Is human height based on a Lucas sequence relationship between the foot height, tibial length, femur length and upper body length?

Abstract

This is a retrospective chart and radiographic review of 145 patients who underwent full-body EOS imaging; 109 males and 36 females. The mean ages of the female and male subsets are 28.8 (SD = 11.6) years and 29.5 (SD = 11.8) years, respectively. The sum of the foot height (Ft) and the tibial length (T) for each subject was compared to their femur length (Fe). Subsequently, the sum of the tibial (T) and femoral lengths (Fe) were compared to their respective upper body lengths (UB), as measured from the tops of the femoral heads. A linear regression test was performed to determine whether a Lucas sequence-based relationship exists between Ft + T and Fe, and between T + Fe and UB. The regression for the relationship between Ft + T and Fe for the entire cohort (R = 0.82, R2  = 0.70), the female subset (R = 0.94, R2  = 0.88) and the male subset (R = 0.75, R2  = 0.57), all demonstrated a strong positive correlation between Ft + T and Fe and showed that Ft + T is a likely predictor of Fe. The regression test for the entire cohort demonstrated a moderately positive correlation between T + Fe and UB (R = 0.41, R2  = 0.17, F(1, 145) = 29.42, p = 2.4E-07). A stronger correlation was found for the relationship between T + Fe and UB (R = 0.57, R2  = 0.32, F(1,35) = 16.64, p = 2.5E-05) for the female subset relative to the male subset (R = 0.20, R2  = 0.038, F(1, 35) = 4.37, p = 0.04). There appears to be a Lucas sequence relationship between the lengths of the foot height, tibial length, femoral length and upper body length, which together make up standing height. This mathematical proportion relationship is stronger in females than males.