The dynamics of human body weight change

Linking neuronal brain activity to the glucose metabolism

BACKGROUND

Energy homeostasis ensures the functionality of the entire organism. The human brain as a missing link in the global regulation of the complex whole body energy metabolism is subject to recent investigation. The goal of this study is to gain insight into the influence of neuronal brain activity on cerebral and peripheral energy metabolism. In particular, the tight link between brain energy supply and metabolic responses of the organism is of interest. We aim to identifying regulatory elements of the human brain in the whole body energy homeostasis.

METHODS

First, we introduce a general mathematical model describing the human whole body energy metabolism. It takes into account the two central roles of the brain in terms of energy metabolism. The brain is considered as energy consumer as well as regulatory instance. Secondly, we validate our mathematical model by experimental data. Cerebral high-energy phosphate content and peripheral glucose metabolism are measured in healthy men upon neuronal activation induced by transcranial direct current stimulation versus sham stimulation. By parameter estimation we identify model parameters that provide insight into underlying neurophysiological processes. Identified parameters reveal effects of neuronal activity on regulatory mechanisms of systemic glucose metabolism.

RESULTS

Our examinations support the view that the brain increases its glucose supply upon neuronal activation. The results indicate that the brain supplies itself with energy according to its needs, and preeminence of cerebral energy supply is reflected. This mechanism ensures balanced cerebral energy homeostasis.

CONCLUSIONS

The hypothesis of the central role of the brain in whole body energy homeostasis as active controller is supported.

Mathematical modeling of the human energy metabolism based on the Selfish Brain Theory

Deregulations in the human energy metabolism may cause diseases such as obesity and type 2 diabetes mellitus. The origins of these pathologies are fairly unknown. The key role of the brain is the regulation of the complex whole body energy metabolism. The Selfish Brain Theory identifies the priority of brain energy supply in the competition for available energy resources within the organism. Here, we review mathematical models of the human energy metabolism supporting central aspects of the Selfish Brain Theory. First, we present a dynamical system modeling the whole body energy metabolism. This model takes into account the two central control mechanisms of the brain, i.e., allocation and appetite. Moreover, we present mathematical models of regulatory subsystems. We examine a neuronal model which specifies potential elements of the brain to sense and regulate cerebral energy content. We investigate a model of the HPA system regulating the allocation of energy within the organism. Finally, we present a robust modeling approach of appetite regulation. All models account for a systemic understanding of the human energy metabolism and thus do shed light onto defects causing metabolic diseases.

Systemic modelling of human bioenergetics and blood circulation

This work reviews the main aspects of human bioenergetics and the dynamics of the cardiovascular system, with emphasis on modelling their physiological characteristics. The methods used to study human bioenergetics and circulation dynamics, including the use of mathematical models, are summarised. The main characteristics of human bioenergetics, including mitochondrial metabolism and global energy balance, are first described, and the systemic aspects of blood circulation and related physiological issues are introduced. The authors also discuss the present status of studies of human bioenergetics and blood circulation. Then, the limitations of the existing studies are described in an effort to identify directions for future research towards integrated and comprehensive modelling. This review emphasises that a multi-scale and multi-physical approach to bioenergetics and blood circulation that considers multiple scales and physiological factors are necessary for the appropriate clinical application of computational models.

Why do individuals not lose more weight from an exercise intervention at a defined dose? An energy balance analysis

Weight loss resulting from an exercise intervention tends to be lower than predicted. Modest weight loss can arise from an increase in energy intake, physiological reductions in resting energy expenditure, an increase in lean tissue or a decrease in non-exercise activity. Lower than expected, weight loss could also arise from weak and invalidated assumptions within predictive models. To investigate these causes, we systematically reviewed studies that monitored compliance to exercise prescriptions and measured exercise-induced change in body composition. Changed body energy stores were calculated to determine the deficit between total daily energy intake and energy expenditures. This information combined with available measurements was used to critically evaluate explanations for low exercise-induced weight loss. We conclude that the small magnitude of weight loss observed from the majority of evaluated exercise interventions is primarily due to low doses of prescribed exercise energy expenditures compounded by a concomitant increase in caloric intake.

