The purpose of this study was to compare small-angle neutron and X-ray scattering from cortical bone for a systematic analysis of the possible complementarity of the two techniques. Comparing SANS and SAXS patterns from the same specimen allows for a detailed interpretation of the scattering and the specimen nanostructure. We have found that the nanostructure of cortical bone gives rise to the same small-angle scattering pattern when using neutrons as when using X-rays. Both in terms of q- and angular dependence, the data showed striking similarities for all specimens (Fig. 2 and Supplementary Figs. 13). This strongly points to a two-component system at the nanoscale, i.e. a matrix that consists mainly of type-I collagen as organic component, and hydroxyapatite (HAp) as inorganic component.

The main difference in scattering intensity between the SANS and SAXS data was seen at high q, where the SAXS intensity drops two orders of magnitude following the plateau at ~ 0.08 Å−1 (Fig. 2a–b and Supplementary Figs. 13a,b), after which internal structures of the mineral crystals give rise to diffraction peaks4. It is worth noting that the SAXS data was offset, with the specimen and measurement specific proportionality constant calculated based on the scattering contrast, to overlap with the SANS data at low q. A Guinier region is seen in both SANS and SAXS data at ~ 0.07 Å−1 (Fig. 2 and Supplementary Figs. 13). This region yields information about the radius of gyration, corresponding to the average size of the mineral platelets in bone. Curve-fitting has previously been employed to obtain the thickness of the mineral platelets4,14,16. This was not done in the current study, where it was instead chosen to focus on the full overlapping q-range comparison of SANS and SAXS data. For neutrons, there is a contribution of incoherent scattering to the data, mainly due to hydrogen, which results in a constant offset. Subtracting this offset from the SANS data is expected to increase the similarities to the corresponding SAXS data. However, there is no simple way to assess this constant offset since no measurements of isotopic composition were done. In addition, the data is shown in log–log scale, meaning the subtraction needs to be very precise. Therefore, no correction for incoherent scattering was done for the SANS data. At high q, probing shorter length scales, the scattering results from the internal structure of the mineral platelets and possibly also the collagen fibres. Here, a difference between SANS and SAXS intensities is expected as it rather reflects the relative differences in atomic cross sections, which are different for SANS and SAXS. This difference at high q is further substantiated by the findings of previous neutron and X-ray diffraction studies of mineralised tissues, where the techniques have been used specifically to focus on the different constituents (mineral and collagen) at high q18,19,20,21,22,23,24,25. The ovine specimens (both longitudinal and radial) had slightly higher values for the intensity difference evaluated over the full q-range (Eq. 2) than the other specimens (Table 2). The q-dependent difference (Eq. 1) showed that the intensities started deviating at lower q for the radial ovine specimen in comparison to the others (Fig. 2c), which explained the higher overall difference. For the longitudinal ovine specimen, clear collagen peaks in the SAXS data reduced the similarity with the SANS data. Different from the other specimens, the radial bovine and porcine specimens, both displayed larger variations (std) in intensity differences at higher q (Fig. 2c). Comparing the scattering curves for each individual measurement position showed that, for all but the radial bovine and radial porcine specimens, the scattering curves from both SANS and SAXS were overlapping almost perfectly. For the radial bovine specimen, the three measurement positions had slightly varying SAXS scattering amplitudes. For the porcine specimen, the SAXS intensity amplitude was slightly lower for one measurement point than the others. These discrepancies resulted in more varying intensity differences between the SANS and SAXS data for these two specimens than for the others. However, for all specimens and measurements the data from each of the three measurement positions matched closely. The normalised root-mean-square-errors (NRMSEs) were 2.8 ± 2.7% and 1.5 ± 1.7% (mean ± std) for SAXS and SANS measurements, respectively. This indicates a homogeneous nanostructure throughout each specimen.

