THE STRENGTH AND ELASTICITY OF BONE IN RATS ON A RACHITOGENIC DIET
Authors: De V. Weir J. B. , Bell G. H. , Chambers J. W. 
Published: February 2018

One of the aims of this work was to find criteria by which the quality of bone as a supporting tissue might be judged. This inevitably involves discussion and, if possible, assessment, of the relative importance of the inorganic and organic material of the bone. It is relatively easy to measure the mineral content, and for that reason it has always received more than its due share of attention.

In the present experiment the composition of the ash of all bones was remarkably constant, with a Ca/P ratio of 2. Furthermore, X-ray crystallography showed that the structure of the inorganic material was the same in all cases. The great difficulty of measuring variations in the quality of the organic material which is, of course, protein in nature makes it impossible to say how much it influences bone strength. Since at least 40 per cent. of the bone is collagen, either a quantitative or a qualitative alteration might alter bone strength. X-ray crystallography revealed no qualitative differences in the collagen material of bones of the three groups; so that for the present it would seem safer to assume that alterations in the physical properties of the bones are due to variations in the relative proportions of organic and inorganic constituents (Dawson 1946, Bell et al. 1947).

These experiments show that the three diets produce highly significant differences in the percentage of ash, in SB, and in E. It is possible that some variations in the percentage of ash are due to variations in the absolute collagen (weight of collagen in unit volume of bone substance); but the range of variation in the percentage of ash leaves no reasonable doubt that differences in percentage ash between the diet groups are due essentially to differences in absolute ash. Presumably the collagen contributes something to the strength of the bone; but the indications are that it plays a minor part and that the relative weakness and flexibility of rachitic bones is due to decrease in the absolute ash content. Within any one diet group, the relation between percentage ash and the other two variables, SB and E, is masked by other sources of variation such as those associated with the many measurements involved; and thus the correlation between percentage ash and SB, and also between percentage ash and E, is not significant.

At first sight, the scatter diagrams (Figs. 5 and 6) appear to indicate a correlation between ash and SB, and between ash and E. Closer inspection shows, however, that the apparent trend is due largely to differences between the means of the diet groups, and that the points within any one group show no such obvious trend. Figure 7 shows that the position with regard to correlation between SB and E is very different. Here there is an obvious trend within each diet group; the amount of scatter is very much less. Calculation shows that, even when the differences between the means of diet groups is excluded, there is still a significant correlation between SB and E. The question of the correlation between the three variables is discussed more fully in the addendum to this paper.

Although the "goodness" of a bone is usually judged by its breaking stress, the experimental findings recorded above suggest that it may be assessed equally well on the basis of elastic properties as shown by Young's modulus. Normal bones, group S in these experiments, were elastic up to 79 per cent. of their breaking stress (Table II): the poorer bones of groups R and N were, however, only a little inferior in this respect. In some cases there was no apparent deviation of the load-deflexion curve from a straight line until the bone was about to break. Such a curve was published in the first paper of this series (Bell, Cuthbertson and Orr 1941), but in the light of further experience this curve is scarcely typical. The terminal falling over of the curve is illustrated in Figure 4 and is much more marked in the bones of group R.

While stress at the upper limit of elasticity varies over a wide range in the three groups (Table II and Fig. 4), the strain at this point is remarkably constant at about 1Â·5 per cent. This same percentage displacement must occur between the molecules of the bone material at the elastic limitâand it may be that, up to this amount of molecular displacement, the deformation is reversible; but that beyond it, plastic changes occur. We have no evidence as to whether the limiting displacement concerns mineral or protein constituents of the bone, or both.

We have already commented on the remarkable strength of bone material (Bell et al., 1941). The breaking stress of normal rat bone is about the same as that of cast iron, and about half that of mild steel. Young's modulus, however, is only one-tenth that of cast iron and one-twentieth that of steel. Thus bone, despite its lightness (specific gravity about 2Â·5 as compared with 7Â·9 for iron), is remarkably strong and at the same time more flexible than might be expected. Presumably the biological advantage is that greater flexibility helps to absorb sudden impacts. It is unusual in metallic substances to find the elastic modulus proportional to the strength; this is more characteristic of materials like concrete and timber. Another remarkable property of bone is that it remains elastic up to three-quarters of the breaking stress. Most metals show considerable ductility before reaching their breaking point.

While Young's modulus is of interest, both on its own account and as an index of the quality of the bone, its close association with breaking stress suggests that it might be used to predict the maximum load which a bone can carry safely. Since E, unlike SB, can be measured without damage, useful information might be gained by measuring the elasticity of living human bones.