Approximate Entropy as a Measure of Regularity in Hormone Series

1. Introduction Hormones, such as luteinizing hormone (LH), are secreted into the blood in short bursts, called pulses, and removed by a decay process. Using hormone assays from blood samples obtained at equally spaced intervals, investigators study secretion characteristics such as pulse frequency and amplitude to learn whether various diseases affect hormone secretion. Approximate entropy (ApEn) has been used to assess regularity in a series. Although it is not specifically tailored to the identification and characterization of pulses (Pincus and Keefe 1992), the authors state that ApEn evaluates both dominant and subordinate patterns in data and therefore detects differences in pulsatile series even when pulse frequency and height do not differentiate between the secretion patterns. ApEn does distinguish between complex mathematical systems that can generate hormone data (Pincus, 1994), but little has been studied about the sensitivity of ApEn to randomness in the main pulse characteristics (timing, mass, duration, and noise). We were interested in assessing whether ApEn was sensitive to timing, mass, and duration. We generated simulated data with fixed pulse characteristics and then added random effects to the timing, mass, and duration parameters. We studied combinations of fixed and random characteristics under various model assumptions (longer vs. shorter half-life, slow vs. rapid pulsing, and noise vs. no-noise) to assess which parameter characteristics cause changes in the ApEn statistic. Since ApEn is being used to characterize the regularity of secretion we also wanted to assess whether conclusions made in peripheral blood, the samples collected in human studies, could be used to draw conclusions about the regularity of secretion closer to the source. We calculated the ApEn statistics for LH data collected in the portal and peripheral blood in six ewes. This enables us to evaluate the influence of hormone dispersion in the peripheral blood on the ApEn statistic.