Analysis of brain activity reveals the presence of synchronous oscillations over a range of frequencies. These oscillations can be observed using electro-neurological measurements such as electroencephalogram (EEG), magnetoencephalogram (MEG) or electrocorticogram (ECoG) . Further, these rhythms can traverse different connected parts of the brain forming a "system of rhythms". These systems are analyzed in this paper using a lumped-parameter, interconnected, neural mass models. This model allows the analysis of the dynamics of the neural population in the frontal cortex and their synapses using a few state variables. It is assumed here that the neurons share the inputs and synchronizes their activity. The present work is motivated by a recent paper by Bhattacharya et al who have proposed an adaptation of Ursino's neural mass model for the study of the changes in alpha rhythms during the course of Alzheimer's disease. In that work, the synaptic organization and connectivity in the lumped thalmo-cortico-thalmic model was modified using experimental data. The authors were able to reproduce the slowing of alpha rhythms (8-12 Hz) and decrease in power of these rhythms associated with the Alzheimer's disease. Using this research as the basis, the present work employs a pathophysiologic understanding of traumatic brain injury to create a computational model of traumatic brain injury that recreates the multimodal electroencephalographic changes observed to occur with mild, moderate, and severe traumatic brain injury. The focus is on recreating the observed changes in the alpha and gamma rhythms (30-100Hz) due to traumatic brain injury. Eight coupled neural mass models are used to represent the frontal cortex. Numerical simulations are conducted using a well-known software package. It is shown that the present model accurately reproduces the power spectral density of the normal frontal cortex under white-noise excitation conditions. Three degrees of traumatic brain injuries are then modeled by decreasing the connection strengths in the neural mass model. A comparison of the power spectral densities of the outputs of the normal and injured neural mass models indicates that the present model is capable to reproducing clinically-observed changes due to traumatic brain injuries.

The balance of excitation and inhibition within most sensory cortices is co-tuned to a given stimulus. However, unlike other sensory cortices, it has been reported from in vivo recordings that widespread global inhibition governs sparse stimulus-evoked excitation in the piriform cortex. Further in vitro physiology has demonstrated that this global inhibition is achieved through local activation of feed-back inhibition by layer 3 (L3) interneurons, which make perisomatic synapses onto pyramidal cells. L3 interneurons are composed of two major classes of GABA-releasing inhibitory interneurons found in all sensory cortices: somatostatin (SOM) and parvalbumin (PV) expressing neurons. Both SOM and PV neurons have been well characterized as significant contributors to cortical inhibitory networks, yet their functional roles within local circuits remain unknown. Here we attempt to model this circuit using minimum Hodgkin-Huxley type models. First, we adapted previously defined models of thalamic and cortical SOM, PV and pyramidal neurons to fit physiology data recorded from piriform cortex SOM, PV and pyramidal neurons. We then used experimentally derived glutamate and GABA synaptic coupling coefficients to create our neural feedback circuit. We aimed to create simplistic models of these neurons which would describe the relative latencies of inhibition each cell type would contribute onto pyramidal cells.

This project considers the problem of trying to selectively sense and induce activity in individual neurons within a network in a living organism, using a small array of electrodes placed some distance away. We consider a variety of approaches to relate neural behavior to the potential or current at the electrode array. Then we perform a simulation using the simple linear model with uniform conductivity, and demonstrate the ability to resolve axons in the transverse direction. We also demonstrate the use of this same approach to estimate a current at the electrode array to achieve, as best possible, a desired potential difference within the neural tissue.
Measuring and inducing neural activity in neurons using extracellular fields provides great insight into neurons functions and how they process information. This paper will consider the problem of trying to selectively sense and induce activity in neurons within a network in a living organism, using a small array of electrodes placed some distance away. One way to approach this problem is to solve for current source density (CSD) using known local field potentials. This involves solving the electrostatic forward problem where we measure the local filed potentials or low frequency part of the extracellular recorded potential by applying an equally spaced linear array or laminar electrode into the cortex [1]. The standard CSD method, involving a discrete double derivate, is then compared to inverse CSD (iCSD), where the CSD is assumed to have cylindrical symmetry and be localized in infinitely thin discs.

It has been hypothesized that the insertion of cation preferential channels into neuronal cell membranes disrupts homeostasis and function leading to Alzheimer's disease. These channels have been shown to be composed of variable numbers of subunits. The nonhomogenous configuration of these subunits in the channels has introduced difficulties in defining set values of ion conductance. Here we model beta-amyloid (A-beta) channels as a cylinder spanning the cell membrane of variable radius dependent on subunit configuration. Various subunit motifs were examined and the expected conductance for each configuration determined. The theoretically determined conductance was then compared to experimentally observed values and a new mechanism for pore growth through successive subunit addition is proposed. This work will allow for the introduction of these channels into electrodynamic models of neurons to illuminate the effects of channel insertion into the cell membrane and expand our understanding of neurodegenerative diseases.

