A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data

Selgrade, James F.; Harris, Leona A.; Pasteur, R. Drew

doi:10.1016/j.jtbi.2009.06.017

Cited by 26 publications

(20 citation statements)

References 13 publications

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“…The ovarian system of previous models [15,22,35,36] used first-order FSH terms to initiate follicular growth. However, Zeleznik [44] suggests that FSH levels must exceed a threshold to initiate follicular development.…”

Section: The Ovarian Systemmentioning

confidence: 99%

A delay differential equation model of follicle waves in women

Panza

Wright

Selgrade

2015

Journal of Biological Dynamics

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This article presents a mathematical model for hormonal regulation of the menstrual cycle which predicts the occurrence of follicle waves in normally cycling women. Several follicles of ovulatory size that develop sequentially during one menstrual cycle are referred to as follicle waves. The model consists of 13 nonlinear, delay differential equations with 51 parameters. Model simulations exhibit a unique stable periodic cycle and this menstrual cycle accurately approximates blood levels of ovarian and pituitary hormones found in the biological literature. Numerical experiments illustrate that the number of follicle waves corresponds to the number of rises in pituitary follicle stimulating hormone. Modifications of the model equations result in simulations which predict the possibility of two ovulations at different times during the same menstrual cycle and, hence, the occurrence of dizygotic twins via a phenomenon referred to as superfecundation. Sensitive parameters are identified and bifurcations in model behaviour with respect to parameter changes are discussed. Studying follicle waves may be helpful for improving female fertility and for understanding some aspects of female reproductive ageing.

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Section: The Ovarian Systemmentioning

confidence: 99%

A delay differential equation model of follicle waves in women

Panza

Wright

Selgrade

2015

Journal of Biological Dynamics

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“…These simulations are discussed in detail in [15,43] and will be described briefly here. Using appropriate initial conditions, we observe the existence of two locally asymptotically stable periodic solutions for the same set of parameter values.…”

Section: Parameter Estimation and Model Simulationsmentioning

confidence: 99%

“…As such, it is important to determine how sensitive the model is to changes in the model parameters. A local sensitivity analysis of the model parameters was performed by Selgrade et al [43] to determine the effects of small variations in the model parameters on model outputs. In this analysis, a normalized sensitivity coefficient for each model parameter was measured by calculating discrete changes in a model output (relative to the output value) divided by changes in a model parameter (relative to the parameter value).…”

Section: Sensitivity Analysis and Bifurcation Analysismentioning

confidence: 99%

“…Selgrade et al [43] decided to use the height of the E2 mid-cycle peak along the normal cycle as the model output in this analysis because a significant follicular phase rise in E2 stimulates the secretion of LH and causes the LH surge needed for ovulation and normal ovarian function. After computing the normalized sensitivity coefficients for the 44 model parameters, Selgrade et al [43] found that the E2 mid-cycle peak was most sensitive to small variations in six parameters: a; Km LH ; c 2 ; V FSH ; c 1 , and V 0;LH .…”

Section: Sensitivity Analysis and Bifurcation Analysismentioning

confidence: 99%

“…Over the last 10-15 years, we have developed and analyzed mechanistic, deterministic, mathematical models [14,15,17,23,32,39,[41][42][43][44] which predict average serum concentrations of reproductive hormones that agree with data in the biological literature for normally cycling adult women [27,50]. This article reviews the procedure which we and other modelers, e.g., Boer et al [3], Bogumil et al [4,5], Chen and Ward [7], Reinecke and Deuflhard [34], Röblitz et al [35], and Zeeman et al [55], have found effective for modeling hormonal regulation of the female reproductive system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling endocrine regulation of the menstrual cycle using delay differential equations

Harris¹,

Selgrade²

2014

Mathematical Biosciences

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Mathematical Modeling in Neuroendocrinology

Bertram

2015

Comprehensive Physiology

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Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.

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A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data

Cited by 26 publications

References 13 publications

A delay differential equation model of follicle waves in women

A delay differential equation model of follicle waves in women

Modeling endocrine regulation of the menstrual cycle using delay differential equations

Mathematical Modeling in Neuroendocrinology

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