REVIEW

3D X-ray ultra-microscopy of bone tissue

M. Langer1,2 & F. Peyrin1,2

Received: 30 September 2014 /Accepted: 22 July 2015 /Published online: 14 September 2015# International Osteoporosis Foundation and National Osteoporosis Foundation 2015

Abstract We review the current X-ray techniques with 3Dimaging capability at the nano-scale: transmission X-ray mi-croscopy, ptychography and in-line phase nano-tomography.We further review the different ultra-structural features thathave so far been resolved: the lacuno-canalicular network,collagen orientation, nano-scale mineralization and their useas basis for mechanical simulations. X-ray computed tomog-raphy at the micro-metric scale is increasingly considered asthe reference technique in imaging of bone micro-structure.The trend has been to push towards increasingly higher reso-lution. Due to the difficulty of realizing optics in the hard X-ray regime, the magnification has mainly been due to the useof visible light optics and indirect detection of the X-rays,which limits the attainable resolution with respect to the wave-length of the visible light used in detection. Recent develop-ments in X-ray optics and instrumentation have allowed toimplement several types of methods that achieve imaging thatis limited in resolution by the X-ray wavelength, thus enablingcomputed tomography at the nano-scale. We review here theX-ray techniques with 3D imaging capability at the nano-scale: transmission X-ray microscopy, ptychography and in-line phase nano-tomography. Further, we review the differentultra-structural features that have so far been resolved and theapplications that have been reported: imaging of the lacuno-canalicular network, direct analysis of collagen orientation,analysis of mineralization on the nano-scale and use of 3Dimages at the nano-scale to drive mechanical simulations.

Finally, we discuss the issue of going beyond qualitative de-scription to quantification of ultra-structural features.

Keywords 3DX-ray ultra-microscopy . Bone .

Lacuno-canalicular network

Introduction

X-ray imaging is a classic method for bone imaging. Actually,the first application of imaging with X-rays was imaging ofbone on the organ level [1]. X-ray computed tomography(CT) [2, 3], that is cross-sectional imaging, at the micron scalehas progressively become the reference method for bonemicro-structure imaging among other applications [4]. Thisis due to the relatively recent high availability of compactmicro-CT (μCT) systems [5–7]. μCT seems to be the idealmethod to image bone micro-structure thanks to the high pen-etrating power in conjunction with good contrast in bone.Coupled to a monochromatic source, such as a synchrotronsource, the resulting synchrotron radiation μCT (SR-μCT) [8]can be used for functional imaging—direct 3D quantificationof the degree of mineralisation of bone (DMB) at the micro-scale [9]. By functional imaging, we mean here the ability toquantify a marker of activity, for example the concentration ofa given element that accumulates in an organ. In SR-μCT, wecan directly measure the concentration of mineral, and bylongitudinal studies, its evolution in time. It is also possibleto image certain markers, such as nano-particles ingested bymacrophages [10]. While μCT techniques are restricted toex vivo imaging for humans, new generations of systemscalled high-resolution peripheral quantitative CT (HR-pQCT) permit to image bone micro-structure at the tibia andradius in vivo [11, 12].

* M. Langermax.langer@esrf.fr

1 Université de Lyon, CREATIS; CNRS UMR5220; Inserm U1044;INSA-Lyon; Université Lyon 1, Lyon, France

2 ESRF – The European Synchrotron, Grenoble, France

Osteoporos Int (2016) 27:441–455DOI 10.1007/s00198-015-3257-0

Imaging is a fundamental tool in osteoporosis and bone-related research. The mechanisms involved in bone loss andfailure are still not fully elucidated. Although bone mass is animportant determinant of bone strength, it is known not to bethe sole factor. Bone fragility is hypothesized to be the resultof failed material or structural adaptations to mechanical stress[13]. Bone adapts to externally imposed mechanical stressesthrough the remodelling process. It is therefore expected thatthe bone will exhibit changes in its macro-, micro- and ultra-structure during its lifetime.

In this paper, we will particularly focus on imaging boneultra-structure at the scale of the osteocyte system, whichplays a major role in bone mecanotransduction. Osteocytes,which are the most abundant bone cells, reside embedded inthe bone tissue and are differentiated from osteoblasts—thebone forming cells—trapped in the pre-bone matrix duringbone formation. They communicate with each other throughdendritic processes [14–17]. The hollow imprint left in thebone matrix by the osteocytes, the lacunae, and their process-es, the canaliculi, is called the lacuno-canalicular network(LCN) [18]. Osteocytes are thought to be the mechanosensingcells that are responsible for initiating the bone remodellingprocess. Strain could be sensed by interstitial fluid flows cir-culating in the LCN, which are hypothesized to stimulate theosteocytes. Micro-cracks could also be responsible for osteo-cyte stimulation, by interrupting osteocyte processes, andtherefore participate in the transduction to trigger remodellingprocess [19, 20]. There has been an increasing interest instudying the LCN and the osteocytes in the last few years[21–25]. In addition to their presumed role in the initiationof bone remodelling, they have a role in maintaining mineralhomeostasis. They secrete a number of factors, among whichsome are seen as potential therapeutic targets [26].

Apart from the LCN, there is the bone matrix itself. At theultra-structural level, bone can be considered as a nano-composite constituted of mineralized collagen fibres. Thesefibres are organized in a regular fashion around the vessel,or Haversian, canals in units of bone remodelling calledosteons. Between the osteons and remaining older tissue,called interstitial tissue, there is a layer of tissue called thecement line. The cement line is thought to have an importantrole in limiting damage propagation and the overall stiffnessof bone [27–29]. The cement line has previously been char-acterized mainly using quantitative backscatter electron imag-ing (qBEI). It has been disputed whether the cement line ishypomineralized [27, 29] or hypermineralized [30, 31].Collagen fibril orientation analysis has so far been performedin 2D using scanning electron microscopy [32, 33], transmis-sion electron microscopy [34] and atomic force microscopy[35] or indirectly analysed by polarized light microscopy [36]and Raman spectral mapping [37]. Very little 3D data is avail-able on the fine structure of the LCN and the bone matrix onthe nano-scale.

The trend in μCT and other X-ray microscopy techniqueshas been to go towards increasingly higher resolution [38].The properties are clearly tantalising: short wavelength (so alower diffraction limit than with visible light) combined withhigh penetration power yielding good contrast in bone. Thehigh penetration power makes X-rays difficult to focus, how-ever, which has kept the magnification factor available fromthe X-rays fairly low. High-resolution imaging has rather beenachieved by indirect detection: a fluorescent screen, a scintil-lator, with a high efficiency in converting X-rays to visiblelight, imaged by standard visible light microscope optics ontoa CCD camera [39]. This, then, yields a resolution that isdiffraction-limited by the wavelength of the visible light emit-ted by the scintillator, magnified by the microscope and de-tected by the CCD. In the proper sense, we can therefore nottalk about imaging of ultra-structure, since this implies imag-ing at resolutions higher than those achievable with a standardbright field visible light microscope operating in transmissionmode.

Micro-computed tomography has been used extensively tostudy bone tissuemicro-structure. Recently, attention has beengiven to the study of the LCN using μCT [40–46], where thediameter of the canaliculi goes down to ~100 nm. Based onthe standard implementation ofμCT given above,μCTcannotby definition be used to image ultra-structure. This is becausethe resolution is diffraction-limited by the visible light micro-scope used to image the scintillating screen.

Ultra-microscopy using X-ray optics has been achievedfairly recently [47]. The main obstacle has been thatmanufacturing of X-ray optics is challenging. The attractionof high-resolution X-ray imaging is the combination of highpenetration power even of hard tissue, the ability to do true 3Dimaging via tomography, and the short wavelength relative tovisible light, hence promising the possibility to image ultra-structure in 3D. Recently, several methods to achieve this havebeen presented.

