# Comparison of small-angle neutron and X-ray scattering for studying cortical bone nanostructure

## Abstract

In this study, we present a combined small-angle neutron and X-ray scattering (SANS and SAXS) study of the nanoscale structure of cortical bone specimens from three different species. The variation of the scattering cross section of elements across the periodic table is very different for neutrons and X-rays. For X-rays, it is proportional to the electron density while for neutrons it varies irregularly with the atomic number. Hence, combining the two techniques on the same specimens allows for a more detailed interpretation of the scattering patterns as compared to a single-contrast experiment. The current study was performed on bovine, porcine and ovine specimens, obtained in two perpendicular directions with respect to the main axis of the bone (longitudinal and radial) in order to maximise the understanding of the nanostructural organisation. The specimens were also imaged with high resolution micro-computed tomography (micro-CT), yielding tissue mineral density and microstructural orientation as reference. We show that the SANS and SAXS patterns from the same specimen are effectively identical, suggesting that these bone specimens can be approximated as a two-component composite material. Hence, the observed small-angle scattering results mainly from the mineral-collagen contrast, apart from minor features associated with the internal collagen structure.

## Introduction

Bone is a hierarchically structured composite material. Its unique possibility to withstand mechanical loading comes from a combination of its constituents, namely type-I collagen and hydroxyapatite (HAp) crystals, and their complex structural organisation, which is built up from the molecular level to the whole organ1,2,3,4,5. To fully elucidate the contribution from each component, all length scales need to be investigated. This article focuses on the nanoscale of cortical bone where curved plate-shaped HAp crystals are interwoven in a collagen matrix, creating mineralised collagen fibrils2,6,7,8. Collagen is a triple helical molecule with diameter and length of 11 Å and 3,000 Å, respectively. The molecules congregate into fibrils where they are staggered axially such that zones of overlap and gaps form with a specific periodicity of approximately 670 Å. The mineral plates nucleate both within the periodic gap-zones and on the surface of the fibrils, and have a crystal c-axis aligned mainly along the main axis of the collagen fibril1,3,9,10. Water is present in different compartments: in pores and canals (on the micrometre scale), as well as loosely bound to the surfaces of collagen fibrils, and between the collagen and mineral phases, and more tightly bound to the collagen molecule and inside the mineral crystal structure11,12. In cortical bone, the collagen has a preferred orientation along the main axis of loading and the organisation becomes more homogeneous as the tissue matures3,13,14,15. In addition, it has been shown that cortical bone nano-structure is similar for different species4.

Small-angle X-ray scattering (SAXS) has been shown to be useful for investigating the nanostructure of bone as the mineral gives rise to a relatively strong scattering signal. The information obtained from SAXS studies includes average thickness, orientation, and degree of orientation of the mineral plates4,10,14,16,17. Neutron diffraction (ND) has previously been used to study the collagen structure, in terms of meridional and axial spacing of the collagen molecules, in both tendon and bone tissue18,19,20,21,22,23,24,25. Only two studies have briefly used small-angle neutron scattering (SANS) on bone26,27, although it is complementary to SAXS. Furthermore, no efforts have been made to compare the two techniques and clarify their complementarity.

In this study, we systematically compare small-angle neutron and X-ray scattering data from cortical bone tissue specimens from different species. The variation of the scattering cross section of elements across the periodic table is very different for neutrons and X-rays. For X-rays, it is proportional to the electron density while for neutrons it varies irregularly with the atomic number. Hence, combining SAXS and SANS allows for studying a material with two different scattering contrasts, which may give additional structural information compared to the single-contrast experiment. The current study was performed on bovine, porcine and ovine specimens, obtained in two perpendicular directions with respect to the main axis of the bone (longitudinal and radial) to maximise the understanding of the nanostructural organisation. The specimens were also imaged with high resolution micro-computed tomography (micro-CT), yielding tissue mineral density and microstructural orientation as reference.

