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A Mechanistic Model of the Human Menstrual Cycle

Lena Reitinger, Nina Nikic, Esma Hamzic-Jahic, Barbara Arbeithuber, Andreas Springer, Werner Haselmayr, Stefan Angerbauer

arXiv:2610.03053v1cs.ET

TL;DR

Existing menstrual-cycle models either simplify biological mechanisms or incur greater mathematical complexity and computational cost to represent them. This paper develops a comparatively simple ODE model of four cycle-driving hormones with mechanistic detail, and reports that it reproduces published hormone trends while representing a periodic cycle.

  • Problem

    Existing models trade simplified descriptions of biological processes for greater complexity and computational cost as they add physiological detail.

    Source: §I · p. 1, A. State-of-the-Art · p. 2

  • Method

    The authors model FSH, LH, E2, and P4 with a 10-dimensional ODE system, incorporating mechanistic representations of follicular development and the corpus luteum.

    Source: §I · p. 1, B. Follicle and corpus luteum · p. 5

  • Results

    The model reproduces trends in published hormone activity and concentration data, with all four simulated hormone levels ending at their cycle-start values.

    Source: §IV · p. 7, §V · p. 8

  • Takeaways & Limitations

    The authors present the comparatively low-cost model as a systemic background for models of related reproductive processes and as a basis for more comprehensive models.

    Source: §V · p. 8

    The model does not reproduce the commonly assumed temporal shift between the mid-cycle E2 and FSH/LH peaks, a timing refinement the authors relinquished to keep the structure simple.

    Source: §IV · p. 7

Abstract

from arXiv · show

The human menstrual cycle is regulated by complex hormonal feedback mechanisms which are essential for reproductive health. Existing mathematical models either rely on simplified phenomenological assumptions or achieve physiological accuracy at the cost of high mathematical complexity and computational costs. This paper presents a novel mechanistic model which balances biological realism with mathematical simplicity. The proposed framework describes the dynamics of the four central cycle-driving hormones, namely follicle stimulating hormone, luteinizing hormone, estradiol, and progesterone, using a system of ordinary differential equations. Mechanistic detail is incorporated through representations of feedback mechanisms, follicular development, luteinization, vascularization of the corpus luteum, and aspects of hormone synthesis mechanisms. Despite its comparatively low complexity, the model reproduces characteristic trends of hormone activity and concentration dynamics reported in experimental data. Due to its computational efficiency and modularity, the model is well suited as a basis for extended in-silico experiments, including applications in pharmacology and personalized medicine. Our results demonstrate that targeted incorporation of biological mechanisms enables accurate yet tractable modeling of endocrine system dynamics.

I. INTRODUCTION

Existing menstrual-cycle models trade mechanistic detail for mathematical simplicity, or physiological realism for greater complexity and computational cost. This work aims to model four cycle-driving hormones with targeted biological mechanisms while retaining a comparatively simple structure.

I. INTRODUCTION

  • The work seeks to retain mechanistic detail while modeling monthly hormone dynamics for the four central cycle-driving hormones.The introduction identifies the menstrual cycle as important to health and reproductive capacity.Source: §I · p. 1, A. State-of-the-Art · p. 1
  • The proposed model represents FSH, LH, E2, and P4 in a 10-dimensional ODE system with 40 parameters.The authors describe it as physiologically meaningful and practically applicable.Source: §I · p. 1

A. State-of-the-Art

  • Earlier models range from a five-dimensional ODE model with decision functions to models using delayed feedback and more detailed ovarian development.The cited frame model has 13 dimensions and 42 parameters; a GnRH-inclusive model has 33 dimensions and 114 parameters.Source: A. State-of-the-Art · p. 2
  • The model targets the trade-off between simplified descriptions of biology and the complexity and computational cost of more detailed models.The authors propose improving simple mechanistic models through targeted incorporation of biological processes rather than more complex mathematical structures.Source: §I · p. 1, A. State-of-the-Art · p. 2

B. Contributions

The paper presents a comparatively simple mechanistic model and reports that it reproduces published hormone trends. The authors also describe potential uses as a low-cost background for related models and as a starting point for patient-specific and other research questions.

