Sample acquisition and preparation<\/p>\n
Samples originated from male 8-week-old Sprague Dawley rats kept in controlled conditions (12\u201312-h light\u2013dark cycles, 22\u2009\u00b0C and ad libitum access to food and water) at the University of Manchester Biomedical Sciences Facility. All tissue collection procedures were performed in accordance with the UK Animals (Scientific Procedures) Act 1986, local regulations set by the UK Home Office with institutional approval obtained from the University of Manchester Animal Welfare and Ethics Review Board under the Home Office Licence (#70\/8858 or I045CA465). Whole spines were dissected and snap frozen in liquid nitrogen before storage at \u221280\u2009\u00b0C. Thawing and further dissection were performed within 24\u2009h of experimentation, as described by Parmenter et al.22<\/a>. This resulted in whole IVD samples (from vertebral levels thoracic 10 to lumbar 2; Supplementary Table 1<\/a>) with half vertebrae on either side.\u00a0No randomization or blinding was carried out.<\/p>\n Samples were mounted in resin-printed holders (Supplementary Fig. 1<\/a>) using cyanoacrylate glue (VetBond; 3\u2009M Science), with sample alignment designed so that the mid-transverse slice of the IVD was parallel to the loading plates. A Kapton polyimide tube enclosed each specimen, leaving approximately 0.5\u2009mm exposed. Holders were placed in a Deben CT500 micromechanical tester (100\u2009N loadcell, \u00b11% accuracy; Deben) with a custom open-frame design22<\/a> (Supplementary Fig. 1<\/a>). Displacement was recorded using a 10-mm extensometer (3-\u03bcm resolution, 1% linearity). The open-frame configuration facilitated alignment and hydration of samples while minimizing beam-path obstruction during SAXS. Sample hydration was maintained through immersion in phosphate-buffered saline (PBS), supplied via a capillary at the holder base from a 100-ml syringe through a stopped-flow module (Bio-Logic). A continuous flow preserved fluid level despite minor leakage from the 3D-printed holder.<\/p>\n Overview of the SAXS\u2013pCT experiment<\/p>\n Although simultaneous SAXS and pCT would have been ideal, in the absence of a dedicated SAXS\u2013pCT beamline at Diamond Light Source (DLS), a sequential approach was taken (SAXS(I22) preloaded\u2009\u2192\u2009pCT(I13) preloaded\u2009\u2192\u2009pCT(I13) loaded\u2009\u2192\u2009SAXS(I22) loaded), as illustrated in Extended Data Fig. 1<\/a>, with special stabilized sample holders and identical mechanical rigs at both beamlines to ensure comparability (Supplementary Fig. 1<\/a>).<\/p>\n Tomographic SAXS acquisition<\/p>\n SAXS data were acquired at the I22 beamline of the DLS synchrotron (experiment SM29784-8, 12\u201315 December 2023). A Deben CT500 was mounted to a rotation stage, on top of the sample table. A Dectris Pilatus P3-2M detector was placed at a distance of 9\u2009m from the stage, with a vacuum tube in between to minimize air scatter. All SAXS measurements used a beam energy of 14\u2009keV and beam size of 20\u2009\u00b5m. Each sample was first mapped at 0\u00b0 angular orientation using a raster map of approximately 100\u2009\u00d7\u2009100 SAXS frames using a 50-ms exposure time and a 20-\u00b5m step size. Maps were inspected to identify the IVD, and a 5\u2009\u00d7\u20091\u2009mm region of interest was assigned within the IVD for tomographic SAXS scans. SAXS scans were undertaken over raster maps of approximately 250\u2009\u00d7\u200910 SAXS frames with a step size of 20\u2009\u00b5m using 150-ms exposure time for nine equally spaced angular orientations (22.5\u00b0 step) between \u221285\u00b0 and 95\u00b0 (to minimize blocking by mechanical testing support rods). Radiation dose for a full single axis SAXS tomography was 12.2\u2009kGy (Supplementary Note\u00a01<\/a>). A relatively large step size of 22.5\u00b0 was used due to a significant reduction in flux caused by the\u00a0reduced ring current of 200 mA\u00a0during the beamtime. The experiment can be readily scaled to a smaller angular step (greater fraction of fibres intersecting the Ewald sphere). SAXS data for one horizontal slice is available in the Supplementary Dataset<\/a>59<\/a>.<\/p>\n pCT acquisition and reconstruction<\/p>\n pCT was conducted at the Diamond-Manchester Imaging Branchline I13-2, DLS (experiment SM29784-9, 12\u201314 December 2023). The setup followed established protocols22<\/a> (mean energy of 27.6\u2009keV, 1,800 projections, 0.5-m sample\u2013detector distance), with only the exposure time adjusted to 0.15\u2009s to account for the reduced ring current mentioned in the previous subsection. The insertion device gap was set to 5\u2009mm during scanning and widened to 7\u2009mm for alignment and low-resolution scans to reduce dose. Initial scans used a 1.25\u00d7 objective (voxel size of 2.6\u2009\u00b5m and field of view of 6.7\u2009\u00d7\u20095.6\u2009mm) to capture the sample environment, including the Kapton tube for SAXS co-registration. Subsequent scans used a 2\u00d7 objective (voxel size of 1.625\u2009\u00b5m and field of view of 4.2\u2009\u00d7\u20093.5\u2009mm) before and after compression. Radiation doses were 1.35\u2009kGy (voxel size of 2.6\u2009\u00b5m) and 27\u2009kGy (voxel size of 1.625\u2009\u00b5m) per scan (Supplementary Note\u00a02<\/a>). Tomograms were reconstructed using the open source Python library Savu 4.2 (https:\/\/savu.readthedocs.io)<\/a> and further processed using ImageJ 1.54 as previously described22<\/a>. Images of IVD1 are available in the Supplementary Dataset<\/a>60<\/a>.