So far, the options for performing ultra-microscopy imag-ing of bone tissue in 3D have been transmission electron mi-croscopy (TEM), scanning electron microscopy (SEM) andconfocal laser scanning microscopy (CLSM). CLSM offers3D imaging of bone ultra-structure, but the depth of penetra-tion in mineralised tissue is limited, around 60 μm in practice[48]. Further, the spatial resolution is anisotropic: It varieswith the depth of the focus in the sample. Moreover, it is ascanning technique, which implies that data acquisition is rel-atively slow. Finally, the use of advanced staining and samplepreparation is necessary [49]. Serial sectioning using a fo-cused ion beam followed by imaging with scanning electronmicroscopy (FIB/SEM) to image the lacuno-canalicular net-work has been reported [50], which offers excellent spatialresolution. This is a destructive technique, however, whichrequires advanced sample preparation. The repeated section-ing and imaging also yields relatively long acquisition times.

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Finally, electron tomography has been used to image osteo-cyte ultra-structure in situ [51]. This kind of imaging is limitedto very thin sections (3 μm in the cited work). Thus, the 3Dinformation is actually quite limited and only yields a verylocal visualisation of the osteocyte.

In contrast, X-rays have high penetration power, requirelittle to no sample preparation, are non-destructive and pro-vide isotropic 3D imaging. While X-ray imaging has exten-sively been used in the last decade to image bone micro-struc-ture, the developments of new methods to image bone at thecellular scale is emerging. We review here the methods andfindings that have so far been achieved in this domain.We firstgive a brief introduction to high-resolution X-ray imagingphysics. We then continue to describe the different imagingmethods that have been used for ultra-microscopy imaging inbone, along with the results that were obtained. We then out-line the type of analysis that has so far been possible at shorterlength scales than can be seen by visible light. Finally, webriefly discuss what we consider the next step of 3D ultra-structure imaging in bone: the possibility of in situ cell imag-ing in bone using X-ray phase nano-tomography.

X-ray imaging methods

We outline here the imaging methods that have so far beenused to image bone ultra-structure at spatial resolution betterthan ~400 nm and the results that were obtained. To this aim,advancedX-ray microscopymethods have to be used, where asignificant part of the magnification is done on the X-ray side.This is not straightforward, however. The very small deviationfrom unity of the refractive index for X-rays makes it difficultto implement X-ray optics. The methods are surprisingly het-erogeneous in their implementation, relying on attenuationand far-field and near-field diffraction, respectively.

Transmission X-ray microscopy

One way of achieving magnification on the X-ray side is byimplementing a transmission X-ray microscope, directly anal-ogous to a standard visible light microscope. Due to the weakrefraction of X-rays in most practical materials, diffractiveoptics, Fresnel zone plates, can be used instead. Andrewset al. [52] reported on the implementation of a full-field trans-mission X-ray microscope (TXM) using either a rotating an-ode X-ray source or a synchrotron source for bone nano-im-aging. The sample was placed in the focus, on a translation-rotation stage to allow for tomographic imaging. A Fresnelzone plate was used as objective lens to re-focus the beamonto a scintillator-based high-resolution CCD detector with1024×1024 pixels of ~2 μm. The X-ray energy used was inthe range of 4–14 keV. A theoretical resolution limit of~35 nm, and an experimentally achieved resolution of

~50 nm in the projections were reported. With an exposuretimes of 2 s, the total acquisition time for one tomographicscan (~1500 projections) was slightly less than 1 h [53].

Imaging of the LCN was reported using this setup. Part ofone lacuna and its environing canaliculi were imaged in tra-becular bone. For imaging, a trabecular sample was removedfrom a mouse proximal tibia by cutting away the cortical boneusing a microtome, followed by washing with a saline jet toremove marrow. The dry sample was attached to a steel can-nula tip with epoxy. The resulting single trabecula sample wasless than 50 μm thick, approximately the depth of focus of theTXM. Heavy element staining was done with 1 % uranylacetate for 12 h. The images show that the lacuna and cana-liculi well resolved, albeit with fairly weak contrast (Fig. 1).Looking at a volume rendering, the lacuna and its canaliculiare clearly visible. The canaliculi show a surprising rate ofbranching, however, compared to the two other techniquesreported here.

With TXM, the attenuation of the sample is measured, i.e.the same as in standard X-ray μCT. This technique canachieve high spatial resolution without the need for advancedimage reconstruction apart from tomographic reconstruction,such as phase retrieval. The disadvantages seem to be the quitesmall sample size possible, limited by the depth of field, ap-proximately 50μm. The technique also operates in a relativelylow energy range, thereby limiting the thickness of the sam-ples and increasing the X-ray dose absorbed in the sample,and thus the risk of radiation damage.

Ptychographic tomography

Another way to achieve high-resolution imaging with X-raysis to exploit diffraction rather than transmission. This requiresa small spot illumination, either by the use of a pinhole or X-ray focusing optics. A far-field, or Fraunhofer, diffraction pat-tern is then recorded downstream of the object. An imagerecorded like this corresponds to the squared modulus of theFourier transform of the imaged object convolved with theFourier transform of the incident beam. It is in certain casespossible to reconstruct the object transmission function by theuse of adapted phase retrieval algorithms [54–57]. This kindof imaging is usually known as coherent diffraction imaging(CDI) [58, 59]. A very high resolution can be achieved withCDI. Since the recorded image is in the frequency domain, theattainable resolution is limited by how far from the centre ofthe detector signal can be measured. In practice, this meansthat the resolution limit is related to the signal-to-noise ratio inthe recorded diffractograms. This kind of imaging is limited toimaging of isolated particles with a support smaller than theused X-ray beam, however, such as isolated nano-particles[60] or single cells [61].

The small support requirement can be obviated by scanningthe probe across an extended sample while letting the probe

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position overlap at each image position (in practice, the sam-ple is scanned through the beam). By using an iterative recon-struction scheme, a complete phase projection can be recon-structed [62–64]. This is known as ptychographic imaging[65].

Since the phase shift introduced by the object in the X-ray beam can be considered as a straight-line projection, ifwe have access to the phase shift, we can use it to recon-struct the 3D refractive index decrement distribution inthe sample, in analogy to the classical attenuation case.What is particularly attractive with this is that for hard X-rays, the refractive index decrement is proportional to thelocal mass density in the sample [66]. This means that, forexample, the use of X-ray phase tomography images todrive mechanical simulations avoids the need to infer themass density from measurements of the degree ofmineralisation in bone (DMB), which has to be done ifdensity is to be related to the attenuation index [9]. Inpractice, phase tomography is implemented by a two-step process: First, the phase is retrieved at each projec-tion angle and then the refractive index decrement is re-constructed by feeding the resulting phase maps into a

tomographic reconstruction algorithm such as filteredback-projection (FBP) [67–69].

Ptychographic tomography has been used to image boneultra-structure [70]. A human cortical bone sample cut to anapproximately cylindrical shape was imaged using a 2.3-μmpinhole (Fig. 2a). The sample was scanned through theresulting pencil beam so that the X-ray spots lie on concentriccircles, covering a rectangular area of 40μm×32μm (Fig. 2b)for a total of 704 diffraction patterns per projection. In total,180 such projections were recorded over a 180° turn of thesample.