## Materials and methods

### Specimens

Specimens consisted of cortical bone from one bovine (29-months old) and porcine (6-months old) femora, as well as one ovine (7-months old) tibia, all obtained from the local abattoir. Each animal can be considered a young adult. Orthogonal sections in longitudinal and radial directions (Fig. 1a) with a thickness of 1 mm (0.94 ± 0.11 mm, mean ± std) were obtained from the mid-diaphysis using a diamond band saw under constant water irrigation (EXAKT 300 CP, Norderstedt, Germany). The specimens were fixed, placed in 70% ethanol, and kept refrigerated at all times except during measurements.

### Small-angle neutron scattering

SANS measurements were carried out at the D11 beamline, at the Institut Laue–Langevin, Grenoble, France28. The specimens were taken out of the 70% ethanol and the excess solvent was blotted away before placing each in separate 2 mm quartz cuvettes (100-QS, Hellma Analytics) for measurements. The longitudinal sections were placed such that the main orientation of the microstructure was aligned vertically. A wavelength of 5.6 Å in combination with specimen-to-detector distances of 39 m, 8 m and 1.4 m were utilised to acquire data in the q-range 0.00046–0.36 Å−1, using CERCA detectors with pixel size of 3.75 × 3.75 mm2 (Fig. 1c). With a beam spot size of 2 mm, scattering data was collected at three points, which were identified based on transmission measurements along the vertical midline of each specimen. An empty cuvette was measured for background reduction. After completion of the measurements, the specimens were again submerged in 70 vol% ethanol and placed back into refrigeration.

Data reduction, calibration to absolute intensity using the direct beam, and subsequent angular integration over 2π were carried out in LAMP29 and GRASP (GRASansP Barebones v. 8.14, Charles Dewhurst, Institut Laue Langevin, France). Data from each configuration were normalised by the intensity of the attenuated direct beam and the corresponding attenuation factor to reach absolute scale intensity. The beamstop and detector edges were masked away, and the data was integrated both over 360° (full integration), and parallel and perpendicular to the collagen fibre orientation (partial integration for anisotropy analysis). The partial integration was performed as 10 pixels wide strips around the beam centre and extending well beyond the region where counts were detected. The integrated data from the three configurations were merged using Matlab (R2019a, MathWorks Inc., MA, USA) in order to have a continuous q-range. This was done by adjusting the intensities of the mid- and high-q data ranges to overlap the low- and mid-q range data, respectively, using a factor close to 1 (± 10%).

### Small-angle X-ray scattering

SAXS measurements were subsequently carried out at the cSAXS beamline at PSI, Switzerland30. An X-ray photon energy of 12.4 keV, equivalent to a wavelength of 1 Å, was selected using a Si (111) monochromator. The beam size at the specimen position was 150 × 125 µm2 (horizontal × vertical), for which the beam was slightly focused using the beamline optics. The specimens were mounted directly on the specimen stage and hence were measured in air. A specimen-to-detector distance of 7.1 m and exposure time of 100 ms were utilised to acquire data in the q-range of 0.0048–0.109 Å−1, using a Pilatus 2 M detector with pixel size 172 × 172 µm231 (Fig. 1d). A grid scan of 8 × 9 points was performed to cover an area of 1.2 × 1.125 mm2 centred at the same positions as those measured previously with SANS. The 2D scattering data was averaged to simulate the volume measured with SANS. Data reduction, calibration to absolute intensity using a glassy carbon standard32, and subsequent angular integration over 2π were done using in-house Matlab code (R2019a, MathWorks Inc., MA, USA)14,16, as well as the cSAXS Matlab base package33. The beamstop, edges of the detector modules, and bad pixels were masked away, and the data was integrated both over 360° (full integration), and parallel and perpendicular to the collagen fibre orientation (partial integration for anisotropy analysis). The partial integration was realised as 30 pixels wide strips around the beam centre and extending well beyond the region where counts were detected.