<\/p>\n In situ mechanical testing<\/p>\n Samples were held under axial compression, applied in the laboratory vertical z-direction, during scanning. For a reproducible mechanical protocol, two identical Deben CT500 mechanical testing rigs with 100\u2009N load cells were used during the experiment, one placed at beamline I22 (provided by Imperial College London) and the other placed at beamline I13-2 (provided by the University of Manchester at Harwell). A preload of 1\u2009N, corresponding to approximately 40% the animals body weight (260\u2009\u00b1\u200933\u2009g), was applied at I22 before SAXS scanning to prevent over swelling of the nucleus pulposus (Extended Data Fig. 1b<\/a>). Samples were allowed 20\u2009min of stress relaxation before scanning to minimize motion, determined as the time taken for load readings to stabilize (less than 0.01-N change in 1\u2009min). Following SAXS, samples were clamped in position using bespoke 3D-printed sample holders and screws (Supplementary Fig. 1<\/a>) and transferred to I13-2 for pCT (Extended Data Fig. 1b<\/a>).<\/p>\n Clamped samples were placed in the mechanical testing rig at I13-2 and secured at the top (Extended Data Fig. 1c<\/a>). The bottom platen of the rig was slowly raised until screw hole alignment was reached between the rig and the clamped sample holder, which was then secured in place. The clamps were removed from the sample holder before preload pCT scans. After the first pCT scan at 1.6-\u00b5m voxel size, a 50-\u00b5m displacement was applied to the bottom platen of the sample holder in the laboratory z-direction, leading to a 2\u20135% reduction in IVD height (Supplementary Table 1<\/a>). Axial compression was chosen for ease of experimentation and interpretation of results. Again, samples were given 20\u2009min or more of stress relaxation before scanning. After imaging, the sample was clamped in its loaded state before being removed from the rig and transported back to I22 (Extended Data Fig. 1c<\/a>). At I22, the sample was placed back in the mechanical testing rig and clamps were removed before taking the loaded SAXS scans, which used the same protocol as described in the section \u2018Tomographic SAXS acquisition\u2019 (Extended Data Fig. 1d<\/a>).<\/p>\n Fibre tracing and DVC analysis<\/p>\n Fibre tracing of the preload 1.6-\u00b5m images was performed using the Avizo XFiber module (Avizo 3D 2023.2; Supplementary Fig. 2<\/a>), with parameters used for tracing given in Supplementary Note\u00a03<\/a>. After fibre tracing, fibres clearly corresponding to imaging artefacts\u2014such as streaks from mineralized tissues and ring artefacts from reconstruction\u2014were removed from further analysis. Fibre spatial graph data were exported as a .xml file, and fibre identification number was conserved throughout all further analysis.<\/p>\n Fibre orientation and curvature were computed per fibre from a 3D polynomial space-curve fit to the traced fibre centreline4<\/a> (r(s)) using a custom-written MATLAB script (MATLAB R2023a, https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>; Supplementary Note\u20094<\/a>). This resulted in fibre ID, x, y, z, curvature, \u03b1-orientation and \u03b2-orientation values for points placed every 6.5\u2009\u00b5m along each fibre. Fibre ID, \u03b1-values and \u03b2-values were converted to 3D volume images for input into the TomoSAXS reconstruction (Supplementary Note\u00a05<\/a>).<\/p>\n Fibre curvature (k(s)) was evaluated from the first and second derivatives of the fitted curve4<\/a> using the standard 3D definition:<\/p>\n $$k(s)=\\frac{\\Vert {{\\bf{r}}}^{{\\prime} }(s)\\times {{\\bf{r}}}^{{\\prime\\prime} }(s)\\Vert }{{\\Vert {{\\bf{r}}}^{{\\prime} }(s)\\Vert }^{3}}$$<\/p>\n A local DVC analysis with flexible point cloud specification was performed using the open-source software iDVC (https:\/\/tomographicimaging.github.io\/iDVC\/<\/a>)4<\/a>,21<\/a>,22<\/a>,23<\/a>,24<\/a>,61<\/a>. The fibre-based coordinates generated above were used as the DVC point cloud defining the locations of sub-volumes used for tracking (Fig. 2e<\/a>), resulting in 0.7\u20131.4 million DVC measurement points per sub-volumes for each sample (Supplementary Table 1<\/a>). Spherical sub-volumes with a diameter of 40 voxels (65\u2009\u00b5m) were matched between the preload and loaded images using a zero-normalized sum-of-square difference function for optimization and 12 degrees of freedom (translation, rotation and first-order strain; Fig. 2g<\/a>). Six thousand sampling points were placed within each sub-volume for matching. The displacement of the first sub-volume in the point cloud was defined by manually tracking a landmark between the preload and loaded images using ImageJ.