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Characterization of chaotic dynamics in the human menstrual cycle.

Derry G, Derry P - Nonlinear Biomed Phys (2010)

Bottom Line: This result is confirmed by recalculation using the Takens estimator and by surrogate data tests.We interpret this result as an approximation to the fractal dimension of a strange attractor governing chaotic dynamics in the menstrual cycle.Taken collectively, these results constitute significant evidence that the menstrual cycle is the result of chaos in a nonlinear dynamical system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, Loyola University Maryland, Baltimore, MD 21210, USA. gderry@loyola.edu.

ABSTRACT

Background: The human menstrual cycle is known to exhibit a significant amount of unexplained variability. This variation is typically dismissed as random fluctuations in an otherwise periodic and predictable system. Given the many delayed nonlinear feedbacks in the multiple levels of the reproductive endocrine system, however, the menstrual cycle can properly be construed as the output of a nonlinear dynamical system, and such a system has the possibility of being in a chaotic trajectory. We hypothesize that this is in fact the case and that it accounts for the observed variability.

Results: Here, we test this hypothesis by performing time series analyses on data for 7749 menstrual cycles from 40 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Both raw menstrual cycle length data and a formal time series constructed from this data are utilized in these analyses. Employing phase space reconstruction techniques with a maximum embedding dimension of 12, we find appropriate scaling behavior in the correlation sums for these data, indicating low dimensional deterministic dynamics. A correlation dimension of Dc ≈ 5.2 is measured in the scaling regime. This result is confirmed by recalculation using the Takens estimator and by surrogate data tests. We interpret this result as an approximation to the fractal dimension of a strange attractor governing chaotic dynamics in the menstrual cycle. We also use the time series to calculate the correlation entropy (K2 ≈ 0.008/τ) and the maximal Lyapunov exponent (λ ≈ 0.005/τ) for the system, where τ is the sampling time of the series.

Conclusions: Taken collectively, these results constitute significant evidence that the menstrual cycle is the result of chaos in a nonlinear dynamical system. This view of the menstrual cycle has potential implications for clinical practice, modelling of the endocrine system, and the interpretation of the perimenopausal transition.

No MeSH data available.


Related in: MedlinePlus

Examples of data. Menstrual cycle length data during 20-40 year age interval, illustrating typical observed variability (A), and time series constructed from the data using the protocol defined by Equation (1) in text (B). Illustrative subsets of total data record in both cases.
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Figure 1: Examples of data. Menstrual cycle length data during 20-40 year age interval, illustrating typical observed variability (A), and time series constructed from the data using the protocol defined by Equation (1) in text (B). Illustrative subsets of total data record in both cases.

Mentions: Data for the menstrual cycles used in this work was obtained from the database maintained by the Tremin Research Program on Women's Health [14], which contains the results of an ongoing longitudinal study begun in 1934 and includes data records for 3717 women. Since some of the subjects in the Tremin database have data records for more limited age ranges, we first isolated a subset of the subjects with longer records (minimally including the 20-40 year age range) and randomly selected those used in the present work from this set. Some of these subjects (< 10) were rejected due to documented health problems, missing data in the records, and so on. The analyses were ultimately performed on data for 20-40 years of age from 40 women, resulting in a total of 7749 menstrual cycle data points. In the Tremin research project, women prospectively record which days they are menstruating (and which not) on calendar cards, minimizing problems with inaccurate memory recall. The calendar card data was initially converted into a string of menstrual cycle times (defined as the time interval between the first day of menstruation for two consecutive menstrual events lasting at least two days). We only retained those menstrual cycles that were at least 16 days but no more than 54 days long; these were the 5th and 95th percentiles for menstrual cycle length reported for the Tremin population [2] (this protocol eliminated pregnancies, undocumented health problems, and so on). Also, in keeping with definitions used by the Tremin researchers, there had to be at least a two-day gap between bleeding episodes to count as a new cycle. The data for all women is then concatenated. A subset of the resulting menstrual data sequence is shown in Figure 1A.


Characterization of chaotic dynamics in the human menstrual cycle.

