Milne Nick
School of Anatomy, Physiology and Human Biology, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia.
J Theor Biol. 2016 Oct 21;407:18-24. doi: 10.1016/j.jtbi.2016.07.019. Epub 2016 Jul 19.
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.
为什么长骨是弯曲的？长期以来，一个悖论一直存在：许多支撑哺乳动物身体的长骨是弯曲的，因为这种弯曲会导致骨骼承受更大的弯曲，产生更高的应变，从而在负载下有更大的骨折风险。本研究建立了一个理论模型，其中弯曲是对运动需求所施加的弯曲应变的一种响应。特别是，专性四足动物的桡尺骨是由肱三头肌操作的杠杆，肱三头肌引起的弯曲应变抵消了作用在弯曲骨骼上的纵向载荷所产生的弯曲。事实上，该理论模型颠倒了这种逻辑，并表明弯曲本身是对肱三头肌所诱导的可预测弯曲应变的一种响应。这反过来又导致了骨骼、肌肉和肌腱的解剖学排列，形成了一种简单的生理机制，通过这种机制，骨骼可以抵抗由于肱三头肌在支撑和移动身体时的作用而产生的弯曲。通过对比美洲驼桡尺骨的有限元模型与同一根骨骼伸直版本的行为来说明该模型。结果表明，纵向和屈肌力量产生的弯曲应变有效地抵消了弯曲模型中肱三头肌拉力所引起的应变，但在伸直模型中则不然。得出的结论是，这些弯曲骨骼以及其他弯曲骨骼的弯曲通过充当预应力梁或可应变预屈曲支柱，为骨骼增加了弹性。还提出，肱三头肌作用于桡尺骨这一杠杆上所产生的颅骨弯曲应变，可以解释此类骨骼弯曲的形成。
