The structure and mechanics of bone

Abstract

The four levels of hierarchy considered in this review are the nanoscale (the mineralised collagen fibre and the extrafibrillar mineral), the microscale (the structure as visible under the microscope), the mesoscale (particularly the relationship between cancellous and cortical bone) and the whole bone scale. The explosion of papers at the nanoscale precludes any settling on one best model. At the microscale the inadequacies of linear elastic fracture mechanics, the importance of R-curves for understanding what is happening to cracks in bone, and the effect of different histological types are emphasised. At the mesoscale the question of whether cancellous bone is anything but compact bone with a lot of holes in it, and the question of whether cancellous bone obeys Wolff’s ‘law’ is discussed. The problem of not damaging bone when examining it with X-rays is mentioned (though not solved). At the whole bone level the relative roles of genetics and the external forces and the question of the way in which bones are loaded, in bending or compression, is raised, and the question of size effects, long underestimated or ignored by the bone community, is discussed. Finally, the question of why there are hierarchies at all in bone is addressed

Appendix

Panel 1: Enhancements in technology and new technologies that have occurred in the last 30 years or so

Improvements in already adopted methods

• Computer-assisted image analysis

• Light microscopes increasingly sophisticated

• Mechanical testing machines driven by computers (an advance?)

• Transmission and scanning electron microscopes are increasingly sophisticated

• Vast improvements in the power and sophistication of computers

Methods now adopted by the bone community, or new methods

• Atomic force microscopy

• Computational chemistry, including quantum mechanical methods

• Environmental chambers

• Finite element analysis

• Micromilling

• Microtomography

• Nanoindentation

• Non-contact optical deformation mapping

• Scanning confocal microscopy

• Shearography

• Spectroscopy (FTIR, Raman, NMR)

People should remember that new techniques bring new hazards: environmental chambers may mislead people into thinking their specimens are truly in a physiological state; images can be tweaked in Photoshop (a very bad practice); papers on Finite Element Analysis are often what Peter Medawar once called methodological chambers of horrors; not having hard copy output from computers can, indeed often does, lead to archiving problems, and so on.

Panel 2

	Adult human haversian	Bovine fibrolamellar	Whale tympanic bulla	Mesoplodon rostrum	Dry Deer antler	Wet Deer femur
Young’s modulus (GPa)	13–18	11–26	35	45	17	22
Shear modulus (GPa)	3.3	5	–	–	–	–
Tensile strength (MPa)	50–130	30–170	30	Low	–	–
Tensile yield (MPa)	110	160	–	Low	–	–
Ultimate tensile strain	0.007–0.030	0.002–0.030	0.002	Low	High	So so
Compressive strength (MPa)	130–200	–	–	–	–	–
Bending strength (MPa)	–	240	33	50	350	260
Shear strength (MPa)	70	65	–	–	–
Impact absorption	So so	So so	Poor	Poor	High	So so

1. Characteristic mechanical properties of cortical bone. This table merely gives some idea of the mechanical properties of cortical bone and should not be used for reference. Compare the ‘Dry Deer antler’ with the ‘Wet Deer femur’, for they were measured on exactly the same type of specimens. For more definitive information, you should refer to papers and books such as the following: [3, 28, 45, 55, 67, 68]

Panel 3

People who wish to examine the history of the so called Wolff’s law, which is a concept without a legal basis, and which is still used all the time without much thought, might like to follow some of the references in this time-line.

• 1832 Bourgery is probably the first to publish [69] (in French) regarding the architectural structure of cancellous bone, though this had been known in a general way for centuries

• 1867 von Meyer publishes a paper [70] (in German) showing the supposed relationship between the directions of the trabeculae in the proximal human femur and a crane devised by Culmann

• 1870 Wolff ‘took charge of the subject’ [71] and published a paper setting out his ideas in detail [72] (in German). In the years afterwards he was very aggressive in defending his views [71]

• 1881 Roux published (in German) a book that was really about functional adaptation [73]. This got conflated [71] with Wolff’s overspecific mathematical theory about the way in which cancellous bone was arranged, into ‘Wolff’s law’

• 1892 Wolff publishes a book [74] (in German) summarising his views (‘often quoted hardly read’ [71])

• 1922 Triepel publishes a book [75] (in German) about the architecture of human cancellous bone that lists 20 reasons for rebutting Wolff’s ideas

• 1942 D’Arcy Thompson publishes (in English) a rather colourful account [76] of how Culmann came to see von Meyer’s dissection of the end of a bone and said ‘That’s my crane!’

• 1986 [77] English language translation of Wolff’s classic work is published

• 1987 Roesler publishes an article [71] (in English) in the course of which he essentially rebuts the concept of Wolff’s law as being anything of the sort

• 2001 Cowin publishes (in English) a good, and one would have hoped final, rebuttal of Wolff’s ‘law’ [44] Alas, it was not to be!