J. Anat. (1984), 139, 2, pp. 265-273 265With 6 figuresPrinted in Great Britain

A neutron diffraction study of the bones of the foot

G. E. BACON, P. J. BACON* AND R. K. GRIFFITHSt

Department of Physics, University of Sheffield, Sheffield S3 7RH,* Institute of Terrestrial Ecology, Merlewood, Grange-over-Sands,

Cumbria LA11 6JU and t Health Services Research Centre,University of Birmingham Medical School, Vincent Drive, Birmingham B15 2TJ

(Accepted 12 January 1984)

INTRODUCTION

The complicated spongy bone of the foot has fascinated investigators for over onehundred years. Figure 1 shows the oft-repeated drawing of D'Arcy Thompson(1917) which originated with Meyer (1867, 1873). These ideas were gradually turnedinto more refined engineering theories by workers such as Jones (1941), Morton(1935) and Hicks (1955), some of whom tried to quantify the properties of the struc-ture and the forces acting on it. Some workers, such as Preuschoft (1969, 1970), havecarried out quite elaborate theoretical and modelling studies.

In a more general way, the interrelation of bone structure with function has beenapproached by many workers using a variety of techniques. The relative merits ofthese methods have been comprehensively reviewed in relation to the human femurby Gdoutos, Raftopoulos & Baril (1982) who cite a hundred items of research overmore than sixty years. A similar body of work is accumulating in relation to the jawbecause of its significance in dental and maxillofacial prosthetic surgery. A varietyof methods has been used, notably by Hylander (1979 a, b) using strain gauges alliedwith load measurement in vivo; by Mongini, Preti, Calderdale & Barberi (1981)using strain gauges in models; and by Williams, Caputo & Sanders (1981) usingphotoelastic analysis combined with load measurement.

All these methods of analysis demonstrate that the forces acting on bone differconsiderably from point to point and vary with time. The structure of a bone asobserved at any moment is an integration of the effects of these various forces andthe physiological responses to them. A number of workers have attempted to throwlight on the way in which different types of force may be important. Lanyon &Baggott (1976) suggest that stress cycles are significant while Hert, Pribylova &Liskova (1972) show that intermittent forces may be more important than con-tinuous ones. Bouvier & Hylander (1981) have shown how different mechanicalenvironments are reflected in changes in Haversian remodelling. All this work tendsto confirm the idea that bone is selectively and anisotropically deposited in order toresist the patterns of forces to which it is subject.The technique of neutron diffraction allows a very different approach because

the great penetrating power of the neutron beam permits very thick (up to 1 cm)sections of bone to be examined. It provides a quantitative assessment of the textureof the bone in terms of the orientation of the hydroxyapatite crystals. In previousstudies the authors have shown that this orientation is highly correlated with the

G. E. BACON, P. J. BACON AND R. K. GRIFFITHS

Fig. 1. D'Arcy Thompson's diagram of stress lines in the human foot, derived fromMcAlister (1884) after Meyer (1867).

directions in which trabeculae point and also correlates with predominant forcesacting on cortical bone (Bacon, Bacon & Griffiths; 1979a, b). We may regard theorientation as indicating the summation of forces as they are seen by the bone-building machinery ofthe body, whether it be the magnitude ofthe force, the durationof the force, or more probably some combination of the two, which determines theresponse in the bone. Pictures of texture will be easier to interpret for those boneswhich are surrounded by muscles where the direction of pull tends to remain con-stant, although the magnitude of the pull may vary with change of activity duringthe day. For example, in the scapula and the mandible, as the authors have shownelsewhere, the orientation of the apatite crystals is relatively easy to comprehendand to relate to the force pattern generated by the surrounding muscles. The foot ismore complicated because the individual bones move in relation to each other as theman or animal walks or runs or simply changes his stance.