Energy content of weight loss: kinetic features during voluntary caloric restriction

The classic rule stating that restricting intake by 3500 kcal/wk will lead to a 1-lb/wk rate of weight loss has come under intense scrutiny. Generally not a component of most weight loss prediction models, the "early" rapid weight loss phase may represent a period during which the energy content of weight change (ΔEC/ΔW) is low and thus does not follow the classic "rule." The current study tested this hypothesis. Dynamic ΔEC/ΔW changes were examined in 23 Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy Study overweight men and women evaluated by dual-energy x-ray absorptiometry during weight loss at treatment weeks 4 to 24. Changes from baseline in body energy content were estimated from fat and fat-free mass. Repeated-measures analysis of variance was used to determine if ΔEC/ΔW changed significantly over time. The evaluation was expanded with addition of the Kiel 13-week weight loss study of 75 obese men and women to test with adequate power if there are sex differences in ΔEC/ΔW. The analysis of variance CALERIE time effect was significant (P < .001), with post hoc tests indicating that ΔEC/ΔW (kilocalories per kilogram) increased significantly from week 4 (X ± SEM; 4, 858 ± 388) to 6 (6, 041 ± 376, P < .01) and changed insignificantly thereafter; ΔEC/ΔW was significantly larger for Kiel women (6, 804 ± 226) vs men (6, 119 ± 240, P < .05). Sex-specific dynamic relative changes in body composition and related ΔEC/ΔW occur with weight loss initiation that extend for 1 month or more. These observations provide new information for developing energy balance models and further define limitations of the 3500-kcal energy deficit → 1-lb weight loss rule.

Modeling the relationship between body weight and energy intake: a molecular diffusion-based approach

Background

Body weight is at least partly controlled by the choices made by a human in response to external stimuli. Changes in body weight are mainly caused by energy intake. By analyzing the mechanisms involved in food intake, we considered that molecular diffusion plays an important role in body weight changes. We propose a model based on Fick's second law of diffusion to simulate the relationship between energy intake and body weight.

Results

This model was applied to food intake and body weight data recorded in humans; the model showed a good fit to the experimental data. This model was also effective in predicting future body weight.

Conclusions

In conclusion, this model based on molecular diffusion provides a new insight into the body weight mechanisms.

Reviewers

This article was reviewed by Dr. Cabral Balreira (nominated by Dr. Peter Olofsson), Prof. Yang Kuang and Dr. Chao Chen.

Modeling metabolic adaptations and energy regulation in humans

Mathematical modeling of human energy regulation and body weight change has recently reached the level of sophistication required for accurate predictions. Mathematical models are beginning to provide a quantitative framework for integrating experimental data in humans and thereby help us better understand the dynamic imbalances of energy and macronutrients that give rise to changes in body weight and composition. This review provides an overview of the various approaches that have been used to model body weight dynamics and energy regulation in humans, highlights several insights that these models have provided, and suggests how mathematical models can serve as a guide for future experimental research.

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.

A Simple Model Predicting Individual Weight Change in Humans

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.

Quantification of the effect of energy imbalance on bodyweight

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.

