Modelling the metabolism: allometric relationships between total daily energy expenditure, body mass, and height

Abstract

Background/objectives

Accurately predicting energy requirements form a critical component for initializing dynamic mathematical models of metabolism. The majority of such existing estimates rely on linear regression models that predict total daily energy expenditure (TDEE) from age, gender, height, and body mass, however, there is evidence these predictors obey a power function.

Subjects/methods

Baseline, free-living TDEE measured by doubly labeled water (DLW) in 20 studies with no overlapping subjects were obtained from the core lab at the University of Chicago and the University of Wisconsin-Madison (N = 2501 adults, 628 males, 1873 females). Linear regression models of log-transformed equations of the form: ${\rm{TDEE}} = \alpha _1M^{\beta _1}H^{\beta _2}$ and ${\rm{TDEE}} = {\rm{ln}}\left( {\alpha _1M^{\beta _1 + \gamma _1{\rm{Sex}}}H^{\beta _2 + \gamma _2{\rm{Sex}}}} \right)$ were developed to determine the values of the exponents of body mass (M (kg)) and height (H (cm)) along with a gender effect (Sex). A nonlinear curve fit was performed to develop a power model that also includes age ${\rm{TDEE}} = \alpha _1M^{\beta _1}H^{\beta _2} + \alpha _2{\mathrm{Age}}$.

Results

The power for body mass, β₁ = 0.45 and the power for height was β₂ = 1.52 in the database with both genders combined. Adding gender reduced these to β₁ = 0.43 and β₂ = 1.04. All terms were significant (p < 0.01) except for height when including gender. The powers for height in the additive gender-specific models were both closer to 1 and the power for body mass was similar across all models ranging between 0.41 and 0.57.

Conclusions

A nonlinear scaling relationship was found to hold for body mass and needs to be considered when adjusting TDEE for body mass or predicting human energy requirements as a function of body mass especially in individuals with obesity.