Elsevier

The Lancet

Volume 378, Issue 9793, 27 August–2 September 2011, Pages 826-837
The Lancet

Series
Quantification of the effect of energy imbalance on bodyweight

https://doi.org/10.1016/S0140-6736(11)60812-XGet rights and content

Summary

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

References (118)

  • CS Johnston et al.

    Ketogenic low-carbohydrate diets have no metabolic advantage over nonketogenic low-carbohydrate diets

    Am J Clin Nutr

    (2006)
  • M Noakes et al.

    Effect of an energy-restricted, high-protein, low-fat diet relative to a conventional high-carbohydrate, low-fat diet on weight loss, body composition, nutritional status, and markers of cardiovascular health in obese women

    Am J Clin Nutr

    (2005)
  • J Tay et al.

    Metabolic effects of weight loss on a very-low-carbohydrate diet compared with an isocaloric high-carbohydrate diet in abdominally obese subjects

    J Am Coll Cardiol

    (2008)
  • A Kekwick et al.

    Calorie intake in relation to body-weight changes in the obese

    Lancet

    (1956)
  • LW Kinsell et al.

    Calories do count

    Metabolism

    (1964)
  • RL Leibel et al.

    Energy intake required to maintain body weight is not affected by wide variation in diet composition

    Am J Clin Nutr

    (1992)
  • JA Vazquez et al.

    Protein sparing during treatment of obesity: ketogenic versus nonketogenic very low calorie diet

    Metabolism

    (1992)
  • AC Buchholz et al.

    Is a calorie a calorie?

    Am J Clin Nutr

    (2004)
  • M Elia et al.

    The energy cost of triglyceride-fatty acid recycling in nonobese subjects after an overnight fast and four days of starvation

    Metabolism

    (1987)
  • MD Jensen et al.

    Insulin dose response analysis of free fatty acid kinetics

    Metabolism

    (2007)
  • DE Gerstein et al.

    Clarifying concepts about macronutrients' effects on satiation and satiety

    J Am Diet Assoc

    (2004)
  • RR Wing et al.

    Long-term weight loss maintenance

    Am J Clin Nutr

    (2005)
  • SB Heymsfield et al.

    Why do obese patients not lose more weight when treated with low-calorie diets? A mechanistic perspective

    Am J Clin Nutr

    (2007)
  • KD Hall et al.

    Estimating changes of free-living energy intake and its confidence interval

    Am J Clin Nutr

    (2011)
  • DM Thomas et al.

    A computational model to determine energy intake during weight loss

    Am J Clin Nutr

    (2010)
  • B Butland et al.

    Foresight tackling obesities: future choices—project report

    (2007)
  • JO Hill

    Understanding and addressing the epidemic of obesity: an energy balance perspective

    Endocr Rev

    (2006)
  • RL Duyff

    American dietetic association complete food and nutrition guide

    (2006)
  • NHLBI. Aim for a healthy weight: National Institutes of Health, National Heart, Lung, and Blood Institute. Report No:...
  • The practical guide: identification, evaluation, and treatment of overweight and obesity in adults

    (2000)
  • Your Weight Your Health: how to take control of your weight

    (2006)
  • KD Hall

    What is the required energy deficit per unit weight loss?

    Int J Obes (Lond)

    (2008)
  • RL Leibel et al.

    Changes in energy expenditure resulting from altered body weight

    N Engl J Med

    (1995)
  • GW Gustavsen et al.

    The effects of taxes on purchases of sugar-sweetened carbonated soft drinks: a quantile regression approach

    Appl Econ

    (2011)
  • EA Finkelstein et al.

    Impact of targeted beverage taxes on higher- and lower-income households

    Arch Intern Med

    (2010)
  • P Simon et al.

    Menu labeling as a potential strategy for combating the obesity epidemic: a health impact assessment

    (2008)
  • TA Smith et al.

    Taxing caloric sweetened beverages: potential effects on beverage consumption, calorie intake, and obesity

    (2010)
  • NF Butte et al.

    Energy imbalance underlying the development of childhood obesity

    Obesity

    (2007)
  • E Christiansen et al.

    Prediction of body weight changes caused by changes in energy balance

    Eur J Clin Invest

    (2002)
  • JP Flatt

    Carbohydrate-fat interactions and obesity examined by a two-compartment computer model

    Obes Res

    (2004)
  • PR Payne et al.

    A model for the prediction of energy balance and body weight

    Ann Hum Biol

    (1977)
  • B Song et al.

    Dynamics of starvation in humans

    J Math Biol

    (2007)
  • DM Thomas et al.

    A mathematical model of weight change with adaptation

    Math Biosci Eng

    (2009)
  • RL Weinsier et al.

    Predicted effects of small decreases in energy expenditure on weight gain in adult women

    Int J Obes Relat Metab Disord

    (1993)
  • KR Westerterp et al.

    Energy intake, physical activity and body weight: a simulation model

    Br J Nutr

    (1995)
  • CC Chow et al.

    The dynamics of human body weight change

    PLoS Comput Biol

    (2008)
  • KD Hall

    Computational model of in vivo human energy metabolism during semistarvation and refeeding

    Am J Physiol Endocrinol Metab

    (2006)
  • KD Hall

    Body fat and fat-free mass inter-relationships: Forbes's theory revisited

    Br J Nutr

    (2007)
  • KD Hall

    Predicting metabolic adaptation, body weight change, and energy intake in humans

    Am J Physiol Endocrinol Metab

    (2010)
  • KD Hall

    Mathematical modelling of energy expenditure during tissue deposition

    Br J Nutr

    (2010)
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