The strong similarities between the SANS and SAXS patterns indicate that the bone structure at the nanoscale can be seen as a two-component composite, the only effective contrast being between the two main constituents, namely the collagen and the HAp crystals. The collagen matrix makes up the continuous phase, with some additional internal structures, in which the mineral platelets are dispersed. The mechanical properties are greatly affected by the presence of water on all hierarchical length scales12, but our findings indicate that the contribution from water on the scattering is minor. The water that would yield a scattering signal in the probed q-range is that which is loosely bound to the collagen fibrils and mineral platelets. The free water in pores and canals are at a different length scale than what is probed in this study5, and the tightly bound water between collagen molecules and inside the mineral crystals is included as part of the collagen and mineral phase, respectively. Bound water makes up 4–4.5 wt% of cortical bone12, and hence the fraction of loosely bound water is even less. The specimens were stored in 70% ethanol and some of the loosely bound water could hence have been exchanged. However, the degree of exchange should be minor since the specimens were not dried prior to submersion in the solvent. The lack of significant contribution from water/solvent on the scattering data indicates that the amount of loosely bound water in cortical bone is minor when it comes to nano-structural characterisation.

Since, for a binary system, the scattering intensity (Ileft( q right)) can be interpreted as

$$ Ileft( q right)sim Delta rho^{2} S_{eff} left( q right)langle{Pleft( q right)}rangle $$



$$ Delta rho = left( {rho_{m} – rho_{c} } right) $$


is the contrast between the mineral and collagen, (rho_{m}) and (rho_{c}), being the mineral and collagen scattering length densities, respectively. (langle{Pleft( q right)}rangle) is the average form factor of the mineral platelets (averaged over e.g. a polydisperse size/thickness distribution), and (S_{eff} left( q right)) is an effective structure factor, reporting on the distribution of the mineral platelets over the collagen matrix. At low-q, the scattering pattern shows a characteristic strong upturn at lower q-values. This upturn is associated with (S_{eff} left( q right)) and implies that the mineral platelets are not distributed homogeneously, but heterogeneously across the collagen matrix, with domains of higher and lower mineral concentrations. As the mineral platelets are oriented parallel to the collagen fibres, they give rise to an anisotropic scattering pattern with dominating scattering perpendicular to the collagen fibres. Thus, ( S_{eff} left( q right)) mainly reports on the concentration fluctuation in the plane perpendicular to the collagen fibres. We have previously4 described this in terms of a fractal structure factor, using an (S_{eff} left( q right)) of the form (S_{eff} = left( {1 + Aq^{ – D} } right)), where D is a mass fractal dimension and A is a constant related to the size and density of the mineral clusters45. In our previous study using SAXS we obtained D (approx) 2.3 ± 0.2 (mean ± std) when comparing different species4. Here, (D) is obtained from the SANS data, which extends to lower q-values, as D ( approx ) 3.3 ± 0.1. The maximum dimension of a mass fractal is 3. Hence, while (S_{eff} left( q right)) clearly demonstrate a heterogeneous distribution of mineral platelets, it is not clear how to interpret (S_{eff} left( q right)) quantitatively.

As intensity scales with the square of the contrast, which is different for neutrons and X-rays, one can expect a factor between SANS and SAXS of 65 for a pure collagen-HAp composite, based on the scattering length densities shown in Table 1. Assuming a hydrated (10 vol.% water) collagen matrix, i.e. taking into account the loosely bound water discussed previously, reduces the proportionality factor to 50. For all specimens and measurement positions, the absolute SANS intensity was lower than the corresponding absolute SAXS intensity, and hence a proportionality constant larger than one was obtained as the SANS data was adjusted to overlap the SAXS data at low-q in the overlapping q-range. The proportionality constant was similar for all measurements except for the radial ovine specimen. The mean ± std was 28.5 ± 5.2 when excluding the radial ovine specimen, for which the proportionality constant was 72.4 ± 1.5 (mean ± std). The proportionality constant for the radial ovine specimen is a clear outlier, whose origin requires further analysis. The specimen was harvested from the same anatomical site as the longitudinal ovine specimen, and hence no significant compositional differences were expected. Looking at the specimen specific data, it was seen that the radial ovine specimen had overall higher SAXS intensities compared to all other specimens. This explains the higher proportionality constant for this specimen as compared to the others. However, why the proportionality constants of the data differ from the theoretical one is not clear.