Figure 2c, d shows virtual sections through the reconstruct-ed electron density. The bright shell on the surface of thesample is due to the sample preparation; the sample was cutusing a focused ion beam, which deposits a residue of heavyions on the surface (in this case Gallium ions). We can easilysee the lacunae and the canaliculi. Note that the reported elec-tron densities are truly quantitative due to the sample beingcompletely covered by the projections. 3D renderings(Fig. 2e, f) show that the imaged volume contains three partiallacunae. The canaliculi are fairly well resolved, but some spu-rious structures remain.

a

cb

d

5 µm

2 µm

2 µm

Fig. 1 Transmission X-ray mi-croscopy (TXM). a Schematic ofthe experimental setup. b Volumerendering of an osteocyte lacunain an isolated murine trabecula. c,d Virtual cuts through the recon-structed volume showing thecontrast between bone, the lacunaand the canaliculi. Images fromAndrews et al. [52] with permis-sion from Cambridge UniversityPress

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The major strength of ptychographic tomography is that itis capable of attaining very high resolutions without the use ofX-ray optics. In energy ranges probably too low to be practicalfor bone imaging (~6 keV), isotropic 3D resolutions up to16 nm have been reported [71]. A major drawback ofptychographic tomography is its scanning nature. This makesthe acquisition time for a single projection relatively long; inpractice, it limits the number of projections that can be ac-quired, and the field of view that can be covered. In the workof Dierolf et al. [70], only 180 angular positions were ac-quired, normally far too few to achieve correct angular reso-lution, and a relatively small sample was imaged, comprisingonly parts of three lacunae. The duration of the complete ac-quisition was reported to be ~40 h. Another disadvantage,shared with the in-line phase imaging below, is that recon-struction is not always straightforward. Considerable expertise

seems to be needed to perform correct reconstructions. Thesetwo drawbacks taken together seem to limit the applicabilityof ptychographic tomography for quantitative studies.Additionally, ptychography can only reconstruct phase shiftsin the range [0 to 2π]. This means that if the true phase shift islarger than 2π, the reconstruction has to be unwrapped, whichis a problem in itself [72].

In-line phase nano-tomography

A related phase imaging technique that can achieve very highresolution but based on a different experimental setup is in-line phase nano-tomography. It exploits image magnificationwhen the sample is placed after the focus of X-ray focusingoptics, effectively creating a projection microscopy setup.Such an instrument has been implemented by using

d

e f

a b

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5 µm 5 µm

Fig. 2 Ptychographic X-ray to-mography. a Schematic of theexperimental setup. b Illustrationof the scanning pattern of the X-ray spot over the sample to formone projection. c, d Virtual cutsthrough the reconstructed volumeshowing very good contrast be-tween bone and the lacuno-canalicular network (LCN). Thebright shell consists of Galliumions deposited by the focused ionbeam cutting of the sample. eVolume rendering of the completeimaged volume. Three lacunaecan be partially seen and a fairamount of the canaliculi seemwell resolved. f Zoom on one la-cuna and its canaliculi. A fairamount of spurious porosity re-mains. The boxes in (c) and (d)represent areas where histogramswere measured in the originalpublication (not presented here).Images from Dierolf et al. [70]with permission from the NaturePublishing Group

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Kirpatrick-Baez (reflective) optics [73]. As before, the sampleis placed on a translation/rotation stage to enable tomographicimaging, and the camera is mounted on a translation stage.This permits setting the geometrical magnification, which is afunction of the beam divergence after the focus, the focus-to-sample distance, and the focus-to-detector distance. Lettingthe beam propagate after interaction with the object createsnot only a magnification effect but, since the beam used hasa high degree of coherence, also strong phase contrast. Thiscontrast can be used to reconstruct the phase shift in the object.One particularity, however, is that the recorded images willlack information at certain spatial frequencies, due to the prop-erties of the Fresnel propagation transfer function. This makesit necessary to acquire several (at least two) images per pro-jection angle, corresponding to different sample-to-detectordistances. Since imaging of bone samples will always intro-duce a considerable attenuation effect, both attenuation andphase contrast will be present in the recorded images. Thisimposes, in any case, a minimum of two images per projectionangle if introduction of strong assumptions on the imagedobjects in the reconstruction is to be avoided.

As in the ptychographic tomography case, the phasecan be retrieved at each projection angle using adaptedalgorithms. Several algorithms for phase retrieval fromFresnel diffraction patterns have been developed, mostof them relying on linearisations of the contrast modelto achieve efficient solutions [67, 68, 74–77]. In thehigh-resolution case, the non-linear contributions will benon-negligible, however. This makes it necessary to applya non-linear optimisation-based refinement to achieve cor-rect spatial resolutions [78–81].

In-line phase tomography has also been used to image sev-eral ultra-structural features in bone. As shown in the volumerendering (Fig. 3f), the LCN can be imaged over a relativelylarge field of view. The LCN also seems resolved in unprec-edented detail and discrimination (compare for example therendering of the LCN in (Fig. 3g) to that obtained withPtychographic tomography in Fig 2f). One interesting thingto note in the reconstructed tomographic slices (Fig. 3c–e) isthe very strong textured appearance of the bone matrix (cf.Fig. 2c, d). Readers familiar with qBEI [32] and TEM[34] images of bone will recognize the arching structuredue to the oblique cutting of the mineralised collagen fi-brils. This means that the collagen fibre orientation can bestudied directly in 3D using texture analysis, as we will seebelow. This ability should open completely new possibili-ties for studying bone fragility and understanding the me-chanical properties of bone. We can also see that the ce-ment lines are visible in striking contrast. Here, the greylevel corresponds to the mass density of the different tis-sues relative to the background. Through this, we can seethat the cement line has a significantly higher mass densitythan the surrounding osteonal and interstitial tissue.

In-line phase tomography seems to possess several ad-vantages that make it particularly attractive for bone imag-ing. Since it is a full-field imaging technique, it is relativelyfast with respect to the image acquisition. Acquisitiontimes of ~4 h per sample has been reported [78], using fullsets of projections (i.e. 3000 projections using a 2048-element wide detector). This makes quantitative study withthis technique fully feasible. Further, due to the full-fieldnature, relatively large fields of views can be covered. InFig. 3f, we can see that more than 10 osteocyte lacunae arevisible in the reconstructed volume.

The in-line technique shares one disadvantage withptychographic tomography, however: Image reconstructionis currently not straightforward. It relies on advanced recon-struction algorithms that often require assumptions or priorknowledge on the object and considerable expertise to oper-ate. A disadvantage compared to ptychography, at least for themoment, is the achievable spatial resolution. While no precisemeasurement has been made, by inspection of the reconstruct-ed volumes, the true spatial resolution so far achieved seemsto lie in the range of 60–80 nm. Nevertheless, probably due tothe combination of relatively fast acquisitions and reconstruc-tions, and superb contrast in the tissue, in-line phase nano-tomography is so far the only technique that has generatedany follow-up studies on bone at the ultra-structural scale.

Ultra-structure with phase nano-tomography

Recently, in-line phase nano-tomography has been used tostudy certain aspects of the ultra-structure in detail. We sum-marise here these works and their results, on the LCN [78], onnano-scale mineralisation and its relationship to the LCN [82],analysis of the collagen fibril orientation [83], and finally theuse of the nano-mineralisation data to drive mechanical sim-ulation on the cellular length scale [84].

Lacuno-canalicular network

The in-line technique has allowed study of the LCN in un-precedented detail in 3D. In Fig. 4a, the LCN porosity isrendered with a grey-level tomographic slice as backgroundto show the LCN in relation to the cement line (brighter struc-ture running through roughly the centre of the slice). Theporosity is rendered so that colour corresponds to connectedcomponents. We can see that on one side of the cement line,the network is well connected, whereas on the other, hardlyany canaliculi remain and the lacunae are thus completely de-connected.

Zooming on one lacuna close to the cement wall (Fig. 3g),we can see several interesting details of the lacunar and can-alicular morphology. The lacuna has a flattened drop shape,with its tip pointing downwards along the main axis of the

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femur. The canaliculi exhibit multiple branchings (or multipleinterconnections) at several different distances from the lacu-na. Most canaliculi run perpendicular or in parallel to thecement line; most of the ones that start out in that directionmake a sharp turn to continue to approximately parallel to it.There are, however, some canaliculi that attach to or barelytraverse the cement line.

