Brain Activity in Spherical Topology via Neural Field Theory

Abstract

Neural activity is responsible for information processing in the brain. Activity has been found to have natural spatial modes, each of which has a frequency, analogous to the pitch of the notes of a musical instrument. A core aim of this thesis is to analyze large scale brain activity in terms of the eigenmodes of a brain hemisphere and to explore eigenmode dynamics. Electroencephalography (EEG) and evoked response potentials (ERPs) are important measurement techniques used to observe large scale changes in brain activity. EEG is a recording technique, while ERPs are transient electrical responses to brief sensory stimuli. In this thesis analysis of EEG and ERPs is carried out in terms of eigenmodes using an established physiologically based neural field theory, which averages over attribute of neurons to yield a continuum model of brain activity whose parameters are based on the physiology. To explore the effects of boundary conditions and topology, a spherical approximation is used and compared with prior work on planar geometry; we also analyze ERP numerically in the convoluted cortex to find how brain activity is affected by folding. Chapter 1 provides an overview of the background and structure of the thesis, covering basic anatomy of the brain, neuron structure and dynamics, measurements of brain activity, EEG, ERP, eigenmode decomposition of brain activity, and large scale brain modeling using neural field theory. Chapter 2 applies an established corticothalamic neural field theory to spherical geometry to understands how geometry affects measures of the brain activity such as the power spectrum, coherence, and correlation using spherical harmonics. Equations for modal dynamics, spectra, correlations, and coherence are found from this model. These equations explain how modal dynamics and corticothalamic resonance depend on the geometry and affect experimental observations. The main findings include an exploration of the spherical modal structure, understanding of the number of modes that contribute significantly to brain activity, and analysis of the effects of the finite spatial extent of the cortex. It is stressed that only a few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. In Chapter 3 we analyze ERPs analytically and numerically using spherical geometry via neural field theory. In this work we also compare results in planar geometry and spherical geometry. It is found that the ERP peak is slightly delayed at large angles from the stimulus point due to the axonal conduction delays, which cause increasing delays as distance increases from ϑ=0, and it is corresponding to group velocities of 6 - 10 ms-1. During propagation spreading and damping reduce the amplitude. Corticothalamic modal effects are explored and, as in Chap. 2, it is found that a handful modes are responsible for explaining the basic features of the ERPs.