Gestational growth trajectories derived from a dynamic fetal-placental scaling law.

Fetal trajectories characterizing growth rates in utero have relied primarily on goodness of fit rather than mechanistic properties exhibited in utero. Here, we use a validated fetal-placental allometric scaling law and a first principles differential equations model of placental volume growth to generate biologically meaningful fetal-placental growth curves. The growth curves form the foundation for understanding healthy versus at-risk fetal growth and for identifying the timing of key events in utero.

Dynamic model predicting overweight, obesity, and extreme obesity prevalence trends.

OBJECTIVE: Obesity prevalence in the United States appears to be leveling, but the reasons behind the plateau remain unknown. Mechanistic insights can be provided from a mathematical model. The objective of this study is to model known multiple population parameters associated with changes in body mass index (BMI) classes and to establish conditions under which obesity prevalence will plateau. DESIGN AND METHODS: A differential equation system was developed that predicts population-wide obesity prevalence trends. The model considers both social and nonsocial influences on weight gain, incorporates other known parameters affecting obesity trends, and allows for country specific population growth. RESULTS: The dynamic model predicts that: obesity prevalence is a function of birthrate and the probability of being born in an obesogenic environment; obesity prevalence will plateau independent of current prevention strategies; and the US prevalence of overweight, obesity, and extreme obesity will plateau by about 2030 at 28%, 32%, and 9% respectively. CONCLUSIONS: The US prevalence of obesity is stabilizing and will plateau, independent of current preventative strategies. This trend has important implications in accurately evaluating the impact of various anti-obesity strategies aimed at reducing obesity prevalence.

Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model.

OBJECTIVE: To develop a new geometrical index that combines height, waist circumference (WC), and hip circumference (HC) and relate this index to total and visceral body fat. DESIGN AND METHODS: Subject data were pooled from three databases that contained demographic, anthropometric, dual energy X-ray absorptiometry (DXA) measured fat mass, and magnetic resonance imaging measured visceral adipose tissue (VAT) volume. Two elliptical models of the human body were developed. Body roundness was calculated from the model using a well-established constant arising from the theory. Regression models based on eccentricity and other variables were used to predict %body fat and %VAT. RESULTS: A body roundness index (BRI) was derived to quantify the individual body shape in a height-independent manner. Body roundness slightly improved predictions of %body fat and %VAT compared to the traditional metrics of body mass index (BMI), WC, or HC. On this basis, healthy body roundness ranges were established. An automated graphical program simulating study results was placed at http://www.pbrc.edu/bodyroundness. CONCLUSION: BRI, a new shape measure, is a predictor of %body fat and %VAT and can be applied as a visual tool for health status evaluations.

Dynamic energy-balance model predicting gestational weight gain.

BACKGROUND: Gestational weight gains (GWGs) that exceed the 2009 Institute of Medicine recommended ranges increase risk of long-term postpartum weight retention; conversely, GWGs within the recommended ranges are more likely to result in positive maternal and fetal outcomes. Despite this evidence, recent epidemiologic studies have shown that the majority of pregnant women gain outside the target GWG ranges. A mathematical model that predicts GWG and energy intake could provide a clinical tool for setting precise goals during early pregnancy and continuous objective feedback throughout pregnancy. OBJECTIVE: The purpose of this study was to develop and validate a differential equation model for energy balance during pregnancy that predicts GWG that results from changes in energy intakes. DESIGN: A set of prepregnancy BMI-dependent mathematical models that predict GWG were developed by using data from a longitudinal study that measured gestational-changes in fat-free mass, fat mass, total body water, and total energy expenditure in 63 subjects. RESULTS: Mathematical models developed for women with low, normal, and high prepregnancy BMI were shown to fit the original data. In 2 independent studies used for validation, model predictions of fat-free mass, fat mass, and total body water matched actual measurements within 1 kg. CONCLUSIONS: Our energy-balance model provides plausible predictions of GWG that results from changes in energy intakes. Because the model was implemented as a Web-based applet, it can be widely used by pregnant women and their health care providers.