Multimodal 2D and 3D microscopic mapping of growth cartilage by computational imaging techniques – a short review including new research

Being able to image the microstructure of growth cartilage is important for understanding the onset and progression of diseases such as osteochondrosis and osteoarthritis, as well as for developing new treatments and implants. Studies of cartilage using conventional optical brightfield microscopy rely heavily on histological staining, where the added chemicals provide tissue-specific colours. Other microscopy contrast mechanisms include polarization, phase- and scattering contrast, enabling non-stained or ‘label-free’ imaging that significantly simplifies the sample preparation, thereby also reducing the risk of artefacts. Traditional high-performance microscopes tend to be both bulky and expensive. Computational imaging denotes a range of techniques where computers with dedicated algorithms are used as an integral part of the image formation process. Computational imaging offers many advantages like 3D measurements, aberration correction and quantitative phase contrast, often combined with comparably cheap and compact hardware. X-ray microscopy is also progressing rapidly, in certain ways trailing the development of optical microscopy. In this study, we first briefly review the structures of growth cartilage and relevant microscopy characterization techniques, with an emphasis on Fourier ptychographic microscopy (FPM) and advanced x-ray microscopies. We next demonstrate with our own results computational imaging through FPM and compare the images with hematoxylin eosin and saffron (HES)-stained histology. Zernike phase contrast, and the nonlinear optical microscopy techniques of second harmonic generation (SHG) and two-photon excitation fluorescence (TPEF) are explored. Furthermore, X-ray attenuation-, phase- and diffraction-contrast computed tomography (CT) images of the very same sample are presented for comparisons. Future perspectives on the links to artificial intelligence, dynamic studies and in vivo possibilities conclude the article.


Introduction
A thorough knowledge of the anatomical and physiological micro-mechanisms of cartilage development and subsequent bone growth is important for a fundamental understanding of the biological structures including their mechanical properties.Cartilage is a compressible connective tissue protecting the ends of long bones, where the cartilage acts as a cushion and facilitates low-friction movements of the joints.Being able to image in detail the normal cartilage development and bone growth is needed to understand and manage joint diseases, as well as for developing new implants.Common joint disorders include the developmental disease of osteochondrosis (Ekman andCarlson 1998, Ytrehus et al 2007) and the degenerative disease of osteoarthritis (Hunter et al 2014), both of which can have incurable consequences.
Cartilage consists of chondrocytes and the matrix they produce, containing water, collagen fibrils, and proteoglycans, with the latter enabling the tissue to withstand compression through hydration-induced swelling.Chondrocytes (cells) are dispersed in the cartilage matrix in differing patterns depending on the distance from the subchondral bone.Close to the articular (joint) surface of the cartilage, and in fully grown individuals, the chondrocytes arrange tangentially, whereas cells in the deeper layers are arranged randomly or radially.These chondrocytes produce collagen fibres that in grown-ups are arranged in orderly Benninghoff 'arcade' structures (Benninghoff 1925, Iozzo and Schaefer 2015, Klika et al 2016).Deeper into the central regions of the growth cartilage, the chondrocytes are randomly distributed in the extracellular matrix.
During the longitudinal growth of long bones in adolescent individuals, mineralized bone gradually replaces the growth cartilage through endochondral ossification (Ytrehus et al 2007).This process allows the bone, and thus the individual, to grow, while the limb at all times remains capable of bearing weight.Close to the growing bone surface the chondrocytes are arranged in zones in the growth cartilage, where the ordered chondrocytes proliferate, grow (become hypertrophic), and then mineralize, before bone tissue is deposited by osteoblasts.Growth cartilage also contains cartilage canals, which are tubular structures with blood vessels, supplying oxygen and nutrients to the developing tissue.Several recent studies on growth cartilage are focused on osteochondrosis, where mechanical failure of cartilage canals in growth cartilage is linked to necrosis of cartilage and ultimately to fissures occurring in the joint epiphyseal surface (Ytrehus et al 2007, Olstad et al 2015).
Cartilage and endochondral ossification have been extensively studied with optical microscopy or histology (Hunziker et al 1997, Pawlina andRoss 2018).However, a particular challenge when imaging cartilage with optical techniques, is that the different cartilage constituents like cells, extracellular matrix and channels have rather similar optical properties for visible light, and therefore staining is commonly applied.Histological stains such as hematoxylin eosin and saffron (HES) enable discerning the collagen-rich extracellular matrix from the cells, also distinguishing between different cell components.Microscopy studies of cartilage are often done using bright field light microscopy in combination with histological staining, such as the HES standard (Edston and Grontoft 1997), or by immunostaining (using antibodies to select proteins) (Coons et al 1941).However, these approaches typically require that the samples are decalcified, cut, and stained, thus disabling further study of the intact samples, possibly introducing artefacts, and perhaps missing the regions of highest interest.Further, the sample information acquired from histology is largely qualitative, meaning that the observed hues and saturation in the recorded images are difficult to relate to physical properties like density or stoichiometry.Electron microscopy of cartilage is challenging owing to radiation damage and the need for keeping the sample hydrated, yet examples of environmental scanning electron microscopy do exist (Suso et al 2004).We emphasize the considerable difference both in workflow and in the information that can be obtained when moving from having to cut 4-6 μm thick 2D histological sections, towards being able to visualize the structures in 3D.For example, to see where, how and why cartilage canals have defects, 3D methods are generally necessary (Finnøy 2017).
Computational imaging (Zheng et al 2013, Tian et al 2014, Mait et al 2018, Barbastathis et al 2019) is a rapidly expanding field signifying an approach to imaging where the optical hardware is designed for optimal information harvesting, while computer algorithms are used to extract the features of interest, including reconstructing actual images.Computational imaging is an integral part of the on-going revolution towards digitalization and artificial intelligence, which enables additional functionality like super-resolution, threedimensional (3D) imaging, digital aberration corrections, and post-capture refocusing.On one hand the field is closely connected to highly integrated platforms like smartphones, which inherently connects optics with processing (Lee et al 2021).On the other hand, computational imaging also enables new approaches like ghost imaging (Mait et al 2018) and non-line-ofsight imaging (Rapp et al 2020).Two classic examples of 3D computational imaging are x-ray computed tomography (CT) and magnetic resonance imaging (MRI), which remain a field of intense research.
The aim of the present work is to provide an overview of how modern microscopy techniques are advancing to address the physiologically complex and important interface between bone and cartilage.In addition to providing a brief review of relevant literature, we apply several recently developed optical and x-ray microscopy techniques to compare how different structural features near cartilage canals and the ossification front can be highlighted in the developing femur from young piglets.Albeit many works are cited, the combined scope of bone, cartilage and advanced microscopy is vast, and we make no claim of completeness in the selection of techniques and references.For example, computational imaging based on coherent Raman scattering imaging is recently reviewed in (Lin and Cheng 2023), and not considered here.Moreover, the focus is largely put on ex vivo laboratory experiments, rather than clinical aspects.Conventional optical microscopies including bright field, dark field and Zernike phase contrast, are juxtaposed with nonlinear microscopy and compared with FPM and the x-ray microscopies of μCT, phase-and diffraction contrast tomography.

