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- Leona Harris Clark, Paul M Schlosser, James F Selgrade
- Bulletin of mathematical biology
- 2003

This study presents a nonlinear system of delay differential equations to model the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Linear model components for the ovaries and pituitary were previously analyzed and reported separately. Results for the integrated model are now presented here. This model… (More)

A model for hormonal control of the menstrual cycle with 13 ordinary differential equations and 41 parameters is presented. Important changes in model behavior result from variations in two of the most sensitive parameters. One parameter represents the level of estradiol sufficient for significant synthesis of luteinizing hormone, which causes ovulation. By… (More)

- Angelean O Hendrix, Claude L Hughes, James F Selgrade
- Bulletin of mathematical biology
- 2014

Mathematical models of the hypothalamus-pituitary-ovarian axis in women were first developed by Schlosser and Selgrade in 1999, with subsequent models of Harris-Clark et al. (Bull. Math. Biol. 65(1):157-173, 2003) and Pasteur and Selgrade (Understanding the dynamics of biological systems: lessons learned from integrative systems biology, Springer, London,… (More)

- Alison Margolskee, James F Selgrade
- Mathematical biosciences
- 2011

A system of 13 ordinary differential equations with 42 parameters is presented to model hormonal regulation of the menstrual cycle. For an excellent fit to clinical data, the model requires a 36 h time delay for the effect of inhibin on the synthesis of follicle stimulating hormone. Biological and mathematical reasons for this delay are discussed.… (More)

- Alison Margolskee, James F Selgrade
- Journal of theoretical biology
- 2013

A system of 16 non-linear, delay differential equations with 66 parameters is developed to model hormonal regulation of the menstrual cycle of a woman from age 20 to 51. This mechanistic model predicts changes in follicle numbers and reproductive hormones that naturally occur over that time span. In particular, the model illustrates the decline in the pool… (More)

- Angelean O Hendrix, James F Selgrade
- Journal of theoretical biology
- 2014

A system of 16 differential equations is described which models hormonal regulation of the menstrual cycle focusing on the effects of the androgen testosterone (T) on follicular development and on the synthesis of luteinizing hormone (LH) in the pituitary. Model simulations indicate two stable menstrual cycles - one cycle fitting data in the literature for… (More)

- Leona A Harris, James F Selgrade
- Mathematical biosciences
- 2014

This article reviews an effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women. The procedure captures the effects of hormones secreted by several glands over multiple time scales. The specific model described here consists of 13 nonlinear, delay, differential equations with 44 parameters and correctly… (More)

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