I’ve just posted a new paper to the quantitative biology archive: Carson C. Chow and Kevin D. Hall, The dynamics of human body weight change (arXiv:0802.3234). Understanding the dynamics of weight change has important consequences for conditions such as obesity, cancer, AIDS, anorexia and bulimia nervosa. While we know that changes of body weight result from imbalances between the energy derived from food and the energy expended to maintain life and perform physical work, quantifying this relationship has proved difficult. Part of the difficulty stems from the fact that the body is comprised of multiple components and we must quantify how weight change is reflected in terms of alterations of body composition (i.e. fat versus lean mass). In this paper, we show that a model of the flux balances of macronutrients, namely fat, protein and carbohydrates, can provide a general description of the way the body weight will change over time. Under general conditions, the model can be reduced to a two dimensional system of fat and lean body masses, which then can be analyzed in the phase plane. For a fixed food intake rate and physical activity level, the body weight and body composition will approach a steady state. However, the steady state can correspond to a unique body weight (fixed point) or a continuum of body weights (invariant manifold) depending on how fat oxidation depends on the body weight and composition changes. Interestingly, the existing experimental data on human body weight dynamics cannot presently distinguish between these two possibilities. However, this distinction is important for the efficacy of clinical interventions that alter body composition and mass.
Addendum: Here is the link to the published paper in PloS Computational Biology.