277
J. Anat. (1979), 128, 2, pp. 277-283 With 5 figures Printed in Great Britain
Neutron diffraction studies of lumbar vertebrae G. E. BACON*, P. J. BACONt AND R. K.
GRIFFITHSt
*Department of Physics, The University, Sheffield,
tEdward Grey Institute, Department of Zoology, The University, Oxford and $Department of Anatomy, The University, Birmingham
(Accepted 28 February 1978) INTRODUCTION
We have recently described (Bacon, Bacon & Griffiths, 1977) a method of using neutron diffraction to measure the integrated orientation of apatite crystals in bulk samples of bone. We now report the use of this method to gain information about the construction of lumbar vertebrae, in particular to compare the orientation of the apatite crystals in the second and fifth lumbar vertebrae. The body of the second lumbar vertebra was selected as a starting point for several reasons: it is in a region of the spine through which most of the body weight is transmitted, it is unfettered by attachment of ribs, and it is not part of a junction between one functional part of the spine and another. The role of the body of this vertebra is to resist compression in the long axis of the spine. Qualitative observation of spinal movements seems to suggest that any torques and shearing forces to which this body is subjected are symmetrical about the long axis of the spine. The fifth lumbar vertebra on the other hand is connected to the relatively stable sacral platform. The propulsive forces of the legs are transmitted through this connection to the spine, tending to produce shearing forces diagonally across the sagittal and coronal planes from alternate sides as each leg bears weight. In addition, rotatory and bending movements of the trunk will be resisted by the pelvis, thus tending to produce torque and further shear stresses in the junctional region. Although many of these forces may be translated into deformations of the L5/S1 disc, it seems reasonable to presume that they will also produce a more complicated stress environment in the body of L5. We have therefore examined this vertebra, which is reasonably similar in its gross anatomy to the second lumbar, in order to compare the extent to which their different functional roles are reflected in their internal structure. Our attention was drawn to this problem by the papers of Oxnard (1973), who examined the varying reflection of light from the cut surfaces of different vertebrae, and of Spiers & Beddoe (1977) and Beddoe, Darley & Spiers (1976), who determined the dimensions of trabecular cavities from normal and radial scans of radiographs of thin sections. These papers make clear the existence of anisotropy in vertebrae. The last mentioned paper, for example, substantiates the hypothesis that the trabecular structure of the vertebral body is symmetrical about its vertical axis. The measurements which we describe provide a direct assessment of the anisotropy which exists in the vertical plane.
278
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS
Fig. 1. Sagittal section of second lumbar vertebra, with evident differences of trabecular structure at top, central and bottom levels: note that heat treatment appears to have had no effect upon the gross structure.
Horizontal
Fig. 2. Choice of areas for viewing in the neutron beam. The overall assessment was made with the circular aperture of diameter 20mm; top, centre and bottom sections used a rectangular slit 20 x 6 mm. 0 indicates the tilt of the horizontal level in the body from the horizontal plane of the diffractometer. EXPERIMENTAL RESULTS
Our measurements were made using the neutron diffractometer DIB at the Institut Laue Langevin, Grenoble, France, with a neutron wavelength of 024 nm. Sagittal and transverse sections of thickness 7 mm were prepared from the second and fifth human vertebrae and heated to about 550 °C to destroy the collagen which would otherwise confuse the neutron diffraction pattern because of the large incoherent scattering from hydrogen. Visual inspection of these sections cut through the vertebrae makes it very evident that the construction and texture is not uniform over the whole of the section. In Figure 1 from the second lumbar vertebra, for example, there is a significant difference in the appearance of upper, central and lower levels. Accordingly, we made separate observations at each of these levels,
Neutron diffraction of lumbar vertebrae
279
124
104
3140
84 0002
S1Q10 x
o I ~64