<\/p>\n Two strain measurement techniques were applied to the displacement fields measured from the DVC, corresponding to different length-scales probed. For tissue-level strains, the differential of a polynomial fit to the displacement field was used to calculate the Lagrangian strain tensor at each point61<\/a>. The 75 closest points to the measurement point were used for fitting to smooth out noise in the displacement field and improve accuracy. The first principal strain was derived from the maximum positive eigenvalue, and the third principal strain was derived from the maximum negative eigenvalue of the strain tensor. The direction of the corresponding eigenvectors relative to the local fibre direction was calculated as an angle between 0\u00b0 (parallel to fibre direction) and 90\u00b0 (orthogonal to fibre direction; Extended Data Fig. 5g<\/a>). Radial and circumferential strains were calculated by projecting the strain tensor along the local radial and circumferential directions (https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>; Extended Data Fig. 5a<\/a> and Supplementary Note\u20096<\/a>). Fibre strains were calculated using a custom-written MATLAB script (MATLAB 2023a), which performs a polynomial fit to displacement along the fibre direction (https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>; Supplementary Fig.\u20093<\/a> and Supplementary Note\u20097<\/a>).<\/p>\n The double projection zero strain method22<\/a> was used to quantify the accuracy of DVC displacements and strains (Supplementary Note\u00a09<\/a>). Zero-strain displacement accuracy (mean absolute error) was 88.5\u2009nm and precision (standard deviation of absolute error) was 83.5\u2009nm. Tissue zero-strain accuracy was 0.16% and precision was 0.16%. Fibre zero-strain accuracy was 0.08% and precision was 0.10%. The DVC was able to track a virtual deformation of 10% compression with a displacement accuracy of 198\u2009nm, tissue strain accuracy of 0.40% and fibre strain accuracy of 0.45%.<\/p>\n To calculate orientation for the same fibres in each sample after loading, DVC displacements were applied to the fibre points in MATLAB (https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>; Supplementary Note\u200910<\/a>). Orientation of the deformed fibres was calculated, and loaded Fibre ID, \u03b1 and \u03b2 3D volume images generated for input into the TomoSAXS reconstruction.<\/p>\n 3D diffraction modelling<\/p>\n 3D diffraction modelling was applied by simulating the meridional X-ray diffraction peaks of collagen fibrils with nanoscale fibre symmetry, under user-defined experimental conditions (wavelength, lattice spacings and angular tilts), and accounting for the variable intersection of the 3D scattering intensity with the Ewald sphere. Implementation was done in a custom Python library developed by us (https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>) and is a more complex version of the model presented by Badar et al.1<\/a>. In brief, the meridional scattering arising from the D-periodicity is simulated by a set of 3D semi-flat ellipsoidal functions, whose location in 3D space is at multiple harmonics of the inverse D-period (q0n\u2009=\u20092\u03c0n\/D), radial width in q (wa) is related to fibril pre-strain heterogeneity, and angular width (w\u03bc) is related to inverse fibril diameter and intrafibrillar tilting, parameterized by a degree of circularity of the ellipsoid function (\u03b4; 0\u2009=\u2009straight function; 1\u2009=\u2009circular ellipsoid). The need for a semi-flat, rather than completely flat, meridional ellipsoid came from the experimental observation that even for tissues with uniaxial fibril orientation, the meridional ellipse showed some arcing (Supplementary Note\u00a011<\/a>). We believe this may be related to the intrafibrillar tilt of the microfibrils38<\/a>.<\/p>\n Owing to the intersection with the Ewald sphere (radius\u2009\u221d\u20091\/\u03bb), the intensity and pattern of the resulting 2D fibril diffraction depends on user-input 3D tilt angles \u03b1 and \u03b2 of the fibril, which will be a crucial factor in deciding which fibres contribute to scattering, as well as the beam wavelength. The functions for fibril scattering can be calculated at any point across the diffraction condition of the sphere both in 2D (Fig. 2b<\/a>, left panel), as well as in 1D (for example, azimuthal (\u03c7) and radial (q) plots; Fig. 2c<\/a>) by averaging in the complementary axis.