MATERIALS AND METHODS

Thick vertical sections were examined, taken through the midline of the foot fora middle aged male. In all, measurements were made at 16 sites on the lower tibia,talus and calcaneus. The three bones were articulated and midline sagittal sectionswere marked upon them. Sections, 1 cm in thickness, were then cut with a band saw.Figure 2 is a plan of the talus and calcaneus, showing the location of the 1 cmsection. Minor variations in the angle of sectioning caused only very small changesin the orientations which were deduced for the apatite crystals and these were withinthe experimental error of the measurements.As justified elsewhere (Bacon et al. 1979b) samples were employed which had been

pre-heated for 20 minutes at 625 °C to remove collagen and other organic matter, inorder to avoid the troublesome incoherent neutron scattering from the large amountof hydrogen which this contains. It can be seen from Figure 3, which is a photographof an assembly of the three bone sections which were examined, that the texture andfabric of the trabeculae, like their internal arrangement, have not been affected byheating.Most of the measurements were made at the Institut Laue-Langevin in Grenoble,

using a neutron beam of wavelength 2-52 A with a circular cross section of diameter9 mm. A beam of this size yields good positional resolution, between closelyspaced sites on the bone. Although the points chosen for measurements were oftenquite close together, it was possible to associate with them significant changes in the

266

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Talus

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Fig. 2. Plan of calcaneus and talus, showing location of vertical section.

orientation structure. For the measurement of the diffraction pattern, the bone wasmounted in a beam of neutrons so that the sectioning plane (i.e. the plane of Fig. 3)was vertical. This plane was then positioned in azimuth so that the neutrons wereinclined at 11° to the normal to the plane. Under these conditions, a collectingcounter placed to receive the 0002 diffraction peak collected neutrons which hadbeen reflected by any 0002 planes which were both vertical and normal to the planeof Figure 3. The experiment consisted of measuring the change in the number ofneutrons as the bone was rotated about a horizontal axis normal to Figure 3. Eachcounting period lasted about 30 minutes and successive measurements were madeat angular intervals of 10°. An example of a series of measurements appears inFigure 4, which shows data at a site near the bottom edge of the calcaneus. TheCartesian plot at the left hand side of this figure shows how the neutron intensitydiffracted by the 0002 crystal planes in apatite varied with the rotation of the bonesample about the incident beam. This intensity was proportional to the number ofapatite crystals (more correctly, the volume of apatite) with the c-axis aligned in thecorresponding direction in space. On the right hand side of Figure 4 the Cartesianplot has been transformed into a polar diagram, showing how the 0002 planes werepreferentially directed in space. In this particular example, the overall orientation curvecan be resolved into two well defined components which are shown by the broken-line curves in the diagram. The directions in space to which these two curves pointwere yielded by the measurements and, as indicated, they coincided with the direc-tions of the lower foot and the joint with the talus, respectively. Further details ofthe practical procedure and the crystallographic analysis are given in an earlier paper(Bacon et al. 1979 a) which describes a similar series ofmeasurements for the scapula.

RESULTS

A polar diagram of the kind shown in Figure 4 was deduced for each of the 16 sitesand these are shown in Figure 5, placed with the appropriate inclination at each site.There were seven sites on the calcaneus, eight on the talus and one at the base of

267

G. E. BACON, P. J. BACON AND R. K. GRIFFITHS

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Fig. 4. Experimental data for site D of the calcaneus. The left hand diagram shows the variationof the 0002 intensity with change of inclination of the sample. At the right is a polar diagramwhich shows how the 0002 planes are preferentially directed in space; the resultant curve isresolved into two components, directed towards the lower foot and the joint with the talus respec-tively.

the tibia. Accordingly, this Figure summarises how, in sections through the midlineof the foot, the apatite crystals were preferentially directed at each site, under theinfluence it is believed, of the bone-building stresses which were relevant there. Thecircle in the bottom left hand corner of the diagram indicates, on the same scale, the9 mm diameter neutron beam and thus indicates the spatial resolution ofthe measure-ments. The inset diagram in Figure 5 shows a polar diagram measured halfway alongthe first metatarsal bone.

DISCUSSION

The results, as summarised in the composite drawing in Figure 5, show essentiallyhow the body weight is transmitted downwards to the heel, in the bottom rightcorner of the diagram, and leftwards, via the talus into the metatarsals.