2022
1
~~~~~~~~~~~~~~213~2
c
0
o11~~~~~~~~~~~~~~~~0 ~ ~ ~ 21-3
61
11
~~~~~~16
21
26133314
24
21 41 36 26 31 Theta (deg) Fig. 3. Diffraction pattern of the central section of the second lumbar vertebra, oriented so that 0 = 900, photographed from the computer-plotted records. The crystallographic indices are shown for the most intense and best-resolved reflections. 1
6
11
16
using an observation slit measuring 20 x 6 mm; and we also made an overall assessment with a circular aperture of diameter 20 mm. These apertures are shown in relation to the dimensions of the vertebra in Figure 2. A typical diffraction pattern secured in one hour is shown in Figure 3. This particular example is for the central section (sagittal) of the second lumbar vertebra, L2S, when the section was aligned so that the vertical direction of the body lay in the horizontal plane of the diffractometer, i.e. the sample was placed so that P, shown in Figure 2, is equal to 90°. Under these circumstances the intensity of the 0002 reflection, which is the most intense reflection in the pattern, measures the amount of apatite material for which the c-axes lie along the vertical direction of the body. If we then twist the sample about the neution beam, thus reducing the value of 0 in Figure 2 below 900, we observe that the 0002 reflection falls in intensity and, from a succession of measurements at different angles, we can plot a spatial distribution function for the c-axes. The measurements are summarized in Figure 4 for sagittal sections of the second and fifth lumbar vertebrae and a transverse section of the second vertebra. In this Figure we have presented for the sagittal sections the mean of four separate measurements, namely the top, central and lower sections, and the 'whole', as specified in Figure 2. It will be seen that the preferential orientation of the c-axes in the vertical direction of the body, as indicated by the rising curve for 0002 as 0 approaches 900, is substantially larger for L2 than for L5. In contrast, and as might be expected, a transverse section of vertebra L2 shows no variation with angle 0, thus indicating
280
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS 025 X~~~~~-
-
-
-
-
-.-
-
-
-
_
-
_
-
_
_
~
~
L2T-
Powder
(3140)
.*
-
-
_--
L5S
0-15
(0002) 0-10
/ _
_
Powder
_
_
_0_O
L5S
0-O
L2T
0-05
30
60 90 Inclination, (deg) Fig. 4. Variation of the integrated intensity of the 0002 and 3140reflectionswiththeinclination 0 of the sample. The ordinate is the ratio of the intensity of the specified reflection to the sum for the eleven peaks which were indexed in Figure 3. Curves are shown for sagittal sections of vertebrae L2 and L5 and for a transverse section of vertebra L2. In each case the recorded values are the means of four measurements: total, top, centre and bottom as specified in Figure 2. The levels marked as 'powder' are the experimental values measured for an unoriented sample of crumbled trabeculae.
that, so far as the mineral architecture of the trabeculae is concerned, the vertical axis of the body is indeed an effective axis of symmetry. Quantitatively it is important to note that the ordinate for the curves which we have just discussed is the ratio of the intensity of the 0002 reflection to the sum of the eleven most intense, and best resolved, reflections in the diffraction pattern, thus providing a simple method of normalising different patterns. These eleven reflections are the ones for which the crystallographic indices are marked in Figure 3. We draw attention to the level marked 'Powder' in Figure 4 at a value of ordinate equal to 0'09. This is the measured experimental value of the 0002 intensity ratio for a sample of powdered trabeculae, in which of course there will be no preferential orientation
281
Neutron diffraction of lumbar vertebrae
a) +.
co 0 c
0
1.5
of
a)
a)
0
60 30 Inclination, 6 (deg)
X1o~'
of
90
Fig. 5. The variation of orientation with position in the spine, indicated by separate curves for the top, centre and bottom sections of the 2nd and 5th lumbar vertebrae. The ordinates, which are proportional to the 0002 neutron intensity, represent the amount of apatite for which the c-axis is horizontal during the measurement on the diffractometer. In contrast to the ordinates of Figure 4, they have been normalized to a value of unity for 0 = 00. The ordinate at 0 = 90° indicates the amount of apatite preferentially orientated in the vertical direction of the human spine.
