Accurate Mathematical neuron models.

UNiversity of Minnesota Ph.D. dissertation. August 2012. Major: Biomedical Engineering. Advisor: Theoden I. Netoff. 1 computer file (PDF); viii, 143 pages, appendices A-D.Computational models of neurons have provided us with a deeper understanding of neuroscience by allowing us to test hypotheses in ways that can be impossible in experiments. Models are used for simulations of the nervous system, to test a hypothesis of how it works. They can also be useful in identifying gaps in our understanding. Here I propose different methods to generate models that can predict behaviors from neurons. I have developed different models that can describe neuronal activity at different time scales. For a full description of the voltage trace, and sampling rates higher than 1 KHz, an Unscented Kalman Filter (UKF) is used to fit a set of parameters of a given mathematical model. The UKF predicts the voltage of the neuron for the next sampling time. For the study of spike rate variability, I introduce the use of fixed and adaptive linear models. These models are able to predict the neuron's firing rate in response to stimuli. These models were then used to control the neuron's spike rate. Finally, I introduce two new methods to measure how the spiking activity of a given neuron can be modified by synaptic inputs. One method is able to describe the change in the period of a periodically firing neuron given the applied current and the time of the synaptic input. The second method generates a model that can predict the spike times given noisy waveforms in non-regular spiking neurons