A computational model to determine energy intake during weight loss123

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Background: Energy intake (EI) during weight loss is difficult and costly to measure accurately.Objective: The objective was to develop and validate a computational energy balance differential equation model to determine individual EI during weight loss.Design: 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.Results: 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.Conclusion: 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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From the Department of Mathematical Sciences, Montclair State University, Montclair, NJ (DMT); the Department of Nutritional Sciences, University of Wisconsin-Madison, Madison, WI (DAS); the Pennington Biomedical Research Center, Baton Rouge, LA (LAR and CKM); the Mayo Clinic, Rochester, MN (JAL); and Merck & Co, Rahway, NJ (SBH).

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DAS was supported by NIH grant PO1 AG11915. LMR is supported by NIH grants U01 AG20478 [principal investigator (PI): Eric Ravussin] and K99 HD060762 (PI: Leanne Redman). CKM was supported by NIH grants U01 AG20478 (PI: Eric Ravussin) and K23 DK068052 (PI: Corby Martin). JAL was supported by NIH grants DK56650, DK63226, DK662760, and M01 RR00585 and the Mayo Foundation.

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Address correspondence to DM Thomas, Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043. E-mail: [email protected].