of the c-axis and which accordingly gives no variation of intensity as the sample is rotated. As would be expected, the intensities of the L2S and L5S reflections for small values of 0 are lower than the powder level, but exceed the latter when 0 is large. Corresponding curves of intensity variation can indeed be constructed for each of the crystallographic reflections, and the upper part of Figure 4 shows curves for the 3140 prismatic reflection. This is an intense reflection from planes which are parallel to the c-axes of the apatite crystals, whereas the 0002 planes are perpendicular to the c-axes. It will be seen that the variations of intensity with angle 0 are reversed for 3140, compared with 0002. Similarly, the powder value is now as low or lower than the measured values for L2 and L5 at small values of 0, but exceeds the measured values when 'A is large. Furthermore, for 3140, the almost constant level for the transverse section of L2 is markedly higher than the powder level, whereas for the 0002 reflection the reverse is the case. This simply indicates the fact that an excess of 0002 (basal) planes normal to any particular direction in the body implies a shortage of 3140 (prismatic) planes. Similar conclusions are reached from measurements of the weaker prismatic reflections (lOTO), (1120) and (3030), but the statistical errors are naturally larger. We now turn to an examination of the variation of orientation in different portions of a vertebra, utilising the measurements made for the top, cential and bottom portions of the second and fifth vertebrae which we have already mentioned. Our findings are represented by the series of curves drawn in Figure 5. These curves again
show the variation of 0002 intensity with the angular inclination of the sample, but
282
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS
we have normalised the ordinates to a value of unity when 0 = 00 in order to simplify comparison of the shapes of the curves. The results show a steady increase of anisotropy with progression up the lumbar spine, as indicated by the increasing 'vertical' preference of the c-axes, which is represented by the rising sequence of ordinates at 0 = 90° in the Figure. The experimental accuracy seems adequate to establish this general conclusion. Certainly the detailed variation of the anisotropic structure could be specified more precisely by observing at a greater number of angular settings, counting for longer times and, of course, studying a substantial number of different samples. DISCUSSION
It has long been assumed that structural attributes of spongy bone are related to function (Wolff, 1899) and it has further been suggested that the mineral crystalline component is laid down in accordance with functional criteria (Bassett, 1965; Justus & Luft, 1970). We therefore anticipated that the structure of the vertebral body would be symmetrical about the spinal axis when viewed in the transverse plane, and the curves for L2T in Figure 4 show this to be the case. Our earliest results from compact bone (Bacon, Bacon & Griffiths, 1977) suggest that there is a preferential orientation of hydroxyapatite crystals, so that the c-axes of the crystals tend to lie in the direction of maximum imposed stress. This seems to indicate that bone makes use of anisotropic properties of calcium hydroxyapatite to resist stress most efficiently, and analysis of spongy bone in the vertebral spinous processes (Griffiths, Bacon & Bacon, 1978) supports the same conclusion. Likewise, for our present results, Figure 4 reveals marked preferential orientation of apatite in the body of L2 in the direction of the long axis of the spine. By comparison, the curves for L5 show much less relative orientation in the direction of the spinal axis, suggesting that the crystals are indeed organised to resist the much more complicated stresses that bear on this vertebral body. Study of the crystalline organization of bone thus seems to be an effective method of 'bio-assaying' stress in bone, and it should be useful in making comparisons between different bones. In the case of the vertebral bodies the homogeneous distribution about the long axis that we find suggests that a simple measure of cross sectional area could be combined with our measure of the neutron intensity diffracted from longitudinally oriented crystals to give a measure of the relative compressive load resisted by each vertebra. This could be useful not only in understanding the function of the human spine but also in studies of the comparative morphology of different locomotor groups in other animals. It may be that the functional attributes of the mineral elements of bone are sufficiently constant to enable absolute measurements of neutron intensity diffracted from particular crystal planes to be compared with those from standard of powders of mineral apatite to predict specific mechanical properties. Such absolute measurements of intensity are easily made with neutrons. The measurements taken from different zones of the two vertebral bodies vary sufficiently to suggest that the stress on the bone changes as we move through the vertebral body along the spinal axis. The differences between the zones may tell us something about the nature of the forces acting at the junction between vertebral body and intervertebral disc, and may in part help to estimate the differing loads to which successive discs are subjected. We intend in the future to measure a sequential