<\/p>\n TomoSAXS algorithm overview<\/p>\n Here the foregoing library (https:\/\/github.com\/DiamondLightSource\/tomosaxs<\/a>), in conjunction with the pCT or DVC data (for \u03b1 and \u03b2), was used to reconstruct the third-order collagen diffraction peak (which typically has intensity between wavevectors of approximately 0.26\u20130.32\u2009nm\u22121). The TomoSAXS implementation works via a series of discrete modules in the Python (3.10) environment, summarized here.<\/p>\n Module 1 spatially co-registers the pCT and SAXS scans, from which the individual collagen fibres in each SAXS beam path at all tomographic rotations can be found.<\/p>\n Module 2 performs background correction of the SAXS signals, accounting for PBS, Kapton tube and air scattering, building on the adcorr Python package62<\/a>. The pCT and co-registered SAXS scans from module 1 allows accurate correction using the variable thickness of the sample through each SAXS beam path by adjusting the proportion of dispersant to sample, compared with assuming a uniform thickness in Pauw et al.62<\/a>.<\/p>\n Module 3 provides initial estimates for per-fibre SAXS amplitude, using singular-value decomposition (SVD) and the 3D diffraction model.<\/p>\n Module 4\u2014the core of the reconstruction\u2014extracts the nanoscale parameters in an iterative way, by scanning through the SAXS tomography along \u03c7 and rotation axes to find angular regions where either a single fibre, a pair of fibres or triplet of fibres dominates the observed scattering over a given angular sector (10\u00b0 in width). Fibres are isolated at the single, double or triplet level when one, two or a maximum of three fibres contribute predominantly (more than 90%) to total scattering across at least a 10\u00b0 sector around the circumferential \u03c7 axis of individual SAXS frames (Fig. 2c<\/a>, top panel). By calculating SAXS radial intensity profiles within this azimuthal sector at three equally spaced angular positions (for example, at 0\u20133.33\u00b0, 3.33\u20136.66\u00b0 and 6.66\u20139.99\u00b0 from the start of a 10\u00b0 sector), and fitting each radial profile with 3D diffraction models, the parameters mean D-period (inverse to radial peak centre; equation (1)); variation in D-period (peak width along q); and fibril radius (inversely related to peak width along \u03c7) can be estimated. For double-fibre and triple-fibre fits, to avoid degenerate cases where multiple fibres are pointing in the same direction and with similar fibril parameters, we enforced a minimum separation of 5\u00b0 between fibrils, as well as minimum predicted intensity levels from each fibre to avoid dominance by one (for doublet) or two (for triplet) fibres.<\/p>\n To iteratively solve for the fibre parameters, a two-stage process was followed (Supplementary Fig. 7<\/a>). First, a sweep was conducted across all rotations and beam paths to isolate and fit single fibres with sufficient independence in scattering intensity across \u03c7, until no more individually isolatable fibres were solvable. The process was then repeated to include fitting for single, double and triple sets of fibres across all beam paths and rotations, looping until no further fibres were solved in a single sweep through all angles and rotations.<\/p>\n Module 5 spatially reconstructs and outputs the estimated metrics and estimates fibril-level (nanoscale) strain in biomechanical loading, using DVC estimates of per-fibre (microscale) deformation to locate the same fibre in the unloaded and loaded datasets.<\/p>\n Module 1: spatial co-registration<\/p>\n Spatial co-registration of SAXS and pCT datasets was achieved through identifying fiducial markers (such as the mineralized vertebral endplates) in the samples, which gave distinct signals in SAXS and pCT. The Kapton tube of the sample environment was used for horizontal alignment and the mineralized tissues of the vertebral endplates used for vertical alignment. High-resolution (1.625\u2009\u00b5m) pCT images did not capture enough Kapton tube for co-registration, so were spatially registered to low-resolution (2.6\u2009\u00b5m) images. Both sets of images were downsampled to a voxel size of 6.5\u2009\u00b5m and the offset between them calculated in x, y and z coordinates. Fibre orientation tiff stacks (absolute voxel size of 8.125\u2009\u00b5m) were padded to the size of the original high-resolution (1.625\u2009\u00b5m) reconstruction (512\u2009\u00d7\u2009512\u2009\u00d7\u2009432 voxels) and centred using the offset between high-resolution and low-resolution images, so that all pCT data were spatially aligned (Supplementary Note\u00a012<\/a>).