In this thesis, the transmission of spike trains in a neuron model is studied in order to obtain a better understanding of the role played by stochastic activity, i.e. uncorrelated spikes, in the auditory pathway. Fluctuations of the neuron membrane potential are given by a first-order stochastic differential equation, using a leaky integrate-and-fire model. In contrast to most previous studies the model has a finite number of synapses, and the usual diffusion approximation does not hold. / The input signal is modeled by spike trains with spiking times described by inhomogenous Poisson processes. The membrane potential is a shot noise process for which statistical properties are derived with a Gaussian approximation. The statistics of the output spike train are obtained by using the property that a pool of a large number of output spike trains can be modeled by an inhomogeneous Poisson process. It is shown that, under certain conditions, the addition of uncorrelated input spikes, i.e. noise, can enhance the transmission of periodic temporal information. This phenomenon, called stochastic resonance, is demonstrated analytically and supported by computer simulations. / Results are compared with those obtained from the traditional leaky integrate-and- fire neuron receiving a continuous waveform input. The shot-noise property of the membrane potential, which implies that its variance is de facto modulated by the input stimulus, is shown to enhance the phenomenon of stochastic resonance. Indeed, for a given average noise level, a modulated noise gives a higher output signal-to-noise ratio than an unmodulated noise with the same average amplitude. / The derivation is then extended to certain polyperiodic stimuli mimicking vowel sounds. The fact that the addition of uncorrelated input spikes can enhance the transmission of information is discussed in the context of cochlear implants. The results provide supportive evidence to the postulate that a cochlear implant speech coding strategy that elicits stochastic firing neural activity might benefit the user.

Presented in this work is the investigation and successful illustration of a coupled model of the human nerve fiber. SPICE netlist code was utilized to describe the electrical properties of the human nervous membrane in tandem with COMSOL Multiphysics, a finite element analysis software tool. The initial research concentrated on the utilization of the Hodgkin-Huxley electrical circuit representation of the nerve fiber membrane. Further development of the project identified the need for a linear circuit model that more closely resembled the McNeal linearization model augmented by the work of Szlavik which better facilitated the coupling of both SPICE and COMSOL programs. Related literature was investigated and applied to validate the model. This combination of analysis tools allowed for the presentation of a consistent model and revealed that a coupled model produced not only a qualitatively comparable, but also a quantitatively comparable result to studies presented in the literature. All potential profiles produced during the simulation were compared against the literature in order to meet the purpose of presenting an advanced computational model of human neural recruitment and excitation. It was demonstrated through this process that the correct usage of neuron models within a two dimensional conductive space did allow for the approximate modeling of human neural electrical characteristics.

This work focuses on modeling a demyelinated Hodgkin and Huxley (HH) neuron with Simulated Program with Integrated Circuit Emphasis (SPICE) platform. Demyelinating disorders affect over 350,000 people in the U.S and understanding the demyelination process at the cellular level is necessary to find safe ways to treat the diseases [9]. Utilizing a previous SPICE model of an electrically small cell neuron developed by Szlavik [32], an extended core conductor myelinated neuron was produced in this work. The myelinated neuron developed has seven active Nodes of Ranvier (nodes) separated by a myelin sheath. The myelin sheath can be successfully modeled with a resistive and capacitive network known as internodes. Both the Nodes of Ranvier and internode equivalent circuits were implemented in P-SPICE sub-circuit library files. Properties of the neuron can be changed in the library files to simulate neurons of different electrical or geometric properties. Using the P-SPICE code developed in this work, a myelinated neuron’s action potential was simulated and the action potential at each node was recorded. The action potential at each node was uniform in amplitude and pulse width. The conduction velocity of the action potential was calculated to be 57.15 m/s. Demyelination can be modeled by decreasing the capacitance and increasing the resistance of the myelin [34]. Two demyelinated neuron models were simulated in this work. The first model had one internode segment demyelinated, and the second model was of three consecutive internode segments. The resulting conduction velocity was calculated for both simulations. For one and three internode segment demyelinated the conduction velocity was slowed to 44.15 m/s, and 27.15 m/s respectively. This model successfully showed that an HH neuron implemented in SPICE could show the effects of demyelination on conduction velocity The goal of this work is to develop a demyelinated neuron so that treatments for Multiple Sclerosis (MS) and other demyelinated neurons could be simulated to test various treatments’ effectiveness. A current treatment for MS is ion channel blockers. Future work would be to use this model to test current ion channel blocker therapy and to validate if such therapies alleviate conduction slowing.

