Body Circumferences: Clinical Implications Emerging from a New Geometric Model

Background: Body volume expands with the positive energy balance associated with the development of adult human obesity and this "growth" is captured by two widely used clinical metrics, waist circumference and body mass index (BMI). Empirical correlations between circumferences, BMI, and related body compartments are frequently reported but fail to provide an important common conceptual foundation that can be related to key clinical observations. A two-phase program was designed to fill this important gap: a geometric model linking body volume with circumferences and BMI was developed and validated in cross-sectional cohorts; and the model was applied to the evaluation of longitudinally monitored subjects during periods of voluntary weight loss. Concepts emerging from the developed model were then used to examine the relations between the evaluated clinical measures and body composition.

Methods: Two groups of healthy adults (n = 494 and 1499) were included in the cross-sectional model development/testing phase and subjects in two previous weight loss studies were included in the longitudinal model evaluation phase. Five circumferences (arm, waist, hip, thigh, and calf; average of sum, C), height (H), BMI, body volume (V; underwater weighing), and the volumes of major body compartments (whole-body magnetic resonance imaging) were measured.

Results: The evaluation of a humanoid geometric model based a cylinder confirmed that V derived from C and H was highly correlated with measured V [R2 both males and females, 0.97; p < 0.001). Developed allometric models confirmed model predictions that C and BMI (represented as V/H) are directly linked as, C = (V/H)0.5. The scaling of individual circumferences to V/H varied, with waist the highest (V/H~0.6) and calf the lowest (V/H~0.3), indicating that the largest and smallest between-subject "growth" with greater body volume occurs in the abdominal area and lower extremities, respectively. A stepwise linear regression model including all five circumferences2 showed that each contributed independently to V/H. These cross-sectional observations were generally confirmed by analysis of the two longitudinal weight loss studies. The scaling of circumference ratios (e.g., waist/hip) to V/H conformed to models developed on the scaling of individual circumferences to V/H, indicating their relations to BMI are predictable a priori. Waist, hip, and arm/calf circumferences had the highest associations with whole-body visceral adipose tissue, subcutaneous adipose tissue, and skeletal muscle volumes, respectively.

Conclusion: These observations provide a simple geometric model relating circumferences with body size and composition, introduce a conceptual foundation explaining previous empirical observations, and reveal new clinical insights.