<\/p>\n Vertical registration between SAXS and pCT involved identifying the border of the mineralized vertebral endplates in the SAXS intensity map generated during coarse mapping at 0\u00b0, and in the 2D total phase-contrast intensity maps of a sample along the same angular orientation from the pCT data and calculating the vertical offset between them. Horizontal registration was achieved by identifying the Kapton tube from its characteristic peaks in SAXS intensity, and manual segmentation of the tube from the pCT data. For each SAXS tomography orientation (n\u2009=\u20099, \u221290\u00b0 to 90\u00b0), the fibre orientation, index and Kapton data for vertically isolated SAXS slices were rotated to the corresponding angle (using a custom function for maintaining fibre data integrity during rotation; Supplementary Note\u00a013<\/a>). The location of the left-hand edge of the Kapton tube was then compared and aligned between the SAXS and pCT data. This allowed finding the indexed fibres that contributed to SAXS scattering along each beam path of the raster scan in the specific SAXS slice. For each frame, the orientation, index and number of CT voxels comprised by each indexed fibre along its beam path were saved, along with the calculated distance between each fibre and the centre of the beam path, which was used as a weighting factor for model fitting. This data were saved as individual matrices, along with the calculated total specimen thickness (along beam path) for each frame.<\/p>\n Module 2: background correction<\/p>\n Background correction was undertaken for each individual SAXS frame following the method outlined in Pauw et al.62<\/a>. A separate scan using the same parameters as the SAXS tomography was undertaken for a single slice (a slice represents a 1D scan\u2009\u00d7\u2009n\u2009=\u20099 rotations) through (1) an empty Kapton tube, and (2) a Kapton tube filled with PBS, to represent background SAXS signals from both the sample holder (Kapton tube) and the dispersant (PBS). These signals were algorithmically subtracted from each sample SAXS frame using the adcorr Python library (https:\/\/github.com\/DiamondLightSource\/adcorr<\/a>), adjusting the ratio between the sample and dispersant based on the sample thickness for the respective frame (module 1). The resultant background-corrected data were saved as .h5 files for each TomoSAXS slice.<\/p>\n Module 3: SAXS amplitude estimation<\/p>\n The first analytical step in the TomoSAXS algorithm makes an initial estimate of the amplitude of SAXS scattering for individual fibres using the SVD, using a mean value for the other peak characteristics such as position, radial and angular widths (Supplementary Table\u20092<\/a> and Supplementary Note\u00a014<\/a>). This was justified by the small variability of the peak position (from 2D data) across different sample locations. The estimation step was used to identify locations of strong scattering for specific fibres enabling fibre-by-fibre solution in the next module 4 step.<\/p>\n At a given beam path in the sample x, and a rotation angle r, the angular intensity of the third-order collagen peak q0 can be written as<\/p>\n $${I}_{x}^{r}\\,(\\chi )=\\mathop{\\sum }\\limits_{i}^{F}{w}_{i}{I}_{i}^{r}(\\chi ;{q}_{0},\\Delta {q}_{0},\\alpha ,\\beta )$$<\/p>\n where the sum in i is taken over all fibres in the volume, with weighting factors either 0 (if outside of the beam path) or proportional to the intensity at the fibre location (assuming a Gaussian beam profile with known shape). As all fibres are taken to have the same average peak location and width parameters in this initial estimation step, the contribution from each fibre \\({I}_{i}^{r}(\\chi ;{q}_{0},\\Delta {q}_{0},\\alpha ,\\beta )\\) can be calculated up to a scaling factor proportional to the amplitude factor Ai, including the geometrical transformations needed to account for fibre orientation with respect to the beam. Hence, when represented for each \\(x,\\chi ,r\\) the above equation can be expanded into an overdetermined set of linear equations, which can be solved by SVD.<\/p>\n A Python dictionary was created with entries for each SAXS frame comprising of 0\u2013180\u00b0 intensity(\u03c7) (herein I(\u03c7)) radial integrations between 0.26 and 0.32\u2009nm\u22121 in\u00a0q, binned to 36 averaged points across \u03c7 and smoothed using 1D Savitzky\u2013Golay filtering (window length of 9 and polynomial order of 1). Two matrices were then created: the first consisting of a single vector comprising the concatenated I(\u03c7) integrations for all SAXS frames (left-hand side (LHS) in the equation above); and the second with columns comprising the contribution of each fibre to the same binned I(\u03c7) intervals predicted for each SAXS frame using 3D diffraction modelling (right-hand side (RHS) in the equation above). The amplitude for each fibre was then estimated by non-negative linear least squares regression, regressing predicted versus measured I(\u03c7) data. A Python dictionary was constructed, with entries for each indexed fibre consisting of its index, \u03b1 and \u03b2 angles and an empty entry for fitted nanoscale parameters. This dictionary was used to calibrate registration matrices (see above) for each rotation angle of the SAXS tomography, creating a series of other dictionaries.