Abstract

OBJECTIVE:

To elucidate the mathematical relationship between longitudinal changes of body composition and the adaptations of substrate utilization required to produce those changes.

DESIGN:

We developed a simple mathematical model of macronutrient balance. By using an empirical relationship describing lean body mass as a function of fat mass, we derived a mathematical expression for how substrate utilization adapts to changes of diet, energy expenditure and body fat such that energy imbalances produced the required changes of body composition.

RESULTS:

The general properties of our model implied that short-term changes of dietary fat alone had little impact on either fat or non-fat oxidation rates, in agreement with indirect calorimetry data. In contrast, changes of non-fat intake caused robust adaptations of both fat and non-fat oxidation rates. Without fitting any model parameters, the predicted body composition changes and oxidation rates agreed with experimental studies of overfeeding and underfeeding when the measured food intake, energy expenditure and initial body composition were used as model inputs.

CONCLUSION:

This is the first report to define the quantitative connection between longitudinal changes of body composition and the required relationship between substrate utilization, diet, energy expenditure and body fat mass. The mathematical model predictions are in good agreement with experimental data and provide the basis for future study of how changes of substrate utilization impact body composition regulation.