Department of Mathematical Sciences, Montclair State University, Montclair, NJ, USA.
Nutr Metab (Lond). 2010 May 9;7:39. doi: 10.1186/1743-7075-7-39.
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.
福布斯方程将去脂体重（FFM）与脂肪量（FM）相关联，用于预测体重变化期间 FFM 的纵向变化，但与一维能量平衡微分方程结合使用时存在重要局限性。在一维能量平衡微分方程中直接使用福布斯模型需要针对研究中的特定人群校准平移参数。将平移参数与美国代表性人群样本进行比较表明，该参数反映了年龄、身高、种族和性别等因素的影响。
我们开发了一类将 FFM 与 FM 相关联的四阶多项式方程，将年龄、身高、种族和性别作为协变量，无需针对基线受试者数据进行参数校准，同时提供了 FFM 的有意义的个体估计值。此外，这些多项式方程的截距是非负的，与在严重的索马里饥荒期间测量到的非常低的 FM 观察结果一致。与来自几项纵向体重变化研究的结果相比，这些模型保留了福布斯模型对身体成分变化的预测能力。
新开发的 FFM-FM 模型为比较经历体重变化的个体与能量平衡的个体、分析个体参数的身体成分以及在与能量平衡微分方程结合时预测体重变化期间的身体成分提供了新的机会。
