#### Date of Award

Summer 2011

#### Document Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Biomedical Engineering

#### First Advisor

Beardsley, Scott

#### Second Advisor

Scheidt, Robert A.

#### Third Advisor

Struble, Craig A.

#### Abstract

Recurrently connected neural networks, in which synaptic connections between neurons can form directed cycles, have been used extensively in the literature to describe various neurophysiological phenomena, such as coordinate transformations during sensorimotor integration. Due to the directed cycles that can exist in recurrent networks, there is no well-known way to a priori specify synaptic weights to elicit neuron spiking responses to stimuli based on available neurophysiology. Using a common mean field assumption, that synaptic inputs are uncorrelated for sufficiently large populations of neurons, we show that the connection topology and a neuron's response characteristics can be decoupled. This assumption allows specification of neuron steady-state responses independent of the connection topology.

Specification of neuron responses necessitates the creation of a novel simulator (computational framework) which allows modeling of large populations of connected spiking neurons. We describe the implementation of a spike-based computational framework, designed to take advantage of high performance computing architectures when available. We show that performance of the computational framework is improved using multiple message passing processes for large populations of neurons, resulting in a worst-case linear relationship between the number of neurons and the time required to complete a simulation.

Using the computational framework and the ability to specify neuron response characteristics independent of synaptic weights, we systematically investigate the effects of Hebbian learning on the hemodynamic response. Changes in the magnitude of the hemodynamic responses of neural populations are assessed using a forward model that relates population synaptic currents to the blood oxygen dependant (BOLD) response via local field potentials. We show that the magnitude of the hemodynamic response is not a accurate indicator of underlying spiking activity for all network topologies. Instead, we note that large changes in the aggregate response of the population (>50%) can results in a decrease in the overall magnitude of the BOLD signal. We hypothesize that the hemodynamic response magnitude changed due to fluctuations in the balance of excitatory and inhibitory inputs in neural subpopulations. These results have important implications for mean-field models, suggesting that the underlying excitatory/inhibitory neural dynamics within a population may need to be taken into account to accurately predict hemodynamic responses.