Mathematical modelling of energy expenditure during tissue deposition

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Abstract
Predicting the magnitude and rate of weight gain for a given increase of energy intake requires a model of whole-body energy expenditure that includes the energy cost of tissue deposition. Here, I introduce a mathematical framework for modelling energy expenditure that elucidates conceptual problems with the classical Kielanowski method for estimating the efficiencies of body fat and protein deposition. An alternative approach uses the theoretical biochemical efficiencies for protein and fat synthesis in combination with models of energy expenditure that include body fat and protein turnover costs. I illustrate this alternative approach using a simple mathematical model applied to previously published data from growing rats and human infants and compare the simple model results with the classical Kielanowski model. While both models fit the data reasonably well (R2>0·87 in rats and R2>0·67 in infants), the Kielanowski method resulted in parameter estimates that varied widely across experiments, had poor precision, and occasionally produced efficiency estimates greater than 1. In contrast, the new method provided precise parameter values and revealed consistencies across different experiments. The proposed mathematical framework has implications for interpreting studies of animal nutrition as well as providing a roadmap for future modelling efforts.