### Micro-computed tomography

Micro-CT measurements were carried out at the 4D Imaging Lab, Division of Solid Mechanics, Lund University, Lund, using a 3D X-ray microscope (Zeiss Xradia XRM520), in order to determine tissue mineral density, porosity, and orientation of the microstructures. The specimens were stacked and wrapped in saline soaked gauze during imaging. Two HAp phantoms (0.75 g/cm3 and 0.25 g/cm3, respectively) were imaged to calibrate the tissue mineral density of the specimens. A tube voltage of 80 kV and power of 70 W was used to collect 2,501 projections over 360°, each with 5 s exposure. The field-of-view (FOV) was approximately 18 × 18 mm, and the isotropic voxel size in the reconstructed images was 9.25 µm.

The micro-CT images were analysed using ImageJ v1.52i34. For each specimen, the three positions measured with SANS and SAXS were identified based on known distances obtained from the transmission measurements from the scattering experiments, and specific structural and compositional parameters were calculated after thresholding in the grey scale range of 140–255 (8-bit images), representing the tissue fraction above 1.0 g/cm3 of mineralised bone. The minimum intensity projection was used to visualize the micro-porosity for analysis of the microstructural orientation, yielding a specimen specific predominant orientation (Fig. 1b), using OrientationJ35. Tissue mineral density was evaluated by comparing the mean grey value to that of the phantoms and extrapolating from their known mineral density. The porosity was calculated using BoneJ36.

### Comparison of scattering data

The integrated scattering intensities (360°) from SANS and SAXS were compared in the overlapping q-range (0.0048–0.109 Å−1), using the common definition of q as $$q = 4\pi \cdot \sin \left( {\theta /2} \right)/\lambda$$, where $$\theta$$ is the angle between the direct and scattered beam. The intensities were adjusted by a proportionality constant, specific to the specimen and measurement position, to overlap at low q. The difference at each q, defined as the interval between two sequential SANS data points (Δq = 9.7e−4 ± 8.4e−4 Å−1, mean ± std), was calculated to find q-range dependent differences between the techniques, as per

$$\delta I\left( q \right) = \left( {I_{X} \left( q \right) - I_{N} \left( q \right)} \right)/\left( {I_{X} \left( q \right) + I_{N} \left( q \right)} \right)$$
(1)

with $${\text{I}}_{{\text{X}}} \left( q \right)$$ and $${\text{I}}_{{\text{N}}} \left( q \right)$$ being the scattering intensity at a specific $$q$$ for SAXS and SANS, respectively. Also, the difference for the entire overlapping q-range was investigated, as per

$$\delta I_{full} = \left( {\sqrt {\left( {I_{X} - I_{N} )} \right)} } \right)/\left( {\sqrt {\sum \left( {I_{N} } \right)^{2} } } \right)$$
(2)

with $${\text{I}}_{{\text{X}}}$$ and $${\text{I}}_{{\text{N}}}$$ being the scattering intensity for the entire q-range. Equations (1) and (2) were also used to explore the anisotropy using the partial integration (parallel and perpendicular to the collagen fibre orientation). For this the overlapping q-range was slightly smaller (0.0048–0.088 Å−1) due to the reduced signal-to-noise ratio at high q. In addition, integration as a function of azimuthal angle covering four partial q-ranges (0.005–0.008 Å−1, 0.020–0.027 Å−1, 0.060–0.067 Å−1, and 0.90–0.96 Å−1) was used to elucidate possible differences in anisotropy as a function of q. The partial q-ranges were chosen in between collagen peaks to avoid interference from the collagen-specific scattering (Fig. 3a,b,d). The anisotropic scattering patterns were analysed in terms of an order parameter, S, quantifying the orientational order of the mineral crystal plates, assuming uniaxial symmetry. Here, S is defined as the second order Legendre polynomial, as per

$$S = \frac{1}{2}\langle3\cos^{2} \theta - 1\rangle$$
(3)

