Investigating the Interplay Between Reproductive Hormones and Ovarian Follicles

Menstrual-cycle-related disorders—such as dysmenorrhea, menorrhagia, premenstrual syndrome, endometriosis, and polycystic ovary syndrome (PCOS)—are not uncommon among people who experience menstrual cycles. Symptoms of menstrual disorders include pain, heavy bleeding, anxiety, depression, and fatigue, all of which can significantly affect one’s ability to work, engage with the public, and become a parent. In many cases, the underlying causes of menstrual-based conditions are poorly understood. Given the considerable impact of menstrual disorders on individuals and society as a whole, it is crucial that we better understand menstrual health norms, the root causes of menstrual-cycle-related diseases, and potential enhancements that will improve overall quality of life.

Key steps in the human menstrual cycle are as follows: 

1. Maturation of ovarian follicles (the cellular unit that carries the egg cell)
2. Release of (usually) one egg cell via ovulation 
3. Preparation of the uterus lining for the implantation of a fertilized egg cell
4. Shedding of the uterus lining via menstruation in the absence of fertilization. 

The menstrual cycle comprises two distinct phases: (i) the follicular phase, which begins with menstrual bleeding and ends with ovulation, and (ii) the luteal phase, which begins after ovulation and ends with the onset of menstruation.

The characteristic series of menstrual cycle events is controlled by feedback actions between hormones that are secreted from the hypothalamus, pituitary gland, and ovaries, which are collectively known as the hypothalamic-pituitary-gonadal (HPG) axis (see Figure 1). The hypothalamus outputs distinct patterns of the gonadotropin-releasing hormone, which regulates the release of the follicle-stimulating hormone (FSH) and the luteinizing hormone (LH). The concentration of FSH increases at the beginning of a menstrual cycle, triggering the growth of a group of ovarian follicles that produce estradiol (E2). The subsequent rise in E2 levels then inhibits FSH secretion from the pituitary gland; FSH levels consequently decrease and the FSH-dependent stimulation of follicular growth ceases. At this point of the menstrual cycle, one follicle is usually mature enough to continue to grow without FSH stimulation and further increase its E2 production.

This increase in E2 concentration stimulates the release of LH from the pituitary gland. The resulting LH peak occurs mid-cycle and triggers ovulation for the mature follicle (in rare cases, more than one follicle may ovulate). After ovulation, the follicle’s E2 production stops and its cellular parts become the corpus luteum: a temporary structure with a vital function in hormone production. The corpus luteum is now the primary source of E2 and progesterone (P4), the simultaneous release of which suppresses the release of FSH. If the egg cell from the previous ovulation was not fertilized, the production of E2 and P4 halts with the degradation of the corpus luteum, and menstruation commences.

As evidenced, regulation of the menstrual cycle spans multiple time scales and organizational levels. Mathematical modeling can thus help portray the menstrual cycle as a multidimensional, interactive, dynamic, and nonlinear complex system [6]. To systematically understand the relationship between the cyclic maturation of ovarian follicles and the dynamics of reproduction hormones, we developed a mechanistic model in the form of a system of ordinary differential equations (ODEs) and algebraic equations [2, 4]. The mathematical description of the time evolution of hormone concentrations is based on synthesis-clearance relationships and encodes the feedback actions between hormones with Hill functions. Each emerging ovarian follicle is described by a single ODE; while this ODE has the same structure for every follicle, their unique parametrizations result in varying growth behaviors. In particular, every follicle that is initialized within a simulation run carries two follicle-specific properties: time of initialization and sensitivity to FSH.

Our proposed menstrual cycle model enables the simulation of hormone profiles and the growth of ovarian follicles over consecutive menstrual cycles (see Figure 2). These simulated hormone profiles agree with clinical observations of a healthy menstrual cycle in terms of profile shapes, hormone concentration ranges, and average cycle length. Figure 2e depicts the growth trajectories of ovarian follicles. One follicle maturates fully and ovulates within each simulated cycle, while all other follicles undergo atresia (degeneration). Which follicle ovulates depends on multiple factors, including initialization time and endocrine environment. As Figure 2f illustrates, the first follicle that is initialized is not necessarily the one that will ovulate. In our simulation results, ovarian follicles also grow in so-called waves (groups of follicles that mature together); this emergent property aligns with ultrasound measurements that describe ovarian follicular wave dynamics in women [1].