A first order collagen peak was seen in the integrated SANS and SAXS data for all longitudinal specimens, as well as in the SAXS data for the radial bovine and porcine specimens (Supplementary Figs. 13). The peak location corresponded to a collagen d-spacing of ~ 640 Å, which is in agreement with previous studies on mineralised bone18. The peak was more defined in the SAXS data than in the SANS data, most likely due to the higher instrument resolution for SAXS. The collagen signal from the longitudinal ovine specimen was stronger than for the other specimens in both SANS and SAXS measurements. The clear first order collagen peak seen in all measurements on the longitudinal ovine specimen was initially thought to be due to a lower mineral content compared to the other specimens. However, the tissue mineral density measured from the micro-CT images indicated the same amount of mineral in all specimens. Nevertheless, it is still possible that the collagen/mineral ratio was larger in the ovine specimens than in the others, possibly due to them being taken from a different anatomical location (tibia as opposed to femur). The collagen fibril structure is periodic in the axial direction and a more regular periodicity of the collagen fibrils can be assumed for the ovine specimens due to the higher intensity of the collagen peaks with respect to the bovine and porcine specimens. In fact, also higher order peaks were distinguishable in the SAXS data in the fibre direction (Supplementary Fig. 4). The partially integrated SAXS signal from the longitudinal ovine specimen again showed clearer collagen peaks than any of the other specimens, resulting in a larger overall difference between integrated SAXS and SANS intensities (Table 2). Due to the anisotropic scattering pattern, the data is smeared differently parallel and perpendicular to the fibre direction. However, this difference seems to be negligible for these specimens as the SANS and SAXS curves are very similar for both integration directions (Supplementary Figs. 45).

Also the azimuthal plots at different q-bands showed striking similarities between SANS and SAXS data (Fig. 3c). It revealed that the nanostructural organisation in the radial specimens, determined from both SANS and SAXS data, remained at a lower orientational order (S = 0.47 ± 0.14, mean ± std) compared to the longitudinal specimens, where all measurements showed a higher orientational order (S = 0.66 ± 0.09, mean ± std) (Fig. 3e). The spread (std = 0.09 and 0.08 for SANS and SAXS, respectively) in orientational order among the longitudinal specimens was low, indicating a homogeneous nanostructure. For the radial specimens, the lower orientational order and the larger spread (std = 0.13 and 0.12 for SANS and SAXS, respectively) showed a more heterogeneous nanostructure, as was expected and discussed elsewhere14, and in agreement with the orientational parameters obtained from the micro-CT analysis (Table 3). Previous studies have reported a different measurement of orientational order, degree of orientation, and although not directly comparable, the values of the order parameter S reported here are in agreement with the previously reported degree of orientation, for both longitudinal and radial specimens in that longitudinal sections show a higher order of organisation than radial sections14,16. The longitudinal ovine specimen showed higher orientational order (S = 0.77 ± 0.03, mean ± std) for all measurement points and q-bands as compared to the longitudinal bovine and porcine specimens (S = 0.59 ± 0.03 and S = 0.60 ± 0.04, respectively, mean ± std). However, the low standard deviations showed that the orientational order remained constant for each specimen over all investigated q-ranges. The same trend was seen for the radial specimens, with S = 0.49 ± 0.10, S = 0.50 ± 0.07, and S = 0.38 ± 0.23 (mean ± std) for the bovine, porcine, and ovine specimen, respectively, over all investigated q-ranges. The high std for the radial ovine specimen could at a first glance indicate the opposite, i.e. a change in orientational parameter over the investigated q-ranges. However, when looking at the order parameter for each measurement position on the specimen, it is seen that the variations are due to one measurement position on the specimen being an outlier in that it displays lower values than the other positions, especially for lower q. This could indicate inhomogeneities in the specimen or an issue with the measurement, the latter reason being more credible since the SAXS data does not show the same trend.

The orientational parameters obtained from the micro-CT measurements indicated a well aligned microstructure in the longitudinal specimens, with a predominant orientation parallel with the main axis of the bone (vertical axis of the specimen) for the bovine and ovine specimens (Table 3). For the porcine specimen, the predominant orientation angle of 52.1° indicated that the microstructure was not aligned parallel to the vertical axis of the specimen. However, the low variation of microstructural orientation in the specimen (low std of the predominant orientation) meant that the specimen could still be considered longitudinal, and the discrepancy in orientation angle is due to imperfect specimen machining rather than improper choice of anatomical location. For the radial specimens, no clear predominant orientation was seen (high std). As has been discussed previously, this lack of a clear dominant orientation comes from the concentric lamellae seen when looking at radial cross sections of cortical bone containing osteons14,16.


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