Comparing the renderings from ptychographic tomography(Fig. 2e, f) and in-line phase tomography (Fig. 3f, g), we canclearly see the larger field of view covered by the in-linetechnique (17 lacunae entirely or partly imaged) compared

to the ptychographic one (3 lacunae partly imaged). The con-trast also seems rather higher in the in-line technique; therendered lacuna in Fig. 3g is much cleaner than the one ren-dered in Fig. 2f, where also some of the background noise isrendered as porosity.

Finally, a drawback compared to the in-line technique (seebelow) is that ptychographic tomography seems less sensitiveto density variations. If we compare the virtual slices in Figs. 2and 3, the bone matrix appears much more homogeneous inthe ptychographic tomography case, whereas in the in-linephase tomography images, several structures due to density

c d e

f g

a b Fig. 3 In-line phase tomography.a Schematic of the experimentalsetup. b Schematic of the phaseretrieval process. c–e Virtual cutsthrough the reconstructedvolume. Note the high contrastbetween the LCN and the bonematrix, and also the strongcontrast in the matrix presumablydue to oblique cutting of themineralised collagen fibres, aswell as the well-resolved cementline. f Volume rendering of allLCN porosity in the sampleshowing a relatively large numberof lacunae. g Zoom on one lacunaand its canaliculi (pink) and thecement line (green). The LCN isrendered in unprecedented detail,and its relationship to the cementline can be studied. Images fromLanger et al. [78] (free for useunder the Creative Commons At-tribution Licence) (Colour figureonline)

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variations are visible: cement lines, mineralisation variationsin the peri-lacunar tissue, and texture due to the variation incollagen orientation. Despite this, ptychographic tomographyhas yielded unique and superbly detailed images on the LCNand seems to currently be the technique of choice if spatialresolution is the most important requirement.

Nano-scale mineralisation

As can be seen in Fig. 3c–e, there is quite strong contrastinside the matrix in the in-line PCT images, correspondingto variations in the local mass density. Hence, using phasenano-tomography, not only the porosities can be analysed.The spatial distribution of mass density in the peri-lacunarand peri-canalicular bone tissue was investigated usingsynchrotron radiation phase nano-CT with 50-nm voxelsize, in human jaw bone specimens originating from four

healthy donors and four treated with high-dosage bisphos-phonate (Fig. 4a). Lacunae and canaliculi were segmentedby applying a hysteresis method based on two thresholdlevels. Small features, considered to be noise, were re-moved using a morphological opening operation with ker-nel radius of two voxel and cleaning of islands smaller than0.2 μm3. The osteocyte lacuna was separated from the can-aliculi using morphological opening with 10 voxelsfollowed by a dilatation with 3 voxels (Fig. 4b). The dis-tance of the mineralized tissue to the LCN was quantifiedusing the distance transform with the Euclidean metric(Fig. 4c). The histogram and its cumulative distributionfunction (Fig. 4d) were used to approximate the thicknessof the peri-LCN mineralized tissue matrix layer. Fifty per-cent of the bone tissue is within about 1.2-μm distance tothe canaliculi, whereas only about 5 % of the bone tissuelies within this distance to the lacunae. Further, the authors

Fig. 4 Study of nano-mineralisation of the bone matrixand its relationship to the LCNusing in-line phase nano-tomog-raphy. a Virtual cut through onelacuna and its canaliculi. b Thelacuna (red) and canaliculi(green) are segmented separately.The inset shows a detail of abranching canaliculus. c Distancemap from each point in the matrixto the nearest pore. d Plot of therelative amount of bone tissue as afunction of the distance to cana-liculi and lacunae. eVariation plotof the mass density as a functionof the distance from lacunae and fcanaliculi. Images from Hesseet al. [82], with permission as co-author (Colour figure online)

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provided the first experimental evidence that mass densityin the direct vicinity of both lacunae and canaliculi is dif-ferent from the mean matrix mass density, resulting in gra-dients with respect to the distance from both pore-matrixinterfaces. The density gradient was more pronouncedaround the lacunae than around the canaliculi (Fig. 4e, f),which was explained by geometrical considerations in theLCN morphology. With tissue age, the average mass den-sity increases and the gradients disappear. The authors con-cluded that the observed mass density gradients are unlike-ly to be impacted by short-term exchanges occurring inmineral homeostasis.

Collagen orientation

Analysing further the density variations visible in Fig. 3c–e,we can see that the characteristic arcing pattern arising fromthe collagen texture is visible. This kind of structure has onlybeen seen on electron microscopy images previously, hence in2D. Here, this texture is present in 3D, however, and can beused to estimate the local collagen orientation in each point inthe reconstructed volume. Varga et al. [83] developed a pro-tocol based on image correlation to perform this orientationestimation. Sub-volumes co-oriented with the lamellar struc-ture were virtually cut at several places in the reconstructedvolume. The Fourier transform of the in-plane autocorrelationfunction was then calculated plane by plane roughlytransversally to the normal of the lamellae. The in-plane ori-entation was calculated by segmenting this Fourier transformand calculating main axis of the resulting spot. The orientationcan then be overlaid as bars on the gray-level images (Fig. 5a–g).

In lamellar bone, the collagen fibrils are assumed to have aplywood-like arrangement, but due to experimental limita-tions, the 3D fibril structure was only deduced from sectionsurfaces and the findings have been divergent. Synchrotronradiation X-ray phase nano-tomography (SR-PNT) gaveaccess to direct 3D information on the bone structure at thenano-scale. It was confirmed that the fibrils are unidirectionalin quasi-planes of sub-lamellae and that two specific dominat-ing patterns, oscillating and twisted plywood, coexist in asingle osteon. Both patterns exhibit smooth orientation chang-es between adjacent quasi-planes. Further, the periodic chang-es of collagen fibril orientation is independent of fluctuationsof local degree of mineralization.

As verification, the local orientation was used to simulatethe collagen structure using a rod model. In Fig. 5h, a virtuallycut block is shown, clearly showing the arcing structureresulting from the oscillating plywood structure. The orienta-tion is then showed along one line, so that the oscillation inorientation is clearly visible. Finally, a homogeneous block ofsuch bars is generated and subsequently virtually cut in the

same way as the grey-level volume. This reveals the samekind of arcing texture visible in the grey-level image.

Mechanical simulation

Finally, we report on the work of Varga et al. [84], where in-line phase tomography images were used as input to drivemechanical simulation on the cellular scale. Again, based onSR-PNT images (Fig. 6a), lacunae and canaliculi were seg-mented separately. They were then meshed using finite ele-ment modelling (FEM, Fig. 6b). Based on observations fromelectron microscopy [85, 86], an FEM model of the osteocyteand its processes was also generated (Fig. 6c). The completeFE model including the extracellular matrix is shown inFig. 6d. Results of the FEM simulations are shown inFig. 6e–g, in the ECM, in the peri-cellular matrix and in theosteocyte respectively. We can see that the shape of the cana-liculi, their branches and attachments to the lacuna effectivelyact as a strain amplifier: Red in the figures indicate a strainmagnification factor of at least 10.

In summary the authors demonstrated the potential of SR-PNT to provide unprecedented geometrical details of theLCN. FE models of osteocytes, including the detailed LCNgeometry, predicted that the externally applied deformationmay be amplified by a factor of up to 50–70, localized at thecell body–dendrite junctions, and that in 30–60 % of this celltissue volume, the strain is at least 10 times higher than the oneapplied externally. Other high strain concentrations werefound to occur along the dendrites. The predicted strain mag-nitudes were compatible with deformations reported to stim-ulate osteocytes in vitro.

