Huiskes R
Orthopaedic Research Laboratory, University of Nijmegen, The Netherlands.
J Anat. 2000 Aug;197 ( Pt 2)(Pt 2):145-56. doi: 10.1046/j.1469-7580.2000.19720145.x.
In the 19th century, several scientists attempted to relate bone trabecular morphology to its mechanical, load-bearing function. It was suggested that bone architecture was an answer to requirements of optimal stress transfer, pairing maximal strength to minimal weight, according to particular mathematical design rules. Using contemporary methods of analysis, stress transfer in bones was studied and compared with anatomical specimens, from which it was hypothesised that trabecular architecture is associated with stress trajectories. Others focused on the biological processes by which trabecular architectures are formed and on the question of how bone could maintain the relationship between external load and architecture in a variable functional environment. Wilhelm Roux introduced the principle of functional adaptation as a self-organising process based in the tissues. Julius Wolff, anatomist and orthopaedic surgeon, entwined these 3 issues in his book The Law of Bone Remodeling (translation), which set the stage for biomechanical research goals in our day. 'Wolff's Law' is a question rather than a law, asking for the requirements of structural optimisation. In this article, based on finite element analysis (FEA) results of stress transfer in bones, it is argued that it was the wrong question, putting us on the wrong foot. The maximal strength/minimal weight principle does not provide a rationale for architectural formation or adaptation; the similarity between trabecular orientation and stress trajectories is circumstantial, not causal. Based on computer simulations of bone remodelling as a regulatory process, governed by mechanical usage and orchestrated by osteocyte mechanosensitivity, it is shown that Roux's paradigm, conversely, is a realistic proposition. Put in a quantitative regulatory context, it can predict both trabecular formation and adaptation. Hence, trabecular architecture is not an answer to Wolff's question, in the sense of this article's title. There are no mathematical optimisation rules for bone architecture; there is just a biological regulatory process, producing a structure adapted to mechanical demands by the nature of its characteristics, adequate for evolutionary endurance. It is predicted that computer simulation of this process can help us to unravel its secrets.
19世纪,几位科学家试图将骨小梁形态与其机械承重功能联系起来。有人提出,根据特定的数学设计规则,骨骼结构是对最佳应力传递需求的一种回应,是将最大强度与最小重量相匹配。运用当代分析方法,对骨骼中的应力传递进行了研究,并与解剖标本进行了比较,据此推测骨小梁结构与应力轨迹相关。其他人则关注骨小梁结构形成的生物学过程,以及在功能多变的环境中骨骼如何维持外部负荷与结构之间关系的问题。威廉·鲁克斯引入了功能适应原理,将其作为一种基于组织的自组织过程。解剖学家兼矫形外科医生尤利乌斯·沃尔夫在他的《骨重塑定律》(译本)一书中,将这三个问题交织在一起,为我们这个时代的生物力学研究目标奠定了基础。“沃尔夫定律”与其说是一条定律,不如说是一个问题,它探讨的是结构优化的要求。在本文中,基于骨骼应力传递的有限元分析(FEA)结果,有人认为这是一个错误的问题,让我们走上了歧途。最大强度/最小重量原理并不能为结构形成或适应提供理论依据;骨小梁方向与应力轨迹之间的相似性只是偶然的,并非因果关系。基于对骨重塑作为一种受机械使用支配并由骨细胞机械敏感性精心调控的调节过程的计算机模拟,结果表明,相反,鲁克斯的范式是一个现实的命题。在定量调节的背景下,它可以预测骨小梁的形成和适应。因此,从本文标题的意义上来说,骨小梁结构并不是对沃尔夫问题的答案。骨骼结构不存在数学优化规则;只有一个生物调节过程,通过其特性本质产生一种适应机械需求的结构,足以实现进化耐久性。据预测,对这一过程的计算机模拟能够帮助我们揭开其奥秘。