Pathologies of the skeleton are among the most common morbidities worldwide. Age-related bone loss (osteoporosis) is supposed to increase in its clinical significance with the current demographic development. Its detrimental result are fragility fractures that remain difficult to treat. Bone quality is a result of the complexity of the bone micro- and nano-structure and the tissue remodelling process. The cellular network of the osteocytes in bone has emerged as key factor of bone remodelling executed by bone-resorbing osteo-clasts and bone-forming osteoblasts. It has been demonstrated that the osteocytes govern a local volume of matrix surrounding the osteocyte lacunae (perilacunar matrix), which is actively turned over by the osteocytic activity [118, 119, 120]. Osteocytes acidify their
5.2 Bone matrix mineralisation 105
Fig. 5.2.1: Simultaneous ptychography and X-ray fluorescence (XRF) of a thin and un-stained human bone section at 7.15 keV. (A) shows the Ca distribution as obtained by XRF mapping and (B) the ptychographic phase shift. Both (A,B) allow to identify a Haversian canal (H) and concentric lamellae (L). In (A), the Ca depletion areas (black arrows) indicate perilacunar matrices of two osteocyte lacunae, while the corresponding areas in (B) exhibit no change in phase shift, which is proportional to the projected density.
lacuno-canalicular volume to demineralise the local bone matrix [118]. This mechanism appears to serve as a response to an increased calcium demand, e.g. during lactation. Yet, mechanistic studies show that osteocytes utilise a far less acidic pH than osteoclasts to dissolve the bone mineral [121]. Therefore, the perilacunar matrix would need to be more susceptible to the demineralisation by means of a differential elemental or structural com-position. Perilacunar matrix governed by osteocytes is hypothesised to be distinctively different from the remaining bone matrix. It is supposed to allow demineralisation by the osteocytic bone resorption and easier lacuna-shape adaptation in differential loading scenarios.
As a second application, concurrent X-ray fluorescence and ptychographic imaging was used to investigate human perilacunar matrix mineralisation by means of its spatially-resolved calcium concentration map. For this purpose, an unstained and resin-embedded thin human cortical bone section was prepared on a silicon-nitride membrane. Detailed sample preparation protocol is provided in Appendix B.2.
5.2.1 Results
Based on the visible-light image of the entire section, a 70×70 µm2 area of the cortical bone matrix in the proximity of a Haversian canal was preselected. It was subsequently scanned with a nano-focussed X-ray beam at a photon energy of 7.15 keV. Detailed ex-perimental parameters are provided in Tab. C.2 (Appendix C). Fig. 5.2.1 shows the Ca map (A) and the ptychographic phase (B) of the selected bone region. It is possible to identify a fragment of the resin-filled Haversian canal (H), concentric lamellae rings (L), and two osteocyte lacunae (black arrows). The surrounding bone matrix was partially affected by typical cutting artefacts during sample preparation causing ruptures without any embedding medium.
106 High-throughput multimodal X-ray imaging of biological specimens
Fig. 5.2.2: Orthogonalised probe modes of the human cortical bone section in Fig. 5.2.1B.
(A), (B), and (C) indicate the first, second, and third mode, respectively. The fractions of the total incident photon flux of 3.75×108photon s−1 are indicated in the upper-right image corners. The probe size was assessed to equal 200×400 nm2 (h×v).
The raw Ca map in Fig. 5.2.1A was obtained using the spectra batch-fitting in the PyMca X-ray Fluorescence Toolkit [94]. The map was further refined with the interfer-ometer positions to eliminate the distortions observed in the motor encoder positions. It was realised with scipy.interpolate.griddata routine from the SciPy Python library.
The ptychographic dataset was reconstructed using 100 iterations of the difference map algorithm and three orthogonal probe modes. Further increase of the probe modes number did not result in any qualitative improvement of the reconstructed object image. Fig. 5.2.2 shows the intensity distributions of the reconstructed, orthogonalised probe modes, with the respective intensity fractions in the upper-right corners of the sub-figures. The overall probe size was estimated to 200×400 nm2 (h×v). The scan was acquired with an incident photon flux of 3.75×108photon s−1 at a horizontal fly-scan speed of 2 µm s−1. It consisted of 326×326 scan points with a scan step size of 200 nm, equal in both directions. This resulted in a rather sparse linear overlap in the horizontal direction, causing artefacts in the ptychographic image due to the grid-scan pathology [122].
5.2.1.1 Spatial resolution analysis
While spatial resolutions of X-ray fluorescence mapping are inherently limited by the size of the X-ray beam footprint on the sample, the use of spatially coherent illumination and iterative phase retrieval instead of an objective lens makes ptychography surpass that limit. The X-ray fluorescence and ptychographic images of the human bone matrix shown in Fig. 5.2.1 are both rich in structural details and can be used to evaluate spatial resolution limits of both imaging techniques. For this purpose, two distinct Fourier-transform-based methods – suitable for each measurement – were employed.
The resolution of the X-ray fluorescence calcium map (Fig. 5.2.1A) was derived from its power spectrum. An edge-softening Tukey window function was applied to the image.
