Body fat and fat-free mass inter-relationships: Forbes's theory revisited

A theoretical equation was developed by Forbes that quantifies the fat-free proportion of a weight change as a function of the initial body fat. However, Forbes's equation was strictly valid only for infinitesimal weight changes. Here, I extended Forbes's equation to account for the magnitude and direction of macroscopic body weight changes. The new equation was also re-expressed in terms of an alternative representation of body composition change defined by an energy partitioning parameter called the P-ratio. The predictions of the resulting equations compared favourably with data from human underfeeding and overfeeding experiments and accounted for previously unexplained trends in the data. The magnitude of the body weight change had a relatively weak effect on the predicted body composition changes and the results were very similar to Forbes's original equation for modest weight changes. However, for large weight changes, such as the massive weight losses found in patients following bariatric surgery, Forbes's original equation consistently underestimated the fat-free mass loss, as expected. The new equation that accounts for the magnitude of the weight loss provides better predictions of body composition changes in such patients.