Abstract
Introduction
Research studies have established mathematical correlations between the lengths of bone segments and the possible biomechanical implications of these correlations. The Lucas sequence comprises a series of integers that adhere to the same recurrence relation as the Fibonacci sequence; it differs in that it can start with any two initial integers. The purpose of this study is to determine whether segmental lengths of the foot height, tibia, femur, and upper body follow a Lucas sequence pattern.
Method
This was a retrospective radiographic review of patients who underwent full-body EOS scans. The AP scan was used to measure standing foot height (Ft), tibial length (T), femoral length (Fe), upper body length (UB), and full body length. 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.
Result
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).
Conclusion
This study demonstrates that total height is made up of sequential segments whose lengths approximate a Lucas series. The Fibonacci sequence is therefore once again implicated in human body proportions.