<\/p>\n Module 4: TomoSAXS fittingInitial intensity simulation<\/p>\n As shown in Fig. 2f\u2013h<\/a>, TomoSAXS reconstruction was based on fitting fibre diffraction models of intensity to measure I(q) profiles across the azimuthal\u00a0angular ranges (Fig. 2g<\/a>) of independent scattering signals from either (1) a single fibre, (2) a pair, or (3) a triplet of overlapping fibres (Supplementary Table 2<\/a>). We first calculate simulated angular SAXS intensity profiles using estimated amplitudes from module 4. A Python fibre dictionary was constructed, containing its index, \u03b1 and \u03b2 angles, initial estimated scattering amplitude and a dictionary for fitted nanoscale parameters. The dictionary was referenced against registration matrices (see above, module 1) for each rotation angle of the SAXS tomography, creating a series of individual orientation-specific dictionaries, indexed by beam path.<\/p>\n For each beam path in the orientation-specific dictionary, a dictionary indexed by fibre index stored information for every fibre in the beam path (including initial estimated amplitude), with a weighting term from the calculated distance of the fibre to the beam centre (Supplementary Note\u00a013<\/a>) where d is the distance from the beam centre and w the beam diameter:<\/p>\n $${\\mathrm{weighting\\; factor}=e}^{{-d}^{2}\/2{w}^{2}}$$<\/p>\n These dictionaries were used to create simulations of the angular scattering intensity of the third-order meridional peak of every beam path using 3D diffraction modelling, using tilt angles obtained from pCT and the averaged nanoscale peak metrics (q0\u2009=\u20090.2856\u2009nm\u22121, wa\u2009=\u20090.005\u2009nm\u22121, w\u00b5\u2009=\u20090.2\u2009nm\u22121 and \u03b4\u2009=\u20090.5; see Supplementary Note\u00a014<\/a> for rationale).<\/p>\n Fitting single, double and triplets of fibres<\/p>\n The angular intensity profile was scanned to iteratively solve individual or small groups of fibres, rather than fitting all fibres to the data, simultaneously (Supplementary Note\u00a016<\/a>).<\/p>\n Single-fibre fit. For each fibre k in a beam path p at a rotation r, its individual angular intensity contribution \\({I}_{k}^{p}(\\chi ;{r})\\) to the total intensity \\({I}^{p}(\\chi ;{r})\\) was calculated. If the following condition was fulfilled for an angular range \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta \\chi ]\\) between 0 and 2\u03c0 (\u0394\u03c7\u2009=\u200910\u00b0), and a single-fibre dominance threshold ts\u2009=\u20090.90:<\/p>\n $${I}_{k}^{p}(\\chi ;r) > {t}_{s}{I}^{p}(\\chi ;r);{\\chi }_{k;1}^{p} < \\chi < {\\chi }_{k;1}^{p}+\\Delta \\chi $$<\/p>\n then the fibre k was identified as being the dominant contribution to the SAXS signal in the \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta \\chi ]\\) angular range. The index, beam-path location and angularly independent sector \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta \\chi ]\\) was recorded for all fibres that met the user-defined criteria for independent scattering were stored in a Python list.<\/p>\n Next, these fibres were fitted to extract the nanoscale (fibrillar) peak metrics, by calculating \\({n}_{\\chi ,c}\\) (default\u2009=\u20093) equally spaced radial\u00a0slices (azimuthally integrated)\u00a0across the \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta ]\\) angular region, with a width \\(\\Delta {\\chi }_{c}\\) (default\u2009=\u20096\u00b0). These were simultaneously fitted with 3D diffraction models for the fibre, using the minimize() function of the lmfit Python library (https:\/\/lmfit.github.io\/lmfit-py\/fitting.html<\/a>) and the Nelder\u2013Mead algorithm. The angles \u03b1 and \u03b2 and the weighting factor of the fibre were fixed parameters, and q0, wa, w\u03bc, amplitude and \u03b4 were set as fit parameters (see Supplementary Table 2<\/a> for settings and Supplementary Note\u00a015<\/a> for rationale). If the fits passed several quality thresholds, both relating to absolute values of the parameters and statistical quality of fit (for standard error, threshold\u2009=\u200925%), the fit values were added to the dictionary entry for the respective fibre. Instances in which the fit to the fibre did not meet quality thresholds were saved and added to a separate Python list allowing them to be discarded from future investigation. This process was repeated for all the fibres in the list.<\/p>\n As successful fits allowed more potential single-fibre instances to be identified (already fitted fibres could be deconvolved from the scattering in all beam paths where they occur), the process was repeated until no more instances of independent scatter for single fibres could be found for any beam paths in the SAXS tomography.<\/p>\n The above process isolated and fitted the instances with the strongest independent scattering signal (approximately 10\u201320% of indexed fibres per slice), providing robust fits for further deconvolution and fitting of other fibres occurring in the next step of the reconstruction algorithm.