The time accuracy of the auditory neuronal pathway in its sound localization branch is high, compared to other sensory systems. The time differences in the sound arrival between the left and right ear are distinguished by the neural circuit in this branch. The accuracy achieved here is in the order of tens of microseconds. This phenomenon has not yet been definitively clarified. In this master thesis, a model of a neuron central to this neural circuit is presented. This neuron is called binaural (neuron of the two ears) and is located in the medial superior olive (MSO) neural nucleus. The properties of the MSO neuron are described. Specifically, the neuron acts as a coincidence detector, and this is necessary for the circuit functioning. Main result of the thesis is the theory explaining how the function of the coincidence detector can be described based on the interaction of the post-synaptic potentials on the spike-response model neuron. Generality and implications for the auditory pathway are then discussed.

No description available.

The pre-Botzinger complex (pBC) is a sub-circuit of the respiratory central pattern generator. The pBC is required for eupnea and is contained in a transverse slice of the ventrolateral medulla. In the slice, pBC cells are responsible for generating the respiratory rhythm, and hypoglossal motoneurons (HMs) are responsible for transmitting the rhythm out of the brainstem to the muscles. Understanding how the transverse slice rhythm is generated and transmitted is a first step in understanding how this process occurs in vivo. To understand this network, we developed ionic current models of the individual network components and explored how the various ion channels affect single-cell firing characteristics and network dynamics. First, we used the considerable amounts of experimental data from neonatal HMs to develop an HM model. The model was used to explore the roles of ion channels in shaping the complex dynamics of the neonatal HM action potential (AP) and to investigate the age-dependent changes in HMs. We used a genetic algorithm to optimize the HM model to more closely fit experimental measures of AP shape. A comparison of feature-based and template-based fitness functions revealed that a feature-based fitness function performs best when optimizing the HM model to fit characteristics of the neonatal HM AP. Next, we used our existing pBC models to understand how different ionic currents affect rhythmogenesis in the pBC. Our results indicate that intrinsic bursters increase the robustness of rhythm generation in the pBC. Finally, we developed an improved pBC neuron model and explored how various ion channels affect bursting dynamics at the single-cell level. The HM and pBC models developed in this study will be used in future network models of the transverse slice.

Modern neuron models are large, complex entities. The ability to better simulate these complex models has been iven by the development of ever more powerful and cheap computers. The capacity to manage and understand the models has lagged behind improvements in simulation ability almost from the inception of neuron modeling. Despite the computing power currently available, more powerful simulation platforms and strategies are needed to cope with current and next generation neuron models. This thesis develops methodologies aimed at better characterizing motoneuron models. The hypothesis presented is that relationships between model outputs in addition to the relationships between model inputs (parameters) and outputs (behaviors) provide a characteristic description of the model that describes the model in a more useful way than just model behaviors. This description can be used to compare a model to different implementations of the same motoneuron and to experiment data. Data mining and data reduction techniques were used to process the data. Principal component analysis was used to indicate a significant, consistent reduction in dimensionality in an intermediate, mechanistic layer between model inputs and outputs. This layer represents the non-linear relationships between input and output, implying that if the non-linear relationships of a model were better understood and accessible, a model could be manipulated by varying the mechanism layer members, or rather the model parameters that primarily affect a mechanism layer member. Hierarchical cluster analysis showed similarity between sensitivity analyses data from models with random parameter sets. A main cluster represented the main region of model behavior with outlying clusters representing non-physiological behavior. This indicates that sensitivity analysis data is a good candidate for a model signature. The results demonstrate the usefulness of cluster analysis in identifying the similarities between data used as a model characterization metric or model signature. Its application is also valuable in identifying the main region of useful activity of a model, thus helping to identify a potential 'average' parameter set. Furthermore, factor analysis also proves functional in identifying members of the mechanism layer as well as the degree to which model outputs are affected by these members.

