG and similar systems have interesting implications for problems in cognitive science and philosophy of mind. In particular, the results of this project dovetail with previous work on Godel's first incompleteness theorem and its relevance to the study of minds as physical systems. The relevance of Godel's theorem to the physical basis of cognition is not universally accepted among cognitive scientists. The BG and similar system exhibit the properties of what Hofstadter calls a "strange loop". Our results, and those of others, provide first steps towards a mechanistic account of how the brain might physically instantiate a strange loop through the BG and other closed neural circuits. |
