ABSTRACT Time series analysis, based on the idea that female reproductive endocrine physiology can be construed as a nonlinear dynamical system in a chaotic trajectory, is performed to measure the correlation dimension of the menstrual cycle data from subjects in two different age cohorts. The dimension is computed using a method proposed by Judd (Physica D, vol. 56, 1992, pp. 216-228) that does not assume the correlation dimension to be necessarily constant for all appropriate time scales of the system’s strange attractor. Significant time scale differences are found in the behavior of the dimension between the two age cohorts, but at the shortest time scales the correlation dimension converges to the same value, approximately 5.5, in both cases.
Cite this paper
G. Derry and P. Derry, "Age Dependence of the Menstrual Cycle Correlation Dimension," Open Journal of Biophysics, Vol. 2 No. 2, 2012, pp. 40-45. doi: 10.4236/ojbiphy.2012.22006.
 H. G. Burger, G. E. Hale, L. Dennerstein, and D. M. Robertson, “Cycle and Hormone Changes during the Perimenopause: The Key Role of Ovarian Function,” Menopause, Vol. 15, No. 4, 2008, pp. 603-612.
 P. S. Derry and G. N. Derry, “Menstruation, Perimenopause, and Chaos Theory,” Perspectives in Biology and Medicine, Vol. 55, No. 1, 2012, pp. 26-42.
 A. Treloar, R. Boynton, B. Behn, and B. Brown, “Variation of the Human Menstrual Cycle through Reproductive Life,” International Journal of Fertility, Vol. 12, No. 1, 1967, pp. 77-126.
 L. D. Lisabeth, S. D. Harlow, B. Gillespie, X. Lin. and M. Sowers, “Staging Reproductive Aging: a Comparison of Proposed Bleeding Criteria for the Menopausal Transition,” Menopause, Vol. 11, No. 2, 2004, pp. 186-197.
 R. J. Ferrell and M. Sowers, “Longitudinal, Epidemiologic Studies of Female Reproductive Aging,” Annals of the New York Academy of Sciences, Vol. 1204, No. 1, 2010, pp. 188-197.
 S. D. Harlow and P. Paramsothy, “Menstruation and the Menopausal Transition,” Obstetrics & Gynecology Clinics of North America, Vol. 38, No. 3, 2011, pp. 595-607.
 G. N. Derry and P. S. Derry, “Characterization of Chaotic Dynamics in the Human Menstrual Cycle,” Nonlinear Biomedical Physics, Vol. 4, No. 1, 2010, Article # 5.
 J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, “Fractal Physiology,” Oxford University Press, Oxford, 1994.
 K. Prank, H. Harms, G. Brabant, R. Hesch, M. Dammig, and F. Mitschke, “Nonlinear Dynamics in Pulsatile Secretion of Parathyroid Hormone in Normal Human Subjects,” Chaos, Vol. 5, No. 1, 1995, pp. 76-81.
 T. Noguchi, N. Yamada, M. Sadamatsu, and N. Kato, “Evaluation of Self-similar Features in Time Series of Serum Growth Hormone and Prolactin Levels by Fractal Analysis: Effects of Delayed Sleep and Complexity of Diurnal Variation,” Journal of Biomedical Science, Vol. 5, No. 3, 1998, pp. 221-225. doi:10.1007/BF02253472
 I. Ilias, A. N. Vgontzas, A. Provata, and G. Mastorakos, “Complexity and Non-linear Description of Diurnal Cortisol and Growth Hormone Secretory Patterns Before and After Sleep Deprivation,” Endocrine Regulations, Vol. 36, No. 2, 2002, pp. 63-72.
 P. Mansfield and S. Bracken, “Tremin: A History of the World’s Oldest Ongoing Study of Menstruation and Women’s Health,” East Rim Publishers, Lemont, 2003.
 R. Castro and T. D. Sauer, “Forecasting and Dimension Calculations from Event Timing Data,” Nonlinear Phenomena in Complex Systems, Vol. 2, No. 3, 1999, pp. 42-51.
 F. Takens, “On the Numerical Determination of the Dimension of an Attractor,” In: B. Braaksma, H. Braer, and F. Takens, Eds., Dynamical Systems and Bifurcations, Springer-Verlag, Berlin, 1985, pp. 99-106.
 P. Grassberger and I. Procaccia, “Characterization of Strange Attractors,” Physical Review Letters, Vol. 50, No. 5, 1983, pp. 346-349. doi:10.1103/PhysRevLett.50.346
 K. Judd, “An Improved Estimator of Dimension and Some Comments on Providing Confidence Intervals,” Physica D, Vol. 56, No. 2-3, 1992, 216-228.
 K. Judd, “Estimating Dimension From Small Samples,” Physica D, Vol. 71, No. 4, 1994, pp. 421-429.
 L. H. Clark, P. M. Schlosser, and J. F. Selgrade, “Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle,” Bulletin of Mathematical Biology, Vol. 65, No. 1, 2003, pp. 157-173.
 I. Reinecke and P. Deuflhard, “A Complex Mathematical Model of the Human Menstrual Cycle,” Journal of Theoretical Biology, Vol. 247, No. 2, 2007, pp. 303-330.
 R. J. Bogumil, M. Ferin, J. Rootenberg, L. Speroff, and R. L. Vande Wiele, “Mathematical Studies of the Human Menstrual Cycle. I. Formulation of a Mathematical Model,” Journal of Clinical Endocrinology & Metabolism, Vol. 35, No. 1, 1972, pp. 126-142.