The relationship between body fat mass and fat-free mass.

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Abstract
It has been suggested that there is a curvilinear relationship between lean body or fat-free mass and body fat mass. In order to confirm this relationship, body composition was measured by determining body density and total body water using deuterium-labeled water in subjects varying widely in body fat mass. There were 29 males and 75 females with body mass index ranging from 20 to 66 kg/m2. The relationship between fat-free mass and fat mass appeared to be linear over the range of body fat from 10 to 90 kg: males R2 = 0.67 (p less than 0.0001) and females, R2 = 0.47 (p less than 0.0001). The amount of variance explained was not greater when the log of fat mass was used in place of fat mass alone. Multiple regression analysis demonstrated that the relationship between fat-free mass and fat mass remained significant (p less than 0.001) after adjusting for body height, age, and fat distribution. It is concluded that over the range of body fat extending from 10 to 90 kg there is a positive and linear relationship between fat-free body mass and fat mass.