The structure of growth cartilage
In this section, we describe in simple terms the main structural features of growth cartilage, exemplified in figure 1 with conventional histology applied to the very same sample as discussed throughout this article, cf Results.
In mature individuals, long bone ends are covered only by mature articular cartilage, which has chondrocytes organized in four distinct cell layers: a superficial tangential layer, an intermediate (random) layer, a deep radial layer, and finally, a calcified layer that fixes the cartilage to the bone.The wellknown Benninghoff arcades develop late in skeletal growth, several months after birth, during endochondral ossification (Benninghoff 1925, Ytrehus et al 2004, Iozzo and Schaefer 2015, Klika et al 2016).The arcade structure pertains to the collagen fibres and has a similar organization as the mature articular cartilage with a tangentially oriented superficial layer, and with the deep collagen fibres being radially oriented.This structure aids with shock absorption and load distribution.Joint inflammation ('arthritis') might be reversible, but if the collagen fibres of the Benninghoff arcades get disrupted, this signals the onset of irreversible osteoarthritis, emphasizing their clinical importance.The Benninghoff arcades cannot be repaired, they only form during growth and are not re-formed if broken later in life.We note that it has not proven feasible to construct an implant that genuinely integrates within native Benninghoff arcades-the implants tend to detach in a matter of years.
In skeletally immature individuals, the bone ends are covered by (i) immature articular cartilage, which is not yet organized in the four layers of mature articular cartilage, and (ii) vascularized growth cartilage.The superficial layer of immature articular cartilage in skeletally immature joints contains no vascular cartilage canals.These young individuals are engaged in the additional physiological function of bone growth by the abovementioned endochondral ossification, which occurs within the specialized growth cartilage.As shown in figure 1, growth cartilage self-organises into four zones (not to be confused with the layers of mature cartilage): I a superficial resting zone; II a proliferative zone where growth takes place by cell division and an increase in cell number; III a hypertrophic zone where growth occurs by an increase in cell size; and IV a zone where the matrix becomes mineralised in preparation for subsequent invasion by osteoblasts and bone production at the continually advancing ossification front.
Growth cartilage also distinguishes itself by containing vascular cartilage canals (Ytrehus et al 2007).Each cartilage canal contains one arteriole, its capillary bed and one or more draining venules.The vessels are made of endothelial cells and contain red blood cells (aka.erythrocytes) with iron-carrying hemoglobin molecules.The vasculature within these canals is organised as anatomical end arteries, meaning that an arteriole courses into and out of the cartilage via one and the same blindending canal.This organization renders the canal vulnerable to failure because there is no collateral supply/ back up system, implying that if one canal fails, the surrounding cartilage will undergo ischemic chondronecrosis, which leads to focally delayed ossification (osteochondrosis) and can result in pathological fracture and fragmentation at the joint surfaces (osteochondrosis dissecans) (Ytrehus et al 2007).Large, central canals additionally contain several perivascular mesenchymal cells (PMCs) that both divide and make chondrocytes, and produce collagen fibers, both of which are pushed out of the canal into the surrounding cartilage, thus contributing to growth.

Review of microscopy techniques applied to cartilage
Visual light microscopy Optical microscopy and histology Bright-field (BF), dark-field (DF) and polarized microscopy are the conceptually simplest and best-known optical microscopy methods for investigating histological samples (Mertz 2019).A well-known limitation of standard light microscopy is that the field of view (FoV) and the resolution are coupled, as choosing a higher magnification objective will give a smaller FoV.A common practical solution to this limitation is to stitch together a series of micrographs obtained by mechanically scanning the sample, thereby covering a larger region with high resolution.
Staining and more specialized histochemistry are performed to obtain specific types of information about bone, cartilage, and relative extracellular matrix, under normal and pathological conditions (Musumeci et al 2014, Rieppo et al 2019).Hematoxylin & eosin is the most common staining and is used for both decalcified and undecalcified specimens.Both Goldner's trichrome staining and von Kossa staining allow differentiating osteoid from mineralized bone matrix.Giemsa, toluidine blue, methylene blue/basic fuchsin and Masson's trichrome can detect acidophilic bone tissue; Alizarin-S staining can be used to distinguish bone from the calcified matrix; and periodic acid-Schiff can pinpoint pathological tissue.Other common stains for cartilage include safranin O/fast green and alcian blue, ink and Indian ink-all excelling for different specific tasks.
Barium (strictly, barium sulphate BaSO 4 ) perfusion of pigs and foals is often combined with Spalteholz tissue clearing and stereomicroscopy (Ytrehus et al 2004).The barium sulphate used is micronized to a guaranteed median particle size of <0.7 micrometres, being one tenth the size of a red blood cell.Consequently, the barium can get into the capillary beds, showing up as 'clouds' of barium surrounding the arterioles when viewed in a stereomicroscope.The barium fills the arteriole side, and enters or becomes stuck in the capillary beds, while the venous side does not get filled and hence cannot be visualized.Barium-formalin solution hardens and sets within the vessels and does not run back out when the samples are sawed.Barium is only for post-mortem work and is optically dense.For in vivo staining, one uses iodine, which is liquid, rather than particulate.If using (colourless) iodine, colour must be added to see it in cleared samples, and e.g., gelatine has to be added to make it set within the vessels and not run out when sawed.
Using certain advanced microscopy techniques, cartilage can however be imaged also without sample staining.Zernike phase-contrast (ZPC) microscopy was the first and is perhaps still the simplest realization of phase contrast, where the light scattered by the specimen is purposely separated from the background illumination, given a ±90°phase shift, and then made to interfere to give measurable stationary intensity variations (Zernike 1942).ZPC gives a significantly enhanced contrast, enabling otherwise similar biological tissues, including cartilage variants, to be distinguished.