In the calcaneus, the most striking feature is the extremely high orientation at siteC where the crystals are contained within the small angle which comprises the zone

of contact between calcaneus and talus. Moreover, this preferential orientation maybe regarded as accentuated by the need for the top edge of the calcaneus, from F to C,to function as a beam which can withstand the anticlockwise moment exerted by theAchilles tendon. It is noteworthy that there are no muscle attachments along thisedge, and, accordingly, no need for vertically oriented crystals to withstand theirpull. On the other hand, on leaving site C and moving clockwise around the heelfrom A to G to D, there is a region of continuous muscular and ligamentous attach-ment, namely first the plantar aponeurosis, followed by a second layer of musclesand then the long plantar ligament. While the first two of these lie parallel to eachother, and roughly horizontal, the third inclines a little above the horizontal as itruns up under the arch of the foot towards its distal attachment. Accordingly, thepolar diagrams at A, G and D have a well defined dual character, one preferred

269

G. E. BACON, P. J. BACON AND R. K. GRIFFITHS

Fig. 5. A section through the foot, indicating the sites at which measurements were made. Ateach site a polar diagram is drawn, showing the amount of apatite with its c-axis in any direction.Inset, but not in location, is a similar diagram showing the very high orientation at the centreof the first metatarsal bone. The circle at the bottom left hand corner indicates the size of theneutron beam.

direction being that of the muscles and ligaments just mentioned and the other one,which is the predominant feature, being the more nearly vertical direction towardsthe joint with the talus. The contrast is emphasised between the very sharply definedsingle orientation at C with what is observed at the group of sites A, G and D. Thusthe sophistication of the technique of measurement demonstrates the differentimpact on the bone of the powerful, localised pull of the Achilles tendon comparedwith the broad group of tensions arising from the plantar ligaments and muscles.Turning to the two sites E and F near the talocalcaneal joint, it is seen that at E theorientation is substantially in the direction of the toes but that there is a small,though well defined, group of crystals directed at the joint itself. At F the distributionis not so sharp and the direction is tempered by the need to withstand the verticalload coming from the tibia. Site B is clearly a junctional region where the boneexperiences forces from a number of directions, related both to the ankle and thefoot joints and to the attachment of the Achilles tendon, the plantar fascia and theplantar muscles. Accordingly the crystals at B show a broad polar diagram, though

270

Neutron diffraction of bones offootthere is still predominance along the length of the foot. Of all the sites whichhave been examined on the calcaneus in the present study, the diagram at Bapproaches most nearly to the circle which would be displayed by a randomlyoriented powder. An appropriate dotted circle on the diagram has been included.Quantitatively, it is found that in the direction of maximum orientation at B, thenumber of crystals is only 30 % greater than that which would be found in a powder.This is the smallest value which has been found among the seven sites. By contrast,at site C, the number of crystals lying in the preferred direction is greater than thatin a powder by a factor of 2-6.

In the talus, Figure 5 shows that the crystals are notably highly oriented at sitesW and Y. At the former they lie predominantly in an almost horizontal direction,transmitting the load from the tibia towards the toes and the ball of the foot. At Y,the 'stress' is in an approximately vertical direction, leading to the heel via the jointwith the calcaneus. At S, where the load arrives from the tibia, the crystal orientationis symmetrically arranged about the vertical but it is very broadly distributed, asbefits the fact that the load bearing forces coming down through the ankle joint mustvary in direction over a considerable angular range as the talus moves inside themortice of the ankle joint when the foot is in motion. This emphasises earlier com-ments made by the authors that the texture of the bones in the foot must cope withthe substantial changes of position and inclination which take place between neigh-bouring bones. Indeed the whole of the central region of the talus, in the neighbour-hood of sites M, Q and T, shows relatively little preferred orientation; such as existsis predominantly vertical. The pattern is most distinctive at T which clearly marksa junctional region in the bone where the forces coming from the calcaneus, thosecoming from the lower parts of the foot and those coming down from the ankle, allimpinge to create a region where the apatite crystals can provide strength in manyspecific directions. On moving to M and Q, there is a noticeably better definedvertical component of orientation on approaching the region of contact with thetibia.The single measurement at the centre of the first metatarsal bone shows a very

high preferential orientation along the length of the bone: the number of crystalslying along the length is greater than in a random powder by a factor of 3-5, thelargest value observed in the foot.These observations suggest that arguments about whether the trabecular patterns

