Quantification of the effect of energy imbalance on bodyweight

Abstract

Obesity interventions can result in weight loss, but accurate prediction of the bodyweight time course requires properly accounting for dynamic energy imbalances. In this report, we describe a mathematical modelling approach to adult human metabolism that simulates energy expenditure adaptations during weight loss. We also present a web-based simulator for prediction of weight change dynamics. We show that the bodyweight response to a change of energy intake is slow, with half times of about 1 year. Furthermore, adults with greater adiposity have a larger expected weight loss for the same change of energy intake, and to reach their steady-state weight will take longer than it would for those with less initial body fat. Using a population-averaged model, we calculated the energy-balance dynamics corresponding to the development of the US adult obesity epidemic. A small persistent average daily energy imbalance gap between intake and expenditure of about 30 kJ per day underlies the observed average weight gain. However, energy intake must have risen to keep pace with increased expenditure associated with increased weight. The average increase of energy intake needed to sustain the increased weight (the maintenance energy gap) has amounted to about 0·9 MJ per day and quantifies the public health challenge to reverse the obesity epidemic.

Figure 1. Predicted bodyweight and fat-mass changes by use of a dynamic simulation model of human metabolism

Error bars are ±1SD. (A) Predicted and measured average changes of bodyweight and fat mass during 25% caloric restriction in 12 overweight men and women. (B) Predicted and measured average changes of bodyweight and fat mass during 12·5% caloric restriction plus exercise in 12 overweight men and women. (C) Predicted and measured average changes of bodyweight and fat mass during a very low energy liquid diet followed by weight maintenance diet in 12 overweight men and women. (D) Daily weight changes in two obese women during a very low energy liquid diet. Model predictions are shown as solid blue curves and the dotted curves illustrate the uncertainty of the predictions based on the inherent imprecision of estimating baseline energy expenditure, assuming an uncertainty in the initial energy expenditure rate of ±1 MJ per day. (E) Average weight change during a 30-day fast in 18 obese men and (F) 58 obese women.

Figure 2. Predicted long-term bodyweight change trajectories

(A) Bodyweight time course of a 100 kg man following a step decrease in dietary energy intake of 2 MJ per day. The dashed curves indicate the expected inter-individual variability of weight loss due to imprecise estimates of the initial state of energy balance (arising solely from an initial uncertainty in the energy expenditure rate of ±300 kJ per day or about 5%). (B) Differences of weight change between people with different initial body composition. People with a higher initial body fat mass lose more weight but the time to reach the plateau is longer. (C) Predicted effect of a step change of physical activity compared with an energy equivalent step change of dietary energy intake. Physical activity has an effect on both the magnitude and the timescale of bodyweight change.

Figure 3. Web-based simulation for setting goals for weight loss and weight-loss maintenance

The panel located on the top-left part of the simulator window specifies the baseline characteristics of the individual person or population average values. This example selects a 100 kg, 180 cm tall, 23-year-old man. The top-middle panel specifies the goal weight (80 kg) and desired time interval to achieve the goal (180 days). Running the simulation displays the required changes of dietary energy intake to meet the goal and then maintain the weight change. The simulated bodyweight trajectory is graphically displayed in the lower panel. Users can also modify the physical activity to examine how combinations of diet and exercise interventions can achieve the same goal.

Figure 4. Energy balance dynamics underlying the typical out-patient weight loss, plateau, and regain trajectory

(A) A typical range of bodyweight trajectories for patients engaged in an out-patient weight-loss programme. The solid blue curve is the mean bodyweight time course and the dashed curves indicate the expected inter-individual weight loss variability due to a ±0·65 MJ per day imprecision in the estimate of the initial energy expenditure rate. Datapoints are mean ±SD from Svetkey and colleagues. (B) The model predicted average energy intake (black) and energy expenditure (red) rates underlying the typical bodyweight loss and regain trajectory.

Figure 5. Simulating the increasing average adult bodyweight gain of the US population

(A) Average simulated adult bodyweight along with data from the NHANES. (B) The simulated linear increase of average energy intake and energy expenditure underlying the observed increase in average bodyweight. The energy imbalance gap is the small difference between the energy intake and expenditure rates. The maintenance energy gap is the change of energy intake required to maintain the final bodyweight compared with the initial weight. (C) Plotting of the simulated average energy expenditure rate versus the average bodyweight gives the red curve with a slope very close to that of the regression line fit to cross-sectional energy expenditure data. The slope indicates that every 100 kJ per day increment of energy intake would eventually lead to about 1 kg change of average bodyweight. NHANES=National Health and Nutrition Examination Survey.

Figure 6. Prediction of the effect of a policy intervention on the population average weight

Simulated average weight change of a 20% tax on caloric sweetened beverages. The average energy-intake change was specified in a recent report by the US Department of Agriculture (USDA) and initial population average weight of 81 kg corresponded to the most recent measurement in the USA. Rather than produce the progressive weight loss predicted by the static model, the same decrease of energy intake led to a simulated modest weight-loss plateau.