Pregnancy and mathematics

Summary: Various mathematical models help describe issues related to conception, diseases associated with pregnancy, and population dynamics.

Much of the conclusions drawn in medicine, in particular in obstetrics and gynecology, are often based on heuristics, limited observations, and sometimes even biased data. Mathematicians and statisticians have recently attempted to develop general theoretical models that can be adapted to specific situations in order to facilitate the understanding of various aspects of human pregnancy. Specifically, more recent studies have been conducted regarding conception time, disease prediction related to pregnancy, and the effect of pregnancy on population growth.

Modeling the Most Efficient Time to Conceive

One of the most fundamental and important research topics in the study of human pregnancy is the so-called time-to-pregnancy (TTP). TTP can be defined scientifically as the number of menstrual cycles it takes a couple engaging in regular sexual intercourse with no contraception usage to conceive a child. Fittingly, statisticians attempt to generate as much data as possible from various couples regarding their personal TTP experiences. The data are collected in a way that is as unbiased as possible—it is intended to accurately represent couples in the general population attempting to conceive a child. From the data, both qualitative and quantitative statistical methods are implemented in order to ascertain the most efficient method to achieve conception.

For example, some social trends increase the age at which a woman attempts to become pregnant. When this situation arises, women are often concerned about achieving conception before the onset of infertility, which proceeds menopause. In fact, couples that are unsuccessful in conceiving within one year are clinically classified as infertile. When this condition occurs, medical doctors often recommend that the couple engage in assisted reproductive therapy (ART). However, ART can be very expensive and often increases the risk of adverse outcomes for the offspring, including various birth defects. Therefore, statistical models have been developed that pose an alternative to ART. These models are developed using Bayesian decision theory, named for Thomas Bayes, and search for optimal approaches for a couple to time intercourse in order to achieve conception naturally, without the potentially disadvantageous ART. These models quantitatively incorporate various biological aspects, including menstrual cycles and basal body temperature, as well as the monitoring of electrolytes—among other phenomena—in order to be as efficient as possible.

Predicting Diseases Associated With Pregnancy

Medical evidence supports the notion that women often repeat reproductive outcomes. In particular, women with a history of bearing children with adverse outcomes often have up to a two-fold increase in subsequent risk. Therefore, researchers in the mathematical and statistical sciences realized the necessity for statistical analyses that address this issue. In fact, statistical research has been conducted in order to promote a consistent strategy that assesses the risks each woman may face in a subsequent pregnancy. The goal is for these types of models to become increasingly more accurate, as they incorporate statistical data regarding the recent reproductive history of the woman, among other biological factors, which were not fully taken into account in previous studies.

Mathematical epidemiology (the study of the incidence, distribution, and control of diseases in a population) attempts to better comprehend, diagnose, and predict various diseases incorporated with pregnancy, and this field is ever-expanding. By designing and implementing various statistical approaches and mathematical models to better predict realistic outcomes, mathematicians and statisticians have studied congenital defects and growth restrictions, as well as preterm delivery, pre-eclampsia, and eclampsia.

For example, pre-eclampsia is a pregnancy condition in which high blood pressure and high levels of protein in urine develop toward the end of the second trimester or in the third trimester of pregnancy. The symptoms of this condition may include excessive weight gain, swelling, headaches, and vision loss. In some cases this condition can be fatal to the expectant mother or the child. The exact causes of pre-eclampsia are unknown at the beginning of the twenty-first century, and the only cure for the disease is the delivery of the child. Therefore, it is apparent that determining which women are prone to develop pre-eclampsia is an exceedingly important area of research.

Empirical evidence indicates that a woman’s heart rate is a deterministic factor in the prediction of pre-eclampsia. In recent times, statisticians have therefore developed a novel and non-invasive approach to detect abnormalities in pre-eclamptic women that distinguishes from women with non-pre-eclamptic pregnancies. This approach is accomplished by comparing the dynamical complexity of the heart rates of women that are pre-eclamptic with those that are non-pre-eclamptic. The analysis revealed that the heart rate of pre-eclamptic women demonstrated a more regular dynamic behavior than those women that were not pre-eclamptic, which substantiates the empirical notion that diseased states may be associated with regular heart rate patterns.

Population Dynamics

Mathematicians have long developed models to analyze population dynamics. One contemporary model also incorporates how pregnant women directly influence such dynamics. This model consists of an equation that describes the evolution of the entire population and an equation that analyzes the evolution of pregnant women. These equations are coupled—they are studied simultaneously. Moreover, this particular system of equations can be analyzed as a linear model (not sensitive to initial data), with or without diffusion (permitting members of the population to travel large distances), or as a nonlinear model (sensitive to initial data) without diffusion. The asymptotic behavior of the solutions to this system (the long-term behavior of the population) was also addressed.

Bibliography

Fragnelli, Ginni, et al. “Qualitative Properties of a Population Dynamics System Describing Pregnancy.” Mathematical Models and Methods in Applied Sciences 4 (2005).

Germaine B., et al. “Analysis of Repeated Pregnancy Outcomes.” Statistical Methods in Medical Research 15 (2006).

Salazar, Carlos, et al. “Non-Linear Analysis of Maternal Heart Rate Patterns and Pre-Eclamptic Pregnancies.” Journal of Theoretical Medicine 5 (2003).

Savitz, David A., et al. “Methodologic Issues in the Design and Analysis of Epidemiologic Studies of Pregnancy Outcome.” Statistical Methods in Medical Research 15 (2006).

Scarpa, Bruno, and David B. Dunson. “Beyesian Methods for Searching for Optimal Rules for Timing Intercourse to Achieve Pregnancy.” Statistics in Medicine 26 (2007).

Scheikle, Thomas H., and Niels Keiding. “Design and Analysis of Time-to-Pregnancy.” Statistical Methods in Medical Research 15 (2006).