An integrate-and-fire model of a one dimensional cellular neural network was developed to assess the effects of receptive field interconnectivity on image processing. Using this model it was found that negative inhibition of neighboring fields pronounced the edges of areas of activation, and was linearly dependent on the strength of the connection, the magnitude of the inputs, and spatial frequency of inputs. Similar effects were seen in second neighbor interactions, however with a non-linear relationship in the magnitude dependence and no relation for frequency dependence.

The main motivation behind this project comes from the observation that topological structures of neural networks intended for engineering purposes often seem to be chosen more or less arbitrarily or with a rule of thumb. This project seeks to explore a biological inspired method for autonomous development and pruning of non-noisy back-propagating neural networks. Learning will be divided in to three distinct phases development, pruning and apoptosis where the network will initially overexpand then contract to a more computationally tractable valency and topology. Thus, the actual computational efficiency of learning will be neglected in favor of ease of implementation and computational efficiency in actual usage.

Retinas can process image information efficiently; consuming only 16.2 nW per ganglion cell. Here I describe novel and extremely efficient circuits that perform the spatial and temporal filtering attributed to the retinal layers between photoreceptors and ganglion cells. CMOS transistors of 90nm process compose the circuit, and when the circuit is integrated with photoreceptors and retinal ganglion cells, it can operate with a supply voltage of as little as 0.5 V and consumes less than 1/1000th of the power consumption of previous neuromorphic designs. The power consumption per pixel (3.16 nW) is comparable to the mammalian retina.

Spike Timing-Dependent Plasticity (STDP) is a Hebbian form of learning that captures the temporal relationship between pre- and postsynaptic spikes. Recent studies have uncovered that the relative concentration of neuromodulators, in addition to the timing of pre- and postsynaptic spikes, can affect the polarity of STDP. In this paper we sought to modify existing STDP rule implementing neural networks to account for experimental findings and observe the corresponding changes in the synaptic weights. Initial conclusions support the notion that minimal changes in A_P or A_D have little effect on rate of synaptic changes however further work must be done to verify or refute these findings.

During the course of brain development there exists a brief period of exuberant synaptic formation followed by an equally impressive pruning and strengthening of surviving synapses that eventually form the basis of the adult brain. The root factor in shaping this process is the information we receive from the world in this critical period of development, the effects of which last a life-time. As we learn neural circuits are fine tuned to accomplish meaningful tasks be they locomotion, communication or any other of the myriad of cognitive facilities we possess. In the process uncertainty gives way to programmatic perfection, those shaky first steps become effortless strides. With this in mind I hypothesized that learning reduces chaos in neural circuits. Below is an initial proof of concept for accessing the chaotic nature of neural circuits.

Accurate detection of seizure onset as well as identification of neuronal regions critically involved in initiating and propagating a seizure remains an important area of research. Understanding the dynamics of neural processes underlying different stages of a seizure can help in devising novel methods of seizure detection, intervention and treatment. In this paper we analyze linear neuronal dynamics during epileptic seizures using adaptive multivariate autoregressive (VAR) models applied to maximally-independent (ICA) sources of intracranial EEG (iEEG, ECoG) data recorded from subdural electrodes implanted in a human patient for presurgery monitoring. We analyze the time-frequency dynamics of directed information flow between sources using a multivariate granger-causal method (dDTF), identifying distinct patterns of information flow in different stages of the seizure. We then further examine the spatial distribution in the cortical source domain of causal sources and sinks of ictal activity using a novel combination of causal flow metrics and Sparse Bayesian Learning-based source localization. Finally, we apply an eigendecomposition method to decompose the VAR model into a system of decoupled oscillators and relaxators (eigenmodes) with characteristic damping times and frequencies. We demonstrate that analysis of a small subset of the most dynamically important eigenmodes may allow effective detection of ictal onset and offset, while also yeilding insight into the dynamical structure of the neuronal system.

The axon initial segment (AIS) is the portion of the neuronal membrane responsible for action potential generation in many neural cell types. Recent work by Matthew Grubb and Juan Burrone (2010) show that the AIS can shift its location in an activity-dependent manner: long-term depolarization induced by high extracellular potassium concentrations in cultures of dissociated hippocampal neurons results in a distal shift of the AIS from the soma. In a computational model of a hippocampal CA1 pyramidal neuron, we show that moving the AIS distally from the soma results in an overall decrease of the excitability of the cell. This spatial shift effectively functions as a mechanism for homeostatic plasticity.

The hippocampal formation is necessary for spatial learning and memory in rats. One aspect of this cognitive function, the ability to remember path sequences, is thought to be achieved through phase precession. The two components of phase precession are a strong theta rhythm (8-12 Hz) in the local field potential and place-selective neurons, which fire selectively while the rat is in a particular area or "place field" of an enclosed arena. As a rat enters and leaves each place field, the respective neuron will fire most strongly in the center and less strongly in the periphery, but in addition to changing firing rate the cell will also fire at progressively earlier phases of the theta rhythm. This ultimately allows for the recent path of the rat to be represented by neuronal firing within one theta cycle, possibly reducing the time between place cell firing to allow for effective spike timing dependent plasticity. We test whether phase precession is required for sequence learning in a small recurrent network of Izekevich neurons with place fields either around the circumference of a closed circular track or forming a grid across a closed square arena with synaptic weights updated according to a spike timing dependent plasticity rule. In either environment, we find that phase precession of place cell responses, as opposed to purely spatially tuned responses, is required for heteroassociative recall and spatial sequence learning.