Neutron diffraction of lumbar vertebrae
283
set of vertebral bodies, and the results may be helpful to workers who are using mathematical methods to study stress, or to model the behaviour of the spine. We appreciate that these interpretations must remain speculative until we have made a more rigorous assessment of the effects of individual variations, and of the influence of age and other factors. Nevertheless our results do suggest the existence of a sophisticated and quantifiable control system which organizes the mineral structure of bone to meet the functional demands. SUMMARY
Neutron diffraction measurements of the orientation of the apatite crystals show a significant preference of their c-axes for the vertical direction. This preference increases from bottom to top of each vertebral body and is substantially greater for the second than for the fifth lumbar vertebrae. This is in line with the predominantly vertical forces which the former withstands. We acknowledge the support of the Science Research Council in providing access to the services of the Institut Laue Langevin and the assistance of Monsieur J. L. Buevoz, at that Institute, with the experimental measurements and the design and construction of the rotating sample-holder. REFERENCES BACON, G. E., BACON, P. J. & GiuFFiTHs, R. K. (1977). The study of bones by neutron diffraction. Journal of Applied Crystallography 10, 124-126. BASSETT, C. A. (1965). Electrical effects in bone. Scientific American 213, 18-25. BEDDOE, A. H., DARLEY, P. J. & SPIERs, F. W. (1976). Measurements of trabecular bone structure in man. Physics in Medicine and Biology 21, 589-560. GRIFFITHS, R. K., BACON, G. E. & BACON, P. J. (1978). The mechanical role of the vertebral processes investigated by neutron diffraction. Proceedings of a Conference on Orthopaedic Engineering, September 1977, Oxford. Biological Engineering Society. JusTUs, R. & LuFr, J. H. (1970). A mechanochemical hypothesis for bone remodelling induced by mechanical stress. Calcified Tissue Research 5, 222-235. OXNARD, G. E. (1973). Form and Pattern in Human Evolution. University of Chicago Press. SPIERS, F. W. & BEDDOE, A. H. (1977). Radial scanning of trabecular bone. Physics in Medicine and Biology 22, 670-680. WOLFF, J. (1899). Die Lehre von der funktionellen Knochengestalt. Virchows Archiv far pathologische Anatomie und Physiologie 155, 256.
J. Anat. (1979), 128, 2, pp. 277-283 With 5 figures Printed in Great Britain
Neutron diffraction studies of lumbar vertebrae G. E. BACON*, P. J. BACONt AND R. K.
GRIFFITHSt
*Department of Physics, The University, Sheffield,
tEdward Grey Institute, Department of Zoology, The University, Oxford and $Department of Anatomy, The University, Birmingham
(Accepted 28 February 1978) INTRODUCTION
We have recently described (Bacon, Bacon & Griffiths, 1977) a method of using neutron diffraction to measure the integrated orientation of apatite crystals in bulk samples of bone. We now report the use of this method to gain information about the construction of lumbar vertebrae, in particular to compare the orientation of the apatite crystals in the second and fifth lumbar vertebrae. The body of the second lumbar vertebra was selected as a starting point for several reasons: it is in a region of the spine through which most of the body weight is transmitted, it is unfettered by attachment of ribs, and it is not part of a junction between one functional part of the spine and another. The role of the body of this vertebra is to resist compression in the long axis of the spine. Qualitative observation of spinal movements seems to suggest that any torques and shearing forces to which this body is subjected are symmetrical about the long axis of the spine. The fifth lumbar vertebra on the other hand is connected to the relatively stable sacral platform. The propulsive forces of the legs are transmitted through this connection to the spine, tending to produce shearing forces diagonally across the sagittal and coronal planes from alternate sides as each leg bears weight. In addition, rotatory and bending movements of the trunk will be resisted by the pelvis, thus tending to produce torque and further shear stresses in the junctional region. Although many of these forces may be translated into deformations of the L5/S1 disc, it seems reasonable to presume that they will also produce a more complicated stress environment in the body of L5. We have therefore examined this vertebra, which is reasonably similar in its gross anatomy to the second lumbar, in order to compare the extent to which their different functional roles are reflected in their internal structure. Our attention was drawn to this problem by the papers of Oxnard (1973), who examined the varying reflection of light from the cut surfaces of different vertebrae, and of Spiers & Beddoe (1977) and Beddoe, Darley & Spiers (1976), who determined the dimensions of trabecular cavities from normal and radial scans of radiographs of thin sections. These papers make clear the existence of anisotropy in vertebrae. The last mentioned paper, for example, substantiates the hypothesis that the trabecular structure of the vertebral body is symmetrical about its vertical axis. The measurements which we describe provide a direct assessment of the anisotropy which exists in the vertical plane.
