Evaluation of self-similar features in time series of serum growth hormone and prolactin levels by fractal analysis: effect of delayed sleep and complexity of diurnal variation.

We assayed the diurnal concentrations of growth hormone (GH) and prolactin (PRL) in 6 healthy male volunteers to evaluate the self-similar features in the time series of each hormone on the basis of fractal theory and to determine the fractal dimension as an index of the complexity of the diurnal variation. In addition, we assessed the effects of a 6-hour delay in the sleep period on the complexity of the diurnal variation of these hormones. There was a statistically significant fractal feature in the serum levels of GH both under the nocturnal-sleep and delayed-sleep conditions in all subjects. The time series of the serum PRL concentrations also showed a statistically significant fractal feature under the nocturnal-sleep and delayed-sleep conditions in all subjects. The fractal dimensions of the patterns of the GH or PRL levels were 1.879 and 1.929 or 1.754 and 1.785 under the nocturnal-sleep and delayed-sleep conditions, respectively. Two-way ANOVA revealed no significant difference in the fractal dimension between the two sleep conditions but did reveal a significant difference between the fractal dimensions of the GH and PRL levels. These results showed (1) that delayed sleep had no significant effect on the complexity of the diurnal pattern of these hormones, and (2) that the diurnal pattern of the GH levels was more complex than that of the PRL levels.