Modeling spike-band extracellular background activity using Johnson's Su Distribution

Abstract

Extracellular neural recordings are collected in awake behaving subjects (e.g. rats) via microelectrode arrays that are chronically implanted into the brain. These recordings contain important information about the activity of individual neurons and the functioning of the brain. In order to detect the action potentials, or spikes, in the recordings, the recordings are first bandpass filtered with cut-off frequencies that are appropriate for spike detection. Now the signal consists of spikes and background activity. Here, background activity is produced by neurons relatively far from the electrode. It is critical to distinguish the spikes from the background activity. In the literature, this problem is usually solved by amplitude thresholding. However, currently, the threshold value is usually determined by multiplying a coefficient determined subjectively by the researcher by the estimated standard deviation of the data under an assumption of Normality. By contrast, purely data-driven thresholding can be performed with truncation thresholds calculated with the truncated Normal distribution, truncation thresholds calculated with the truncated Johnson's SU (JSU) distribution, and an Otsu-based method. In the present study, completely data-driven amplitude thresholding methods are examined and compared against each other. Realistic simulated extracellular neural recording data having 21 different firing rate levels were used in the analyses. The methods were compared in terms of the accuracy with which they allowed the standard deviation of the background activity to be estimated. The best method was found to be the Otsu-based method. In addition, the distribution of the data encompassed by the Otsu-based threshold values was examined. It was found that the truncated Normal distribution could pass the Kolmogorov-Smirnov (KS) test only at two firing rates, while the truncated JSU distribution could pass the test at all firing rates tested. JSU is a distribution with 4 parameters (γ, δ, ξ, and λ) and therefore provides more flexibility in modeling than the Normal distribution. However, when computational costs are compared, the JSU method has the highest computational cost. Reducing the cost is important in terms of being useful for real-time applications. Therefore, four different parameter-fixed JSU distributions (JSU γ, JSU δ, JSU ξ, and JSU λ) are proposed in this study, in which each parameter is fixed to its initial value (estimated before any truncation) and the other three different parameters are estimated after truncation. By fixing one parameter (except for ), the calculation time can be reduced to approximately 1/7 of JSU all. The thresholding performance of these methods has been studied and JSU ξ has been shown to give better results than JSU all. However, the parameter-fixed models were not as successful as JSU all in fitting the data encompassed by the Otsu-based threshold values. All the analyses were also performed on a real data segment of 1 second duration.