Multiphoton and nonlinear microscopy
Nonlinear microscopy (Sheppard and Kompfner 1978, Hoover and Squier 2013, Parodi et al 2020) is based on the optical response of nonlinear media where the polarization response to the electric field of the light is nonlinear.Nonlinear microscopy has gained widespread use and is available in commercial instruments, including both absorptive (non-parametric, like TPEF; vide infra) and parametric processes like second-and third-harmonic generation (SHG/THG), and coherent Raman scattering (CRS).In a parametric process, the quantum state of the nonlinear material is not changed by the interaction.Notably, two photon excitation fluorescence (TPEF), which is based on the simultaneous absorption of two photons by a single endogenous fluorophore, is realized with near-infrared femtosecond lasers.Because the exceedingly low probability of such events effectively confines the process to the focal plane of the incoming beam where the electric field is the strongest, TPEF can be used to obtain clear images deep (>100 μm) into disordered and strongly scattering media.These nonlinear optical microscopy techniques allow material-specific imaging, implemented in laser-scanning microscopy setups (Mertz 2019).Short pulses of high-intensity light focused to small volumes promote nonlinear effects, effectively also enabling thick sections to be scanned to obtain 3D images.
For second-harmonic generation (SHG), noncentrosymmetric molecules generate photons of half the wavelength of the incoming light.The emitted frequency-doubled photons are selected using a filter and recorded by a detector.In several biological tissues, such as cartilage, collagen are the only molecules that provide a second harmonic signal, and thus SHG microscopy is often used for studying collagen (Mansfield et al 2008).Peptide bonds in the collagen triple helix molecular structure act as harmonophores (Deniset-Besseau et al 2009), and SHG has been used to study cartilage since 2005 (Yeh et al 2005).Collagen fibrils and chondrocytes in growth cartilage can advantageously be studied by SHG or TPEF microscopy (Finnøy 2017).SHG intensity variations might be caused by either density inhomogeneities, or structural arrangements of the collagen fibrils, as the packing motif of the fibrils is known to modify the SHG signal (Chen et al 2012).TPEF also allows identification of chondrocytes in the extracellular matrix of the cartilage and erythrocytes (red blood cells) in the cartilage canal vasculature (Mertz 2019).In a study by Finnøy et al (Finnøy 2017), early osteochondrosis lesions were tracked in 3D using SHG and TPEF to find the site of vascular failure, while at the same time visualizing the structures inside the canals.They observed two types of failure: (i) dilated vessels, and (ii) broken vessels with free erythrocytes within the canals.The etiology, i.e., why the vessels burst, is known to be, at least partially, of genetic origin.
While nonlinear microscopies excel in deeper penetration and tissue specificity, they also have the limitations that the laser beams employed have to be intense (giving risk of sample damage); for SHG the materials have to be non-centrosymmetric; and the setups are arguably (still) rather bulky, complex and costly (Mertz 2019).

Ultramicroscopy
Techniques like Stimulated Emission Depletion (STED) (Hell and Wichmann 1994) and Stochastic Optical Reconstruction Microscopy (STORM) (Betzig et al 2006), earning the inventors the Nobel Prize for Chemistry 2013 (Möckl et al 2014), have enabled extreme lateral resolution in the tens of nanometre range.However, also these techniques are complex and costly, and their need of fluorescing molecules to function render them somewhat outside the scope of the current article.

Quantitative phase imaging and Fourier ptychography
Quantitative phase imaging (QPI) (Park et al 2018) has become a mature technology, with several competing implementations, such as Fourier ptychographic microscopy (FPM) (Zheng et al 2013), spatial light interference microscopy (SLIM) (Wang et al 2011b), and digital holography (Park et al 2018).QPI has the huge advantage that it opens for density determination and hence to estimate the material composition.The essence of QPI is that both the amplitude A and the phase f of the complex wave, ψ(x, y) = A(x, y)exp(if(x, y)), are obtained through interference.
FPM is a recent breakthrough in the blooming field of computational imaging (Zheng et al 2013, Tian et al 2014, Mait et al 2018, Barbastathis et al 2019).In FPM, many (∼100 s) images are captured, typically with a low numerical aperture (NA) microscope objective which gives a large FoV.Illumination from distinct light emitting diode (LED) sources gives (partially) coherent light from distinct directions.Using iterative phase-retrieval algorithms the partially coherent exposures are combined to form high-resolution amplitude and quantitative phase images (Zheng et al 2013, Ou et al 2014, Tian et al 2014, Tian and Waller 2015, Konda et al 2020, Hasanzade et al 2022, Tekseth et al 2023).FPM has several advantages compared to conventional bright-field and phase-contrast microscopy techniques.The combination of low-NA objective lenses and partially coherent illumination with angular diversity gives a series of wide FoV exposures, allowing images to be synthesized with a substantially higher space bandwidth product (SBP) than what is achievable in conventional microscopyeffectively bypassing the diffraction limit of the microscope objective (Zheng et al 2013).Thereby, high-resolution images can be obtained while simultaneously having a large FoV.FPM has also been demonstrated in 3D, however with modest axial resolution, using multilayer propagation models (Tian and Waller 2015, Horstmeyer et al 2016, Zheng et al 2021).
FPM augmented with polarized light enables preferred orientations and strain to be visualized (Song et al 2021, Dai et al 2022, Gholami-Mayani et al 2022), see also (Ferrand et al 2018).With suitable algorithms, also the aberrations of the optical system can be retrieved and compensated, thereby relaxing the need for high-quality optical elements (Ou et al 2014).Consequently, as low-cost optics can often be used, FPM setups can be relatively inexpensive, while still achieving comparable performance to much costlier and bulkier setups.FPM has also been demonstrated in handheld portable devices (Lee et al 2021), holding promise of easy and widespread use of microscopy in the field and/or in poor communities, e.g., for drinking water or wound diagnostics in underdeveloped areas (McLeod andOzcan 2016, Zheng et al 2021).
Having the full quantitative description of the complex light field (amplitude and phase) propagating through the object also allows calculating the scattering coefficients (Wang et al 2011a, Horstmeyer et al 2015), describing the light transport properties through the sample.The anisotropy of the random scattering process can be described by the anisotropy parameter g = 〈cosχ〉, where χ denotes the scattering angle with respect to the forward direction.The parameter g is thus zero for isotropic scattering, while g > 0 implies that there is an overweight of scattering in the forward direction.Analogously to the description of absorption μ a by Beer-Lambert's law, the reduced forward intensity because of scattering can be described with a scattering coefficient μ s , such that the total attenuation becomes μ att = μ a + μ s , and the remaining intensity after propagating a distance Δ through the material is I 0 exp(−μ att Δ), where I 0 denotes the incoming intensity.The anisotropic scattering can be approximated as the sum of the reduced scattering (1-g) and the forward scattering g.Defining the scattering probability distribution p(Ω) to be normalized, ∫p(Ω) dΩ = 1, it follows naturally that p(Ω) = g δ(χ) + (1-g)/(4π), where the Dirac delta function δ(χ) ensures that the first term describes radiation in the forward direction, and the second term models the remaining signal intensity as isotropically scattered into 4π.
As described by the scattering-phase theorem (Xu 2011, Wang et al 2011a, Horstmeyer et al 2015), there are close connections between the phase map f (x, y) and the scattering properties of the sample.Specifically, the scattering coefficient μ s can be expressed as implying that the spatial variance of the phase map is related to the sample's scattering coefficient μ s .Here, L is the sample thickness, and is the spatial average of the quantitative phase map f(x, y).The spatial average 〈•〉 Δ x ,Δ y denotes a running average with a spatial kernel of size Δx, Δy.Also, the phase gradient is related to the reduced scattering coefficient μ s ′, through (Horstmeyer et al 2015) CT instruments in university laboratories and hospitals usually operate with a wide energy spectrum to give a high photon flux and short measurement times.Consequently, it gets more challenging to interpret the obtained images because the different wavelengths of the energy spectrum will be absorbed differently by a given material.A related challenge is beam hardening, which is an artefact arising because the attenuation generally (i.e., away from absorption edges) decreases with increasing photon energies.Consequently, the mean energy of the x-ray spectrum is shifted towards higher energies as the beam traverses through the sample.
Analogously to light microscopy, phase-contrast is helpful for improving contrast in x-ray imaging (Snigirev et al 1995).X-ray CT is often implemented at synchrotron sources with propagation-based phase contrast (PPC-CT) by letting the radiation field propagate an extended distance between the object and the detector (Horng et al 2014, Mürer et al 2021a).In synchrotron propagation-based phase-contrast x-ray CT (PPC-CT) the image contrast is formed from the refraction of x-rays in addition to the attenuation, thus giving a much improved signal for weakly absorbing soft organic materials (Cloetens et al 1999).For PPC-CT, the sample is illuminated by a full-field beam, and the transmitted intensity measured on the detector is dependent on both the attenuation and the phase-shift caused by the sample.Phase contrast gives substantially better contrast between weakly attenuating soft materials, thereby facilitating chondrocytes and cartilage canals to be studied non-destructively in 3D (Coan et al 2010).As for attenuation-based CT, tomographic reconstruction methods can be used for multi-projection phase-contrast data to retrieve a 3D image.Talbot-Laue interferometry (Momose et al 2003, Bech et al 2010, Esmaeili et al 2015) and diffuser-based phase contrast (Zdora 2018) are other phase-contrast techniques that currently receive much attention, not just for synchrotrons but also for home-laboratory setups based on x-ray tubes (Pfeiffer et al 2006, Zanette et al 2014, Sarapata et al 2015).