of the foot are a dome or whether the foot is a series of arches or a series of beamsare perhaps oversimplifications. The trabecular patterns are clearly a pragmaticsolution to a number of varied and changing problems throughout the foot structure.The strong resultant force created between the plantar fascia and the Achilles tendoninevitably creates the appearance of a dome in the heel part of the calcaneus.Similarly the apatite at site E on the calcaneus and W on the talus show how theforces are transmitted from these two bones down the length of the foot, and thisagain tends to look like a dome. The weight-bearing forces coming down from theankle mortice impinge on this dome and require a complicated arrangement ofapatite to transmit them and this complexity is demonstrated by the patterns at X,M, T and perhaps Z. Site S, on the other hand, reminds us that the dome is notloaded simply from above like the stand of a tailor's dummy, but receives forces ina variety of directions as the ankle joint moves.

It is tempting to try to produce a revised version of D'Arcy Thompson's drawingin the light of the data obtained in this study. A tentative suggestion is presented in

271

G. E. BACON, P. J. BACON AND R. K. GRIFFITHS

Fig. 6. A tentative revised version of D'Arcy Thompson's diagram.

Figure 6 for the bones which have been examined. Much of the diagram is unchangedand the overall impression is similar, but there are two substantial differences. Abroad sweep of roughly horizontal stress lines has been added across the middleregion of the talus, following the plantar muscles from the neighbourhood of sitesZ, T; at the same time the beam feature has been added along the edge of the cal-caneus near C. It is difficult to take account of both the direction and magnitude ofstress when drawing continuous lines: we really need a pictorial representation suchas that provided by iron filings when used to display a magnetic field. An exampleof the difficulty is the region between sites B, D and G where the sparseness oftrabeculae, evident in Figure 3, is well known. D'Arcy Thompson indicates this byabruptly terminating his lines. Our own diagram concentrates on the general iso-tropy of stress here, but cannot display its small value. With hindsight we shouldhave done well to examine the region which is distal to site D and where there are nomuscle attachments. Less radical changes may be necessary to the directions of theThompson stress lines in some places: these probably reflect local forces betweenthe bones which D'Arcy Thompson (and Meyer before him) may have consideredless important than the overall pattern. Such local forces are probably more signifi-cant in determining the shape of the individual bones and might be more important ifpathological conditions alter the functional relationship between the bones.

SUMMARY

The preferential orientation of the apatite crystals in the lower tibia, talus andcalcaneus, as determined by neutron diffraction, serves as an indicator of the linesof stress in the foot. The main stress flows down from the tibia to the heel and theball of the foot and there is noteworthy orientation along the line of the plantaraponeurosis which acts as a tie. Orientation is particularly marked above the pointof attachment of the Achilles tendon, where the edge of the calcaneus functions asa beam. The centre of the talus serves as a junctional region for forces and is rela-tively unoriented.

272

Neutron diffraction of bones offoot 273We acknowledge the support of the Science and Engineering Research Council

in enabling us to use the nuclear reactor at the Institut Laue-Langevin, Grenoble,France, and the assistance of Dr P. Convert, there, with the experimental work. Wealso thank Mr R. Avery of the Department of Anatomy, University of Birmingham,for preparation of the samples.

REFERENCES

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BACON, G. E., BACON, P. J. & GRIFFITHS, R. K. (1979b). The orientation of apatite crystals in bone.Journal of Applied Crystallography 12, 99-103.

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HERT, J., PRIBYLOVA, E. & LISKOVA, M. (1972). Reaction of bone to mechanical stimuli. 3. Microstructureof compact bone of rabbit tibia after intermittent loading. Acta anatomica 85, 218-230.

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MCALISTER, SIR DONALD (1884). How a bone is built. English Illustrated Magazine, 640-649.MEYER, H. (1867). Die Architektur der Spongiosa. Archiv fur Anatomie und Physiologie 47, 615-628.MEYER, H. (1873). Die Statik und Mechanik des menschlichen Knochengerdistes. Leipzig.MONGINI, F., PRETI, G., CALDERDALE, P. M. & BARBERI, G. (1981). Experimental strain analysis on themandibular condyle under various conditions. Medical and Biological Engineering and Computing 19,521-523.

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