278
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS
Fig. 1. Sagittal section of second lumbar vertebra, with evident differences of trabecular structure at top, central and bottom levels: note that heat treatment appears to have had no effect upon the gross structure.
Horizontal
Fig. 2. Choice of areas for viewing in the neutron beam. The overall assessment was made with the circular aperture of diameter 20mm; top, centre and bottom sections used a rectangular slit 20 x 6 mm. 0 indicates the tilt of the horizontal level in the body from the horizontal plane of the diffractometer. EXPERIMENTAL RESULTS
Our measurements were made using the neutron diffractometer DIB at the Institut Laue Langevin, Grenoble, France, with a neutron wavelength of 024 nm. Sagittal and transverse sections of thickness 7 mm were prepared from the second and fifth human vertebrae and heated to about 550 °C to destroy the collagen which would otherwise confuse the neutron diffraction pattern because of the large incoherent scattering from hydrogen. Visual inspection of these sections cut through the vertebrae makes it very evident that the construction and texture is not uniform over the whole of the section. In Figure 1 from the second lumbar vertebra, for example, there is a significant difference in the appearance of upper, central and lower levels. Accordingly, we made separate observations at each of these levels,
Neutron diffraction of lumbar vertebrae
279
124
104
3140
84 0002
S1Q10 x
o I ~64
2022
1
~~~~~~~~~~~~~~213~2
c
0
o11~~~~~~~~~~~~~~~~0 ~ ~ ~ 21-3
61
11
~~~~~~16
21
26133314
24
21 41 36 26 31 Theta (deg) Fig. 3. Diffraction pattern of the central section of the second lumbar vertebra, oriented so that 0 = 900, photographed from the computer-plotted records. The crystallographic indices are shown for the most intense and best-resolved reflections. 1
6
11
16
using an observation slit measuring 20 x 6 mm; and we also made an overall assessment with a circular aperture of diameter 20 mm. These apertures are shown in relation to the dimensions of the vertebra in Figure 2. A typical diffraction pattern secured in one hour is shown in Figure 3. This particular example is for the central section (sagittal) of the second lumbar vertebra, L2S, when the section was aligned so that the vertical direction of the body lay in the horizontal plane of the diffractometer, i.e. the sample was placed so that P, shown in Figure 2, is equal to 90°. Under these circumstances the intensity of the 0002 reflection, which is the most intense reflection in the pattern, measures the amount of apatite material for which the c-axes lie along the vertical direction of the body. If we then twist the sample about the neution beam, thus reducing the value of 0 in Figure 2 below 900, we observe that the 0002 reflection falls in intensity and, from a succession of measurements at different angles, we can plot a spatial distribution function for the c-axes. The measurements are summarized in Figure 4 for sagittal sections of the second and fifth lumbar vertebrae and a transverse section of the second vertebra. In this Figure we have presented for the sagittal sections the mean of four separate measurements, namely the top, central and lower sections, and the 'whole', as specified in Figure 2. It will be seen that the preferential orientation of the c-axes in the vertical direction of the body, as indicated by the rising curve for 0002 as 0 approaches 900, is substantially larger for L2 than for L5. In contrast, and as might be expected, a transverse section of vertebra L2 shows no variation with angle 0, thus indicating
280
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS 025 X~~~~~-
-
-
-
-
-.-
-
-
-
_
-
_
-
_
_
~
~
L2T-
Powder
(3140)
.*
-
-
_--
L5S
0-15
(0002) 0-10
/ _
_
Powder
_
_
_0_O
L5S
0-O
L2T
0-05
30
60 90 Inclination, (deg) Fig. 4. Variation of the integrated intensity of the 0002 and 3140reflectionswiththeinclination 0 of the sample. The ordinate is the ratio of the intensity of the specified reflection to the sum for the eleven peaks which were indexed in Figure 3. Curves are shown for sagittal sections of vertebrae L2 and L5 and for a transverse section of vertebra L2. In each case the recorded values are the means of four measurements: total, top, centre and bottom as specified in Figure 2. The levels marked as 'powder' are the experimental values measured for an unoriented sample of crumbled trabeculae.