where $$\theta$$ is the angular deviation from the average orientation, and <  > refers to an ensemble average. The definition of $$\theta$$ is illustrated in Fig. 1e. Azimuthal plots $$I\left( \theta \right)$$ for a given q-band typically showed two peaks, that were fitted with Gaussian functions (Fig. 1e), obtaining a standard deviation $$\sigma$$, describing the width of the peaks. From $$\sigma$$, the order parameter was calculated, as per

$$S = \frac{3}{2}\frac{{\mathop \smallint \nolimits_{0}^{\pi } \exp \left\{ { - (\theta - \theta_{0} )^{2} /2\sigma^{2} } \right\}\sin \theta \cos^{2} \theta d\theta }}{{\mathop \smallint \nolimits_{0}^{\pi } \exp \left\{ { - \left( {\theta - \theta_{0} } \right)^{2} /2\sigma^{2} } \right\}\sin \theta d\theta }} - \frac{1}{2}$$
(4)

### Scattering contrast

The scattering length densities of collagen and mineral were calculated using the NIST Neutron activation and scattering calculator (https://www.ncnr.nist.gov/resources/activation/), assuming chemical formulae and mass densities presented in Table 1. The partial carbonation of the bone mineral (ca. 5 wt% CO32− substitution37,38,39,40) has only a negligible effect on the scattering length densities and was hence omitted from the calculations.

## Results

Striking similarities between SANS and SAXS data were apparent for all measurements. Comparing the fully integrated (360°) scattering intensities in the overlapping q-region showed very small differences (≤ 15.4%) for all specimens (Table 2), with a proportionality constant of 35.9 ± 17.5 (mean ± std) for overlap of low q data in the overlapping q-range.

For all measurements, the difference between the techniques increased slightly as a function of q, with the SAXS intensity at higher q being lower compared to the SANS intensity (Fig. 2). Data from all specimens are available in Supplementary Figs. 13. For the partial integration parallel to the collagen fibre orientation, the strong collagen peaks in the SAXS data, especially from the longitudinal ovine specimen, gave rise to large differences in intensity for the longitudinal specimens (Supplementary Fig. 4). However, integration perpendicular to the collagen fibre orientation for the longitudinal specimens, and both parallel and perpendicular to the collagen fibre orientation for the radial specimens, showed the same variation (differences increased as a function of q) as the fully integrated data (Supplementary Figs. 15).

The q-dependent azimuthal plot (Fig. 3) revealed that the orientational order (S), remained constant around 0.66 and 0.47 for both longitudinal and radial specimens in both SANS and SAXS (S = 0.66 ± 0.09, and S = 0.47 ± 0.14 (mean ± std), for longitudinal and radial specimens, respectively).

The micro-CT analysis of the microstructure indicated a homogeneous specimens set in terms of bone porosity and tissue mineral density (Table 3). The orientational analysis (Fig. 1b and Supplementary Fig. 9) showed a predominant orientation parallel to the long axis of the bone for the longitudinal sections (low standard deviation), and more disperse orientation for the radial sections.

## Discussion

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 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 $$I\left( q \right)$$ can be interpreted as

$$I\left( q \right)\sim \Delta \rho^{2} S_{eff} \left( q \right)\langle{P\left( q \right)}\rangle$$
(5)

where

$$\Delta \rho = \left( {\rho_{m} - \rho_{c} } \right)$$
(6)

is the contrast between the mineral and collagen, $$\rho_{m}$$ and $$\rho_{c}$$, being the mineral and collagen scattering length densities, respectively. $$\langle{P\left( q \right)}\rangle$$ 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.

## Limitations

Due to the selection of beamstop for the high-q SANS measurements (1.4 m sample-detector distance), no overlap between mid- and high-q ranges were obtained after 2π integration of the 2D scattering, resulting in lack of data in the q-range of 0.064–0.075 Å−1. However, no significant features are expected in this q-range, and by comparing the data integrated over 2π to data where also the corners of the detector banks were included (“full-detector integration”), it is clear that no significant information was lost (Supplementary Figs. 68). Merging of the mid- and high-q ranges was done such that it matched the merged full-detector integration.