Body composition and appetite: fat-free mass (but not fat mass or BMI) is positively associated with self-determined meal size and daily energy intake in humans

The idea of body weight regulation implies that a biological mechanism exerts control over energy expenditure and food intake. This is a central tenet of energy homeostasis. However, the source and identity of the controlling mechanism have not been identified, although it is often presumed to be some long-acting signal related to body fat, such as leptin. Using a comprehensive experimental platform, we have investigated the relationship between biological and behavioural variables in two separate studies over a 12-week intervention period in obese adults (total n 92). All variables have been measured objectively and with a similar degree of scientific control and precision, including anthropometric factors, body composition, RMR and accumulative energy consumed at individual meals across the whole day. Results showed that meal size and daily energy intake (EI) were significantly correlated with fat-free mass (FFM, P values < 0·02-0·05) but not with fat mass (FM) or BMI (P values 0·11-0·45) (study 1, n 58). In study 2 (n 34), FFM (but not FM or BMI) predicted meal size and daily EI under two distinct dietary conditions (high-fat and low-fat). These data appear to indicate that, under these circumstances, some signal associated with lean mass (but not FM) exerts a determining effect over self-selected food consumption. This signal may be postulated to interact with a separate class of signals generated by FM. This finding may have implications for investigations of the molecular control of food intake and body weight and for the management of obesity.

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

BACKGROUND

Free-living energy intake in humans is notoriously difficult to measure but is required to properly assess outpatient weight-control interventions.

OBJECTIVE

Our objective was to develop a simple methodology that uses longitudinal body weight measurements to estimate changes in energy intake and its 95% CI in individual subjects.

DESIGN

We showed how an energy balance equation with 2 parameters can be derived from any mathematical model of human metabolism. We solved the energy balance equation for changes in free-living energy intake as a function of body weight and its rate of change. We tested the predicted changes in energy intake by using weight-loss data from controlled inpatient feeding studies as well as simulated free-living data from a group of "virtual study subjects" that included realistic fluctuations in body water and day-to-day variations in energy intake.

RESULTS

Our method accurately predicted individual energy intake changes with the use of weight-loss data from controlled inpatient feeding experiments. By applying the method to our simulated free-living virtual study subjects, we showed that daily weight measurements over periods >28 d were required to obtain accurate estimates of energy intake change with a 95% CI of <300 kcal/d. These estimates were relatively insensitive to initial body composition or physical activity level.

CONCLUSIONS

Frequent measurements of body weight over extended time periods are required to precisely estimate changes in energy intake in free-living individuals. Such measurements are feasible, relatively inexpensive, and can be used to estimate diet adherence during clinical weight-management programs.

Simulation models of obesity: a review of the literature and implications for research and policy

Simulation models (SMs) combine information from a variety of sources to provide a useful tool for examining how the effects of obesity unfold over time and impact population health. SMs can aid in the understanding of the complex interaction of the drivers of diet and activity and their relation to health outcomes. As emphasized in a recently released report of the Institute or Medicine, SMs can be especially useful for considering the potential impact of an array of policies that will be required to tackle the obesity problem. The purpose of this paper is to present an overview of existing SMs for obesity. First, a background section introduces the different types of models, explains how models are constructed, shows the utility of SMs and discusses their strengths and weaknesses. Using these typologies, we then briefly review extant obesity SMs. We categorize these models according to their focus: health and economic outcomes, trends in obesity as a function of past trends, physiologically based behavioural models, environmental contributors to obesity and policy interventions. Finally, we suggest directions for future research.

A dynamical model for describing behavioural interventions for weight loss and body composition change

We present a dynamical model incorporating both physiological and psychological factors that predicts changes in body mass and composition during the course of a behavioral intervention for weight loss. The model consists of a three-compartment energy balance integrated with a mechanistic psychological model inspired by the Theory of Planned Behavior (TPB). The latter describes how important variables in a behavioural intervention can influence healthy eating habits and increased physical activity over time. The novelty of the approach lies in representing the behavioural intervention as a dynamical system, and the integration of the psychological and energy balance models. Two simulation scenarios are presented that illustrate how the model can improve the understanding of how changes in intervention components and participant differences affect outcomes. Consequently, the model can be used to inform behavioural scientists in the design of optimised interventions for weight loss and body composition change.

