Modeling endocrine regulation of the menstrual cycle using delay differential equations

Toward an optimal contraception dosing strategy

Anovulation refers to a menstrual cycle characterized by the absence of ovulation. Exogenous hormones such as synthetic progesterone and estrogen have been used to attain this state to achieve contraception. However, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This study utilizes optimal control theory on a modified menstrual cycle model to determine the minimum total exogenous estrogen/progesterone dose, and timing of administration to induce anovulation. The mathematical model correctly predicts the mean daily levels of pituitary hormones LH and FSH, and ovarian hormones E2, P4, and Inh throughout a normal menstrual cycle and reflects the reduction in these hormone levels caused by exogenous estrogen and/or progesterone. Results show that it is possible to reduce the total dose by 92% in estrogen monotherapy, 43% in progesterone monotherapy, and that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. Finally, we show that by combining estrogen and progesterone the dose can be lowered even more. These results may give clinicians insights into optimal formulations and schedule of therapy that can suppress ovulation.

Reduced model for female endocrine dynamics: Validation and functional variations

A normally functioning menstrual cycle requires significant crosstalk between hormones originating in ovarian and brain tissues. Reproductive hormone dysregulation may cause abnormal function and sometimes infertility. The inherent complexity in this endocrine system is a challenge to identifying mechanisms of cycle disruption, particularly given the large number of unknown parameters in existing mathematical models. We develop a new endocrine model to limit model complexity and use simulated distributions of unknown parameters for model analysis. By employing a comprehensive model evaluation, we identify a collection of mechanisms that differentiate normal and abnormal phenotypes. We also discover an intermediate phenotype-displaying relatively normal hormone levels and cycle dynamics-that is grouped statistically with the irregular phenotype. Results provide insight into how clinical symptoms associated with ovulatory disruption may not be detected through hormone measurements alone.

In silico modeling of endocrine organ-on-a-chip systems

The organ-on-a-chip (OoC) is an artificially reconstructed microphysiological system that is implemented using tissue mimics integrated into miniaturized perfusion devices. OoCs emulate dynamic and physiologically relevant features of the body, which are not available in standard in vitro methods. Furthermore, OoCs provide highly sophisticated multi-organ connectivity and biomechanical cues based on microfluidic platforms. Consequently, they are often considered ideal in vitro systems for mimicking self-regulating biophysical and biochemical networks in vivo where multiple tissues and organs crosstalk through the blood flow, similar to the human endocrine system. Therefore, OoCs have been extensively applied to simulate complex hormone dynamics and endocrine signaling pathways in a mechanistic and fully controlled manner. Mathematical and computational modeling approaches are critical for quantitatively analyzing an OoC and predicting its complex responses. In this review article, recently developed in silico modeling concepts of endocrine OoC systems are summarized, including the mathematical models of tissue-level transport phenomena, microscale fluid dynamics, distant hormone signaling, and heterogeneous cell-cell communication. From this background, whole chip-level analytic approaches in pharmacokinetics and pharmacodynamics will be described with a focus on the spatial and temporal behaviors of absorption, distribution, metabolism, and excretion in endocrine biochips. Finally, quantitative design frameworks for endocrine OoCs are reviewed with respect to support parameter calibration/scaling and enable predictive in vitro-in vivo extrapolations. In particular, we highlight the analytical and numerical modeling strategies of the nonlinear phenomena in endocrine systems on-chip, which are of particular importance in drug screening and environmental health applications.

Characterization of salivary progesterone in female smokers

INTRODUCTION

Fluctuations in ovarian hormones have been associated with changes in cigarette smoking behavior, which can be measured through both serum or less invasive salivary procedures. The primary aim of this exploratory study is to characterize the progesterone profiles of salivary progesterone measurements and to compare that with the profiles estimated from a previously measured serum sample.

METHODS

Non-treatment seeking, cigarette smoking women (n=82; ages 18-45) provided daily salivary hormone samples every morning for 14 consecutive days. Time dependent random effects functions were used to approximate daily salivary progesterone (ng/ml) levels over the course of a standardized menstrual cycle. Serum measures of progesterone from a previous study of female cigarette smokers were examined for consistency with established profiles and compared to the salivary profile using the same methodology.

RESULTS

The salivary model fit exhibits relative stability during the follicular phase and a clear unimodal peak during the luteal phase. Parameter estimates from the non-linear function show correspondence to serum data. Although the profiles estimated from salivary and serum data agree in functional form, we observed larger between-subject heterogeneity both in the follicular level and the peak luteal level in salivary measures.

CONCLUSIONS

The pattern of salivary and serum progesterone measured across the menstrual cycle is similar in form, which is noteworthy given that the saliva and serum samples were drawn from independent sample of female smokers. Inter- and intra-individual variation in salivary measures may be greater than in serum measures.

IMPLICATIONS

Measuring progesterone level variation across the menstrual cycle via saliva samples has several benefits relative to serum sampling methods in that they are easily obtained, non-invasive and low-cost. Inter- and intra-individual variation in measurements may be greater than those in serum measurements. However, the functional form of the salivary progesterone profile is isomorphic to serum progesterone.

A phenomenological-based model of the endometrial growth and shedding during the menstrual cycle

The human endometrium presents a remarkable growth dynamic with an outstanding regenerative capacity. This work aims to develop a phenomenological-based dynamic model to predict the volume changes in the functional layer of the endometrium in each phase of the menstrual cycle. This model considers changes in the endometrial tissue, the blood flow through the spiral arteries, the shedding of the endometrial cells, and the menstrual blood flow. The input variables are estrogen and progesterone; these hormone dynamics are taken from a pre-existing and validated model. Key parameters are modified in order to know their effect on the state variables. The model response was quantitatively assessed using the experimental data of the endometrial cycle reported in the literature. The proposed model provides a better insight into the interactions between ovarian hormones and the endometrial cycle by coupling both physiological processes.

Computational Models for Diagnosing and Treating Endometriosis

Endometriosis is a common but poorly understood disease. Symptoms can begin early in adolescence, with menarche, and can be debilitating. Despite this, people often suffer several years before being correctly diagnosed and adequately treated. Endometriosis involves the inappropriate growth of endometrial-like tissue (including epithelial cells, stromal fibroblasts, vascular cells, and immune cells) outside of the uterus. Computational models can aid in understanding the mechanisms by which immune, hormone, and vascular disruptions manifest in endometriosis and complicate treatment. In this review, we illustrate how three computational modeling approaches (regression, pharmacokinetics/pharmacodynamics, and quantitative systems pharmacology) have been used to improve the diagnosis and treatment of endometriosis. As we explore these approaches and their differing detail of biological mechanisms, we consider how each approach can answer different questions about endometriosis. We summarize the mathematics involved, and we use published examples of each approach to compare how researchers: (1) shape the scope of each model, (2) incorporate experimental and clinical data, and (3) generate clinically useful predictions and insight. Lastly, we discuss the benefits and limitations of each modeling approach and how we can combine these approaches to further understand, diagnose, and treat endometriosis.