Application of Mathematical Models in the Management of Obesity during Pregnancy and the Postpartum Period in Reproductive Age Women

Abstract

Obesity is a complex pandemic, and its effective management involves addressing many different factors. This complexity has given rise to novel analytic methods, integrating intensive computational, engineering and statistical techniques. Mathematical models are currently applied to inform clinical practice. At the 2017 The Korean Nutrition Society 50th Anniversary International Conference, the development of such models and their application to improve data accuracy and patient care during the pregnancy and postpartum periods was discussed.

1. Introduction

Overweight and obesity has nearly tripled worldwide since 1975 [1]. Reproductive age women in middle and high income countries are not spared from the obesity pandemic with approximately 50% of women in the United States, 30% in Europe, and 10% in Asia entering pregnancy with overweight or obesity [2–4]. Overweight and obesity complicates pregnancies and increases risk of negative maternal and fetal outcomes such as fetal and neonatal death, birth defects, macrosomia, pre-eclampsia, gestational diabetes, and caesarian sections [5, 6]. In addition, gestational weight gain is positively correlated with short and long-term maternal weight change. While average postpartum weight retention is relatively small and thus has little impact on weight trajectory throughout life, there is large variability in postpartum weight retention [5]. Excessive gestational weight gain and postpartum weight retention are indicators of overweight and obesity decades after pregnancy [6, 7]. Thus, proper weight management during the periconception period is important for overall weight control throughout life.

2. Use of a novel weight calculator to determine weight at conception

Defining pre-pregnancy weight is critical in the proper medical management of pregnancy as gestational weight gain guidelines are based on the mother’s pre-pregnancy weight. However, obtaining an accurate pre-pregnancy weight is difficult as the initial obstetric visit occurs well into the first trimester, and clinicians seldom have access to documented weights at the time of conception [8]. Therefore, clinicians and researchers often use the weight obtained at the first doctor’s visit typically within three months of conception or self-reported pre-pregnancy weight as a proxy for the weight at conception. While there is a correlation between a patient’s self-reported pre-pregnancy weight and a measured weight, this information can vary considerably for women especially among those with a higher body mass index (BMI) [8–10]. Due to the difficulty and importance of obtaining an accurate pre-pregnancy weight for proper pregnancy management, Thomas et al. [10] developed a mathematical model which utilizes easily obtained clinical data (current gestational age, current weight, height, maternal age, and self-reported pre-pregnancy weight) to predict pre-pregnancy weight. The regression model used to predict pre-pregnancy weight was derived from the Project Viva study [11] and considered maternal age, height, race/ethnicity, parity, and first trimester weight as covariates. The final algorithm was validated against measured pre-pregnancy weights obtained in the Fit For Delivery study [9] and the Programming Research in Obesity, Growth, Environment and Social Stressors study [12, 13]. Clinicians are able to input a patient’s data into the pre-pregnancy weight calculator software and identify a potentially misreported pre-pregnancy weight across a range of patient BMI classifications. We routinely utilize the pre-pregnancy calculator in our research studies to 1) derive a more accurate estimate of pre-pregnancy weight and 2) correctly classify pre-pregnancy BMI, to deliver an appropriate and effective lifestyle intervention.

3. Weight gain during pregnancy

In addition to pre-pregnancy obesity, weight gain during pregnancy is independently associated with maternal and fetal health [3, 14, 15]. To reduce the incidence of adverse maternal and infant outcomes, the 2009 Institute of Medicine (IOM) weight gain guidelines recommend that women with a pre-pregnancy BMI of 18.5 – 24.9 kg/m² limit total weight gain in pregnancy to 11.5–16 kg (25–35 lb.), women with a pre-pregnancy BMI of 25 – 29.9 kg/m² to 7–11.5 kg (15–25 lb.), and women with obesity (all classes) to 5–9 kg (11–20 lb). Ideally, this weight gain is distributed as 27% maternal reserves (i.e. fat mass), 35% extracellular fluid, uterine tissue, and breast tissue, 11% amniotic fluid and placenta, and 27% is the fetus [16]. However, most women exceed the IOM guidelines (40% of women with normal pre-pregnancy weight, 66% with overweight, and 58% with obesity) [2]. Excess weight gain is primarily comprised of maternal fat mass which contributes to the deleterious effects postpartum weight retention that results in higher pre-pregnancy weight (and adiposity) for future pregnancies [17].

