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Objectives: Mathematical models of lean- and fat-mass growth with diet are useful to help describe and potentially predict the fat- and lean-mass change with different diets as a function of consumed protein and fat calories. Most of the existing models do not explicitly account for interdependence of fat-mass on the lean-mass and vice versa. The aim of this study was to develop a new compartmental model to describe the growth of lean and fat mass depending on the input of dietary protein and fat, and accounting for the interdependence of adipose tissue and muscle growth. Methods: The model was fitted to existing clinical data of an overfeeding trial for 23 participants (with a high-protein diet, a normal-protein diet, and a low-protein diet) and compared with the existing Forbes model. Results: Qualitatively and quantitatively, the compartment model data fit was smoother with less overall error than the Forbes model. The root means square error were 0.39, 0.93 and 0.72 kg for the new model, the Forbes model, and the modified Forbes model, respectively. Additionally, for the present model, the differences between some of the coefficients (on the cross dependence of fat and lean mass as well as on the intake diet dependence) across different diets were statistically significant (P < 0.05). Conclusions: Our new Dey-model showed excellent fit to overfeeding data for 23 normal participants with some significant differences of model coefficients across diets, enabling further studies of the model coefficients for larger groups of participants with obesity or other diseases.

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