that, so far as the mineral architecture of the trabeculae is concerned, the vertical axis of the body is indeed an effective axis of symmetry. Quantitatively it is important to note that the ordinate for the curves which we have just discussed is the ratio of the intensity of the 0002 reflection to the sum of the eleven most intense, and best resolved, reflections in the diffraction pattern, thus providing a simple method of normalising different patterns. These eleven reflections are the ones for which the crystallographic indices are marked in Figure 3. We draw attention to the level marked 'Powder' in Figure 4 at a value of ordinate equal to 0'09. This is the measured experimental value of the 0002 intensity ratio for a sample of powdered trabeculae, in which of course there will be no preferential orientation
281
Neutron diffraction of lumbar vertebrae
a) +.
co 0 c
0
1.5
of
a)
a)
0
60 30 Inclination, 6 (deg)
X1o~'
of
90
Fig. 5. The variation of orientation with position in the spine, indicated by separate curves for the top, centre and bottom sections of the 2nd and 5th lumbar vertebrae. The ordinates, which are proportional to the 0002 neutron intensity, represent the amount of apatite for which the c-axis is horizontal during the measurement on the diffractometer. In contrast to the ordinates of Figure 4, they have been normalized to a value of unity for 0 = 00. The ordinate at 0 = 90° indicates the amount of apatite preferentially orientated in the vertical direction of the human spine.
of the c-axis and which accordingly gives no variation of intensity as the sample is rotated. As would be expected, the intensities of the L2S and L5S reflections for small values of 0 are lower than the powder level, but exceed the latter when 0 is large. Corresponding curves of intensity variation can indeed be constructed for each of the crystallographic reflections, and the upper part of Figure 4 shows curves for the 3140 prismatic reflection. This is an intense reflection from planes which are parallel to the c-axes of the apatite crystals, whereas the 0002 planes are perpendicular to the c-axes. It will be seen that the variations of intensity with angle 0 are reversed for 3140, compared with 0002. Similarly, the powder value is now as low or lower than the measured values for L2 and L5 at small values of 0, but exceeds the measured values when 'A is large. Furthermore, for 3140, the almost constant level for the transverse section of L2 is markedly higher than the powder level, whereas for the 0002 reflection the reverse is the case. This simply indicates the fact that an excess of 0002 (basal) planes normal to any particular direction in the body implies a shortage of 3140 (prismatic) planes. Similar conclusions are reached from measurements of the weaker prismatic reflections (lOTO), (1120) and (3030), but the statistical errors are naturally larger. We now turn to an examination of the variation of orientation in different portions of a vertebra, utilising the measurements made for the top, cential and bottom portions of the second and fifth vertebrae which we have already mentioned. Our findings are represented by the series of curves drawn in Figure 5. These curves again
show the variation of 0002 intensity with the angular inclination of the sample, but
282
G. E. BACON, P. J. BACON AND R. K. GRIFFITHS
we have normalised the ordinates to a value of unity when 0 = 00 in order to simplify comparison of the shapes of the curves. The results show a steady increase of anisotropy with progression up the lumbar spine, as indicated by the increasing 'vertical' preference of the c-axes, which is represented by the rising sequence of ordinates at 0 = 90° in the Figure. The experimental accuracy seems adequate to establish this general conclusion. Certainly the detailed variation of the anisotropic structure could be specified more precisely by observing at a greater number of angular settings, counting for longer times and, of course, studying a substantial number of different samples. DISCUSSION