B. Contributions

  • The proposed model is simpler than existing models while using more detailed mechanistic understanding to represent biological processes.The authors attribute the reduction in complexity to more concise mathematical representations of those processes.Source: B. Contributions • · p. 2
  • Its comparatively low computational cost makes the model a proposed background for models of related reproductive processes and a starting point for pharmacological and pathology-related research.Examples of related processes include embryo implantation and endometrial recovery.Source: B. Contributions • · p. 2
  • The model reproduces trends from published data with estimated parameters and is described as personalizable to an individual patient's trends.The published FSH, LH, E2, and P4 courses in Fig. 3 are the stated simulation target.Source: B. Contributions • · p. 3, Figure 3 · p. 3

II. THE MENSTRUAL CYCLE

The menstrual cycle involves monthly rebuilding and shedding of the uterine lining, regulated by coordinated hormone interactions. This process prepares the uterine environment for possible pregnancy; without pregnancy, the lining breaks down and menstruation follows.

II. THE MENSTRUAL CYCLE

  • The endometrium is approximately monthly shed and rebuilt during the menstrual cycle.The endometrium is the inner lining of the uterus.Source: §II · p. 3
  • Rebuilding the uterine lining prepares an environment where a blastocyst can implant and develop if pregnancy occurs.Source: §II · p. 3
  • When pregnancy does not occur, the uterine environment is destructed and breakdown of the lining results in menstruation.Source: §II · p. 3
  • Hormones regulate the menstrual-cycle processes through coordinated interactions.Source: §II · p. 3

A. Phases of the menstrual cycle

The average cycle lasts about 28 days and is divided into menstruation, follicular, ovulatory, and luteal phases. The phases encompass endometrial shedding and regrowth, follicle maturation and ovulation, and post-ovulatory transformation of the follicle's remaining cells.

A. Phases of the menstrual cycle

  • The average cycle lasts approximately 28 days and comprises menstruation, follicular, ovulatory, and luteal phases.In Fig. 3, the time axis is centered on ovulation, so menstruation begins at day -14.Source: A. Phases of the menstrual cycle · p. 3
  • During menstruation, the endometrium's functional layer is shed while its basal layer remains and supports subsequent regrowth.The functional layer starts to regrow from the residual basal layer after menstruation.Source: A. Phases of the menstrual cycle · p. 3
  • During the follicular phase, FSH induces maturation of 5 to 11 follicles, after which the follicle responding best to its growth environment becomes dominant.The other follicles are degraded; FSH and LH stimulate proliferation of granulosa and theca cells, respectively.Source: A. Phases of the menstrual cycle · p. 3
  • A rapid LH surge triggers ovulation, releasing the mature oocyte from the follicle into the neighboring fallopian tube.Ovulation is described as occurring for approximately one day around day 15.Source: A. Phases of the menstrual cycle · p. 3
  • After ovulation, LH-associated luteinization transforms the ruptured follicle's granulosa and theca cells into the corpus luteum, which is later degraded unless pregnancy occurs.The transformation includes cessation of cell-cycle progression, altered gene expression, and proliferation of vascular endothelial cells that form a dense capillary network.Source: A. Phases of the menstrual cycle · pp. 3–4

B. Hormonal interactions

FSH and LH secretion responds to hypothalamic GnRH pulses and steroid feedback, while ovarian steroid production shifts from the growing follicle to the corpus luteum. E2 feedback changes from inhibitory to stimulatory at sustained high levels, and P4 inhibits gonadotropin synthesis during the luteal phase.