<\/p>\n Overlapping fibre fit. In the next step, the reconstruction algorithm included fitting of instances where two to three fibres produced a combined scattering that meets the thresholds for independent scatter. For example, for all pairs of fibres \\({k}_{1},{k}_{2}\\) in the beam path \\(p\\), we checked whether the following condition was fulfilled for any \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta \\chi ]\\) and a double-fibre dominance threshold td\u2009=\u20090.95:<\/p>\n $$({I}_{{k}_{1}}^{p}+{I}_{{k}_{2}}^{p})(\\chi ;r) > {t}_{d}{I}^{p}(\\chi ;r);{\\chi }_{k;1}^{p} < \\chi < {\\chi }_{k;1}^{p}+\\Delta \\chi $$<\/p>\n For multiple-fibre fits, validation simulations (Supplementary Note\u00a015<\/a>) have shown that the dominance of one fibre\u2019s scattering intensity can bias the fit of the other fibre (or fibres) and lead to inaccuracies in fits. Hence, upon identification of a pair of fibres \\({k}_{1},{k}_{2}\\), the relative combination of scatter from each fibre was estimated. Only instances in which each fibre represented a minimum of \\({t}_{d}^{1},{t}_{d}^{2}\\)\u2009=\u200920% of the total scatter across >\u200990% (0.90) of\u00a0the angular sector \\([{\\chi }_{k;1}^{p},{\\chi }_{k;1}^{p}+\\Delta \\chi ]\\) were considered for fitting. Instances that passed this test were then fitted using the minimize() function as above.<\/p>\n After each fit, the parameter database was updated, and each angular intensity profile was scanned to identify any new solvable fibres (single, double or triple), which could be fitted by deconvolving already fitted fibres.<\/p>\n The foregoing steps were looped through all beam paths at all rotations, for a user-defined maximum number nl\u2009=\u200910 times, recording the ratio of fitted versus total indexed fibres at the end of each loop. If no increase in fitted fibres was observed at the end of a loop, the loop was terminated as all possible fibres had been fitted.<\/p>\n The entire TomoSAXS pipeline was conducted on a per-slice basis (per-horizontal 20-\u00b5m SAXS tomography slice) using cluster computing (specifically the DLS computing cluster). This allowed each slice to be run in parallel to maximize efficiency. The complete process across each of the five modules was completed within 6\u20137 days, with each module triggered individually in an iterative manner. TomoSAXS fitting (4\u20135 days) resulted in a mean proportion of fitted fibres of 60.08% per slice. This included multiple fits for differing instances of individual fibres found within different TomoSAXS slices. It is important to note that this does not correspond to the proportion of the total sample represented in each slice being fitted, as TomoSAXS operates on a per-fibre basis as opposed to a per-voxel basis (as in SAXS-TT28<\/a>). Reconstructions are spatially heterogeneous and dependent on the density and orientation of fibres within the respective slice.<\/p>\n Module 5: TomoSAXS reconstruction<\/p>\n Once fitting was complete, fitted parameters were spatially reconstructed for scanned fibres to create volumetric maps of per-fibre values. This was performed per slice for each parameter, by creating blank maps of the same shape as fibre index maps (created during the registration process; Supplementary Note\u00a013<\/a>) and assigning metric values to the voxels assigned to the index of every solved fibre in index maps. For fibres with fitted values in multiple TomoSAXS slices, if slices remained unfitted between these points, they were provided with values between fitted values estimated using linear interpolation.<\/p>\n Per-fibre nanoscale strain reconstruction<\/p>\n To estimate strain in nanoscale parameters under compressive load, indexed fibres were isolated that provided fits in both unloaded and loaded data. For each unloaded fit, the estimated vertical deformation of this point (and thus position in the loaded TomoSAXS scan) was estimated using the vertical (z axis) deformation measurements provided by DVC analysis (Supplementary Note\u00a017<\/a>). Strain in each parameter was calculated as the percentage difference between unloaded and loaded TomoSAXS fits for each point.<\/p>\n Validation using digital phantoms<\/p>\n The spatial calibration between pCT and SAXS data allowed estimation of the accuracy of fits supplied by the TomoSAXS technique, by providing known artificial nanoscale parameters to each indexed fibre in each TomoSAXS slice (maintaining fibre orientation, initial estimated scattering amplitude and per-instance weighting; Supplementary Note\u00a018<\/a>). Experimental noise was added to the simulated SAXS data, and accuracy and precision of nanoscale parameter estimates calculated as mean absolute error and standard deviation of absolute error.<\/p>\n Laboratory TomoSAXS analysis<\/p>\n Chicken foot tendons were dissected and air cured under differing tare loads of 0.5\u2009N, 1.5\u2009N and 3.5\u2009N to generate different levels of pre-strain in the collagen. Three tendons were arranged at different overlapping orientations and superglued to a 3D-printed sample holder (Extended Data Fig. 2a<\/a>). SAXS scans were performed using a Xenocs Xeuss 3.0 (DLS) with a beam size of 400\u2009\u00b5m and exposure time of 5\u2009min. Nine angular rotations between 0\u00b0 and 180\u00b0 were used, with 11 beam paths per rotation. \u00b5CT of the sample was performed using a Phoenix V|tome|x (Research Complex at Harwell) with a voxel size of 14.3\u2009\u00b5m.