Open Access Research

New fat free mass - fat mass model for use in physiological energy balance equations

Diana Thomas1*, Sai Krupa Das2, James A Levine3, Corby K Martin4, Laurel Mayer5, Andrew McDougall6, Boyd J Strauss7 and Steven B Heymsfield8

Author Affiliations

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

2 Energy Metabolism Laboratory, Jean Mayer USDA Human Nutrition Center at Tufts University, Boston, MA, USA

3 Department of Medicine, Endocrine Research Unit, Mayo Clinic and Mayo Foundation, Rochester, MN, USA

4 Ingestive Behavior Laboratory, Pennington Biomedical Research Center, Baton Rouge, LA, USA

5 Columbia University, College of Physicians and Surgeons, The New York State Psychiatric Institute, New York City, NY, USA

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

7 Monash University Department of Medicine, Monash Medical Centre, Clayton, Victoria, Australia

8 Merck & Co, Rahway, NJ, USA

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Nutrition & Metabolism 2010, 7:39  doi:10.1186/1743-7075-7-39

Published: 9 May 2010



The Forbes equation relating fat-free mass (FFM) to fat mass (FM) has been used to predict longitudinal changes in FFM during weight change but has important limitations when paired with a one dimensional energy balance differential equation. Direct use of the Forbes model within a one dimensional energy balance differential equation requires calibration of a translate parameter for the specific population under study. Comparison of translates to a representative sample of the US population indicate that this parameter is a reflection of age, height, race and gender effects.


We developed a class of fourth order polynomial equations relating FFM to FM that consider age, height, race and gender as covariates eliminating the need to calibrate a parameter to baseline subject data while providing meaningful individual estimates of FFM. Moreover, the intercepts of these polynomial equations are nonnegative and are consistent with observations of very low FM measured during a severe Somali famine. The models preserve the predictive power of the Forbes model for changes in body composition when compared to results from several longitudinal weight change studies.


The newly developed FFM-FM models provide new opportunities to compare individuals undergoing weight change to subjects in energy balance, analyze body composition for individual parameters, and predict body composition during weight change when pairing with energy balance differential equations.