B. Hormonal interactions

  • Pulsatile GnRH release from the hypothalamus stimulates pituitary FSH and LH production, with lower and higher pulse frequencies linked to the respective hormones.Both hormones act on the ovaries; FSH also supports follicular growth and estrogen synthesis.Source: B. Hormonal interactions · p. 4
  • As the dominant follicle grows, rising E2 first inhibits FSH and, to a lesser extent, LH, then sustained high E2 stimulates both hormones and induces their peaks.The account links the feedback switch to sustained high E2 levels.Source: B. Hormonal interactions · p. 4
  • After luteinization, the corpus luteum produces P4 while continuing lower E2 production, and these steroids inhibit FSH and LH; without pregnancy, P4 falls and luteolysis begins another cycle.With pregnancy, hCG maintains high P4 levels.Source: B. Hormonal interactions · p. 4

III. METHODS

The methods develop an ODE model for the temporal concentrations of FSH, LH, E2, and P4, aiming to include biological mechanisms without high mathematical complexity. Hill functions represent hormone feedback, with the model overview linking GnRH, gonadotropins, and ovarian steroid production.

III. METHODS

  • The model aims to predict temporal concentrations of FSH, LH, E2, and P4 while keeping mathematical complexity low through mechanistic detail.The corresponding equations are derived in the methods, and Fig. 5 depicts the main components.Source: §III · p. 4
  • The model overview links GnRH levels to FSH and LH synthesis through pulse-frequency encoding and shows E2 and P4 feedback on GnRH synthesis.The ovarian follicle and its successor, the corpus luteum, produce the steroid hormones; E2 can stimulate or inhibit feedback at high or lower levels, respectively.Source: Figure 5 · p. 4
  • Hill functions represent feedback by modeling interactions between hormones and receptors on ovarian or pituitary neuronal cells.The Hill coefficient n controls curve steepness, while K regulates its turning point; K corresponds to the feedback-hormone concentration triggering that turning point.Source: §III · pp. 4–5

A. Gonadotropic hormones (FSH, LH)

FSH and LH dynamics are modeled as synthesis and degradation shaped by E2 and P4 feedback. E2 inhibits gonadotropins during the early cycle, stimulates a mid-cycle surge at high levels, and P4 contributes inhibition during the luteal phase.

A. Gonadotropic hormones (FSH, LH)

  • FSH and LH synthesis depends on E2 feedback, with basal synthesis rates and constant blood-degradation rates included in their dynamics.Initial hormone levels are set above zero to reflect reported activity near the cycle's beginning and end.Source: A. Gonadotropic hormones (FSH, LH) · p. 5
  • During menstruation and the follicular phase, rising E2 increasingly inhibits gonadotropin secretion, corresponding to declining FSH and LH levels during the first 12 cycle days.The passage notes a slight initial FSH increase before inhibition.Source: A. Gonadotropic hormones (FSH, LH) · p. 5
  • At high E2 levels, activating feedback produces mid-cycle peaks in FSH and LH, after which gonadotropin levels decrease as E2 falls.The activating Hill-term parameters are specified as the E2 levels inducing those peaks.Source: A. Gonadotropic hormones (FSH, LH) · p. 5
  • During the luteal phase, increasing E2 and P4 concentrations inhibit FSH and LH synthesis through a separate feedback term.The passage describes the term as decreasing as the combined steroid concentration rises.Source: A. Gonadotropic hormones (FSH, LH) · p. 5

B. Follicle and corpus luteum

Follicular growth is represented through proliferating cell-cycle phases, followed by LH-triggered arrest and luteinization into corpus-luteum cells. The model treats the follicle and its luteinized remnant as steroid-production sites.