<\/p>\n The orientation of collagen fibrils within each tendon was assumed to be aligned with the principal axis of the tendon. The sample was divided into an 11\u2009\u00d7\u200911 grid for TomoSAXS reconstruction rather than individual fibres, for the purpose of a simplified, proof-of-concept reconstruction (Extended Data Fig. 2<\/a>). TomoSAXS reconstruction followed modules 4 and 5 of our pipeline, with no background correction or SVD analysis of scattering amplitude applied.<\/p>\n TomoSAXS of human IVD<\/p>\n Static imaging of a whole, formalin-fixed, human IVD (spinal level thoracic 11\u201312, 64-year-old male donor, no known spinal pathologies) was performed at the BM18 beamline of the ESRF using hierarchical pCT45<\/a> (Supplementary Note\u00a021<\/a>). Donation and dissection were performed at the Laboratoire d\u2019Anatomie des Alpes Fran\u00e7aises in November 2023, in accordance with French legislation governing body donation. Subsequent transport and imaging protocols were approved by the UK Health Research Authority through the Integrated Research Application System (#200429) and the French Ministry of Health.<\/p>\n The entire IVD was captured with a voxel size of 10\u2009\u00b5m and a local zoom with a voxel size of 4\u2009\u00b5m performed centrally to enable clear visualization of collagen fibres throughout the complete organ (Fig. 4b,d<\/a>). Fibre tracing was performed on the 10-\u00b5m scan using the Avizo XFiber module (Avizo 3D 2023.2), with parameters used for tracing given in Supplementary Note\u00a021<\/a>. Correlative high-energy (75\u2009keV, beam size of 100\u2009\u00b5m) tomographic SAXS was performed at ESRF beamline ID31 at 24 angles (Supplementary Note\u00a022<\/a>).<\/p>\n TomoSAXS reconstruction of a single slice of human IVD followed a modified pipeline to overcome the increased number of angular rotations, the 103 increase in sample volume and concomitant increase in fibre density per beam path. In principal, this involved three primary modifications. First, \u03b1 and \u03b2 fibre-angle maps were independently quantized by k-means clustering of non-zero angles rounded to 3\u00b0 increments, then combined pixel-wise into a 3D orientation label map of unique vertical\u2013horizontal fibre pairs, reducing fibre indices from more than 26,000 to approximately 3,600. Second, we extended the multiple-fibre fitting strategy to include four-fibre and five-fibre clusters across the angular \u03c7 axis. Finally, to handle the larger number of beam paths and greater amount of indexed objects per beam path, we introduced parallel processing. Instead of running rotations sequentially, each rotation was processed in parallel on a computing cluster, with all rotations reading from and updating a shared database of fitted fibres so that they could inform one another during execution. For more details of these modifications, see Supplementary Note\u00a022<\/a>.<\/p>\n Statistical analysis<\/p>\n Two-sided ordinary least squares regression analysis was used to test the agreement of known versus estimated properties of digital phantom data with and without the addition of experimental noise (Extended Data Table 1<\/a>). Correlations between per-fibre mean values of fibre strain, D-period, D-period variation and D-period strain were tested using ordinary least squares regression (Extended Data Table 2<\/a>). No adjustments were made for multiple comparisons.<\/p>\n","protected":false},"excerpt":{"rendered":"Sample acquisition and preparation Samples originated from male 8-week-old Sprague Dawley rats kept in controlled conditions (12\u201312-h light\u2013dark…\n","protected":false},"author":2,"featured_media":675341,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[3041,2026,61,21703,60,2027,178582,82,207487],"class_list":["post-675340","post","type-post","status-publish","format-standard","has-post-thumbnail","category-science","tag-biomedical-engineering","tag-humanities-and-social-sciences","tag-ie","tag-imaging-techniques","tag-ireland","tag-multidisciplinary","tag-nanoscale-biophysics","tag-science","tag-tissues"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/675340","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/comments?post=675340"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/posts\/675340\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media\/675341"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/media?parent=675340"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/categories?post=675340"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/ie\/wp-json\/wp\/v2\/tags?post=675340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}