How does the relative wall thickness of human femora follow the biomechanical optima? An experimental study on mummies.

We studied how the ratio (K) of the internal:external diameter of human femora follows the biomechanical optima derived earlier by other researchers for marrow-filled tubular bones with circular cross section and minimum mass designed to withstand yield and fatigue, or stiffness, or bending fracture, or impact strengths. With evaluation of radiographs of 107 femora from 57 human mummies the values of K were measured. We found that K(posterior)=0.498+/-0.085 for the posterior radiographic view, and K(medial)=0.589+/-0.070 for the medial view with K(min)=0.345 and K(max)=0.783. The theoretical optima for K depend on the ratio (Q) of the marrow:bone density. Accepting the assumption of earlier authors that Q=0.50, our data show that human femora are optimised to withstand bending fracture, or yield and fatigue strengths. There were no sex-, age- and length-specific differences in K, and the means of K of the right and left femora of individuals were statistically not significantly different. The biomechanical optimization for K of human femora is not finely tuned. Compared with fox femora, K of human femora follows the biomechanical optimum to a much lesser extent. Although the relative wall thickness W=1-K of human femora are optimised, the very low relative mass increment due to deviation of K from the optimum and the considerable intraspecific variance of K make it probable that an accurate optimization of the relative wall thickness is irrelevant in humans.