Implementation of the gestational weight gain recommendations requires an understanding of the energy needs during pregnancy. A landmark trial led by Dr. Butte [18] enrolled women prior to pregnancy who were planning to become pregnant and used a series of objective assessments of energy intake and expenditure (measured pre-pregnancy weight, underwater weighing, room calorimetry, doubly labelled water, activity, etc.) to estimate energy requirement during pregnancy. Due to the rigorous study design and objective assessments, many secondary analyses have come from this rich dataset including mathematical modeling and the development of a maternal energy intake calculator [19, 20]. A dynamic energy-balance model was developed using the Butte data including gestational changes in fat-free mass, fat mass, total body water, and total energy expenditure to predict gestational weight gain in women with low, normal and high pre-pregnancy BMI. Two independent studies were used for validation, and the original model predictions matched actual measurements within 1 kg. The model was implemented as a Web-based applet (https://www.pbrc.edu/research-and-faculty/calculators/gestational-weight-gain/) in which clinicians or research interventionists can enter the woman’s age, height, and pre-pregnancy weight to generate a recommended weight gain graph together with trimester specific kilocalorie intake targets [20]. The maternal energy intake model and graph were incorporated into an eHealth lifestyle intervention which was systematically tested against an in-person and standard of care intervention in pilot randomized controlled trial [21]. Fifty-four women were randomized to one of three groups, 1) Usual Care who were asked to follow the advice from their physician, 2) SmartMoms Clinic who received an in-person intensive lifestyle program via weekly (2^nd trimester) and biweekly (3^rd trimester) individual and group sessions from 13 weeks gestation until delivery in addition to usual care, or 3) SmartMoms Phone who received identical material and recommendations as the SmartMoms Clinic group, but the information was delivered via a SmartPhone application, “SmartMoms®” developed by the investigators. Objective energy intake and exercise data was obtained automatically from the free-living participants via Bluetooth enabled devices. The SmartMoms® application included the personalized weight graph with trimester-specific energy intake goals generated by the maternal energy intake model, regular behavior change lessons focusing on modifying energy intake and expenditure, and self-monitoring of body weight, food intake, and exercise. Approximately 58% of the participants in the SmartMoms Phone group exceeded the IOM gestational weight gain guidelines compared to 84.6% in the Usual Care group (p=0.04). The SmartMoms Phone and Clinic groups were equivalent (55.6% in SmartMoms Clinic). Of note, recent studies have shown that the model estimates of energy intake may not be valid for women with morbid obesity [22]. This discrepancy is likely to be multifactorial including differences in body composition, energy expenditure, and the small numbers of women with obesity previously studied [17–19, 23].

4. Postpartum Weight Loss

Women who gain above the IOM weight gain guidelines are more likely to retain the excess weight in the postpartum period. Women who gain above the guidelines are on average 5 kg heavier 3 years postpartum and 20 kg heavier 20 years postpartum [24]. In addition, BMI is positively correlated with parity supporting the notion that excess gestational weight gain leads to increased postpartum weight retention and increased pre-pregnancy BMI for subsequent pregnancies [25, 26]. To combat postpartum weight retention and facilitate postpartum weight loss, we enrolled 40 women who were 6 to 8 weeks postpartum and receiving Women, Infants, and Children (WIC) postpartum benefits. The participants were randomized to one of two groups, 1) WIC Moms who received usual care from the WIC clinic and 2) WIC E-Moms who received a SmartPhone based lifestyle intervention in addition to WIC usual care. Similar to the SmartMoms® application, SmartLoss® [27] includes a personalized weight graph generated from a validated dynamic energy balance model which determines the amount of weight an individual will lose over time if they are adherent to a given energy intake prescription [28–30]. Body weight and physical activity data is collected via Bluetooth enabled body weight scale and step counter and transferred to the participants’ and interventionist’s program interface. The interventionist is then able to provide personalized feedback to the participant in near real-time thus improving behavior change. Tracking of body weights on a personalized weight loss graph allowed nutritional counseling to target an individualized energy gap. Participants were not given a daily kilocalorie target and asked to count calories. Instead, participants were oriented to the weight graph at the beginning of the intervention and they used body weight as a proxy to dietary prescription adherence. If the participant’s weight was above the weight graph zone, the participant knew energy intake needed to be adjusted downward and/or diet quality altered. This self-regulation was particularly helpful where counting calories may be difficult in diverse, health disparate populations, and underreporting of energy intake even via food intake SmartPhone applications is common [31].

5. Conclusions

Mathematical models of body weight have proven to be helpful and effective in weight management interventions in various populations during the reproductive cycle (Figure 1). However, development and subsequent validation of these models requires large amounts of precise, accurate and objective data of energy balance. There are limited trials which collect such data as doubly-labeled water due in part to expense. In addition, model development requires multidisciplinary teams of researchers including experts in metabolism, energy balance, and mathematics. There is a need to develop dynamic energy balance models for other situations and specific populations such as for individuals who are Asian since assumptions related to fat and fat-free mass changes commonly adopted in these models (ie. Forbes function) are invalid. Thus, static body weight values can be predicted in such models whereas dynamic changes cannot. At this time, there is a lack of data in particular populations and races to develop and validate more specific models.

Figure 1. The use of mathematical models to optimize weight management in reproductive-age women.

When integrated into patient centered behavioral lifestyle interventions, mathematical models are a powerful tool which can aid in successful weight management during pregnancy and in the postpartum period.

Highlights:

• A mathematical model was developed to predict pre-pregnancy weight

• Mathematical models may improve weight management interventions

• More high-quality data is needed for model development in other populations

Abbreviations:

BMI

Body Mass Index

IOM

Institute of Medicine

WIC

Women, Infants, and Children