Spectral CT
Dual energy CT (DE-CT) denotes efforts to further distinguish materials that give similar attenuation 'gray values'.In DE-CT, acquisitions with two (or more) broad energy spectra are made, which gives an additional handle to distinguish materials.In hospital scanners DE-CT is often achieved using two pairs of source and detector, typically one operating at 140 kV and the other at 80 kV.A prime example of the clinical use of DE-CT is to distinguish crystalline deposits of uric acid (so-called tofi) from bone and cartilage in gouty patients (Johnson 2012).
In recent years photon counting detectors are also increasingly used in CT.These detectors register the individual photons absorbed in each pixel, rather than integrating the total deposited energy.Thereby the (approximate) energy spectrum is recorded, which allows spectral (energy resolved) CT.Photon-counting CT (PC-CT) as developed by Siemens Healthineers was approved by the US Food and Drug Administration (FDA) in 2021.The main advantages of PC-CT compared with ordinary CT are improved spatial resolution and that the signal-to-noise ratio is improved, allowing better images and/or the dose to be reduced.Moreover, the energy resolution allows multiple contrast agents to be used (Schlomka et al 2008, Shikhaliev 2008, Taguchi and Iwanczyk 2013).A drawback is the large volumes of data that are generated.Using several energy thresholds, discrete energy bins can be defined, effectively giving an approximation to the x-ray spectrum.As for DE-CT, this information enables the material composition of each voxel to be determined, rather than the average linear attenuation coefficient obtained in conventional CT.Such decomposition, based on at least two energy bins, increases the ability of differentiating between different tissues.The spectral information can be used to remove beam hardening artifacts as mentioned above.PC-CT has several advantages over DE-CT.Having several energy bins gives more freedom to define reconstruction schemes to highlight the specific features of interest.
X-ray diffraction computed tomography (XRD-CT) is a 3D generalization of the conceptually simpler 2D

Overview
To investigate the structural features in growth cartilage from a young pig, we cut a ∼3 × 3 × 3 mm 3 cube from the femorotibial joint and imaged the very same sample with multiple optical and x-ray microscopy modalities, see Materials and Methods for details.First, this cubeshaped bulk sample was measured with home-laboratory attenuation-contrast μCT and with synchrotron propagation-based phase-contrast CT (PPC-CT).Thereafter, the sample was decalcified and cut into 4 μm thin sections for optical microscopy.All the unstained microscopy results presented in this article were measured for this very same section.The histological hematoxylin eosin saffron (HES) stained section was obtained immediately adjacent to the unstained section, and thus presents essentially the same features.
Standard HES-based histology is shown in figure 1, effectively also giving an overview of the most prominent features present in growth cartilage.Figure 1(b) is a zoomed-in view of figure 1(a), emphasizing the fact that these huge images contain much more information than can be appreciated from these small-figure visualizations.
The standard HES section (cf figure 1) clearly delineates two main regions: the growth cartilage and bone.The yellow-stained region corresponds to the collagen-rich extracellular matrix.The cartilage canals contain erythrocytes in arterioles and venules that give rise to the pink stained regions.The collagen-containing trabeculae in bone turn orange, while the spacings in-between the trabeculae, containing blood vessels and (immature) bone marrow, get purple stained.

Multimodal mapping of cartilage using x-ray and optical microscopies
A cross-section from the three-dimensional (3D) attenuation-contrast μCT scan is shown in figure 2(a).As is well-known and described above, attenuationbased μCT is particularly good at distinguishing mineralized bones from soft tissue, and we note from figure 2 that only the mineralized phase of the bone and the mineralized cartilage close to the ossification front provided a sufficient contrast under 'standard' measurement conditions.

Fourier ptychographic microscopy of growth cartilage
The same unstained section of cartilage as presented in figures 2 and 3 was measured with our custom-built home laboratory FPM setup, cf figure 4. Notably, the whole section of cartilage could be placedwithin the FoV, as a low NA objective lens (Edmund Optics, 2x/ NA 0.055) was used.Quantitative phase images of the full FoV were obtained through iterative phase retrieval (Ou et al 2014).While the amplitude part of the reconstructed complex-valued image shown in figure 4(a) at first glance appears similar to the lowresolution bright field image (figure 3 Even though the fundamental image formation process is different between the (coherent) BF intensity and the FPM-phase images, it is instructive to compare their respective spatial resolution, cf figure 5, where the signals have been normalized.While these curves are expected to be different, they are still sufficiently similar to each other that it becomes apparent that the iterative FPM algorithm based on a 10x (NA 0.28) objective yields resolution comparable to the 50x (NA 0.55) objective, suggesting that the resolution has been roughly doubled as a result of the FPM phase retrieval process.We note that the resolution in FPM is given by λ/NA synth , where NA synth = NA obj + NA illum , and λ is the LED photon wavelength (Zheng et al 2013).The subscripts synth, obj and illum stand for synthetic, objective and illumination, respectively.In the present case, having used a single on-axis LED for the 50x objective, the corresponding resolution is λ/NA obj .Note that with an optimally matched incoherent illumination, the resolution with the 50x objective would ideally have been improved to λ/ (2 NA obj ) (Goodman 2017).