It has long been assumed that structural attributes of spongy bone are related to function (Wolff, 1899) and it has further been suggested that the mineral crystalline component is laid down in accordance with functional criteria (Bassett, 1965; Justus & Luft, 1970). We therefore anticipated that the structure of the vertebral body would be symmetrical about the spinal axis when viewed in the transverse plane, and the curves for L2T in Figure 4 show this to be the case. Our earliest results from compact bone (Bacon, Bacon & Griffiths, 1977) suggest that there is a preferential orientation of hydroxyapatite crystals, so that the c-axes of the crystals tend to lie in the direction of maximum imposed stress. This seems to indicate that bone makes use of anisotropic properties of calcium hydroxyapatite to resist stress most efficiently, and analysis of spongy bone in the vertebral spinous processes (Griffiths, Bacon & Bacon, 1978) supports the same conclusion. Likewise, for our present results, Figure 4 reveals marked preferential orientation of apatite in the body of L2 in the direction of the long axis of the spine. By comparison, the curves for L5 show much less relative orientation in the direction of the spinal axis, suggesting that the crystals are indeed organised to resist the much more complicated stresses that bear on this vertebral body. Study of the crystalline organization of bone thus seems to be an effective method of 'bio-assaying' stress in bone, and it should be useful in making comparisons between different bones. In the case of the vertebral bodies the homogeneous distribution about the long axis that we find suggests that a simple measure of cross sectional area could be combined with our measure of the neutron intensity diffracted from longitudinally oriented crystals to give a measure of the relative compressive load resisted by each vertebra. This could be useful not only in understanding the function of the human spine but also in studies of the comparative morphology of different locomotor groups in other animals. It may be that the functional attributes of the mineral elements of bone are sufficiently constant to enable absolute measurements of neutron intensity diffracted from particular crystal planes to be compared with those from standard of powders of mineral apatite to predict specific mechanical properties. Such absolute measurements of intensity are easily made with neutrons. The measurements taken from different zones of the two vertebral bodies vary sufficiently to suggest that the stress on the bone changes as we move through the vertebral body along the spinal axis. The differences between the zones may tell us something about the nature of the forces acting at the junction between vertebral body and intervertebral disc, and may in part help to estimate the differing loads to which successive discs are subjected. We intend in the future to measure a sequential
Neutron diffraction of lumbar vertebrae
283
set of vertebral bodies, and the results may be helpful to workers who are using mathematical methods to study stress, or to model the behaviour of the spine. We appreciate that these interpretations must remain speculative until we have made a more rigorous assessment of the effects of individual variations, and of the influence of age and other factors. Nevertheless our results do suggest the existence of a sophisticated and quantifiable control system which organizes the mineral structure of bone to meet the functional demands. SUMMARY
Neutron diffraction measurements of the orientation of the apatite crystals show a significant preference of their c-axes for the vertical direction. This preference increases from bottom to top of each vertebral body and is substantially greater for the second than for the fifth lumbar vertebrae. This is in line with the predominantly vertical forces which the former withstands. We acknowledge the support of the Science Research Council in providing access to the services of the Institut Laue Langevin and the assistance of Monsieur J. L. Buevoz, at that Institute, with the experimental measurements and the design and construction of the rotating sample-holder. REFERENCES BACON, G. E., BACON, P. J. & GiuFFiTHs, R. K. (1977). The study of bones by neutron diffraction. Journal of Applied Crystallography 10, 124-126. BASSETT, C. A. (1965). Electrical effects in bone. Scientific American 213, 18-25. BEDDOE, A. H., DARLEY, P. J. & SPIERs, F. W. (1976). Measurements of trabecular bone structure in man. Physics in Medicine and Biology 21, 589-560. GRIFFITHS, R. K., BACON, G. E. & BACON, P. J. (1978). The mechanical role of the vertebral processes investigated by neutron diffraction. Proceedings of a Conference on Orthopaedic Engineering, September 1977, Oxford. Biological Engineering Society. JusTUs, R. & LuFr, J. H. (1970). A mechanochemical hypothesis for bone remodelling induced by mechanical stress. Calcified Tissue Research 5, 222-235. OXNARD, G. E. (1973). Form and Pattern in Human Evolution. University of Chicago Press. SPIERS, F. W. & BEDDOE, A. H. (1977). Radial scanning of trabecular bone. Physics in Medicine and Biology 22, 670-680. WOLFF, J. (1899). Die Lehre von der funktionellen Knochengestalt. Virchows Archiv far pathologische Anatomie und Physiologie 155, 256.
