A method of estimating the rate of miniature end-plate potential occurrences based on parametric time series modeling

This paper presents a parametric method of estimating the rate of miniature end-plate potential (MEPP) occurrences. We consider the case where the rate of MEPP occurrences is raised by the constant deporalization of presynaptic terminals by using high-concentration potassium solutions. Under such conditions, since MEPP occurrences cannot be identified by eye due to waveform superposition, it is necessary to estimate the rate with the aid of statistical techniques instead of counting the occurrences by eye. In this paper it is assumed according to the literatures that the MEPP data are modeled as a stationary Poisson impulse process filtered by the linear system the impulse response function of which is the sum of two exponentials. Then, the discretized MEPP data are shown to be a second-order autoregressive (AR(2)) process, driven by the sum of 2 first-order moving average (MA(1)) processes (the residual time series). An explicit formula for estimating the rate can be derived by combining the second- and third-order moments of the residual time series. The validity of the proposed estimation method is verified through Monte Carlo simulations in which the rate is varied ranging from 100 to 10,000 s-1. Likewise, the proposed method is applied to estimation of the rate of actual MEPP data, which were observed at the frog's neuromuscular junction under high-concentration potassium solutions.