Discussion and Conclusions

In this review, we have focused on state of the art X-ray im-aging techniques to analyse bone ultra-structure. The respec-tive strengths and weaknesses of the methods presented hereare summarised in Table 1. Ptychographic tomography is thetechnique that has permitted the highest resolution so far. Thiscomes at the cost of it being a scanning technique, meaningthat acquisition time is generally long since it depends on thefield of view that is covered. In terms of field of view, in-linephase tomography currently offers the largest, due to it being afull-field technique and not being limited in focal depth, un-like TXM. In-line phase tomography seems to also to be themost sensitive technique, based on the images presented here,followed by ptychographic imaging. However, the two tech-niques have never been compared so far on the same samples.Finally, TXM has the advantage of not requiring any otherdata processing for the reconstruction than standard tomogra-phy algorithms, compared to phase-based imaging techniquesuch as ptychography and in-line phase tomography. To

Osteoporos Int (2016) 27:441–455 449

compare to other non-X-ray imaging techniques, we have in-cluded CLSM and FIB/SEM. With the progress made in non-linear optical imaging and the possibility to exploit differentmode of contrasts, this technique, although limited by thepenetration of optical light into hard mineralize samples, hasa real potential to image large sections of bone samples (a fewsquare centimetres). FIB/SEM has also to be mentioned sinceit has the potential to reach the highest spatial resolution at thecost of being destructive and time consuming.

So far, in-line phase tomography is the only one of thetechniques presented here that has had follow-up studies onbone tissue, and none of the techniques have yet been used inquantitative studies. This is mainly due to all three techniquesbeing new techniques. All three techniques are also so farsynchrotron radiation techniques, which means that availabil-ity is low. This, coupled with them being relatively time-consuming techniques has also contributed to their limiteduse so far. Challenges include the need to acquire data fromsufficiently large volumes to be representative despite the highresolution. In ptychographic imaging, more scanning points

could be used, but this increases acquisition times. In TXMand SR-PCT, larger detectors could be used to increase thefield of view, at the cost of increased data size and processingtime. In the two-phase-based techniques, reconstruction algo-rithms need to be further developed and validated to make theimaging routine for all types of samples.

Another concern is the exploitation of the data provided bythese new techniques. Imaging at high resolution, in 3D andon sufficiently large fields of view generates complex andmassive data sets. They typically include the raw experimentaldata necessary to reconstruct the image plus the final 3D im-age itself. The size of the later is directly proportional to cubicpower of the field of view in one direction, which means forinstance 256 GB for a (4K) [3] image. The extraction of quan-titative parameters of bone ultra-structure is a new topic due tothe emerging nature of the imaging techniques. It generallyinvolves two steps, the segmentation of the structures of inter-est and the calculation of parameters. Generally, the segmen-tation of lacunae and canaliculi has been obtained bythresholding techniques (by simple thresholding [50, 70,

Fig. 5 Analysis of collagen orientation from SR-PNT images. a Virtualcut transversal to the lamella orientation. b–g Schematic of the textureanalysis protocol for the extraction of the local collagen orientation. hVirtual cut of the reconstructed volume to show the arching structure in an

oblique cut. i Bar representation of the local orientation through the blockin (h) along one line. j Simulated volume using a bar model to representthe oriented collagen fibres, cut like in (h). The arching structure is wellreproduced. Images from Varga et al. [83]

450 Osteoporos Int (2016) 27:441–455

98], or by region growing [42]). However, the problem ofsegmenting canaliculi is more challenging than that ofsegmenting lacunae due to the small size of these channels

and noise. To our knowledge, the only methods proposed sofar have been based on region growing after non-linear filter-ing [46, 99] and minimal paths [100].

Fig. 6 Mechanical simulation based on one lacuna and its canaliculi. aVirtual cutout of one lacuna from the reconstructed volume. b Lacuna andcanaliculi segmented separately. c The corresponding osteocyte and itsdendrites, inferred based on TEM images [85, 86]. d Complete FEM

model of the osteocyte, the LCN and the bone matrix. e Contour plot ofthe minimum principal strain in the bone matrix, f in the peri-cellularmatrix and g in the osteocyte. Images from Varga et al. [84] withpermission

Table 1 Summary of the described 3D imaging methods

Voxel size (nm) Pros Cons Features Ref

X-ray methods

SR-μCT 300×300×300 Limited spatial resolution,acquisition time

Lacunae, displayof canaliculi

[87, 88, 89]

TXM 30×30×30 [90]

Ptychography 65×65×65 Spatial resolution Acquisition time [91]

In-line phasenano-tomography

50×50×50 Full Field, sensitivity Sample geometry Lacunae, canaliculi,collagen texture,density

[92, 93, 94]

Other methods

CLSM 300×300×1500 Large areas, staining Penetration depth Lacunae, canaliculi [95]

FIB/SEM 10×10×10 Spatial resolution upto nm

Destructive,small FOV

Lacunae, canaliculi, [96, 97]

The methods discussed in this review are highlighted in grey

SR-μCTsynchrotron radiation micro-CT, TXMX-raymicroscope,CLSM confocal laser scanningmicroscopy, FIB/SEM focused ion beamwith scanningelectron microscopy

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Concerning the extraction of quantitative parameters at thelevel of lacunae, Carter et al. have studied lacunae density,volume and shape based on SR micro-CT images in humanfemoral bone [43, 44]. An automated image analysis methodto segment lacunae and extract 3D shape descriptors includinglacunae volume surface and lengths has been proposed andapplied to large population of cells in human femoral bone[41]. Another, more extended framework including tensorrepresentations was described with application to mice bone[101]. The calculation of the number of canaliculi associatedto each lacuna from SR-μCT images has been described[102]. It is clear that further works concerning image analysisand quantification have to be performed to take full advantageof the information within these new images at the nano-scale.

In summary, understanding the mechanisms occurring atthe cellular scale is a major concern today. X-ray nano-tomog-raphy shows great promise as a method to image bone ultra-structure quantitatively in 3D. Several implementations exist,using different contrast modes: attenuation in TXM-CT,Fraunhofer diffraction in ptychographic tomography, andFresnel diffraction in in-line phase tomography. For quantita-tive study, in-line phase tomography currently seems to be themethod of choice, as it offers high resolution (albeit currentlysomewhat lower than ptychographic tomography), a relativelylarge field of view, relatively fast acquisitions and somewhatsimpler data reconstruction. This is further supported by therecent works where in-line phase tomography has been usedto analyse nano-mineralisation and collagen orientation and asa basis for mechanical simulation. To be truly useful, the qual-itative observations, such as those reviewed here, must betranslated into quantifiable and meaningful parameters. Thisalso requires the development of post-processing steps to seg-ment the image and extract relevant information. This willconstitute an important work for the few years to come. It isthen expected that such techniques, coupled to complementa-ry physical means of investigations, will provide new insightsinto the function of osteocytes, the mineralisation of the ex-tracellular matrix and the organisation of collagen fibres andfibrils in animal models of humans.

Acknowledgments The authors would like to thank Bernhard Hesse,Alexandra Pacureanu, Peter Varga and Loriane Weber for helpful sugges-tions and discussions, as well as the support of the ESRF scientists, inparticular Peter Cloetens and Heiki Suhonen. This work was performedwithin the framework of the LABEX PRIMES (ANR-11-LABX-0063) ofUniversité de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

Conflicts of interest None.

