Curved bones: An adaptation to habitual loading.

Why are long bones curved? It has long been considered a paradox that many long bones supporting mammalian bodies are curved, since this curvature results in the bone undergoing greater bending, with higher strains and so greater fracture risk under load. This study develops a theoretical model wherein the curvature is a response to bending strains imposed by the requirements of locomotion. In particular the radioulna of obligate quadrupeds is a lever operated by the triceps muscle, and the bending strains induced by the triceps muscle counter the bending resulting from longitudinal loads acting on the curved bone. Indeed the theoretical model reverses this logic and suggests that the curvature is itself a response to the predictable bending strains induced by the triceps muscle. This, in turn, results in anatomical arrangements of bone, muscle and tendon that create a simple physiological mechanism whereby the bone can resist the bending due to the action of triceps in supporting and moving the body. The model is illustrated by contrasting the behaviour of a finite element model of a llama radioulna to that of a straightened version of the same bone. The results show that longitudinal and flexor muscle forces produce bending strains that effectively counter strains due to the pull of the triceps muscle in the curved but not in the straightened model. It is concluded that the curvature of these and other curved bones adds resilience to the skeleton by acting as pre-stressed beams or strainable pre-buckled struts. It is also proposed that the cranial bending strains that result from triceps, acting on the lever that is the radioulna, can explain the development of the curvature of such bones.