Autocorrelation and Fourier Analysis for Detecting Periodic Cell Potentials in a Simulated Inhibitory Neural Network

Abstract

The field of Computational Neuroscience is best described as a mathematical approach to the study of neural systems reducing neural systems to a set of computational tasks. Computer models are an important part of this analysis for their insight into the phenomenon. In order to begin a meaningful study, one has to find a pattern that exists throughout the brain. Experimental studies have shown that isolated neurons can be naturally periodic repeating almost "clock-like". However, due to inter-neuron interactions, signals from cells in networks are neither perfectly periodic nor completely random. The goal of my analysis was to characterize periodic behavior of inhibitory neurons. I created a network model of a hundred neurons, in which I could influence the percentage of periodic neurons by changing the number of connections or their strength. During the simulations, membrane potential traces were recorded from each of the one-hundred cells. Then, I developed three methods for the detection of periodic neurons. The first method was the Autocorrelation Function (AC), which I computed using Matlab. I improved this method by modifying several functions, allowing for the removal of initial transients in each simulation. AC's tells us how well a signal correlates with itself when one copy is shifted by a time ¢t. Because an animal's behavior has correlates with activity in the µ frequency (4¡10Hz), we filtered out other frequencies. For example, REM sleep correlates with µ activity. I then fitted an exponential function to the local maxima of the AC. Decay constants of the exponentials were recorded for each cell and the cell was identified as periodic when the decay was greater than a threshold. Despite this well thought out method, some cells were identified incorrectly, based on our visual inspection of the raw data. Therefore, I implemented a Fast Fourier Transform (FFT) algorithm. A Fourier plot gives the activity of a signal for each frequency. I created a method to take an integral of the FFT over the µ range. As with the AC method, cells with values over a threshold were labelled periodic. My data show that the FFT method identifies periodic cells more accurately than the AC method. After a few initial tests, this model was assumed to be biologically accurate for the purposes of my project. It is my hope that the creation and implementation of more accurate methods will allow for a further understanding of periodicity in the Medial Septum.