References

1. Röntgen WC (1896) On a new kind of rays. Nature 53:274–277

2. Hounsfield GN (1972) A method of and and apparatus for examina-tion of a body by radiation such as X-ray or gamma radiation. http://www.google.com/patents/US3944833. Accessed 13 Aug 2015

3. Cormack AM (1963) Representation of a function by its line in-tegrals, with some radiological applications. J Appl Phys 34:2722

4. Bonse U (2002) Developments in X-ray tomography II. In: Proc.of SPIE Vol. 4503. SPIE

5. Engelke K, Karolczak M, Lutz A, Seibert U, Schaller S, KalenderW (1999) Micro-CT. Technology and application for assessingbone structure. Radiologe 39(3):203–212

6. Bouxsein ML, Boyd SK, Christiansen BA, Guldberg RE, JepsenKJ, Müller R (2010) Guidelines for assessment of bone micro-structure in rodents using micro-computed tomography. J BoneMiner Res 25(7):1468–1486. doi:10.1002/jbmr.141

7. Hildebrand T, Laib A,Müller R, Dequeker J, Rüegsegger P (1999)Direct three-dimensional morphometric analysis of human cancel-lous bone: microstructural data from spine, femur, iliac crest, andcalcaneus. J BoneMiner Res 14(7):1167–1174. doi:10.1359/jbmr.1999.14.7.1167

8. Salomé M, Peyrin F, Cloetens P et al (1999) A synchrotron radi-ation microtomography system for the analysis of trabecular bonesamples. Med Phys 26(10):2194. doi:10.1118/1.598736

9. Nuzzo S, Peyrin F, Cloetens P, Baruchel J, Boivin G (2002)Quantification of the degree of mineralization of bone in threedimensions using synchrotron radiation microtomography. MedPhys 29:2672–2681. doi:10.1118/1.1513161

10. Marinescu M, Langer M, Durand A, Olivier C, Chabrol A, RositiH, Chauveau F, Cho TH, Nighoghossian N, Berthezène Y, PeyrinF, Wiart M (2013) Synchrotron radiation X-ray phase micro-com-puted tomography as a new method to detect iron oxide nanopar-ticles in the brain. Mol Imaging Biol.15(5):552-559. doi:10.1007/s11307-013-0639-6

11. Boutroy S, Bouxsein ML, Munoz F, Delmas PD (2005) In vivoassessment of trabecular bone microarchitecture by high-resolution peripheral quantitative computed tomography. J ClinEndocrinol Metab 90(12):6508–6515. doi:10.1210/jc.2005-1258

12. Burghardt AJ, Pialat J-B, Kazakia GJ et al (2013) Multicenterprecision of cortical and trabecular bone quality measures assessedby high-resolution peripheral quantitative computed tomography.J Bone Miner Res 28(3):524–536. doi:10.1002/jbmr.1795

13. Seeman E, Delmas PD (2006) Bone quality–the material andstructural basis of bone strength and fragility. N Engl J Med354(21):2250–2261. doi:10.1056/NEJMra053077

14. Nijweide PJ, Burger EH, Klein Nulend J (2002). The Osteocyte.In Bilezikian JP, Raisz LG, Rodan GA (eds.) Principles of BoneBiology, second edition, vol. 1. Academic Press, San Diego, CA,USA, p 93–108

15. Knothe Tate ML, Adamson JR, Tami AE, Bauer TW (2004) Theosteocyte. Int J Biochem Cell Biol 36(1):1–8

16. Klein-Nulend J, Bacabac RG, Mullender MG (2005)Mechanobiology of bone tissue. Pathol Biol (Paris) 53(10):576–580. doi:10.1016/j.patbio.2004.12.005

17. Bonewald LF (2006) Mechanosensation and Transduction inOsteocytes. Bonekey Osteovision 3(10):7–15. doi:10.1138/20060233

18. Burger EH, Klein-Nulend J (1999)Mechanotransduction in bone–roleof the lacuno-canalicular network. FASEB J 13(Suppl):S101–S112

19. Hazenberg JG, Freeley M, Foran E, Lee TC, Taylor D (2006)Microdamage: a cell transducing mechanism based on rupturedosteocyte processes. J Biomech 39(11):2096–2103. doi:10.1016/j.jbiomech.2005.06.006

20. Taylor D, Hazenberg JG, Lee TC (2007) Living with cracks: dam-age and repair in human bone. Nat Mater 6(4):263–268. doi:10.1038/nmat1866

21. Rochefort GY, Pallu S, Benhamou CL (2010) Osteocyte: the un-recognized side of bone tissue. Osteoporos Int 21(9):1457–1469.doi:10.1007/s00198-010-1194-5

452 Osteoporos Int (2016) 27:441–455

22. Bonewald LF (2011) The amazing osteocyte. J Bone Miner Res26(2):229–238. doi:10.1002/jbmr.320

23. Bonewald LF, Kneissel M, Johnson M (2013) Preface: the osteo-cyte. Bone 54(2):181. doi:10.1016/j.bone.2013.02.018

24. Klein-Nulend J, Bakker AD, Bacabac RG, Vatsa A, Weinbaum S(2013) Mechanosensation and transduction in osteocytes. Bone54(2):182–190. doi:10.1016/j.bone.2012.10.013

25. Kalajzic I, Matthews BG, Torreggiani E, Harris MA, DivietiPajevic P, Harris SE (2013) In vitro and in vivo approaches tostudy osteocyte biology. Bone 54(2):296–306. doi:10.1016/j.bone.2012.09.040

26. Seeman E (2006) Osteocytes–martyrs for integrity of bonestrength. Osteoporos Int 17(10):1443–1448. doi:10.1007/s00198-006-0220-0

27. Burr DB, Schaffler MB, Frederickson RG (1988) Composition ofthe cement line and its possible mechanical role as a local interfacein human compact bone. J Biomech 21(11):939–945

28. O’Brien FJ, Taylor D, Lee TC (2003) Microcrack accumulation atdifferent intervals during fatigue testing of compact bone. JBiomech 36(7):973–980

29. Schaffler MB, Burr DB, Frederickson RG (1987) Morphology ofthe osteonal cement line in human bone. Anat Rec 217(3):223–228. doi:10.1002/ar.1092170302

30. Skedros JG, Holmes JL, Vajda EG, Bloebaum RD (2005) Cementlines of secondary osteons in human bone are not mineral-defi-cient: new data in a historical perspective. Anat Rec A: DiscovMol Cell Evol Biol 286(1):781–803. doi:10.1002/ar.a.20214

31. Davies JE (2007) Bone bonding at natural and biomaterial surfaces.Biomaterials 28(34):5058–5067. doi:10.1016/j.biomaterials.2007.07.049

32. Kingsmill VJ, Boyde A (1998) Mineralisation density of humanmandibular bone: quantitative backscattered electron image anal-ysis. J Anat 192(Pt 2):245–256

33. Pannarale L, Braidotti P, d’Alba L, Gaudio E (1994) Scanningelectron microscopy of collagen fiber orientation in the bone la-mellar system in non-decalcified human samples. Acta Anat(Basel) 151(1):36–42

34. Giraud-Guille M-M, Besseau L, Martin R (2003) Liquid crystal-line assemblies of collagen in bone and in vitro systems. JBiomech 36(10):1571–1579

35. Hassenkam T, Fantner GE, Cutroni JA, Weaver JC, Morse DE,Hansma PK (2004) High-resolution AFM imaging of intact andfractured trabecular bone. Bone 35(1):4–10. doi:10.1016/j.bone.2004.02.024

36. Bromage TG, Goldman HM, McFarlin SC, Warshaw J, Boyde A,Riggs CM (2003) Circularly polarized light standards for investi-gations of collagen fiber orientation in bone. Anat Rec B NewAnat 274(1):157–168. doi:10.1002/ar.b.10031

37. Kazanci M, Roschger P, Paschalis EP, Klaushofer K, Fratzl P(2006) Bone osteonal tissues by Raman spectral mapping: orien-tation-composition. J Struct Biol 156(3):489–496. doi:10.1016/j.jsb.2006.06.011

38. Peyrin F, Salomé M, Nuzzo S, Cloetens P, Laval-Jeantet AM,Baruchel J (2000) Perspectives in three-dimensional analysis ofbone samples using synchrotron radiation microtomography. CellMol Biol 46(6):1089–1102

39. Labiche J-C, Mathon O, Pascarelli S et al (2007) Invited article:the fast readout low noise camera as a versatile x-ray detector fortime resolved dispersive extended x-ray absorption fine structureand diffraction studies of dynamic problems in materials science,chemistry, and catalysis. Rev Sci Instrum 78(9):091301. doi:10.1063/1.2783112