Improved knowledge of human nerve function and recruitment would enable innovation in the Biomedical Engineering field. Better understanding holds the potential for greater integration between devices and the nervous system as well as the ability to develop therapeutic devices to treat conditions affecting the nervous system. This work presents a three-dimensional volume conductor model of the human arm for coupling with code describing nerve membrane characteristics. The model utilizes an inhomogeneous medium composed of bone, muscle, skin, nerve, artery, and vein. Dielectric properties of each tissue were collected from the literature and applied to corresponding material subdomains. Both a fully anatomical version and a simplified version are presented. The computational model for this study was developed in COMSOL and formatted to be coupled with SPICE netlist code. Limitations to this model due to computational power as well as future work are discussed. The final model incorporated both anatomically correct geometries and simplified geometries to enhance computational power. A stationary study was performed implementing a boundary current source through the surface of a conventionally placed electrode. Results from the volume conductor study are presented and validated through previous studies.

One-dimensional neural networks comprised of large numbers of Integrate-and-Fire neurons have been widely used to model electrical activity propagation in neural slices. Despite these efforts, the vast majority of these computational models have no analytical solutions. Consequently, my Ph.D. research focuses on a specific class of homogeneous Integrate-and-Fire neural network, for which analytical solutions of network dynamics can be derived. One crucial analytical finding is that the traveling wave acceleration quadratically depends on the instantaneous speed of the activity propagation, which means that two speed solutions exist in the activities of wave propagation: one is fast-stable and the other is slow-unstable. Furthermore, via this property, we analytically compute temporal-spatial spiking dynamics to help gain insights into the stability mechanisms of traveling wave propagation. Indeed, the analytical solutions are in perfect agreement with the numerical solutions. This analytical method also can be applied to determine the effects induced by a non-conductive gap of brain tissue and extended to more general synaptic connectivity functions, by converting the evolution equations for network dynamics into a low-dimensional system of ordinary differential equations. Building upon these results, we investigate how periodic inhomogeneities affect the dynamics of activity propagation. In particular, two types of periodic inhomogeneities are studied: alternating regions of additional fixed excitation and inhibition, and cosine form inhomogeneity. Of special interest are the conditions leading to propagation failure. With similar analytical procedures, explicit expressions for critical speeds of activity propagation are obtained under the influence of additional inhibition and excitation. However, an explicit formula for speed modulations is difficult to determine in the case of cosine form inhomogeneity. Instead of exact solutions from the system of equations, a series of speed approximations are constructed, rendering a higher accuracy with a higher order approximation of speed.

We present a multi-layer multi-column computational model of neocortex that is built based on the activity and connections of known neuronal cell types and includes activity-dependent short term plasticity. This model, a network of spiking neurons, is validated by showing that it exhibits activity close to biology in terms of several characteristics: (1) proper laminar flow of activity; (2) columnar organization with focality of inputs; (3) low-threshold-spiking (LTS) and fast-spiking (FS) neurons function as observed in normal cortical circuits; and (4) different stages of epileptiform activity can be obtained with either increasing the level of inhibitory blockade, or simulation of NMDA receptor enhancement. The aim of this research is to provide insight into the fundamental properties of vertical and horizontal inhibition in neocortex and their influence on epileptiform activity. The developed model was used to test novel ideas about modulation of inhibitory neuronal types in a developmentally malformed cortex. The novelty of the proposed research includes: (1) design and implementation of a multi-layer multi-column model of the cortex with multiple neuronal types and short-time plasticity, (2) modification of the Izhikevich neuron model in order to model biological maximum firing rate property, (3) generating local field potential (LFP) and EEG signals without modeling multiple neuronal compartments, (4) modeling several known conditions to validate that the cortex model matches the biology in several aspects,(5) modeling different abnormalities in malformed cortex to test existing and to generate novel hypotheses.