Cycle Detection: A Technique for Estimating the Frequency and Amplitude of Episodic Fluctuations inBlood Hormone and Substrate Concentrations*

Abstract

Investigation of episodic endocrine secretion has been hampered by inadequate analytical techniques for describing patterns of blood concentrations over time. Although standard time series methods, such as autocorrelation and power spectral analysis, are available, their use is limited to special cases in which rhythms are regular. To facilitate the analysis of our own episodic LH data, we have developed a process for determining the frequency and amplitude of both regular and irregular endocrine rhythms (signals) in the presence of high levels of random measurement errors (noise). This process, called cycle detection, engages an iterative, computerized procedure which scans data identifying sequential increases and decreases greater than an initial, preset threshold value. One complete cycle is defined as two increases greater than threshold separated by a decrease which is also greater than threshold. For an initial first pass estimate of frequency and amplitude, the threshold is set at 2.7 times the noise standard deviation. On the next pass, the threshold is readjusted, based on an mpirically derived formula, and the data are scanned again. his process is repeated until the threshold reaches a stable value. We have tested the reliability of the cycle detection process by simulating irregular rhythm fluctuations of different frequencies, corrupted by various levels of noise and evaluating the signal characteristics with cycle detection analysis. These tests indicate that cycle detection provides excellent estimates of cycle frequency and amplitude, even with signal to noise ratios as low as 1.5. The ability of this process to analyze cyclic signals of almost any shape, with either regular or irregular rhythms, should make it a valuable tool in the hands of endocrine researchers.