The electrophysiology of cardiac myocytes is tightly coupled to mechanics. One aspect of this is apparent in the effects of mechanical strain on cardiac action potential dynamics. These can be considered through adjustments to classic electrophysiological models. The standard FitzHugh Nagumo model is a reduced two-variable model from Hodgkin-Huxley that can reproduce basic mechanisms of action potential dynamics. A modified formulation that adapts the model to ventricular cardiomyocytes is considered. The Luo-Rudy model is also a Hodgkin-Huxley-derived model for action potentials driven by ionic currents in cardiac myocytes. The Healy-McCulloch model predicts a decrease in time for 20% action potential repolarization and variable time for 90% action potential duration as seen in rabbit ardiomyocytes based on tiered conductance values. Recently, Lunze and Leonhardt provide a mathematical relation for stretch-activated conductance and strain in smooth muscle. This paper determines whether the Lunze-Leonhardt model for stretch-activation of ionic currents can be applied to a cardiomyocyte model. Using Matlab and Continuity, we will develop a modified model derived from the FitzHugh Nagumo and Luo-rudy models by incorporating a strain-dependent ion channel. We will simulate several coupled cardiomyocytes in Matlab with this modified model to reproduce the results of the Healy-McCulloch model. The modified FitzHugh Nagumo model is also implemented in a finite element simulation study the effects of a strain field on action potential propagation.

Recurrence is one of the fundamental functions attributed to neocortex. Classically, studies of recurrence in cortex have focused on higher-order association areas, such as prefrontal cortex, involved in working memory tasks and showing neural correlates of representation maintenance. However, the role of recurrence in primary sensory cortices is debated. Recurrence is thought to orchestrate, on a moment-by-moment basis, the balance of excitation and inhibition within a local network. What is controversial is the degree to which recurrence in primary sensory areas also enables the maintenance of a representation over time. We may begin to tackle this question using optogenetic methods. Genetic manipulations in the mouse allow the expression of channelrhodopsin (ChR) in parvalbumin-positive (PV+) interneurons, which comprise 95% of the cortical interneurons. By synchronous activation of many inhibitory cells, we can transiently interrupt recurrent activity in primary visual cortex (V1) after a stimulus and determine the effect of this manipulation on maintenance of the cortical representation. Furthermore, many of these effects can be recapitulated in a rate model of two simple, coupled cortical areas, to allow insights into the subtleties of the studied system and to suggest theories for the observed phenomena. The model explains the preferentially sustained network response in the gamma frequency range (30-80 Hz) and the ability of the representation to return to V1after transient silencing. This model suggests that, in vivo, a different cortical area may store the representation of the visual stimulus, while V1 is silenced, and then feed that representation back into V1.

Rhythmicity is a ubiquitous feature of neural activity that results from an interaction between intrinsic currents and extrinsic network properties. The most prominent rhythm during sleep appears in extracranial EEG as a large amplitude, ~ 1Hz Slow Oscillation (SO) with ~10,000 cycles per night. SO is known to orchestrate activity across the cortex during slow-wave sleep and may be involved in important restorative functions and memory consolidation. Understanding the biophysical basis and spatiotemporal dynamics of the oscillation would provide direct insight into fundamental aspects of sleep function. Conflicting evidence from animal and human studies with different recording techniques has produced multiple theories that have yet to be resolved. One question that must be answered for this research to advance is does the SO occur synchronously or propagate across the cortex, and what are the underlying mechanisms governing the dynamics? To address the question of potential generating mechanisms, I studied a thalamocortical network model of the SO and developed an approach to model specification that facilitates model comparison.

Studying the cortex via columnar organization of neurons is a perspective. One which is more holistic than single cell models but still far less ambitious than studying diverse networks [1]. Though there are confusions in terminology, studying columnar organization instead of neurons have allowed many researchers to attain a functional understanding of and ability to model processes such as map cell placement [9] and pattern recognition. We report an extension to a model proposed by A.G. Hashmi, M.H. Lipasti. We discuss the biological plausability of cortical column modeling and show a two level implementation.

Stimulus-evoked neural activity increases both local oxygen metabolism and blood flow in active regions of the brain. However, multiple imaging modalities including functional magnetic resonance imaging and positron emission tomography have demonstrated that the degree of coupling between metabolism and blood flow is highly non-linear. Specifically oxygen metabolism appears to peak and decline at significantly lower levels of stimulus than does blood flow. This model attempts to explain this phenomenon as a consequence of balanced excitation and inhibition in a network of neurons in the primary visual cortex.

The digestion of the food in the gastro-intestinal tract is aided by the peristaltic contractions of the gastric muscles. This gastric motility is a result of the sponta- neous rhythmic pacemaker activity produced by the interstitial cells of Cajal(ICC), which line the gastro-enteric system. The interstitial cells of Cajal are a special- ized group of neuro-muscular cells and are derived from fibroblasts. These cells generate periodic action potentials termed as slow waves, which are responsible for gastric motility. The objective of this project is to implement a VLSI model of a simple ICC network capable of producing slow waves generated by the ICC network of the stomach. The cells of the network are designed using a mathematical model where the membrane voltage of the ICC is based on the flow of C a2+ ions and N a+ ions.