Schedule, Notes/Handouts & Videos

Many transgender (trans) men and nonbinary AFAB (assigned female at birth) individuals choose to undergo testosterone replacement therapy, TRT, where they take exogenous testosterone (T) to bring about masculinizing changes in the body. One of these changes is the loss of the menstrual cycle. T has a negative feedback effect on the hypothalamic-pituitary axis (H-P axis) which dampens secretion of luteinizing hormone (LH). LH allows for secondary follicles to develop until the ovulatory phase and then prompts ovulation; therefore, as LH levels decrease, follicles are less likely to complete the ovulatory stage, thus disrupting the regular menstrual cycle. Our model explores the effects of varying dosages of T on the dynamics of the eventual loss of the menstrual cycle.

Endometriosis is a disorder in which endometrial tissue grows on or outside the uterus. While endometriosis affects roughly 190 million females around the world, little research exists exploring both the causes of endometriosis and preventative treatment of progressive factors. One theory for endometriosis is an imbalance of estradiol, E2, and progesterone, P4, in the body. An elevated ratio of E2 to P4 can indicate the growth of endometriosis lesions, which are another source of E2 production. Such lesions disrupt regular E2 levels throughout the menstrual cycle, resulting in continuous endometrium growth. The relationship between E2 levels and lesion growth – and an increased ratio of E2 to P4 – was demonstrated using Margolskee et al.’s 2013 model of the menstrual cycle and Arbel´az-G´omez et al.’s 2022 model of endometrium growth. Periodic exogenous E2 suppression was shown to be an effective treatment for preventing excessive endometrial tissue volume in the presence of lesions.

Type 2 diabetes (T2D) is a disease caused by an excess of blood glucose and insulin resistance in the body. Stress, which is any reaction the body has to environmental changes that threaten its homeostasis, causes the release of hormones such as cortisol. Extended periods of stress from weeks to months, called chronic stress, result in abnormally high levels of glucose, -cell death, and insulin resistance which are all associated with T2D. We were interested in modeling the connection between chronic stress and diabetes. We modified an existing model to analyze the relationship between glucose, insulin, and stress. Then we merged the modified model with an existing model on the Hypothalamic-Pituitary-Adrenal (HPA) Axis that describes cortisol levels under chronic stress. Finally, with the merged model, we examined the response of glucose, insulin, and -cell mass to periodic intervals of stress over extended periods of time.

The female reproductive endocrine system primarily consists of gonadotropin releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), estrogen (estradiol or E2), and progesterone (P4). Pulses of GnRH prompt the production of LH and FSH, which in turn stimulates estradiol and progesterone growth. While a monthly model of these hormones is widely known, our bodies have a circadian rhythm, and certain hormones fluctuate on a daily basis. Studies suggest that these hormones more closely follow a circadian rhythm during the follicular phase. Thus, this research paper will map the fluctuation of the hormones most involved in the menstrual cycle on a minute-by-minute scale, under the influence of melatonin, to demonstrate circadian rhythm during the follicular phase.

Beta cells are cells located in the pancreas that produce insulin. Type 2 diabetes occurs when the body becomes resistant to insulin, causing glucose levels to increase. Patients with type 2 typically experience beta cell apoptosis (cell death) and beta cell dysfunction (failure to secrete insulin). Our research focuses on exogenous 17-Beta estradiol and its impacts on beta cells in people with type 2 diabetes. One of our main research interests was relating metabolism to the reproductive system. We discovered that there is a bidirectional relationship between insulin and estrogen. Using this relationship, we worked to connect two existing models: the BIG model of beta-cells, insulin, and glucose and a model of the menstrual cycle that included estrogen, progesterone, LH, and FSH. To connect the models, we added new terms and parameters to represent the new relationships. Preliminary results showed that due to estrogen’s influence on insulin secretion rate, increasing estrogen increased beta-cell mass.

Gestational Diabetes Mellitus (GDM) is a condition that causes high blood sugar levels in pregnant women, with an observed increased risk of pregnancy complications and developing Diabetes Mellitus (DM) post-pregnancy. Approximately 10.5 pregnancies per 100 deliveries were affected by GDM in 2020, according to the CDC, representing an increase from 4.5 pregnancies per 100 deliveries in 2000. Overall, it affects 5-9% of pregnant women annually in the US. Despite its prevalence and increasing risk for DM, little mathematical modeling has been done to understand the population flow of women diagnosed with GDM into the diabetic population. Understanding the dynamics of a non-diabetic non-pregnant population into a newly diabetic population may serve as a foundation for researching effective interventions at the population level, before, during, and after pregnancy to reduce both the incidence of GDM and DM. We developed a model of pregnant women, focusing exclusively on women without diabetes who develop GDM. Using primarily CDC data to estimate initial parameter values, and assuming a fixed population growth rate, we observed the non-diabetic population converges to roughly 55.5 million and the diabetic population to approximately 470 thousand. The model also captures the dynamic of pregnant women who develop Gestational Diabetes-related complications, and the increased risk factor of developing DM from previous GDM. Equilibrium analysis was conducted to determine the steady state of the solution to the system of ODEs, and we were able to show the positivity and uniform boundedness of the solution. Additionally, sensitivity analysis was conducted on uncertain parameters.