Energy balance, energy turnover, and risk of body fat gain

Dear Editor:

We read with great interest the article by Hume et al. (1), “Low energy intake plus low energy expenditure (low energy flux), not energy surfeit, predicts future body fat gain.” The study used the energy balance equation to determine the relation between energy balance, energy flux, and long-term changes in percentage of body fat. First, we show here that the study’s representation of energy balance is equivalent to weight stability, and hence, the study is simply examining baseline expenditures in weight-stable individuals against long-term changes in percentage body fat, which has been well studied (2, 3). Second, we show that the established fat-free mass (FFM)–fat mass (FM) relation and the baseline relation between total energy expenditures (TEEs) adjusted for FFM and percentage body fat affect the dynamics of fat gain. Finally, we point out that examining the true influence of low energy turnover on fat gain requires adjusting TEE by resting metabolic rate (RMR). When adjusted accordingly, existing studies did not find high energy turnover to be protective against fat gain (2, 3).

By using the energy balance equation, ES = TEI − TEE, where TEI represents total energy intake and ES represents changed body energy stores, the study computed baseline TEI by using the following formula:

where ΔW is the change in weight over the baseline 2-wk doubly labeled water (DLW) measures of TEE. In this case, . The study’s primary analysis excluded individuals in whom TEI was >33% or <33% of their TEE. Formulaically, this is represented by the following inequality:

The use of Equation 1 and substituting the mean values of TEE for studies 1 and 2 provided in the article’s Supplemental Table 1 transforms the inequality to one in terms of ΔW:

Thus, participants who remained in “energy balance” are essentially the weight-stable participants whose magnitude of weight change remained within 1.5 kg of baseline measures during the 2-wk DLW measurement period.

Second, we point out that several well-established relations influence the study results. The study defines energy flux as TEI + TEE. With the use of Equation 1 and considering only the weight-stable participants, where ΔW ≈ 0, we have

This relation influences a potentially spurious relation between RMR and EnFlux (energy flux) in the article’s Figure 2 (1). Because RMR + TEF + AEE = TEE, where TEF is the thermic effect of feeding and AEE represents activity energy expenditures, plotting RMR against 2TEE should automatically result in a positive correlation.

The authors’ Figure 1 essentially plots EnFlux = 2TEE/FFM₀ compared with change in percentage of body fat. Because FFM is algebraically related to FR through the validated Forbes model (4),

where , a second relation in the study’s Figure 1 automatically exists. Moreover, individuals with a higher percentage of fat have a lower energy flux per kilogram of FFM (5), especially when both sexes are combined, as in the study’s Figure 1A (1). This property is shown in the plots of the publicly available Institute of Medicine’s DLW database (6) of TEE per kilogram of FFM compared with percentage fat (Figure 1). The Forbes equation indicates that individuals with higher baseline FM gain more FM than do their lean counterparts. Finally, the study’s stated conclusions imply that individuals with a low energy turnover (or physically inactive individuals) are at risk of increased fat accretion over time. To show that physical inactivity is a risk factor for fat gain, TEE/RMR or the physical activity level (PAL) would need to be compared against change in percentage of fat. High PAL has not been found to protect against increased fat gain (2, 3).

FIGURE 1.

 Sex-specific plots of TEE per kilogram of FFM compared with percentage of fat (6). FFM, fat-free mass; TEE, total energy expenditure.

In summary, the complex calculations presented in this study reduce simply to considering the relation between baseline TEE in weight stable participants to long-term changes in FM. In addition, the study omitted established relations between changes in fat and lean mass along with the property that individuals with higher percentage of fat have lower TEE per kilogram of lean mass. These omissions may have contributed to the correlations observed in the study results. Finally, to capture the role of activity on the risk of fat gain, the study should examine the relation of PAL compared with change in percentage of fat.