The viability of spike-timing-dependent plasticity (STDP) to explain learning processes is controversial, although recent developments of reward-modulated STDP (RM-STDP) models provide a plausible substrate. However, evidence has also emerged to show that rewards themselves can modify the STDP rule. In this modeling study, we use a dynamic STDP rule to show that such modification can lead to network instability, and furthermore that inhibitory STDP may be able to balance networks to restore asynchronous, stochastic firing. We conclude that further experimental and modeling work is necessary to arrive at a biologically plausible mechanism of learning.

Findings that sub-threshold Voltage signals were propagated from Soma to Axon terminal may change the way we view Cortical Coding. How these signals were never considered before is a surprising error in both theoretical and experimental neuroscience. I address this by studying the effects of Heterogeneities in axon parameters, specifically membrane and internal resistances. Numerical studies will show how these heterogeneities affect the spatial decay of Voltage in a passive axon.

I implement a Hodkin-Huxley neuron that can be stimulated with a voltage clamp of a timecourse of a neuron stimulated by Channelrodopsin-2. I test this on a model network of four neurons that includes a recurrent loop and inhibitory feedback to explore how the dynamics vary with stimulation type.

A connection between sleep spindles and epilepsy or in particular seizures has been stated in previous research. This is a project aiming to evaluate if this connection can be shown in a spatially extended cortical model. The model has earlier been used to generated spike and wave discharges, seizures, and it can therefore be thought to be able to show the wanted connection. The evaluation is made by changing the parameters in the cortical system when an external current is put into it. The external current is either a current of random spiking behavior or it has the pattern of sleep spindles. The conclusion of the evaluation is that this model is not sufficient enough to show the connection between sleep spindles and epilepsy.

The intricate neural circuit in the retina is responsible for detecting and converting light into electrical signal. Basic imaging processing occurs within the network. This paper analysed the convergence of information within the retina at a cellular level. It found significant non-linear behaviour at the amacrine level. Possible accounts for this phenomenon have been presented.

A network-centric view of brain function that is becoming more widely accepted would benefit from the directional interaction information that occurs between multiple neurons. Granger causality has been used previously to address this need, but previous methods can only operate on continuos-value data sets. This prevents it from being directly applied directly to neural spike train data so previous attempts have involved smoothing, binning, etc. to address this. Recently a point process framework that enables Granger causality to be applied to point process data was proposed. The newly proposed framework was used to investigate network interactions proposed in previous assignments to verify that the correct minimal generative model graph could be recovered from just the raw simulated neural spike train data. The interactions and non interactions present in the simulated networks were indeed recovered.

Neural growth is directed by extracellular signal molecules that can either deter or encourage growth. Those molecules cause internal signal response that effects gene expression and ultimately cell fate. These dynamic signal molecules can be quantified at the systems scale with the nascent fields of proteomics and metabolomics. Molecular-scale "omics" measures can be combined with cell-level phenotypic and fluorescence microscopy methods as a collective input to theoretical models, which are used to validate assumptions and generate testable hypothesis. A complete model of neurodynamic growth, once complete, promises to expedite generation of therapeutic targets and cures for neurological diseases. Here I describe the implementation of a model that allows scalable input from systems signal molecule measures and microscopy data. The package written in Java is named "Axon." I envision this package will in the future accept real-time imaging data, histological data, and omicscale molecular measures independently. This provides a publicly available framework that bridges computational and experimental biology.

The transient receptor potential (TRP) channels are group of ion channels on mammal neurons plasma membrane that have an important role in some inflammatory and nociceptive processes. This study investigates the impact of magnetic electrical field-induced external sinusoidal voltage application on the pattern of action potential (AP) firing of a modified Hodgkin-Huxley neuron. The impact of frequency and amplitude variation of the external sinusoidal voltage is investigated with different TRP-like channel activity.

Cardiac myocytes are non-neural cells that possess the capacity to propagate regenerative depolarizing potentials. This allows them to coordinate the exquisite timing necessary to orchestrate millions of these individual muscle cells to generate a heartbeat. Abnormalities of cardiac conduction and cardiac electrophysiology are central to many disease processes and account for significant morbidity and mortality. Several of the various pharmacologic therapies used in clinical cardiology to treat those aberrations modulate the ionic conductances that generate the cardiac action potential. This project uses electrophysical models of cardiac myoctes in order to study the effects of pharmacologic intervention.

Many motor system impairments are debilitating not because they destroy previously acquired motor control policies but because they impair the ability to learn and incorporate error signals in moving. The cerebellum is of chief importance in nearly all motor learning tasks, and is a hypothesized location of storage for internal models important to movement. This model hypothesizes that plasticity in the parallel fibers that connect granule cells and Purkinje cells in the cerebellar cortex are the biological mechanism of policy learning. The model implements the granule cells and Purkinje cells as a neural network connected to a 2-degreeof- freedom simulated arm and two plasticity rules, one for long-term potentiation and one for long-term depression. The activity of the network and behavior of the simulated arm are captured and analyzed.