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The Effect of Gonadotropin-Releasing Hormone (GnRH) on the Regulation of Hormones in the Menstrual Cycle: A Mathematical Model

Abstract: 

Gonadotropin Releasing Hormone (GnRH) is the drving force for hormonal regu- lation during the menstrual cycle. GnRH signals the anterior pituitary gland to secrete follicle stimulating hormone (F SH) and luteinizing hormone (LH) which promotes the release of estradiol (E2) and progesterone (P4). Interferences in the cyclic interactions have been shown to cause irregularities in the menstrual cy- cle. In this study, the non-linear dynamics of GnRH, F SH, LH, E2, and P4 are examined. A simplified model of six non-linear ordinary differential equations is developed to model the effect of GnRH on the dynamics of hormones in the men- strual cycle. A mathematical analysis is performed to observe the regulation of GnRH in a monthly cycle. Our findings suggest that the relationship between E2 and GnRH plays an important role in concentrations and patterns of release of the hormones involved in the menstrual cycle.

 

Year: 2018

Authors:

Shanell S. George - Lehman College, The City University of New York, Bronx, NY

Laura O. Mora Mercado - University of Puerto Rico, Mayaguez, PR

Corina Y. Oroz - Pomona College, Claremont, CA

X. Tallana-Chimarro - Yachay Tech University, Urcuqu´ı, Ecuador

Juan R. Melendez-Alvarez - Arizona State University, Tempe, AZ

Anarina L. Murrillo - University of Alabama at Birmingham, Birmingham, AL

Carlos W. Castillo-Garsow - Eastern Washington University, Cheney, WA

Karen R. Rios-Soto - University of Puerto Rico, Mayaguez, PR  
 

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