We present a novel mathematical model of the dynamics of body weight, fat mass, fat free mass, energy expenditure and food intake dynamics in rats, based on nonlinear ordinary differential equations with delay. This model is based on leptin, ghrelin and glucose variations and take into account a memory of the previous food consumption in the system.

The rat is a model organism to study regulation of body weight in the context of multiple diets. Gain in body weight, fat mass and fat free mass depends on the composition and the amount of food consumed. Food consumption is submitted to regulations within the organism, occurring at short-time scale and at long-time scale, influencing hunger. The main regulators of food consumption are the level of fat reserves and the memory of the previous meals. Signals are integrated in the brain via concentrations of hormones, such as leptin, an indicator of adiposity, and ghrelin, an hormone produced by the stomach, and nutrients in plasma, such as glucose.

To validate our model, we performed experiments on 4 groups of rats submitted to different patterns of food availability. In addition to a control group (Ad libitum food), three groups received a reduced amount of food providing the same amount of energy overall but with different dynamics. Surprisingly, despite equivalent amounts of energy intake, final body weights were significantly different. Using part of the data set to evaluate the model parameters, we were able to predict quite accurately both body weight and food intake on the validating set. We modelled adaptation of energy expenditure using a delay model and we showed that adaptation of energy expenditure depends on previous food consumption dynamics on a time scale of 8 days. This is probably an important mechanism to react to changes in food availability, in order to maintain some energy reserves.

physiological model; body-weight dynamics; energy expenditure