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Related Concept Videos

The Menstrual Cycle01:19

The Menstrual Cycle

The menstrual cycle is a recurrent sequence of changes in the uterine endometrium, specifically its functional layer, the stratum functionalis. This cycle prepares the uterus for potential pregnancy. This cycle typically spans 21–35 days, averaging 28 days, and aligns with the ovarian cycle, regulated by fluctuating levels of ovarian hormones, primarily estrogen and progesterone.
The menstrual phase occurs from days 1 to 5 and involves the shedding of the stratum functionalis, as a uterine...
Hormonal Regulation of the Menstrual Cycle01:22

Hormonal Regulation of the Menstrual Cycle

The ovarian cycle regulates endometrial changes throughout a single menstrual cycle via the coordinated action of gonadotrophin-releasing hormone (GnRH) and gonadotrophins.
At puberty, GnRH begins a pulsatile release pattern, which triggers the anterior pituitary gland to secrete follicle-stimulating hormone (FSH) and luteinizing hormone (LH). The frequency and amplitude of GnRH pulses vary across the menstrual cycle, with faster pulses favoring LH release and slower pulses favoring FSH release.
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
Ovarian Cycle01:27

Ovarian Cycle

The menstrual cycle includes a critical component known as the ovarian cycle, which undergoes two main phases each month—the follicular phase and the luteal phase. The follicular phase is variable and averaging around 14 days. Ovulation, triggered by a surge in luteinizing hormone (LH), marks the transition between the two phases. The second phase, the luteal phase, is relatively consistent, lasting approximately 14 days, and is marked by the activity of the corpus luteum. While a cycle length...
Hormonal Control of the Ovarian Cycle01:30

Hormonal Control of the Ovarian Cycle

The ovarian cycle is meticulously regulated by the hypothalamic-pituitary-gonadal axis. This cycle orchestrates the release of a mature oocyte, essential for reproduction.
Before puberty, the hypothalamus releases GnRH in a low frequency, low amplitude pulsatile manner. This along with the immature hypothalamic-pituitary-gonadal axis activity, results in low estrogen levels and the absence of a fully functional ovarian cycle.  At puberty, GnRH secretion increases in both frequency and...
Menses Phase01:18

Menses Phase

The uterine cycle begins with the menstrual phase, which is considered day one of the cycle and typically lasts about five days. This phase is characterized by the degeneration and shedding of the stratum functionalis, the functional layer of the endometrium.
When fertilization does not occur, the corpus luteum deteriorates, causing a significant drop in the levels of estrogen and progesterone in the body. This hormonal decrease triggers the release of prostaglandins, which cause the uterine...

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Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle
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Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle

Published on: August 30, 2021

A mathematical model for the human menstrual cycle.

C Y Chen1, J P Ward

  • 1Department of Applied Mathematics, The National University of Kaohsiung, Kaohsiung, Taiwan.

Mathematical Medicine and Biology : a Journal of the IMA
|January 19, 2013
PubMed
Summary
This summary is machine-generated.

A mathematical model of the human menstrual cycle reveals normal and abnormal hormonal patterns. The model framework, including receptor down-regulation, aligns with physiological observations for hormonal therapies.

Keywords:
Hopf bifurcationdelay differential equationsmathematical modellingmenstrual cycleperiodic solutions

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Area of Science:

  • Reproductive endocrinology
  • Mathematical modeling
  • Computational biology

Background:

  • The human menstrual cycle involves complex hormonal interactions within the hypothalamus-pituitary-ovaries axis.
  • Understanding these dynamics is crucial for identifying cycle abnormalities and developing effective hormonal therapies.

Purpose of the Study:

  • To develop a mathematical model framework for the human menstrual cycle's hormonal interactions.
  • To extend the model to simulate processes disrupting normal cycle function, such as receptor down-regulation.
  • To assess the model's ability to represent physiological observations, including responses to hormonal therapies.

Main Methods:

  • Development of a simple mathematical model for the hypothalamus-pituitary-ovaries axis hormonal regulation.
  • Analysis of model's periodic solutions to identify characteristics of normal and abnormal menstrual cycles.
  • Extension of the basic model to incorporate receptor down-regulation for simulating pituitary desensitization.

Main Results:

  • The basic model yielded multiple periodic solutions, with one exhibiting key features of a normal menstrual cycle.
  • Other solutions indicated potential abnormalities observed in women of reproductive age.
  • The extended model qualitatively agreed with physiological observations of pituitary desensitization during hormonal therapy.

Conclusions:

  • The developed mathematical framework effectively models the hormonal dynamics of the human menstrual cycle.
  • The model provides insights into both normal cycle function and potential abnormalities.
  • The framework is adaptable for simulating disruptions and evaluating hormonal therapies, such as those used for uterine fibroids.