The Dynamics of Human Body Weight Change

Citation: Chow CC, Hall KD ( The Dynamics of Human Body Weight Change Carson C. Chow 0 Kevin D. Hall 0 Philip E. Bourne, University of California San Diego, United States of America 0 Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health , Bethesda, Maryland , United States of America An imbalance between energy intake and energy expenditure will lead to a change in body weight (mass) and body composition (fat and lean masses). A quantitative understanding of the processes involved, which currently remains lacking, will be useful in determining the etiology and treatment of obesity and other conditions resulting from prolonged energy imbalance. Here, we show that a mathematical model of the macronutrient flux balances can capture the long-term dynamics of human weight change; all previous models are special cases of this model. We show that the generic dynamic behavior of body composition for a clamped diet can be divided into two classes. In the first class, the body composition and mass are determined uniquely. In the second class, the body composition can exist at an infinite number of possible states. Surprisingly, perturbations of dietary energy intake or energy expenditure can give identical responses in both model classes, and existing data are insufficient to distinguish between these two possibilities. Nevertheless, this distinction has important implications for the efficacy of clinical interventions that alter body composition and mass. - Obesity, anorexia nervosa, cachexia, and starvation are conditions that have a profound medical, social and economic impact on our lives. For example, the incidence of obesity and its co-morbidities has increased at a rapid rate over the past two decades [1,2]. These conditions are characterized by changes in body weight (mass) that arise from an imbalance between the energy derived from food and the energy expended to maintain life and perform work. However, the underlying mechanisms of how changes in energy balance lead to changes in body mass and body composition are not well understood. In particular, it is of interest to understand how body composition is apportioned between fat and lean components when the body mass changes and if this energy partitioning can be altered. Such an understanding would be useful for optimizing weight loss treatments in obese subjects to maximize fat loss or weight gain treatments for anorexia nervosa and cachexia patients to maximize lean tissue gain. To address these issues and improve our understanding of human body weight regulation, mathematical and computational modeling has been attempted many times over the past several decades [319]. Here we show how models of body composition and mass change can be understood and analyzed within the realm of dynamical systems theory and can be classified according to their geometric structure in the two dimensional phase plane. We begin by considering a general class of macronutrient flux balance equations and progressively introduce assumptions that constrain the model dynamics. We show that two compartment models of fat and lean masses can be categorized into two generic classes. In the first class, there is a unique body composition and mass (i.e. a stable fixed point) that is specified by the diet and energy expenditure. In the second class, there is a continuous curve of fixed points (i.e. an invariant manifold) with an infinite number of possible body compositions and masses at steady state for the same diet and energy expenditure rate. We show that almost all of the models in the literature are in the second class. Surprisingly, the existing data are insufficient to determine which of the two classes pertains to humans. For models with an invariant manifold, we show that an equivalent one dimensional equation for body composition change can be derived. We give numerical examples and discuss possible experimental approaches that may distinguish between the classes. General Model of Macronutrient and Energy Flux Balance The human body obeys the law of energy conservation [20], which can be expressed as where DU is the change in stored energy in the body, DQ is a change in energy input or intake, and DW is a change in energy output or expenditure. The intake is provided by the energy content of the food consumed. Combustion of dietary macronutrients yields chemical energy and Hesss law states that the energy released is the same regardless of whether the process takes place inside a bomb calorimeter or via the complex process of oxidative phosphorylation in the mitochondria. Thus, the energy released from oxidation of food in the body can be precisely measured in the laboratory. However, there is an important caveat. Not all macronutrients in food are completely absorbed by the body. Furthermore, the dietary protein that is absorbed does not undergo complete combustion in the body, but rather produces urea and ammonia. In accounting for these Understanding the dynamics of human body weight change has important consequences for conditions such as obesity, starvation, and wasting syndromes. Changes of body weight are known to result from imbalances between the energy derived from food and the energy expended to maintain life and perform physical work. However, quantifying this relationship has proved difficult, in part because the body is composed of multiple components and weight change results from alterations of body composition (i.e., fat versus lean mass). Here, we show that mathematical modeling can provide a general description of how body weight will change over time by tracking the flux balances of the macronutrients fat, protein, and carbohydrates. For a fixed food intake rate and physical activity level, the body weight and composition will approach steady state. However, the steady state can correspond to a unique body weight or a continuum of body weights that are all consistent with the same food intake and energy expenditure rates. Interestingly, existing experimental data on human body weight dynamics cannot distinguish between these two possibilities. We propose experiments that could resolve this issue and use computer simulations to demonstrate how such experiments could be performed. effects, we refer to the metabolizable energy content of dietary carbohydrate, fat, and protein, which is slightly less than the values obtained by bomb calorimetry. The energy expenditure rate includes the work to maintain basic metabolic function (resting metabolic rate), to digest, absorb and transport the nutrients in food (thermic effect of feeding), to synthesize or break down tissue, and to perform physical activity, together with the heat generated. The energy is stored in the form of fat as well as in lean body tissue such as glycogen and protein. The body need not be in equilibrium for Equation 1 to hold. While we are primarily concerned with adult (...truncated)