The resolution for the SAXS measurements was considerably higher than for the SANS measurements28,30. Nevertheless, the resolution of the SANS data (Δλ/λ = 9%) is more than enough to properly resolve any characteristic features in the scattering data. As the polydispersity of the mineral platelets is relatively high4, the shape of the scattering curves are due to the polydispersity of the scattering particles rather than the wavelength distribution. The lower resolution of SANS compared to SAXS further explains the intensity differences seen around the collagen peaks and thereby indicates that if the resolution was more equal, there may have been even larger similarities between the techniques.

The difference in beam dimension for SANS and SAXS was in part accounted for by performing grid scans with SAXS. Still, the volumes measured were not exactly the same for the two techniques (3.14 mm3 and 1.35 mm3 for SANS and SAXS, respectively). However, the micro-CT data shows that the micro-structure inside the measured volumes for SANS were very homogeneous. Also, both SANS and SAXS measurements covered a relatively large volume. Hence enough averaging is done for smaller structural discrepancies not to have a noticeable effect on the resulting data.

The specimens were stored in ethanol and measured in air, resulting in dehydration of the tissue from both. It is known that drying and ethanol fixation of non-mineralised tissue has an effect on the collagen33,46. However, due to the mineralisation of the collagen matrix in bone, changes due to dehydration are less prominent11. Since both SANS and SAXS measurements were carried out in the same manner, the same amount of dehydration and potential change of collagen organisation should have occurred. Thus, the data is still comparable. Furthermore, since the specimens were not dried prior to submersion in ethanol, and the fact that the solvent was 70%, we are confident that enough water remain for there to have been a possible contribution to the scattering pattern.

## Conclusions

We have shown that SANS and SAXS patterns from different sections of cortical bone from different species are essentially identical, apart from a contribution of incoherent scattering for SANS, and a proportionality factor reflecting the different in contrast between the techniques, within the studied q-range. This implies that within this q-range the bone specimens can be considered a binary composite material in the analysis of scattering data for structural characterisation, with effective contrast between the organic collagen matrix and the inorganic HAp mineral platelets. Thus, the small-angle scattering from these bone specimens can be fully understood as arising from mineral platelets distributed within a collagen fibre matrix, where the enhanced scattering at lower q-values shows that the mineral distribution is heterogeneous in the plane perpendicular to the collagen fibre axis, with mineral rich and mineral poor domains on the 1,000 Å length scale.

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## Acknowledgements

This research is funded by the Swedish Foundation for Strategic Research (SSF) within the Swedish national graduate school in neutron scattering (SwedNess, GSn15-0008). The authors want to acknowledge the Institut Laue-Langevin, Grenoble, France for providing the beamtime at the D11 beamline (https://doi.org/10.5291/ILL-DATA.8-05-432), the Paul Scherrer Institut, Villigen, Switzerland, for provision of synchrotron radiation beamtime at the cSAXS beamline of the Swiss Light Source, and the 4D Imaging Lab, Division of Solid Mechanics, Lund University, for the micro-tomographic imaging. We also want to thank Isabella Silva Barreto, Dr Maria Pierantoni, and Dr Sophie Le Cann for assistance during the SAXS measurements.

## Funding

Open Access funding provided by Lund University.

## Author information

Authors

### Contributions

Study design: E.T., U.O. and H.I. Data collection: E.T., L.G., S.P. and A.D. Data analysis: E.T., S.P., A.D. Data interpretation: E.T., L.G., S.P., A.D., U.O. and H.I. Drafting manuscript: E.T. All authors revised the manuscript content and approved the final version of the manuscript. E.T. and H.I. take responsibility for the integrity of the data analysis.

### Corresponding author

Correspondence to Elin Törnquist.

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### Competing interests

The authors declare no competing interests.

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Törnquist, E., Gentile, L., Prévost, S. et al. Comparison of small-angle neutron and X-ray scattering for studying cortical bone nanostructure. Sci Rep 10, 14552 (2020). https://doi.org/10.1038/s41598-020-71190-9

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