3D reconstruction of cartilage canals by PPC-CT
Being able to observe and visualize the 3D canal structures in cartilage is important for better understanding diseases but technically difficult for unstained samples because of weak contrast.A well-established work-around is to use barium sulphate (BaSO 4 ) perfusion in combination with attenuation-based μCT (Olstad et al 2008a).
Using PPC-CT, the cartilage canals can be discerned from the cartilage extracellular matrix (see also figure 3(d)).Still similar figures exist in the literature, but then typically obtained for example by tissue clearing methods, see e.g.(Ytrehus et al 2004).By manually segmenting the cartilage canals from the PPC-CT dataset they could be visualized in 3D, as shown in figure 6.Clearly, synchrotron-based PPC-CT allows the cartilage canal wall structure to be studied in 3D.Note that sample III studied by PPC-CT was BaSO 4 -perfused (see Materials and Methods), as often used for attenuation-contrast μCT.Note that a clear limitation of BaSO 4 staining is immediately seen from figure 6, as the staining agent is contained only in the arterioles and is unable to perfuse into the thinnest vessels in the capillary beds.Therefore, albeit practical and relatively easily available, BaSO 4 staining for μCT has limitations when it comes to imaging the full cartilage blood vessel morphology.
Note that Spalteholz clearing combined with perfusion is a well-established and powerful method for visualizing the cartilage canals, see e.g.(Ytrehus et al 2004).In order to use the structural information to better understand diseases, it is necessary to be able to resolve the entire canal morphology, including arteriole contents, walls, capillaries, venules, and perivascular mesenchymal cells.For example, capturing the rupture of a weak-walled venule would be crucial to understand the ensuing cartilage problems.

Orientation of mineralized structures by diffraction-contrast CT
The fine details of the hydroxyapatite (HA) bone mineral distributions close to cartilage canals entering the bone can be studied by tensor tomography or   6 reveals that the HA crystallites exhibit a slight preferred orientation in the mineralized bone in a region close to the bone and cartilage interface, where a cartilage canal is entering the bone.The XRD-TT was performed with an x-ray beam of diameter ∼50 μm, raster scanned with a step length of 50 μm, effectively defining the resolution of the experiment.We note, however, that as the characteristic thickness of the trabeculae is of the same order, a beam being an order of magnitude smaller, as used e.g., in (Grünewald et al 2020), would have given more insight into the mineral orientation across these mesoscale building blocks.Still, the image demonstrates the potential of this technique for future studies of the intricate structure of bone.

Discussion
Practical use While some of the microscopy techniques like BF, DF and μCT used in the present work are well established and in everyday use across the world, others like XRD-TT are still in their infancy and are actively being developed to realize their full potential.Similarly, basic use of BF microscopy is introduced already in primary school, whereas obtaining a good understanding of the more complicated modalities requires years of university training.
This difference in maturity also directly impacts the potential user.Training in ordinary light microscopy is comparatively cheap and readily available, as long as one can rely on standard equipment and procedures without a full immersion in the underlying physics.At the other extreme, nonlinear microscopy and XRD-TT require heavy investments and/or access to a few specialized laboratories world-wide, and these methods also require years of study to fully gather the depths of these cutting-edge techniques.Equipment for Fourier ptychography is a modest capital investment per se (∼10 4 USD), but considerable time and expertise will go into constructing, building, and commissioning the microscope.Figuring out how to use and understand the freely available FPM software also requires time and insight, but this situation is rapidly changing with several groups providing tutorials (Zheng et  With HES staining it is possible to see all the specific cell types relevant for cartilage studies.With the non-staining techniques demonstrated here it is possible to distinguish between chondrocytes and zones because the different zones have different cell density, shape, size, and amount of matrix.Within the canals one can distinguish whether the RBCs are within intact or broken vessels.Certainly, with targeted efforts, using FPM to obtain 3D images of the canal interiors should be feasible. In situ, in operando and clinical aspects An aspect not discussed in this article is in situ or in operando studies.Bone and cartilage are by nature designed for both static and dynamic loads, and many studies within biomechanics are carried out to better understand the mechanical response of bones to loads ranging from repetitive low-load to high-impact fracture-inducing events like crashes (Rho et al 1998).Digital volume correlation (DVC) is increasingly combined with μCT to study strain distributions, see Refs.(Tozzi et al 2020, Davis et al 2024).For dynamic studies, the full-field techniques not relying on scanning clearly have an advantage as they inherently facilitate better time resolution.For 2D-studies, visual microscopy is well adapted for dynamic studies, frequently in combination with digital image correlation to track minute changes within the sample, including strain fields (Pan et al 2009, Palanca et al 2016).While not relying on mechanical scanning, FPM still has a disadvantage for such measurements as several exposures must be made for each time step.
Efforts are made by many groups, also assisted by machine learning (Barbastathis et al 2019, Liu et al 2020), to increase the time resolution of μCT to enable dynamic studies, also known as '4D CT'.Typically, this is done by reducing the number of projections, and compensating for the consequently lacking information by relying on iterative reconstruction algorithms that can also incorporate additional a priori information about the sample, like sparsity in space and/or time (Chen et al 2008).For example, in the field of multiphase flow in porous media, such developments are gaining traction (Bultreys et al 2016).A related method, useful for repetitive dynamics, is to use stroboscopic imaging, often combined with external triggering or gating (Mokso et al 2015, Tekseth et al 2024).Analogous to 2D studies, also in 3D, image correlation techniques are used (Bay et al 1999), like the freeware TomoWarp2 for tracking internal deformations (Tudisco et al 2017).Digital staining based on machine learning (Rivenson et al 2019) is also highly relevant to the cartilage-bone interfaces.
In clinical practice, 'dynamic' applies to both fluoroscopic imaging, and to genuine dynamic volumetric CT acquisitions.Fluoroscopy denotes an imaging mode where a continuous x-ray image is shown on a monitor (originally on a fluorescent screen, hence the name) in real time, which is particularly useful for surgery guidance.An example of fluoroscopy applied to cartilage to observe cartilage motion is found in (Li et al 2005).Magnetic resonance imaging (MRI), positron emission tomography (PET) and combinations of these techniques, albeit highly interesting and promising, are considered outside the scope of this article.
From a bone and cartilage science structure point of view, we emphasize that all the length scales of the hierarchical structures described for bone (Reznikov et al 2014) are covered with the microscopy techniques reported here.While XRD-CT/TT and SAXS-CT provide images with locally averaged nanoscale information like hydroxyapatite orientation, FPM and μCT provide complementary data over larger volumes, like pore structures and interfaces.Phase-contrast methods generally facilitate imaging weakly attenuating objects, while quantitative phase imaging has the demonstrated ability of providing valuable input on physics and/or physiology through traceable numerical values, exemplified with the scattering coefficients.As reviewed, the on-going revolution in computational imaging, and its strong coupling to digitalization and machine learning, bodes for higher spatial resolution, better contrast, and easier analysis including automated segmentation.

