If bone is the answer, then what is the question?

Abstract

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 selforganising 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.

A sclerostin-based theory for strain-induced bone formation

“…In the inhibitory model, mechanical loading (∼ μR) inhibits the secretion of a signal (sc) that inhibits bone formation ( m obl ) bone structure. Osteocytes within the bone (elements with m(x, t) > 0.5) are assumed to sense a mechanical stimulus R, for which we use the local strain-energy-density (SED) rate as a correlate (Brown et al 1990;Huiskes 2000). Note that we use a static load to represent a cyclic load of given amplitude σ and frequency f .…”

Structural Adaptation of Trabecular Bone Revealed by Position Resolved Analysis of Proximal Femora of Different Primates

“…The observation of a nonrandom and anisotropic trabecular architecture, for example in the proximal femur of humans and primates, led Julius Wolff and contemporaries to the conclusion that the bone structure follows a mechanical optimization principle (Huiskes, 2000;Skedros and Baucom, 2007). Much later the concept of a mechanostat controlling the process of bone (re)modeling was proposed (Frost, 1987) to explain functional bone adaptation (Robling et al, 2006;Fratzl and Weinkamer, 2007) during life.…”

Untitled

“…Comprehensive theories relating mechanical forces to biological behavior will underlie this understanding [55]. Such theories, to be useful, should be testable.…”