B. Follicle and corpus luteum

  • Follicular growth is modeled as stroma cells passing through G1, S, G2, and M, with cell-cycle transitions and division represented in the dynamics.The factor 2 in the G1 equation represents one cell becoming two after a cycle; phase-specific death rates are also included.Source: B. Follicle and corpus luteum · p. 5
  • When LH rises above a preset threshold, a switch-like arrest rate withdraws cells from each proliferating phase into a resting state.The resting cells are degraded at a constant rate.Source: B. Follicle and corpus luteum · pp. 5–6
  • With cell-cycle arrest and high LH, non-proliferating cells undergo luteinization and become cells of the corpus luteum.The model represents this transition at a luteinization rate, while luteinized cells also have a death rate.Source: B. Follicle and corpus luteum · p. 6

C. Steroid hormones (E2, P4)

Estradiol and progesterone synthesis is linked to the cells that produce them, with progesterone additionally depending on corpus luteum vascularization. The model represents steroid synthesis pathways and vascularization dynamics with simplifying assumptions about precursor and intermediate states.

C. Steroid hormones (E2, P4)

  • Estradiol is produced by granulosa cells after theca-cell androgens are aromatized, while luteinized theca and granulosa cells synthesize progesterone from cholesterol.Because protein synthesis is fast relative to the model's day-scale dynamics, precursor molecules and intermediates are assumed to be at steady state.Source: C. Steroid hormones (E2, P4) · p. 6
  • The model gives estradiol a basal synthesis rate and constant-rate degradation, with two activating Hill terms involving granulosa and lutein cell numbers.Reported initial estradiol concentrations are approximately 50 pg/mL, and the model uses nonzero initial conditions.Source: C. Steroid hormones (E2, P4) · p. 6
  • Corpus luteum vascularization is modeled as logistic growth limited by its capacity, with vascular-cell death at a constant rate.Vascularization supplies circulating cholesterol to progesterone-producing lutein cells.Source: C. Steroid hormones (E2, P4) · p. 6
  • Progesterone levels depend on both the number of progesterone-producing lutein cells and corpus luteum vascularization.Its synthesis rate is modeled as constant.Source: C. Steroid hormones (E2, P4) · p. 6

IV. RESULTS AND DISCUSSION

Simulations reproduce published hormone trends and return all four hormones to their starting values by cycle end, supporting periodicity.

IV. RESULTS AND DISCUSSION

  • The simulated 28-day cycle reproduces published hormone activity and concentration trends, with all four hormones ending at their starting values.Source: §IV · pp. 6–7, Figure 6 · p. 7
  • FSH reproduces first-half trends and early-follicular and pre-ovulatory peaks, with an additional luteal peak not reported in but seen in patient-specific data.Source: §IV · p. 7
  • LH shows a mid-cycle peak and near-zero levels in other phases; its peak precedes ovulation, while levels remain above zero during the luteal phase.Source: §IV · p. 7
  • E2 shows a preovulatory peak near 300 pg/mL and a second luteal-phase peak, although reported luteal patterns vary across data sources.Source: §IV · p. 7
  • P4 begins rising mid-cycle, peaks around days 19–20, then declines more steeply than reported data to approach zero by cycle end.The steeper decline is intended to support periodicity.Source: §IV · p. 7
  • The model does not reproduce the commonly reported temporal shift between mid-cycle E2 and FSH/LH peaks, retaining tightly coupled feedback to limit complexity.Source: §IV · p. 7

V. CONCLUSION AND OUTLOOK

The paper presents a compact mechanistic model of four cycle-driving hormones that reproduces published trends. It is computationally inexpensive and proposed as a basis for broader physiological and personalized simulations.

V. CONCLUSION AND OUTLOOK

  • The model represents monthly FSH, LH, E2, and P4 courses in a 10-dimensional ODE system with 40 parameters.Source: §V · p. 8
  • Simulations indicate that the structurally simple model reproduces trends in published hormone activity and concentration data without costly delay differential equations.Source: §V · p. 8
  • The model is proposed as a low-cost systemic background for embryo implantation and endometrial recovery models.Source: §V · p. 8
  • Future work could fit parameters to individual patient data for hormone-level simulations in pharmacology or in-vitro fertilization planning.Source: §V · p. 8
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