Predicting changes of body weight, body fat, energy expenditure and metabolic fuel selection in C57BL/6 mice

The mouse is an important model organism for investigating the molecular mechanisms of body weight regulation, but a quantitative understanding of mouse energy metabolism remains lacking. Therefore, we created a mathematical model of mouse energy metabolism to predict dynamic changes of body weight, body fat, energy expenditure, and metabolic fuel selection. Based on the principle of energy balance, we constructed ordinary differential equations representing the dynamics of body fat mass (FM) and fat-free mass (FFM) as a function of dietary intake and energy expenditure (EE). The EE model included the cost of tissue deposition, physical activity, diet-induced thermogenesis, and the influence of FM and FFM on metabolic rate. The model was calibrated using previously published data and validated by comparing its predictions to measurements in five groups of male C57/BL6 mice (N = 30) provided ad libitum access to either chow or high fat diets for varying time periods. The mathematical model accurately predicted the observed body weight and FM changes. Physical activity was predicted to decrease immediately upon switching from the chow to the high fat diet and the model coefficients relating EE to FM and FFM agreed with previous independent estimates. Metabolic fuel selection was predicted to depend on a complex interplay between diet composition, the degree of energy imbalance, and body composition. This is the first validated mathematical model of mouse energy metabolism and it provides a quantitative framework for investigating energy balance relationships in mouse models of obesity and diabetes.

Mechanisms of metabolic fuel selection: modeling human metabolism and body-weight change

Casual observation of any magazine rack or browsing the diet section of any bookshop provides convincing evidence that weight loss is of great interest to the U.S. population. Americans spend more than US$30 billion/year on weight-loss products, and the health cost of obesity was recently estimated to be as high as US$147 billion/year. Understanding the development of obesity and how excess weight can be lost requires knowledge of the physiological mechanisms by which the body uses food to provide fuel for metabolism and how the body copes with imbalances between fuel delivery and utilization.

Cellular bioenergetics as a target for obesity therapy

Obesity develops when energy intake exceeds energy expenditure. Although most current obesity therapies are focused on reducing calorific intake, recent data suggest that increasing cellular energy expenditure (bioenergetics) may be an attractive alternative approach. This is especially true for adaptive thermogenesis - the physiological process whereby energy is dissipated in mitochondria of brown fat and skeletal muscle in the form of heat in response to external stimuli. There have been significant recent advances in identifying the factors that control the development and function of these tissues, and in techniques to measure brown fat in human adults. In this article, we integrate these developments in relation to the classical understandings of cellular bioenergetics to explore the potential for developing novel anti-obesity therapies that target cellular energy expenditure.

New fat free mass - fat mass model for use in physiological energy balance equations

Background

The Forbes equation relating fat-free mass (FFM) to fat mass (FM) has been used to predict longitudinal changes in FFM during weight change but has important limitations when paired with a one dimensional energy balance differential equation. Direct use of the Forbes model within a one dimensional energy balance differential equation requires calibration of a translate parameter for the specific population under study. Comparison of translates to a representative sample of the US population indicate that this parameter is a reflection of age, height, race and gender effects.

Results

We developed a class of fourth order polynomial equations relating FFM to FM that consider age, height, race and gender as covariates eliminating the need to calibrate a parameter to baseline subject data while providing meaningful individual estimates of FFM. Moreover, the intercepts of these polynomial equations are nonnegative and are consistent with observations of very low FM measured during a severe Somali famine. The models preserve the predictive power of the Forbes model for changes in body composition when compared to results from several longitudinal weight change studies.

Conclusions

The newly developed FFM-FM models provide new opportunities to compare individuals undergoing weight change to subjects in energy balance, analyze body composition for individual parameters, and predict body composition during weight change when pairing with energy balance differential equations.