Derry G, Derry P - Nonlinear Biomed Phys (2010)

Examples of data. Menstrual cycle length data during 20-40 year age interval, illustrating typical observed variability (A), and time series constructed from the data using the protocol defined by Equation (1) in text (B). Illustrative subsets of total data record in both cases.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2959058&req=5

Figure 1: Examples of data. Menstrual cycle length data during 20-40 year age interval, illustrating typical observed variability (A), and time series constructed from the data using the protocol defined by Equation (1) in text (B). Illustrative subsets of total data record in both cases.
Mentions: Data for the menstrual cycles used in this work was obtained from the database maintained by the Tremin Research Program on Women's Health [14], which contains the results of an ongoing longitudinal study begun in 1934 and includes data records for 3717 women. Since some of the subjects in the Tremin database have data records for more limited age ranges, we first isolated a subset of the subjects with longer records (minimally including the 20-40 year age range) and randomly selected those used in the present work from this set. Some of these subjects (< 10) were rejected due to documented health problems, missing data in the records, and so on. The analyses were ultimately performed on data for 20-40 years of age from 40 women, resulting in a total of 7749 menstrual cycle data points. In the Tremin research project, women prospectively record which days they are menstruating (and which not) on calendar cards, minimizing problems with inaccurate memory recall. The calendar card data was initially converted into a string of menstrual cycle times (defined as the time interval between the first day of menstruation for two consecutive menstrual events lasting at least two days). We only retained those menstrual cycles that were at least 16 days but no more than 54 days long; these were the 5th and 95th percentiles for menstrual cycle length reported for the Tremin population [2] (this protocol eliminated pregnancies, undocumented health problems, and so on). Also, in keeping with definitions used by the Tremin researchers, there had to be at least a two-day gap between bleeding episodes to count as a new cycle. The data for all women is then concatenated. A subset of the resulting menstrual data sequence is shown in Figure 1A.

Bottom Line: This result is confirmed by recalculation using the Takens estimator and by surrogate data tests.We interpret this result as an approximation to the fractal dimension of a strange attractor governing chaotic dynamics in the menstrual cycle.Taken collectively, these results constitute significant evidence that the menstrual cycle is the result of chaos in a nonlinear dynamical system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Physics, Loyola University Maryland, Baltimore, MD 21210, USA. gderry@loyola.edu.

ABSTRACT

Background: The human menstrual cycle is known to exhibit a significant amount of unexplained variability. This variation is typically dismissed as random fluctuations in an otherwise periodic and predictable system. Given the many delayed nonlinear feedbacks in the multiple levels of the reproductive endocrine system, however, the menstrual cycle can properly be construed as the output of a nonlinear dynamical system, and such a system has the possibility of being in a chaotic trajectory. We hypothesize that this is in fact the case and that it accounts for the observed variability.

Results: Here, we test this hypothesis by performing time series analyses on data for 7749 menstrual cycles from 40 women in the 20-40 year age range, using the database maintained by the Tremin Research Program on Women's Health. Both raw menstrual cycle length data and a formal time series constructed from this data are utilized in these analyses. Employing phase space reconstruction techniques with a maximum embedding dimension of 12, we find appropriate scaling behavior in the correlation sums for these data, indicating low dimensional deterministic dynamics. A correlation dimension of Dc ≈ 5.2 is measured in the scaling regime. This result is confirmed by recalculation using the Takens estimator and by surrogate data tests. We interpret this result as an approximation to the fractal dimension of a strange attractor governing chaotic dynamics in the menstrual cycle. We also use the time series to calculate the correlation entropy (K2 ≈ 0.008/τ) and the maximal Lyapunov exponent (λ ≈ 0.005/τ) for the system, where τ is the sampling time of the series.

Conclusions: Taken collectively, these results constitute significant evidence that the menstrual cycle is the result of chaos in a nonlinear dynamical system. This view of the menstrual cycle has potential implications for clinical practice, modelling of the endocrine system, and the interpretation of the perimenopausal transition.

No MeSH data available.


Related in: MedlinePlus