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

Diana Thomas,Steven B Heymsfield,Corby K Martin,Sai Das,Laurel Mayer,Andrew Mcdougall,James A Levine,Boyd J Strauss

doi:10.1186/1743-7075-7-39

Abstract

BackgroundThe 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.ResultsWe 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.ConclusionsThe 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.

Highlights

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
We show that longitudinal data travels the trend set by National Health and Nutrition Examination Survey (NHANES) and that the new models predict the changes in FFM with equal accuracy to the Forbes model, thereby preserving the most descriptive conclusions derived from the Forbes model
We used the cross-sectional models to answer three main questions related to pairing a FFM model to an energy balance equation: Do the cross-sectional models preserve the accuracy of predictions provided by the Forbes model for changes in FFM during weight change? Do the cross-sectional models have a non-negative intercept that reflects observed data? How do the cross-sectional models vary with age, height, gender and race? To answer these questions we analyzed two existing crosssectional body composition databases consisting of athletes and subjects with anorexia nervosa and five existing weight change databases which reflect changes in body composition due to caloric restriction, caloric restriction

Summary

Introduction

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. Mathematical models based on the energy balance equation provide descriptions of the impact of physiological changes and quantitative predictions of body mass during weight change. Quantitative predictions of body mass during weight change applying minimal individual baseline information. The Hall model [1] is developed around the first approach where a system of five differential equations is carefully determined to reflect the specific flow of macronutrient energy during weight change. The first major simplification assumes glucose/glycogen mass is modeled by a time averaged constant, thereby eliminating the carbohydrate balance equation and its associated parameters and baseline inputs [3]

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Discussion

Conclusion