Cartilage canals
As mentioned, a feature that distinguishes growth cartilage from mature cartilage is the presence of vascular cartilage canals, which contain endothelial, vascular (red and white blood cells) and perivascular mesenchymal cells.Being able to resolve these cells within the canals is key to understanding both the functionalities and several related diseases.To exemplify the clinical importance of the cartilage canals, we mention the study of Finnøy et al based on SHG/TPEF (Finnøy et al 2017), where it was suggested that osteochondrosis is a result of failure of the cartilage canal blood supply to growth cartilage.In early osteochondrosis, the cartilage matrix around failed canals (Finnøy 2017) and the bone trabeculae are reported to both be intact (Olstad et al 2015), thus a current working hypothesis is that the vascular failure occurs within the cartilage canal itself.Specific to osteochondrosis, one might further ask whether it is the arteriole or the venules that fail (Finnøy et al 2017).Topics that still deserve further attention include where, how, and why canal failure occurs.
Of the microscopy techniques described in the present study, the ability to resolve the canal structures varies.A clear advantage of the HES histology approach is the ability to distinguish all the cells inside the canals, including whether they are alive or dead.With most of the new techniques, only the RBCs can be discerned.Being able to see the RBCs without replacing the contents of the circulation with any kind of contrast-enhancing staining (barium sulphate, iodine, gadolinium, ink) is an important step forward in itself, also because the error source of incomplete perfusion is lifted.
Owing to their inherent 3D abilities, several of the techniques described here (CT, FPM) perform much better than histology at tracing 3D canal structures to find points of failure.Other techniques (XRD-TT; PPC-CT) represent long steps forward when it comes to understanding the related topics of the collagen fibril structures and the orientation of HA crystallites.

Knowledge gaps and future possibilities
A main thread in the preceding discussion is how biologically relevant static or dynamic structural information can be extracted from the opaque tissues of bone and cartilage.The large difference in optical properties between bone and cartilage (both for visual light and x-rays) makes it challenging to study their shared interface.We have demonstrated that with μCT, the different contrast mechanisms (attenuation, phase, scattering/diffraction) all yield complementary information.Notably, scattering-based CT provides sub-resolution orientational information, which we believe will prove highly useful to infer both growth mechanisms and mechanical properties.A key ambition for the future will be to further develop these techniques to get a resolution well below the micron scale, while also making the acquisitions faster.Even though light-based microscopy techniques have developed dramatically in recent years, there is still much to desire.3D microscopy techniques are arguably in their infancy, as are the various upcoming techniques for looking through opaque media (Zhu et al 2022).With continued improvements in optics, detectors and algorithms, the discussed new techniques like FPM, possibly combined with digital staining (Rivenson et al 2019), will be able to see the capillaries, venules, and perivascular cells with better contrast, better resolution and hence more details (Jiang et al 2023).
In the future, the microscopy techniques discussed here are likely to help resolving the biologically crucial question of whether the tissue was in a healthy, living, sick or dead state at the time of dissection.Albeit not pursued in this article, including spectroscopic information by energy sensitive methods is an obvious extension of computational imaging.For example, IR or Raman scattering yield spectroscopic molecular 'fingerprints' in the optical regime, and energy-sensitive detectors for x-rays are expected to be increasingly used for chemical contrast in the coming years.Along the path of biomechanics, a combination of the techniques discussed here will allow time resolved dynamics of bone, cartilage, and vessels inside cartilage canals to be tracked simultaneously.Capturing the real-time dynamical response of cartilage to mechanical stimuli will become feasible.Albeit considered here mainly from a materials science perspective, many of these developments are expected to also find their way into clinical practice, as currently being demonstrated for x-ray Talbot imaging (Willer et al 2021).

Conclusions
In this study, we have imaged samples of growth cartilage and subchondral bone from a young piglet using both established HES staining protocols and a series of novel advanced optical microscopy and x-ray techniques, grossly sharing the fact that they can be considered computational imaging techniques.We have compared how the various structures in cartilage appear when using the different techniques, highlighting where appropriate techniques must be selected for specific purposes.We have demonstrated Fourier ptychographic microscopy as applied to cartilage, with amplitude and phase maps numerically reconstructed over a large FoV using a comparatively inexpensive home-built microscopy setup.The close connection between the quantitative phase map and the scattering properties has been exploited to obtain maps of the scattering coefficients.Comparisons to multi-photon microscopy techniques have been presented.X-ray μCT techniques provide complementary information to the visual-light techniques, notably higher resolution and the interior structures of opaque objects.Attenuation-contrast CT is particularly useful for studies of the mineralized bone phase.Phase-contrast CT additionally allows the chondrocyte morphology and the structure of cartilage canals to be mapped in 3D without applying clearing and/or staining protocols.With XRD-CT and XRD-TT, mineral contrast and the orientation of sub-resolution structures can be retrieved in 3D, holding great promise for future investigations of bone growth mechanisms and a deeper understanding of the mechanical properties.Finally, we discussed the prospects of computational imaging, specifically targeting bone and cartilage interfaces as a key biological system of high scientific, but also medical and even socio-economic importance.

Materials and methods
Bone and cartilage samples were cut from the medial femoral condyle from two Landrace pigs, both approximately 80-day old.Cubed sections of approximate dimensions 3 × 3 × 3 mm 3 , were extracted from the condyles with a surgical blade and a saw.A total of three different bulk samples were used; Sample I for attenuation-contrast and PPC-CT, multimodal optical microscopy and histology, Sample II for diffraction-contrast CT, and Sample III for PPC-CT, where the arterioles were barium sulphate perfused.All samples were fixed in formaldehyde and stored on a 70 wt.%ethanol and 30 wt.% water solution.From Sample I, thin sections were decalcified with ethylenediaminetetraacetic acid (EDTA) using established protocols and sectioned with a microtome.Multiple adjacent 4 micrometre thin sections were cut, and one of these were stained with hematoxylin eosin and saffron (HES) by established protocols.
Bright-field and Zernike phase-contrast microscopy was performed on an unstained slide by using a Zeiss AXIO Observer Z1 microscope equipped with a, a Zeiss 10x (NA = 0.3) Plan-Neofluar objective lens and a Hamamatsu C11440-22CU camera.The histology HES slide was measured with bright field microscopy with a VS120 Virtual Slide Microscope (Olympus).An Olympus UPSLSAPO apochromat 20x objective with a NA of 0.75 was used.The exposure time was 2.9 ms.An Olympus VC50 camera was used.By translating the stage, total FoV of 4.0 mm × 6.8 mm was covered with 11641 × 19615 pixels, corresponding to a pixel size of 345 nm.
Second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) were done using a Leica TCS SP8 confocal microscope.A Chameleon Vision S mode-locked Ti:Sapphire femtosecond laser was used for excitation at a wavelength of 890 nm.The SHG signal was collected with a 445 ± 10 nm bandpass filter (from Semrock TM ).For TPEF collection, a filter with a passband of 525 ± 25 nm (Semrock TM ) was used.
Quantitative phase microscopy was done with a custom-built Fourier ptychographic microscopy (FPM) setup.The illumination consisted of a 32 × 32 light emitting diode (LED) array (Sparkfun, product #14646).Edmund optics infinity corrected long working distance objectives with magnifications 2x (NA 0.055), 10x (NA 0.28), and 50x (NA 0.55) were used.Transmission images were recorded using a Hamamatsu C11440-42U30 camera with 2048 × 2048 square pixels of size 6.5 μm and the sensor size (13.3 mm) 2 .Transmission images were recorded for 21 × 21 LEDs (with a 2x microscope objective) and 17 × 17 LEDs (with 10x) with a centre wavelength of 520 nm (green).Synchrotron propagation-based phase-contrast CT (PPC-CT), X-ray diffraction computed tomography (XRD-CT) and tensor tomography (XRD-TT) were done at the beamline ID15A (Vaughan et al 2020) at the European synchrotron radiation facility (ESRF), Grenoble, France.A monochromatic collimated beam of energy 50.00 keV was used.For PPC-CT, full-field illumination was applied with beam dimensions of 7.6 × 3.5 mm 2 .2001 projections were recorded evenly distributed over 180°.3D tomograms were reconstructed with custom Matlab TM macros.For XRD-CT and XRD-TT, a beam cross section of approximately 50 × 50 μm 2 was used.Orientational images were numerically reconstructed using in-house developed Matlab TM macros and the small-angle scattering tensor tomography (SASTT) package (Liebi et al 2015) developed by the coherent x-ray scattering (CXS) group at the Paul Scherrer Institute, Villigen, Switzerland.For further details of the experimental setup and the reconstruction procedure, see Mürer et al (Mürer et al 2021a).

