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.
Introduction
While the complexity of the obesity epidemic is graphically illustrated by the web of interacting variables in the Foresight Obesity Map,1 at the central core of the system map lies a fundamental principle of nutrition and metabolism: bodyweight change is associated with an imbalance between the energy content of food eaten and energy expended by the body to maintain life and perform physical work.2 Any successful intervention targeting obesity (eg, diet, exercise, drugs, bariatric surgery, etc) must tip the balance between energy intake and expenditure. Therefore, to assess the potential of an obesity intervention, its effect on both energy intake and energy expenditure over time needs to be quantified.
Key messages
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Health and nutrition organisations have perpetuated the myth that a reduction of food intake of 2 MJ per day will lead to a steady rate of weight loss of 0·5 kg per week. Because this static weight-loss rule does not account for dynamic physiological adaptations that occur with decreased bodyweight, its widespread use at both the individual and population levels has led to drastically overestimated expectations for weight loss.
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We introduce a validated web-based dynamic simulation model of adult human metabolism that predicts the time course of individual weight change in response to behavioural interventions. Model simulations can be clinically useful to help set personalised weight-loss goals and track adherence to an intervention.
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On the basis of our model, we propose an approximate rule of thumb for an average overweight adult: every change of energy intake of 100 kJ per day will lead to an eventual bodyweight change of about 1 kg (equivalently, 10 kcal per day per pound of weight change) with half of the weight change being achieved in about 1 year and 95% of the weight change in about 3 years.
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Our model simulations show that present limitations on the precision of measuring energy expenditure before a diet intervention result in a substantial expected inter-individual variability of weight loss, since a given diet results in an uncertain degree of energy deficit.
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Applications of dynamic simulation models include: prediction of individual weight changes resulting from energy balance interventions; assessment of effects of policy interventions targeting energy intake or physical activity; estimation of the magnitude of the maintenance energy gap that determines the increased energy intake needed to maintain higher average bodyweights as a result of the obesity epidemic.
Despite the simplicity of this core energy balance principle, calculation of the dynamics of energy imbalance and translation of the imbalance to a change in bodyweight is not straightforward. Widespread official recommendations from the National Health Service in the UK, the National Institutes of Health and the American Dietetic Association in the USA erroneously state that reduction of energy intake by about 2 MJ per day will result in slow and steady weight loss of about 0·5 kg per week.3, 4, 5, 6 This ubiquitous weight-loss rule (also known as the 3500 kcal per pound rule) was derived by estimation of the energy content of weight lost7 but it ignores dynamic physiological adaptations to altered body weight that lead to changes of both the resting metabolic rate as well as the energy cost of physical activity.8 Unfortunately, this static weight-loss rule continues to be used for weight-loss counselling and has been misapplied at the population level to predict the effect of policy interventions on obesity prevalence.9, 10, 11, 12 While it is generally recognised that the static weight-loss rule is overly simplistic, there is a dearth of methods for accurate predictions of how changes of diet or physical activity will translate into weight changes over time.
We address this issue by using a dynamic mathematical modelling approach to human metabolism that integrates our knowledge about how the human body responds to changes of diet and physical activity. Although several mathematical models of human metabolism and weight change have been developed in the past,13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 here, we describe some insights about weight loss resulting from our research group's experience in developing and validating various mathematical models of human metabolism and body-composition change.7, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37 Furthermore, we present a web-based implementation of one of our dynamic mathematical models of human metabolism with which readers can do their own simulations. We show how this dynamic simulation model of human metabolism can predict the time course of weight change at both the individual and population levels.
Section snippets
Quantitative physiology of weight change in adults
An imbalance between energy intake and energy expenditure is accounted for by a gain or loss of body fat and lean tissue which generally change in parallel.30, 38 Thus, quantification of weight change requires both a dynamic assessment of how energy expenditure changes over time as well as how energy imbalances are partitioned between storage or mobilisation of body fat and lean tissue. The energy content per kg change of body fat is 39·5 MJ and 7·6 MJ for a kg of lean mass.7 Thus, to lose the
Modelling of the dynamics of weight change
Figure 1A–C shows our model simulations of weight change and body fat change along with experimental data from the CALERIE study80 that investigated 6 months of 25% caloric restriction, 12·5% caloric restriction plus exercise, and 3 months of a liquid diet of 3·7 MJ per day followed by a period of weight maintenance. The close agreement between the model predictions and the data provides some validation of the mathematical model, since these data were not used for model development. Figure 1D
Setting goals for weight loss and weight-loss maintenance
The long timescale for weight loss in obese and overweight individuals has important implications for clinical weight-loss interventions. For example, implementation of a weight-loss programme in various stages so that a goal weight can be achieved in an abbreviated timeframe might be desirable. The first stage might consist of a more aggressive temporary change in behaviour to achieve the weight loss goal in a specified time, after which the intervention can be relaxed to a permanent
Assessment of obesity interventions and patients' adherence
To assess the mechanisms and comparative effectiveness of various obesity treatments requires understanding their long-term effect on both energy intake and energy expenditure. However, a major difficulty in the field of obesity research is that current methods for assessment of free-living food intake (eg, 24 h recall, food frequency questionnaires, diet diaries, etc) are known to be inaccurate.91, 92 Therefore, to interpret the results of various diet trials (panel) is difficult, as is to
Modelling average weight change in a population
The obesity epidemic is measured at the population level, including the bodyweights of individuals within the population. Accordingly, it is important to develop models that can quantitatively relate individual changes in energy balance and bodyweight to population-level effects. Modelling of the dynamics of the entire population distribution over time is complex and beyond the scope of this report. However, by taking the average of the mathematical model over the US adult population, we
Simulation of the potential effect of policy interventions to address obesity
By modelling the magnitude of the maintenance energy gap we can begin to estimate the potential effect of population-wide policy interventions. For example, the US Department of Agriculture (USDA) recently issued a report12 describing the potential effect on obesity prevalence of taxing caloric sweetened beverages. The authors estimated that a 20% tax would result in a decrease of overall energy intake by about 170 kJ per day (40 kcal per day). Using the rule that every change of diet of 2 MJ
Conclusions
This report describes how mathematical modelling of human metabolism has resulted in several important insights about weight change in adults. We have shown how inter-individual weight-loss variability resulting from the same intervention can be caused by differences in the initial body composition between individuals as well as the uncertainty about the baseline energy expenditure. We also showed that the timescale of human weight change is long and depends on the initial body composition.