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Am J Clin Nutr. 2010 Dec;92(6):1326-31. doi: 10.3945/ajcn.2010.29687. Epub 2010 Oct 20.

A computational model to determine energy intake during weight loss.

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Department of Mathematical Sciences, Montclair State University, Montclair, NJ, USA.



Energy intake (EI) during weight loss is difficult and costly to measure accurately.


The objective was to develop and validate a computational energy balance differential equation model to determine individual EI during weight loss.


An algorithm was developed to quantify EI during weight loss based on a validated one-dimensional model for weight change. By using data from a 24-wk calorie-restriction study, we tested the validity of the EI model against 2 criterion measures: 1) EI quantified through food provision from weeks 0-4 and 4-12 and 2) EI quantified through changes in body energy stores [measured with dual-energy X-ray absorptiometry (DXA)] and energy expenditure [measured with doubly labeled water (DLW)] from weeks 4-12 and 12-24.


Compared with food provision, the mean (±SD) model errors were 41 ± 118 kcal/d and -22 ± 230 kcal/d from weeks 0-4 and 4-12, respectively. Compared with EI measured with DXA and DLW, the model errors were -71 ± 272 kcal/d and -48 ± 226 kcal/d from weeks 4-12 and 12-24, respectively. In every comparison, the mean error was never significantly different from zero (P values > 0.10). Furthermore, Bland and Altman analysis indicated that error variance did not differ significantly over amounts of EI (P values > 0.26). Almost all individual participants' values were within CI limits.


The validity of the newly developed EI model was supported by experimental observations and can be used to determine an individual participant's EI during weight loss.

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