Effect of nutritional supplements on immune function and body weight in malnourished adults

In the United States, approximately 5% of the population is malnourished or has low body weight, which can adversely affect immune function. Malnutrition is more prevalent in older adults and is often a result of energy imbalance from various causes. Dietary supplementation to promote positive energy balance can reverse malnutrition, but has not been assessed for its effect on immune parameters. This 8-week clinical feeding trial evaluated the effect of a commercially available, high-protein, high-energy formula on body weight and immune parameters in 30 adult volunteers with body-mass indices (BMI) <21 kg/m². After the intervention, participants gained a mean of 3.74 lbs and increased BMI by 0.58 kg/m². The intervention improved lean body mass and limited body fat accumulation. However, no clinically significant improvements in immune measures were observed. These results support the use of high-protein, high-energy supplements in the treatment of underweight/malnutrition. Further investigation utilizing feeding studies of longer duration, and/or studying severely malnourished individuals may be needed to detect an effect on immune parameters of weight gain promoted by nutritional supplements.

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

Complex interactions between carbohydrate, fat, and protein metabolism underlie the body's remarkable ability to adapt to a variety of diets. But any imbalances between the intake and utilization rates of these macronutrients will result in changes in body weight and composition. Here, I present the first computational model that simulates how diet perturbations result in adaptations of fuel selection and energy expenditure that predict body weight and composition changes in both obese and nonobese men and women. No model parameters were adjusted to fit these data other than the initial conditions for each subject group (e.g., initial body weight and body fat mass). The model provides the first realistic simulations of how diet perturbations result in adaptations of whole body energy expenditure, fuel selection, and various metabolic fluxes that ultimately give rise to body weight change. The validated model was used to estimate free-living energy intake during a long-term weight loss intervention, a variable that has never previously been measured accurately.

Nutritional systems biology modeling: from molecular mechanisms to physiology

The use of computational modeling and simulation has increased in many biological fields, but despite their potential these techniques are only marginally applied in nutritional sciences. Nevertheless, recent applications of modeling have been instrumental in answering important nutritional questions from the cellular up to the physiological levels. Capturing the complexity of today's important nutritional research questions poses a challenge for modeling to become truly integrative in the consideration and interpretation of experimental data at widely differing scales of space and time. In this review, we discuss a selection of available modeling approaches and applications relevant for nutrition. We then put these models into perspective by categorizing them according to their space and time domain. Through this categorization process, we identified a dearth of models that consider processes occurring between the microscopic and macroscopic scale. We propose a "middle-out" strategy to develop the required full-scale, multilevel computational models. Exhaustive and accurate phenotyping, the use of the virtual patient concept, and the development of biomarkers from "-omics" signatures are identified as key elements of a successful systems biology modeling approach in nutrition research--one that integrates physiological mechanisms and data at multiple space and time scales.

A mathematical model of weight change with adaptation

As obesity and its related health problems grow around the world, efforts to control and manage weight is increasing in importance. It is well known that altering and maintaining weight is problematic and this has led to specific studies trying to determine the cause of the difficulty. Recent research has identified that the body reacts to forced weight change by adapting individual total energy expenditure. Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. Forward time simulations of the model compare well with mean data in both overfeeding and calorie restriction studies.

Estimating the continuous-time dynamics of energy and fat metabolism in mice

The mouse has become the most popular organism for investigating molecular mechanisms of body weight regulation. But understanding the physiological context by which a molecule exerts its effect on body weight requires knowledge of energy intake, energy expenditure, and fuel selection. Furthermore, measurements of these variables made at an isolated time point cannot explain why body weight has its present value since body weight is determined by the past history of energy and macronutrient imbalance. While food intake and body weight changes can be frequently measured over several weeks (the relevant time scale for mice), correspondingly frequent measurements of energy expenditure and fuel selection are not currently feasible. To address this issue, we developed a mathematical method based on the law of energy conservation that uses the measured time course of body weight and food intake to estimate the underlying continuous-time dynamics of energy output and net fat oxidation. We applied our methodology to male C57BL/6 mice consuming various ad libitum diets during weight gain and loss over several weeks and present the first continuous-time estimates of energy output and net fat oxidation rates underlying the observed body composition changes. We show that transient energy and fat imbalances in the first several days following a diet switch can account for a significant fraction of the total body weight change. We also discovered a time-invariant curve relating body fat and fat-free masses in male C57BL/6 mice, and the shape of this curve determines how diet, fuel selection, and body composition are interrelated.

