An auditory nerve model based on Meddis is test in this project. In this model, the input sound was decomposed into different constituent single frequencies, and was therefore responded by individual hair cells. Mechanical amplification during the transduction process was taken into account. The deflection was translated into the change in membrane potential, which was subsequently used as the input to the Meddis model. The spiking patterns were observed under pure tone and human voice stimulations. Phase-lock phenomenon, adaptation, and spiking rate pattern indicate that this model reflects some of the distinct properties of the hair cell.

The number of backwards projecting connections in the visual stream dwarfs the number of forward projecting connections. Yet, we have little understanding of the function of these connections. The primary obstruction to our understanding has been our inability to distinguish between the effect of feed-forward connections and feedback connections on a given neuron. In this work, I propose Cross-Correlation Mapping (CCM) as a means of isolating the effect feedback connections. Cross-Correlation Mapping is a time-embedding manifold method that has been successfully used to show unidirectional causality between two variables in complex dynamical systems [5]. I will, first, run CCM on model neural data for which we know the causal relationshipsto determine the effectiveness of CCM. If I can show that CCM can uncover functional connectivity in neural populations, I will use CCM and fMRI data to create a functional mapping of the feedback connections from V2 onto V1.

In this paper we focus on the two particular properties of myelinated neuron, the increased conduction speed and changeable excitability. First we implemented myelinated neuron using NEURON simulator and verified in simulation the previously known two properties mentioned above. Next we tried to identify in simulation which channels were responsible for changeable excitability. Finally we verified that the structure of dendrites could also affect the changeable excitability.

Synaptic democracy is believed to be an important effect that enables distal synapses to contribute information to the soma. Synaptic democracy is found in hippocampal CA1 pyramidal neurons, which is an important area of the brain for learning and memory. Previous computational work by Sterratt et al [1] show that synaptic democracy arises in a model of a CA1 pyramidal neuron when sufficient synapses are synchronously activated given that the calcium concentration is homeostatically maintained. However, in this work only a 5Hz excitatory postsynaptic potential (EPSP) was tested. We explored how different input vectors might affect the dynamics of synaptic democracy and the neuron as a whole. We found that high frequency stimulation compensated for a sub-threshold number of synapses allowing for synaptic democracy. Interestingly, in the cases with supra-threshold synapse numbers, higher frequency synaptic inputs abolished synaptic democracy.

Genome-scale metabolic networks have been widely used in many different applications to predict and analyze both cellular physiology phenotype of specific cell models. These metabolic networks provide insight into energy usage, gene expression, and pathway architecture of cells. In the context of human brain cells, such metabolic networks not only reveal important information about the overall metabolism of neurons and astrocytes, but also poses the potential to incorporate with neuronal activity. That is, chemical synapses depend upon the concentrations of different types of neurotransmitters in the cell. This allows us to look into the relationship between the concentration of neurotransmitter and the specific electrical activity of these cells for the transmission of information. In this project, we used both systems biology and neurodynamics to model and predict the depletion rates of neurotransmitters due to synaptic release in both normal and Alzheimer neurons. These simulations were based on metabolic fluxes and electrical stimulation rates.

Spinal stimulation for neuropathic treatment was modeled by incorporating and inhibitory junctions and a volume conductor into Hodgkin-Huxley and Frankenhaeuser-Huxley axon models. Results indicate successful merging of the models at low resistivity values but also show that these two mechanisms operate independently of one another. At high resistivity values, the model no longer produces reliable results, most likely due to the effect of capacitive and inductive forces that are produced by thick layers of tissue.

Winnerless competition is a theoretical model used to study cognitive and attention-based processes using the sequential switching between metastable states of a neurodynamical system. This competition is observed in both physical neural networks and in higher-ordered cognition. I demonstrate this principle in a network of three interconnected Fitzhugh-Nagumo neurons and in the working memory model, a more abstract cognitive processes using competitive Lotka-Volterra dynamics.

In this paper we introduce a technique called time-delay synchronization. This technique uses data from a single state-variable measurement at different times to determine the values of unmeasured state variables and parameters in a model of an experiment. We test the technique using simulated data and show that we are able to accurately determine the values of all state variables in a network of two or three Hodgkin-Huxley neurons, using only data from a single voltage measurement. In the case of the two neuron network we are also able to determine the values of GABA and Glutamate conductances in all synapses. In the three neuron network, we are able to to determine all state variables, however we found that determining the parameters of the synapse connections is much harder and were only able to do so for particular cases.