Subsequently, the power of its discrete Fourier transform was calculated. The obtained two-dimensional power spectral density was then averaged vertically and horizontally to account, respectively, for different horizontal and vertical illumination sizes. Fig. 5.2.3A shows two directionally averaged PSD curves whose intersections with the lines denoting twice the noise level [93] correspond to the half-period resolution limits of: 418 nm in
5.2 Bone matrix mineralisation 107
Fig. 5.2.3: Spatial resolutions of the human bone section measurements in Fig. 5.2.1.
(A) presents horizontally- and vertically-averaged power spectral densities (PSD) of the raw Ca K-line map. The cross-sections of the PSD curves and twice the noise floor denotes half-period spatial resolutions of 418 nm×359 nm (h×v), respectively. Spatial resolution of the ptychographic phase image was evaluated by Fourier Ring Correlation (B) between reconstructions of two sub-datasets being complementary halves of the whole set of diffraction patterns. The reconstructions involved position refinement to break the raster-scan periodicity, resulting in grid-pathology artefacts. The cross-section of the FRC curve and the 1/2-bit threshold criterion provides a conservative spatial resolution estimation of 65 nm.
the horizontal direction and 359 nm in the vertical direction. The obtained values remain in very good agreement with the probe size obtained by ptychographic reconstruction (200 nm×400 nm, h×v) broadened horizontally by the 200-nm step of the continuous scanning.
The spatial resolution of the bone matrix ptychographic reconstruction in Fig. 5.2.1B was estimated with the Fourier ring correlation (FRC) method [89]. FRC requires typ-ically two independently acquired images. In the absence of a repeated measurement, phase reconstructions from two complementary sub-datasets can be correlated, provid-ing a more conservative resolution estimation [112]. Here, the sub-datasets were created according to the following pattern: (1) for even scan lines: even-numbered diffraction patterns, for odd scan lines: odd-numbered diffraction patterns; (2) for even scan lines:
odd-numbered diffraction patterns, for odd scan lines: even-numbered diffraction pat-terns. Both sub-datasets were reconstructed using 100 iterations of the difference map algorithm and 3 probe modes. Additionally, refinement of the scan positions was enabled to break the raster-scan periodicity, resulting in step-scan-related grid-scan pathology artefacts. Solid blue line in Fig. 5.2.3B denotes the FRC between the two ptychographic sub-datasets. Its intersection with the 1/2-bit threshold line provides a spatial resolution limit of 65 nm.
5.2.1.2 Ptychography-enhanced calcium distribution
The raw Ca map in Fig. 5.2.1A is intrinsically affected by the projected density and thickness of the specimen called the mass-thickness effect. In the absence of calibration standards, the quantitative phase contrast image acquired simultaneously with the ele-mental map allows for a robust correction of this distortion, free of any scanning artefacts.
Therefore, the lower halves of Figs. 5.2.1A and 5.2.1B were selected for further correction
108 High-throughput multimodal X-ray imaging of biological specimens
Fig. 5.2.4: Spatial distribution of relative Ca concentration of a human bone section us-ing simultaneous ptychography and X-ray fluorescence (XRF) at 7.15 keV. (A) shows the lower half of the Ca map in Fig. 5.2.1A, upscaled bilinearly to the pixel size of the ptycho-graphic reconstruction. (B) shows the corresponding ptychoptycho-graphic phase image. The Ca map in (A) was then divided by the regularised ptychographic phase (B). (C) presents the mass-thickness-corrected Ca map corresponding to the relative Ca concentration. Sample preparation artefacts were masked in white. (D) shows histograms of relative Ca concen-trations values of three bone matrix areas as marked with dashed rectangles in (C). It compares relative Ca concentrations between two regions enclosing the identified perila-cunar matrices (1, 3) and a representative region of the bone matrix (2). Face-filled in blue and red histogram values correspond to actual areas of the perilacunar matrices and span over visibly lower range of relative Ca concentrations than the values from the bone matrix (in green).
of the mass-thickness effect, as described in [108]. Since a background-corrected area un-der the Ca K-line peak is proportional to Ca areal mass and a ptychographic phase shift is proportional to the projected mass per unit area of the sample, the ratio of the two repre-sents a relative Ca concentration map. The bilinearly upscaled Ca map (Fig. 5.2.4A) and the ptychographic phase (Fig. 5.2.4B) were aligned using subpixel image registration [66].
The upscaled Ca map was then divided by the ptychographic phase shift augmented by a regularisation phase offset of 0.1 rad to avoid division by zero. Fig. 5.2.4C shows the mass-thickness-corrected Ca map which corresponds to the relative Ca concentration. In the rupture areas stemming from cutting artefacts, the operation resulted in artificially elevated relative Ca concentrations. They originate from the difference in spatial reso-lution and sensitivity between XRF and ptychographic measurement. These areas were masked in white and excluded from the analysis. The obtained relative Ca concentration map (Fig. 5.2.4C) was used to compare the Ca content around two osteocyte lacunae with respect to the surrounding bone matrix. For this purpose, the relative Ca concentration values of the two perilacunar matrix regions (denoted as 1 and 3 in Fig. 5.2.4C) and a rep-resentative bone matrix area (2) were compared in the histogram in Fig. 5.2.4D. In the case of regions (1) and (3), the face-filled histogram regions represent the actual areas of the perilacunar matrices. The histogram shows depletion of Ca in the two regions around the osteocyte lacunae with respect to the remaining bone matrix area.