The unrelenting obesity epidemic has resulted in intensive basic scientific investigation into the molecular mechanisms of body weight regulation—with the mouse being the organism of choice for such studies. We know that any mechanism of body weight regulation must exert its effect by influencing food intake, energy output, fuel selection, or some combination of these factors over extended time scales (∼weeks for mice). While food intake and body weight can be frequently measured in mice, current methods prohibit corresponding measurements of energy output or fuel selection on such long time scales. We address this deficiency by developing a mathematical method that quantitatively relates measurements of food intake, body weight and body fat to calculate the dynamic changes of energy output and net fat oxidation rates during the development of obesity and weight loss in male C57BL/6 mice. The mathematical model is based on the law of energy conservation, makes very few assumptions, and provides the first continuous-time estimates of energy output and fuel selection over periods lasting many weeks. Application of our methodology to various mouse models of obesity will improve our understanding of body weight regulation by placing molecular mechanisms in their whole-body physiological context.

Models use leptin and calculus to count calories

Thermostats have "set-points" that engineers design with mathematical rigor. Work in this issue of Cell Metabolism (Tam et al., 2009) applies similar modeling strategies to explore the control of murine energy and body weight homeostasis by leptin.

Modeling weight-loss maintenance to help prevent body weight regain

BACKGROUND

Lifestyle intervention can successfully induce weight loss in obese persons, at least temporarily. However, there currently is no way to quantitatively estimate the changes of diet or physical activity required to prevent weight regain. Such a tool would be helpful for goal-setting, because obese patients and their physicians could assess at the outset of an intervention whether long-term adherence to the calculated lifestyle change is realistic.

OBJECTIVE

We aimed to calculate the expected change of steady-state body weight arising from a given change in dietary energy intake and, conversely, to calculate the modification of energy intake required to maintain a particular body-weight change.

DESIGN

We developed a mathematical model using data from 8 longitudinal weight-loss studies representing 157 subjects with initial body weights ranging from 68 to 160 kg and stable weight losses between 7 and 54 kg.

RESULTS

Model calculations closely matched the change data (R(2) = 0.83, chi(2) = 2.1, P < 0.01 for weight changes; R(2) = 0.91, chi(2) = 0.87, P < 0.0004 for energy intake changes). Our model performed significantly better than the previous models for which chi(2) values were 10-fold those of our model. The model also accurately predicted the proportion of weight change resulting from the loss of body fat (R(2) = 0.90).

CONCLUSIONS

Our model provides realistic calculations of body-weight change and of the dietary modifications required for weight-loss maintenance. Because the model was implemented by using standard spreadsheet software, it can be widely used by physicians and weight-management professionals.

State-of-the-art measurements in human body composition: A moving frontier of clinical importance

The measurement of human body composition allows for the estimation of body tissues, organs, and their distributions in living persons without inflicting harm. From a nutritional perspective, the interest in body composition has increased multi-fold with the global increase in the prevalence of obesity and its complications. The latter has driven in part the need for improved measurement methods with greater sensitivity and precision. There is no single gold standard for body-composition measurements in-vivo. All methods incorporate assumptions that do not apply in all individuals and the more accurate models are derived by using a combination of measurements, thereby reducing the importance of each assumption. This review will discuss why the measurement of body composition or human phenotyping is important; discuss new areas where the measurement of body composition (human phenotyping) is recognized as having important application; and will summarize recent advances made in new methodology. Reference will also be made to areas we cannot yet measure due to the lack of appropriate measurement methodologies, most especially measurements methods that provide information on kinetic states (not just static state) and metabolic function.