The role of cross-sectional geometry, curvature, and limb posture in maintaining equal safety factors: a computed tomography study

The limb bones of an elephant are considered to experience similar peak locomotory stresses as a shrew. "Safety factors" are maintained across the entire range of body masses through a combination of robusticity of long bones, postural variation, and modification of gait. The relative contributions of these variables remain uncertain. To test the role of shape change, we undertook X-ray tomographic scans of the leg bones of 60 species of mammals and birds, and extracted geometric properties. The maximum resistible forces the bones could withstand before yield under compressive, bending, and torsional loads were calculated using standard engineering equations incorporating curvature. Positive allometric scaling of cross-sectional properties with body mass was insufficient to prevent negative allometry of bending (F(b) ) and torsional maximum force (F(t) ) (and hence decreasing safety factors) in mammalian (femur F(b) ∞M(b) (0.76) , F(t) ∞M(b) (0.80) ; tibia F(b) ∞M(b) (0.80) , F(t) ∞M(b) (0.76) ) and avian hindlimbs (tibiotarsus F(b) ∞M(b) (0.88) , F(t) ∞M(b) (0.89) ) with the exception of avian femoral F(b) and F(t) . The minimum angle from horizontal a bone must be held while maintaining a given safety factor under combined compressive and bending loads increases with M(b) , with the exception of the avian femur. Postural erectness is shown as an effective means of achieving stress similarity in mammals. The scaling behavior of the avian femur is discussed in light of unusual posture and kinematics.