40. Hesse B, Männicke N, Pacureanu A et al (2014) Accessing oste-ocyte lacunar geometrical properties in human jaw bone on thesub-micron length scale using Synchrotron Radiation μCT. JMicrosc 255:158–168

41. Dong P, Haupert S, Hesse B et al (2014) 3D osteocyte lacunarmorphometric properties and distributions in human femoral cor-tical bone using synchrotron radiation micro-CT images. Bone 60:172–185

42. Hesse B, Langer M, Varga P et al (2014) Alterations of MassDensity and 3D Osteocyte Lacunar Properties in Bisphosphonate-Related Osteonecrotic Human Jaw Bone, a Synchrotron μCTStudy. PLoS One 9(2), e88481. doi:10.1371/journal.pone.0088481

43. Carter Y, Thomas CDL, Clement JG, Peele AG, Hannah K,Cooper DMLL (2013) Variation in osteocyte lacunar morphologyand density in the human femur–a synchrotron radiation micro-CT study. Bone 52(1):126–132. doi:10.1016/j.bone.2012.09.010

44. Carter Y, Thomas CDL, Clement JG, Cooper DML (2013)Femoral osteocyte lacunar density, volume and morphology inwomen across the lifespan. J Struct Biol 183(3):519–526. doi:10.1016/j.jsb.2013.07.004

45. Pacureanu A, Larrue A, Olivier C, Langer M, Lafage-Proust MH,Peyrin F (2013) Adaptive filtering for enhancement of the osteo-cyte cell network in 3D microtomography images. IRBM 34(1):48–52

46. Pacureanu A, Langer M, Boller E, Tafforeau P, Peyrin F (2012)Nanoscale imaging of the bone cell network with synchrotron X-ray tomography: optimization of acquisition setup. Med Phys39(4):2229. doi:10.1118/1.3697525

47. Schroer CG, Meyer J, KuhlmannM et al (2002) Nanotomographybased on hard x-ray microscopy with refractive lenses. Appl PhysLett 81(8):1527. doi:10.1063/1.1501451

48. Centonze VE, White JG (1998) Multiphoton excitation providesoptical sections from deeper within scattering specimens than con-focal imaging. Biophys J 75(4):2015–2024. doi:10.1016/S0006-3495(98)77643-X

49. Sugawara Y, Kamioka H, Honjo T, Tezuka K, Takano-YamamotoT (2005) Three-dimensional reconstruction of chick calvarial os-teocytes and their cell processes using confocal microscopy. Bone36(5):877–883. doi:10.1016/j.bone.2004.10.008

50. Schneider P, Meier M, Wepf R, Müller R (2011) Serial FIB/SEMimaging for quantitative 3D assessment of the osteocyte lacuno-canalicular network. Bone 49(2):304–311. doi:10.1016/j.bone.2011.04.005

51. Kamioka H, Murshid SA, Ishihara Y et al (2009) A method forobserving silver-stained osteocytes in situ in 3-microm sectionsusing ultra-high voltage electron microscopy tomography. MicroscMicroanal 15(5):377–383. doi:10.1017/S1431927609990420

52. Andrews JC, Almeida E, van der Meulen MCH et al (2010)Nanoscale X-ray microscopic imaging of mammalian mineralizedtissue. Microsc Microanal 16(3):327–336. doi:10.1017/S1431927610000231

53. Andrews JC, Brennan S, Patty C et al (2008) A high resolution,hard x-ray bio-imaging facility at SSRL. Synchrotron RadiatNews 21(3):17–26. doi:10.1080/08940880802406067

54. Elser V (2003) Solution of the crystallographic phase problem byiterated projections. Acta Crystallogr Sect A: Found Crystallogr59(3):201–209. doi:10.1107/S0108767303002812

55. Fienup JR (1982) Phase retrieval algorithms: a comparison. ApplOpt 21(15):2758–2769. doi:10.1364/AO.21.002758

56. Gerchberg RW, Saxton WO (1972) A practical algorithm forthe determination of phase from image and diffraction planepictures. Optik (Stuttg) 35:237–246

57. Bauschke HH, Combettes PL, Luke DR (2002) Phase retrieval,error reduction algorithm, and Fienup variants: a view from con-vex optimization. J Opt Soc Am A 19(7):1334. doi:10.1364/JOSAA.19.001334

58. Thibault P, Elser V (2010) X-ray diffraction microscopy. AnnuRev Condens Matter Phys 1(1):237–255. doi:10.1146/annurev-conmatphys-070909-104034

Osteoporos Int (2016) 27:441–455 453

59. Elser V, Rankenburg I, Thibault P (2007) Searching with iteratedmaps. Proc Natl Acad Sci U S A 104(2):418–423. doi:10.1073/pnas.0606359104

60. Schroer C, Boye P, Feldkamp J et al (2008) Coherent X-ray dif-fraction imaging with nanofocused illumination. Phys Rev Lett101(9):090801. doi:10.1103/PhysRevLett.101.090801

61. Huang X, Nelson J, Kirz J et al (2009) Soft X-ray diffractionmicroscopy of a frozen hydrated yeast cell. Phys Rev Lett103(19):198101. doi:10.1103/PhysRevLett.103.198101

62. Maiden AM, Rodenburg JM (2009) An improved ptychographicalphase retrieval algorithm for diffractive imaging. Ultramicroscopy109(10):1256–1262. doi:10.1016/j.ultramic.2009.05.012

63. Thibault P, Dierolf M, Menzel A, Bunk O, David C, Pfeiffer F(2008) High-resolution scanning x-ray diffraction microscopy.Science 321(5887):379–382. doi:10.1126/science.1158573

64. Thibault P, Dierolf M, Bunk O,Menzel A, Pfeiffer F (2009) Proberetrieval in ptychographic coherent diffractive imaging.Ultramicroscopy 109(4):338–343. doi:10.1016/j.ultramic.2008.12.011

65. HoppeW (1969) Beugung im inhomogenen Primärstrahlwellenfeld. I.Prinzip einer Phasenmessung von Elektronenbeungungsinterferenzen.Acta Crystallogr Sect A 25(4):495–501. doi:10.1107/S0567739469001045

66. Guinier A (1994) X-ray diffraction in crystals, imperfectcrystals, and amorphous bodies. Dover Publications (NewYork).

67. Langer M, Cloetens P, Peyrin F (2010) Regularization ofphase retrieval with phase-attenuation duality prior for 3-Dholotomography. IEEE Trans Image Process 19(9):2428–2436

68. Paganin D,Mayo SC, Gureyev TE,Miller PR,Wilkins SW (2002)Simultaneous phase and amplitude extraction from a singledefocused image of a homogeneous object. J Microsc 206(1):33–40. doi:10.1046/j.1365-2818.2002.01010.x

69. Wilkins SW, Gureyev TE, Gao D, Pogany A, Stevenson AW(1996) Phase-contrast imaging using polychromatic hard X-rays.Nature 384(6607):335–338

70. Dierolf M,Menzel A, Thibault P et al (2010) Ptychographic X-raycomputed tomography at the nanoscale. Nature 467(7314):436–439. doi:10.1038/nature09419

71. Holler M, Diaz A, Guizar-Sicairos M et al (2014) X-rayptychographic computed tomography at 16 nm isotropic 3D res-olution. Sci Rep 4:3857. doi:10.1038/srep03857

72. Ghiglia DC, Pitt MD (1998) Two-dimensional phase unwrapping:theory, algorithms, and software. Wiley

73. Mokso R, Cloetens P, Maire E, Ludwig W, Buffière J-Y (2007)Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics. Appl Phys Lett 90(14):144104. doi:10.1063/1.2719653