Our menstrual cycle model exhibits variability in follicular growth, which results in variability in hormone profiles (see Figure 2e) and cycle length. This attribute is a valuable feature of the model, as menstrual cycle length and its variability are essential indicators of reproductive health. However, the model neglects other factors—such as changes in lifestyle or contraception—that may also affect menstrual cycle length.

To validate the model and demonstrate the breadth of its potential applications, we performed in silico trials of protocols for controlled ovarian stimulation (COS). COS is a suite of medical interventions that seek to mature a cohort of ovarian follicles by inducing changes in the endocrine environment. Our recent work provides simulation results of two ovarian stimulation protocols that we implemented in the model by following established pharmacokinetic principles [2]. Figures 3a-3e summarize simulation results for COS in the luteal phase of the menstrual cycle; in this protocol, the stimulation of ovarian follicle growth with FSH begins one to three days after the last ovulation. Figures 3f-3j shows the simulation of COS in the late follicular phase; here, stimulatory treatment with FSH begins when at least one follicle is 14 millimeters in diameter. The protocol’s characteristic feature is that one ovulation occurs within the treatment interval (see Figure 3j). For both procedures, our simulation results agree with clinical reports about treatment duration and response.

Here, we introduce the first mechanistic model of the human menstrual cycle that describes the relationship between key reproductive hormones and individual ovarian follicles over consecutive menstrual cycles. Our population-based model describes certain sources of intra- and interindividual variability in nonpathological menstrual cycles, and coupling it with pharmacokinetic models allows us to simulate COS treatment strategies. In future studies, our model might help optimize treatments in terms of doses and dosing time points; it could even serve as a starting point for the investigation of menstrual cycle characteristics that pertain to pathological cases like PCOS or endometriosis. Eventually, we may be able to fit the model to individual patient data, which would pave the way for its use in clinical decision support.

Sophie Fischer-Holzhausen delivered a minisymposium presentation on this research at the 2023 SIAM Conference on Applications of Dynamical Systems (DS23), which took place in Portland, Ore., last year. She received funding to attend DS23 through a SIAM Student Travel Award. To learn more about Student Travel Awards and submit an application, visit the online page.

SIAM Student Travel Awards are made possible in part by the generous support of our community. To make a gift to the Student Travel Fund, visit the SIAM website.

Acknowledgments: The authors would like to thank Eder Zavala (University of Birmingham) for the invitation to contribute to the DS23 minisymposium.

References

[1] Baerwald, A.R., Adams, G.P., & Pierson, R.A. (2003). Characterization of ovarian follicular wave dynamics in women. Biol. Reprod., 69(3), 1023-1031.
[2] Fischer, S., Ehrig, R., Schäfer, S., Tronci, E., Mancini, T., Egli, M., … Röblitz, S. (2021). Mathematical modeling and simulation provides evidence for new strategies of ovarian stimulation. Front. Endocrinol., 12, 613048.
[3] Fischer-Holzhausen, S. (2023). A matter of timing: A modelling-based investigation of the dynamic behaviour of reproductive hormones in girls and women [Ph.D. thesis, Department of Informatics, University of Bergen]. Bergen Open Research Archive.
[4] Fischer-Holzhausen, S., & Röblitz, S. (2022). Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities. J. Theor. Biol., 547, 111150.
[5] Fischer-Holzhausen, S., & Röblitz, S. (2022). Mathematical modelling of follicular growth and ovarian stimulation. Curr. Opin. Endocr. Metab. Res., 26, 100385.
[6] Zavala, E., Wedgwood, K.C.A., Voliotis, M., Tabak, J., Spiga, F., Lightman, S.L., & Tsaneva-Atanasova, K. (2019). Mathematical modelling of endocrine systems. Trends Endocrinol. Metab., 30(4), 244-257.