In cortex, there are several electrically coupled inhibitory interneuronal networks which are thought to be critical to temporal coordination of cortical and hippocampal oscillations seen in EEG. This is because gap junction mediated networks have many properties, such as speed and bidirectionality, desirable for neural synchronization. Gap junctions exclusively connect GABAergic neurons of the same type, implying distinct functional roles for each type of inhibitory network. Using BRIAN, we built a model simulating Layer IV excitatory neurons, which receive thalamic input and synapse onto gap-junction coupled interlaminar inhibitory neurons, which in turn inhibit Layer VI excitatory neurons. The electrical coupling of the inhibitory layer drives synchronization of neuronal firing in Layer VI which is dependent on the topology the electrically connected inhibitory network. We investigated how lattice (nearest neighbor), random, and small world topologies effect synchronization. Small world networks occur when a percent of connections in a lattice network are rewired randomly, resulting in the path length L between any two neurons scaling with the logarithm of N. Small world networks are less likely to exist in systems where links arise mainly from spatial or temporal proximity. We found that small-world network topology for the gap-junction connected inhibitory network results in the highest correlation between spiking of neurons in the inhibited layer.

It has been posited that biological neural networks, such as a brain, may naturally exist in critical states. We propose two mechanisms for signal transduction in two such networks as encoding strategies which are optimized by criticality. First, we examine compressive sensing in a 2-dimensional Ising model at or near its critical temperature. Secondly, we examine the dynamical synchronization capabilities of a random neural network model as it transitions into chaotic behavior. We propose that both techniques should be most successful at the critical state of either model.

In the event of a traumatic brain injury, three primary physiological outcomes occur: the neurons become inactive at first, but through a process known as homeostatic synaptic plasticity (HSP), TNF-alpha is released from glial cells. This affects the excitatory and inhibitory neurotransmitter balance, which can lead to pro-epileptic effects. The nerve cells are also damaged, causing sodium and potassium channels to become chronically leaky, although ion pumps will respond. Finally, the cortex stimulates a current that yields a smaller frequency in the event of trauma. An extended Morris-Lecar model is used to model the dynamics of a single neuron, coupled PY-PY and PY-IN neurons, and a six neuron network in the event of these effects. The model incorporates features such as neurotransmitter-dependent synaptic currents, ion pump currents, and an excitatory cortical trauma current, which are varied to alter the injured neurons' firing of action potentials. Different trauma volumes and trauma types, such as focal and diffuse, are simulated in the six-neuron network. HSP mechanics, which adjust the neurotransmitter conductivities, are also examined within coupled neurons. Expectations are that with higher pump currents, deafferentation conductivities and trauma volumes, the amplitude of individual spikes are higher, but smaller peaks of bursts also exist, so the spiking rate is less. In the six-neuron network testing, focal trauma yields greater deafferentation effects than diffuse trauma. With HSP, the expectations are that IN reduces the firing rate so it requires a greater conductivity adjustment than with PY neurons.

Many different neuron models have been devised in order to explain the functioning of neurons. The most common being the Integrate and Fire and the Hodkin-Huxley models. The integrate and fire neuron model offers fast simulation with simple description of the system. While Hodkin-Huxley model offers a detailed description of the system with slow simulation time. In order to overcome the shortcomings that either model offers, this paper uses the Izhikevich neuron model to simulate large networks (N > 10000) of excitatory and inhibitory neurons. In addition Synaptic weights between the different types of neurons, time dependent random synaptic input, and random connectivity in the network are included in the model to achieve simulations close to actual observations. Simulation results in output that is analogous to many local field potential measurements for the awake cortex.

Steady-state evoked potential (SSVEP) is a periodic cortical response induced by repeated visual stimuli. This study aims to generate visual evoked potential (VEP) and to simulate SSVEP using existing mathematical models. Assessment of the results will include accuracy of the VEP and SSVEP as a temporal process as well as accuracy of the power spectrum for various input frequencies. The quantitative prediction of SSVEP is a pathway to understand the unexplained properties of SSVEP, and may provide useful information for future SSVEP-based practical applications.