74. Langer M, Cloetens P, Peyrin F (2009) Fourier-wavelet regulari-zation of phase retrieval in x-ray in-line phase tomography. J OptSoc Am A Opt Image Sci Vis 26(8):1876–1881. doi:10.1364/JOSAA.26.001876

75. Guigay JP, Langer M, Boistel R, Cloetens P (2007)Mixed transferfunction and transport of intensity approach for phase retrieval inthe Fresnel region. Opt Lett 32(12):1617–1619. doi:10.1364/OL.32.001617

76. Langer M, Cloetens P, Pacureanu A, Peyrin F (2012) X-ray in-linephase tomography of multimaterial objects. Opt Lett 37(11):2151.doi:10.1364/OL.37.002151

77. Langer M, Cloetens P, Hesse B et al (2014) Priors for X-ray in-linephase tomography of heterogeneous objects. Philos Trans R Soc A372:20130129

78. LangerM, Pacureanu A, SuhonenH, Grimal Q, Cloetens P, PeyrinF (2012) X-ray phase nanotomography resolves the 3D human

bone ultrastructure. PLoS One 7(8), e35691. doi:10.1371/journal.pone.0035691

79. Moosmann J, Hofmann R, Baumbach T (2011) Single-distancephase retrieval at large phase shifts. Opt Express 19:12066–12073.doi:10.1364/OE.19.012066

80. Moosmann J, Hofmann R, Bronnikov A, Baumbach T (2010)Nonlinear phase retrieval from single-distance radiograph. OptExpress 18:25771–25785. doi:10.1364/OE.18.025771

81. Davidoiu V, Sixou B, Langer M, Peyrin F (2013) In-line phasetomography using nonlinear phase retrieval. Ann Univ BucharestMath Ser 4(LXII):115–122

82. Hesse B, Varga P, Langer M et al (2014) Canalicular networkmorphology is the major determinant of the spatial distributionof mass density in human bone tissue - evidence by means ofsynchrotron radiation phase-contrast nano-CT. J Bone MinerRes. doi:10.1002/jbmr.2324

83. Varga P, Pacureanu A, Langer M et al (2013) Investigation of the3D orientation of mineralized collagen fibrils in human lamellarbone using synchrotron X-ray phase nano-tomography. ActaBiomater 9:8118–8127

84. Varga P, Hesse B, Langer M et al (2015) Strains experienced byosteocytes in situ as predicted by case specific finite element anal-ysis. Biomech Model Mechanobiol 14(2):267–282

85. Verbruggen SW, Vaughan TJ, McNamara LM (2012) Strain am-plification in bonemechanobiology: a computational investigationof the in vivo mechanics of osteocytes. J R Soc Interface 9(75):2735–2744. doi:10.1098/rsif.2012.0286

86. McNamara LM, Majeska RJ, Weinbaum S, Friedrich V, SchafflerMB (2009) Attachment of osteocyte cell processes to the bonematrix. Anat Rec (Hoboken) 292(3):355–363. doi:10.1002/ar.20869

87. Vatsa A, Breuls RG, Semeins CM, Salmon PL, Smit TH, Klein-Nulend J (2008) Osteocyte morphology in fibula and calvaria— isthere a role for mechanosensing? Bone 43(3):452–8. doi:10.1016/j.bone.2008.01.030

88. van Hove RP, Nolte PA, Vatsa A, Semeins CM, Salmon PL, SmitTH, Klein-Nulend J (2009) Osteocyte morphology in human tib-iae of different bone pathologies with different bone mineral den-sity–is there a role for mechanosensing? Bone 45(2):321–9. doi:10.1016/j.bone.2009.04.238

89. Pacureanu A, Langer M, Boller E, Tafforeau P, Peyrin F (2012)Nanoscale imaging of the bone cell network with synchrotron X-ray tomography: optimization of acquisition setup. Med Phys39(4):2229. doi:10.1118/1.3697525

90. Andrews JC, Almeida E, van der MeulenMC, Alwood JS, Lee C,Liu Y, Chen J, Meirer F, Feser M, Gelb J, Rudati J, Tkachuk A,Yun W, Pianetta P (2010) Nanoscale X-ray microscopic imagingof mammalian mineralized tissue. Microsc Microanal 16(3):327–36. doi:10.1017/S1431927610000231

91. Dierolf M, Menzel A, Thibault P, Schneider P, Kewish CM, WepfR, Bunk O, Pfeiffer F (2010) Ptychographic X-ray computed to-mography at the nanoscale. Nature 467:436–439. doi:10.1038/nature09419

92. LangerM, Pacureanu A, SuhonenH, Grimal Q, Cloetens P, PeyrinF (2012) X-ray phase nanotomography resolves the 3D humanbone ultrastructure. PLoS One 7(8), e35691. doi:10.1371/journal.pone.0035691

93. Varga P, Pacureanu A, Langer M, Suhonen H, Hesse B, GrimalQ, Cloetens P, Raum K, Peyrin F (2013) Investigation of thethree-dimensional orientation of mineralized collagen fibrils inhuman lamellar bone using synchrotron X-ray phase nano-to-mography. Acta Biomater 9(9):8118–27. doi:10.1016/j.actbio.2013.05.015

94. Hesse B, Langer M, Varga P, Pacureanu A, Dong P, Schrof S,Männicke N, Suhonen H, Olivier C, Maurer P, Kazakia GJ, RaumK, Peyrin F (2014) Alterations of mass density and 3D osteocyte

454 Osteoporos Int (2016) 27:441–455

lacunar properties in bisphosphonate-related osteonecrotic humanjaw bone, a synchrotron μCT study. PLoS One 9(2), e88481. doi:10.1371/journal.pone.0088481

95. Sugawara Y, AndoR, Kamioka H, Ishihara Y, Honjo T, KawanabeN, Kurosaka H, Takano-Yamamoto T, Yamashiro T (2011) Thethree-dimensional morphometry and cell-cell communication ofthe osteocyte network in chick and mouse embryonic calvaria.Calcif Tissue Int 88(5):416–24. doi:10.1007/s00223-011-9471-7

96. Debbie J Stokes, J RTong, J Juhasz, PAMidgley, Serena M Best.Characterisation and 3DVisualisation of Biomaterials and Tissuesusing Focused Ion Beam (E)SEM. University of Cambridge,United Kingdom. Microscopy and Microanalysis. 08/2005;11(S02):1260–1261. doi:10.1017/S143192760550285X

97. Schneider P, Meier M, Wepf R, Müller R (2011) Serial FIB/SEMimaging for quantitative 3D assessment of the osteocyte lacuno-canalicular network. Bone 49(2):304–11. doi:10.1016/j.bone.2011.04.005

98. Varga P, Pacureanu A, Langer M, Hesse B, Peyrin F, Raum K(2013) Case specific finite element analysis of the strains experi-enced by osteocytes. In: V International Conference onComputational Bioengineering

99. Pacureanu A, Larrue A, Langer M et al (2013) Adaptive filtering forenhancement of the osteocyte cell network in 3D microtomographyimages. IRBM 34(1):48–52. doi:10.1016/j.irbm.2012.12.013

100. Zuluaga MA, Orkisz M, Dong P, Pacureanu A, Gouttenoire P-J,Peyrin F (2014) Bone canalicular network segmentation in 3Dnano-CT images through geodesic voting and image tessellation.Phys Med Biol 59(9):2155–2171

101. Mader KS, Schneider P, Müller R, Stampanoni M (2013) A quan-titative framework for the 3D characterization of the osteocytelacunar system. Bone 57(1):142–154

102. Dong P, Pacureanu A, ZuluagaMA, Olivier C, Grimal Q, Peyrin F(2014) Quantification of the 3D morphology of the bone cell net-work from synchrotron micro-CT images. Image Anal Stereol33(2):157. doi:10.5566/ias.v33.p157-166

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