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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

Correlation entropy results. Logarithmic variation of the correlation sums with embedding dimension for a fixed R in the low R limit, illustrating the expected behavior for a chaotic system. Slope of the resulting straight line yields the correlation entropy.
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Figure 3: Correlation entropy results. Logarithmic variation of the correlation sums with embedding dimension for a fixed R in the low R limit, illustrating the expected behavior for a chaotic system. Slope of the resulting straight line yields the correlation entropy.

Mentions: which approximates the Kolmogorov-Sinai entropy of a chaotic system. From this relationship, we see that a plot of -ln[C(d)] vs d for a fixed R should be a straight line with slope K2ΔT. For the smallest experimentally accessible value of R and for large d (consistent with the theoretical validity of Equation 3 in the R→0 and d→∞ limits), we observe behavior consistent with this predicted relationship, as shown in Figure 3. From the slope of the resulting line, we find that K2 ≈ 0.008/τ for this system, where τ is the sampling time used to construct the time series. The fact that the K2 value computed in this way has the correct sign and that the overall behavior of K2 with variations in d and R is consistent with our expectations for chaotic systems offers further evidence of non-linear dynamics in the menstrual cycle.


Characterization of chaotic dynamics in the human menstrual cycle.

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

Correlation entropy results. Logarithmic variation of the correlation sums with embedding dimension for a fixed R in the low R limit, illustrating the expected behavior for a chaotic system. Slope of the resulting straight line yields the correlation entropy.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Correlation entropy results. Logarithmic variation of the correlation sums with embedding dimension for a fixed R in the low R limit, illustrating the expected behavior for a chaotic system. Slope of the resulting straight line yields the correlation entropy.
Mentions: which approximates the Kolmogorov-Sinai entropy of a chaotic system. From this relationship, we see that a plot of -ln[C(d)] vs d for a fixed R should be a straight line with slope K2ΔT. For the smallest experimentally accessible value of R and for large d (consistent with the theoretical validity of Equation 3 in the R→0 and d→∞ limits), we observe behavior consistent with this predicted relationship, as shown in Figure 3. From the slope of the resulting line, we find that K2 ≈ 0.008/τ for this system, where τ is the sampling time used to construct the time series. The fact that the K2 value computed in this way has the correct sign and that the overall behavior of K2 with variations in d and R is consistent with our expectations for chaotic systems offers further evidence of non-linear dynamics in the menstrual cycle.

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