The relationship between rate of venous sampling and visible frequency of hormone pulses

In this paper, a stochastic model of episodic hormone secretion is used to quantify the effect of the sampling rate on the frequency of pulses that can be detected by objective computer methods in time series of plasma hormone concentrations. Occurrence times of secretion pulses are modeled as recurrent events, with interpulse intervals described by Erlang distributions. In this way, a variety of secretion patterns, ranging from Poisson events to periodic pulses, can be studied. The notion of visible and invisible pulses is introduced and the relationship between true pulses frequency and mean visible pulse frequency is analytically derived. It is shown that a given visible pulse frequency can correspond to two distinct true frequencies. In order to compensate for the 'invisibility error', an algorithm based on the analysis of the original series and its undersampled subsets is proposed and the derived computer program is tested on simulated and clinical data.