A Simple Model Predicting Individual Weight Change in Humans

Abstract

Excessive weight in adults is a national concern with over 2/3 of the US population deemed overweight. Because being overweight has been correlated to numerous diseases such as heart disease and type 2 diabetes, there is a need to understand mechanisms and predict outcomes of weight change and weight maintenance. A simple mathematical model that accurately predicts individual weight change offers opportunities to understand how individuals lose and gain weight and can be used to foster patient adherence to diets in clinical settings. For this purpose, we developed a one dimensional differential equation model of weight change based on the energy balance equation is paired to an algebraic relationship between fat free mass and fat mass derived from a large nationally representative sample of recently released data collected by the Centers for Disease Control. We validate the model's ability to predict individual participants' weight change by comparing model estimates of final weight data from two recent underfeeding studies and one overfeeding study. Mean absolute error and standard deviation between model predictions and observed measurements of final weights are less than 1.8 ± 1.3 kg for the underfeeding studies and 2.5 ± 1.6 kg for the overfeeding study. Comparison of the model predictions to other one dimensional models of weight change shows improvement in mean absolute error, standard deviation of mean absolute error, and group mean predictions. The maximum absolute individual error decreased by approximately 60% substantiating reliability in individual weight change predictions. The model provides a viable method for estimating individual weight change as a result of changes in intake and determining individual dietary adherence during weight change studies.

Keywords: dietary adherence; energy balance equation; metabolic adaptation; non-exercise activity thermogenesis.

Figure 1

A simulation of individual weight loss for a period of five years with age held constant (dashed curve) and increasing age (solid curve). The y-axis represents weight in kg and the x-axis time in days. Baseline weight, height, and age are 77 kg, 172 cm, and 44 years. The target caloric intake is 2200 kcal/d.

Figure 2

The 24-week body mass in kg (y-axis) is plotted for each individual calorie restricted subject (x-axis) for actual CALERIE PHASE I measurements (square), Heymsfield model predictions (solid circle) and one dimensional Chow-Hall model predictions (solid triangle). [23].

Figure 3

Each graph is a plot of body mass in kg during weight change (y-axis) versus time in days (x-axis). The solid curves are simulations of the Heymsfield model for an individual subject in the CALERIE Phase I study assuming energy intake was 100% compliant (a),estimating energy intake from DLW/DXA measurements (b), and assuming 100% compliance for 4 weeks followed by intake estimated from DLW/DXA measurements (c). Circles represent actual measurements of body mass.

Figure 4

The 12-week body mass in kg (y-axis) is plotted for each individual calorie restricted subject (x-axis) for actual Racette study measurements (square), Heymsfield model predictions (solid circle) and one dimensional Chow-Hall model predictions (solid triangle) [44].

Figure 5

The 8-week body mass in kg (y-axis) is plotted for each individual overfed subject (x-axis) for actual measurements (square), Heymsfield model predictions (solid circle) and one dimensional Chow-Hall model predictions (solid triangle) [34, 35]

Figure 6

Final measured body mass in kg (y-axis) plotted against the Heymsfield model predicted body mass in kg (x-axis) for subjects in all three studies.