Wall thickness of gas- and marrow-filled avian long bones: measurements on humeri, femora and tibiotarsi in crows (Corvus corone cornix) and magpies (Pica pica).

We studied how the ratio K of the internal to external diameter of gas- and marrow-filled avian long bones follows the biomechanical optima derived for tubular bones with minimum mass designed to fulfil various mechanical requirements. We evaluated radiographs of numerous humeri, femora and tibiotarsi in Corvus corone cornix and Pica pica. The K-values of the gas-filled humerus (K=0.78+/-0.03) and the marrow-filled femur (K=0.79+/-0.02) in Corvus are practically the same, while K of the marrow-filled tibiotarsus (K=0.71+/-0.04) is significantly smaller. The same is true for the gas-filled humerus (K=0.78+/-0.02) and the marrow-filled femur (K=0.77+/-0.02) and tibiotarsus (K=0.67+/-0.05) in Pica. K in Corvus is slightly larger than K in Pica, but the differences are statistically not significant. The standard deviation DeltaK of the tibiotarsi (DeltaK=0.04-0.05) is approximately two times as large as that of the humeri (DeltaK=0.02-0.03) and femora (DeltaK=0.02) in both species. Accepting the assumption of earlier authors that the ratio Q of the marrow to bone density is 0.5, our data show that the marrow-filled tibiotarsi of Corvus and Pica are optimized for stiffness, while the marrow-filled femora are far from any optimum. The relative wall thickness W=1-K of the gas-filled avian humeri studied is much larger than the theoretical optimum W*=1-K*=0.07, and thus these bones are thicker-walled than the optimal gas-filled tubular bone with minimum mass.