British Journal of Nutrition

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British Journal of Nutrition (2010), 104:4-7 Cambridge University Press
Copyright © The Author 2010

Short Communication

Mathematical modelling of energy expenditure during tissue deposition

Kevin D. Halla1 c1

a1 Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, Bethesda, MD 20892, USA
Article author query
hall kd [PubMed]  [Google Scholar]


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.

(Received July 23 2009)

(Revised January 11 2010)

(Accepted January 12 2010)

(Online publication February 05 2010)

Key Words:Mathematical modelling; Energy expenditure; Tissue deposition; Weight gain


c1 Corresponding author: Kevin D. Hall, fax +1 301 402 0535, email


Abbreviations: AA, amino acid