Figure 1 .
Figure 1.Histological image of growth cartilage.(a) Immature articular cartilage with no blood supply is seen at the ~0.2 mm layer closest to the surface.I: Resting zone RZ, containing ovoid chondrocytes separated by extensive matrix.II: Proliferative zone PZ, with flattened, ovoid cells close together, in pairs or fours, in same lacuna or short stacks.III: Hypertrophic zone HZ, with cells increasing in size, being 2-3 times as large as in the resting zone, often assuming a triangular or cuboid shape.IV: Mineralized zone MZ, similar to HZ, except that the matrix septae stain intensely basophilic for calcium mineral.c.c.: Cartilage canals.(b) Close up of the region marked with a rectangle in (a), showing mainly a patent cartilage canal, being open with normal blood flow.RBC: red blood cells/ erythrocytes, which are eosinophilic.WBC: white blood cells.PMCs: Perivascular mesenchymal cells; large, pale, undifferentiated cells that can differentiate into fibroblasts, chondrocytes and contribute to growth.PMCs are found inside the canal, between the blood vessels.A: Arteriole, having a small lumen with thick wall.V: Draining venule; a large, thin-walled lumen.
scanning x-ray microscopy technique(Fratzl et al  1996, Rinnerthaler et al 1999, Paris 2008, Deyhle et al  2011, Granlund et al 2014), capable of mapping out the spatial variations of the hierarchical microstructure of bone(Harding et al 1987, Stock et al 2008, Mürer et al 2018, Mürer et al 2021a) and cartilage(Mürer et al 2021a), by scanning the sample with a pencil beam and using the scattered or diffracted signal to reconstruct 3D images.Recall that owing to the short wavelength of x-rays of ∼1 Å, comparable to the interatomic spacing in condensed matter, x-ray diffraction gives atomic resolution (Als-Nielsen and McMorrow 2011).Consequently, while the imaging resolution for XRD-CT is typically in the tens of micrometre range, the signal used for the reconstruction can have its origin at much shorter length scales.In other words, using XRD-CT for crystalline materials, and, for non-crystalline samples small angle x-ray scattering (SAXS-CT), can give sample overviews based on an ensemble average of the underlying molecular structures (Pauw et al 2010, Jensen et al 2011, Mürer et al 2018, Chattopadhyay et al 2020, Mürer et al 2021a, 2021b).Adding further complexity to the analysis, with so-called tensor tomography (XRD-TT) also the locally averaged orientation of sub-resolution microstructures can be retrieved and studied in 3D (Liebi et al 2015, Schaff et al 2015, Skjønsfjell et al 2016, Grünewald et al 2020, Mürer et al 2021a).X-ray ptychography (Rodenburg and Faulkner 2004, Thibault et al 2008, Esmaeili et al 2013, Patil et al 2016), a technique mathematically closely related to FPM, yet quite different in terms of experimental layout, is an emerging technique which has already been used to study a wide range of materials, including biological materials like silk (Esmaeili et al 2013), bone (Dierolf et al 2010) and teeth (Zanette et al 2015).X-ray Fourier ptychographic microscopy, based on the same principles as optical-light FPM, has also recently been demonstrated (Wakonig et al 2019).
After performing μCT the sample was sectioned, and optical micrographs are shown in figure 1 and again in figure 2(b) to facilitate comparisons.A detailed HES BF micrograph of the chondrocyte cells and the surrounding extracellular matrix is shown in figure 2(b), where the colour variations of the yellowstained extracellular matrix close to the cartilage canal perimeter are likely caused by a non-homogeneous collagen concentration (Finnøy et al 2016).Optical micrographs in figures 2(c), (d) show BF and DF exposures of the cut unstained sample.A low numerical aperture (2x, NA 0.055) objective combined with a scientific-grade CMOS camera was used to capture the full section in a single exposure.Zoomed-in regions of the cartilage containing the cartilage canal are shown in figure 3, corresponding to the red dashed rectangle in figures 1 and 2. The cartilage canal boundary and the internal cells are visible in bright field microscopy.Expectedly, increased contrast for weakly attenuating regions of the specimen is achieved when employing Zernike phase contrast (ZPC), cf figure 3(b).The cells within the cartilage canals are weakly absorbing, and there is little contrast between the cells in the cartilage matrix and the surrounding matrix.Compared to the BF micrograph (figure 3(a)), the details of the chondrocyte and the highly scattering cells within the arterioles in the cartilage canals are more visible.Note, however, that also the ZPC images are qualitative, implying that the contrast cannot be converted into

Figure 2 .
Figure 2. Overview of the bone-cartilage (sample I).(a) Attenuation-contrast μCT cross-section of the sample, measured before cutting to produce the sections displayed in (b)-(d).Note the strong attenuation by the trabecular bone in the mineralized region of the sample, the comparatively featureless cartilage region, and the clear delineation by the ossification front.(b) Adjacent HES-stained cross-section, with bone and cartilage regions indicated.The rectangle outlines a region containing a vascular cartilage canal as found in growth cartilage, an issue that is extensively discussed in the text (see also figure 3).(c) BF exposure obtained using a 2x objective lens with NA = 0.055 and partially coherent illumination using a single LED placed on the optical axis.(d) Dark-field exposure obtained using a 2x, NA 0.055 objective and a single LED placed off the optical axis.
figures 4(d), (h).The maps of μ s ' in figures 4(e), (i) show that the cartilage canal circumference, red blood cells within the arterioles, and the walls surrounding the canals in the matrix are highly scattering.Differences in scattering between healthy and diseased tissue have previously been shown to be associated with the onset of tumours, related to the fact that fast-growing cancerous tissue has different optical properties from healthy tissue (Horstmeyer et al 2015).In figure 4(h) the RBCs stand out, and it is clear that they are inside intact lumina.Even though the fundamental image formation process is different between the (coherent) BF intensity and the FPM-phase images, it is instructive to compare their respective spatial resolution, cf figure5, where the signals have been normalized.While these curves are expected to be different, they are still sufficiently similar to each other that it becomes apparent that the iterative FPM algorithm based on a 10x (NA 0.28) objective yields resolution comparable to the 50x (NA 0.55) objective, suggesting that the resolution has been roughly doubled as a result of the FPM phase retrieval process.We note that the resolution in FPM is given by λ/NA synth , where NA synth = NA obj + NA illum , and λ is the LED photon wavelength(Zheng et al 2013).The subscripts synth, obj and illum stand for synthetic, objective and illumination, respectively.In the present case, having used a single on-axis LED for the 50x objective, the corresponding resolution is λ/NA obj .Note that with an optimally matched incoherent illumination, the resolution with the 50x objective would ideally have been improved to λ/ (2 NA obj ) (Goodman 2017).

Figure 3 .
Figure 3. Multimodal optical imaging of growth cartilage (sample I).The region shown corresponds approximately to the dashed rectangle indicated in figure 2. (a) Unstained BF microscopy, (b) Zernike phase contrast.(c) Composite nonlinear microscopy image, with SHG in red and TPEF in green.(d) Cross-section of x-ray PPC-CT tomogram.Note that all these images are qualitative, and with the unstained images, it is mainly possible to see the RBCs and to some extent whether they are within/outside intact luminal structures/vessels, but with HES, it is possible to see endothelial cells and perivascular mesenchymal cells, and if the cells are alive (nucleated) or dead.

Figure 4 .
Figure 4. Reconstructed high-resolution wide-FoV micrographs of cartilage images by Fourier ptychographic microscopy (sample I).(a)-(b) High-resolution amplitude-and phase-contrast images with a large FoV.(c)-(f) Magnified sections corresponding to the red box indicated in (a).Reconstructed amplitude (c), quantitative phase (d), and reduced scattering coefficient μ s ' (e), the latter displayed with a log intensity scale.(f) Conventional BF histology of an adjacent HES section for comparison.The bottom row contains zoomed-in views of the images in the row above.

Figure 5 .
Figure 5.Comparison between BF and FPM (sample I).(a) Reconstructed quantitative phase-contrast images of cartilage using a 10x, NA 0.28 objective.(b) BF image using a 50x, NA 0.55 objective for comparison.(c) Line plot corresponding to the colored lines in (a)-(c) in normalized units directly comparing the phase and intensity signals.Scalebar: 50 μm.

'
XRD-TT', cf figure 7. The HA mineral provides stiffness to the collagen fibrils (Stock 2015), and is deposited onto the collagen matrix close to the bonecartilage interface during growth of the individual (Ytrehus et al 2007).HA crystallites are oriented with the crystallographic c-axis tending to be parallel to the collagen fibril length axis (Grünewald et al 2020), and the directional information contained in the x-ray diffraction signal can be used in combination with recent numerical reconstruction methods (Liebi et al 2015, Schaff et al 2015, Skjønsfjell et al 2016) to map the HA orientation non-destructively in 3D (Mürer et al 2018, Grünewald et al 2020, Mürer et al 2021a). Figure

Figure 6 .
Figure 6.3D visualization of cartilage canals and bone mineral orientation through phase-and diffraction-contrast CT (sample III).(a) 3D structure of cartilage canals close to the mineralized bone surface (black).The cartilage canal circumference is shown in yellow, and arterioles containing BaSO 4 are shown in green.(b) Same cartilage channel as shown in (a), but in a different orientation.The limitations of the Ba perfusion are clearly seen, as the arterioles apparently are discontinued, and the other structures (venules, wall, capillaries, PMCs) within the canals are not visualized.
al 2013, Zheng et al 2021, Jiang et al 2023) and user-friendly software (Tian and Waller 2015).A pedagogical and detailed description of the use of FPM to study kidney tissue has recently been published (Valentino et al 2023).Submicron-scale quantitative refractive index measurements of rat brain tissue (Lee et al 2023) is another recent example of biological research based on related techniques.Conventional μCT has effectively become a workhorse for materials characterization and limited training is needed to obtain good quality images, aided by the proprietary software typically supplied by these instruments.Still, to get high-quality μCT results fully exploiting the potential of the instrument does of course require substantial effort and a good understanding of the underlying physics.

Figure 7 .
Figure 7. X-ray tensor tomography cross sections showing hydroxyapatite bone mineral orientation (sample II).The dominant local crystallographic hydroxyapatite c-axis orientation is illustrated by the oriented ellipsoids, superposed on three adjacent PPC-CT grayscale images.The diffraction signal disappears in regions containing a cartilage canal protruding into the bone.The color coding corresponds to the Hermans' parameter S, which is a measure of the local degree of orientation, with 0 denoting isotropy and +1 full co-alignment.The inset gives a perspective view of the intact cylinder-shaped sample with the bone-cartilage interface, and the purple arrows indicate a cartilage canal protruding from the bone into the cartilage.The distance between the planes is approximately 64 μm; the voxel size of the underlying PPC-CT data is 3.2 μm, and for the XRD-TT 50 μm.
FPM reconstruction was done with Matlab TM (MathWorks Inc.) using published algorithms (Zheng et al 2013, Ou et al 2014, Konda et al 2020, Aidukas et al 2022, Hasanzade et al 2022).Smaller patches (256 × 256 pixels) were reconstructed individually to ensure sufficient source coherence for each patch, and thereafter stitched together.X-ray attenuation-based μCT was done using a Nikon XT H 225 ST home-laboratory setup.An acceleration voltage of 80 kV and a tube current of 180 μA wereused in with a molybdenum source.No beam condition filter was used.Projection images with 2000 × 2000 pixels were collected on a PerkinElmer (Waltham, USA) 1620 CN CS detector.Projections in cone-beam geometry were recorded with 760 sample rotation angles evenly distributed over 360°.
The invention of attenuation-contrast CT opened for 3D morphologies to be studied nondestructively, earning Hounsfield and Cormack the 1979 Nobel Prize for Physiology or Medicine.With this imaging technique, the contrast is formed by the x-ray beam being attenuated upon propagating through the sample.During the last two decades, the resolution of x-ray CT has reached the sub-micrometre range, making micro-CT (μCT) a highly relevant tool for materials science, still including bone (Kim and Henkin 2015).At lower photon energies the attenuation is predominantly governed by photoelectric absorption, which scales with the atomic number Z to the 3rd-4th power(Heismann et al 2003).In medicine and biology μCT is thus highly sensitive to the Ca-rich (Z = 20) minerals.As opposed to bone, cartilage is much less studied with x-rays because the comparatively low attenuation associated with unmi- (Olstad et al 2008b) imaging has been an immensely important tool to study bone, both in clinical and research settings, since immediately after Prof. Röntgen's discovery in 1895.neralizedbiologicaltissues gives a weak signal (Horng et al 2014), often requiring staining (Descamps et al 2020).For soft tissue, the attenuation starts to be dominated by Compton scattering already from about ∼60 keV.Attenuation-based μCT is also used to study the structure of arteries within cartilage canals, including how they traverse through the ossification front, and these studies are typically performed by perfusion of the arteries using for example barium sulphate solution to enhance contrast(Olstad et al 2008b).We also refer the reader to Kerckhofs et al (Kerckhofs et al 2018, Davis et al 2024), who specifically discuss the CT study of staining agents for cartilage-bone interfaces.