**1. Introduction**

Bone is a highly heterogenous, anisotropic and hierarchical material that is organised at various levels to optimise its mechanical competence [1]. Thus, it is essential to understand the mechanics of its different components and the structural relationships between them at the different dimensional scales [2–4]. This is of fundamental importance since many musculoskeletal pathologies, such as osteoporosis, are associated with alterations in bone quality at the micro- and nanoscale [5]. Therefore, novel techniques aim at characterising the deformation mechanisms of bone in a three-dimensional (3D) manner, from apparent to tissue level, and establishing their links with bone structure [6–8].

To date, the only experimental method that allows for 3D strain measurements within the bone structure is digital volume correlation (DVC) in combination with in situ microcomputed tomography (microCT) testing [9–11]. DVC has been widely used in bone mechanics to investigate full-field

displacement and strain in cortical [12] and trabecular [13,14] bone at different dimensional scales and loading conditions, providing a unique insight to the 3D deformation of such complex material. Nevertheless, in order to characterise bone failure mechanisms at the tissue level, high-resolution microCT is needed [11,15,16]. High-energy synchrotron radiation (SR) microCT has proven to provide fast high-quality image acquisition of bone microstructure with high spatial resolution (~1 μm), and together with in situ mechanical studies, it has allowed for a detailed coupling between 3D bone microstructure and deformation [6,17,18]. Furthermore, recent studies have combined in situ SR-microCT mechanics with DVC to investigate the internal strain and microdamage evaluation of cortical bone [12], trabecular bone [14] and bone-biomaterial systems [19], enhancing the understanding of bone failure at the microscale.

However, it is known that high exposures to SR X-ray radiation lead to a deterioration in the mechanical properties of bone as a consequence of collagen matrix degradation [20,21]. Similarly, ionising radiation, such as gamma rays, commonly used to sterilise bone allografts [22], and X-rays, negatively affects the mechanical and biological properties of the tissue by the degradation of the collagen present in the bone matrix [20,23–27]. Specifically, radiation produces reactive free radicals by the radiolysis of water molecules, which splits the polypeptides chains of the collagen and induces cross-linking reactions, causing collagen denaturation [28–30]. In clinical practice, the adverse effects of gamma radiation during sterilization have been successfully reduced by irradiating the bone while frozen [31,32]. Lowering the temperature is beneficial, as it reduces the mobility of free radicals and, therefore, their ability to interact with collagen molecules [33,34]. Particularly, Hamer et al. [31] observed that cortical bone irradiated at low temperatures ( −78 ◦C) was less brittle and had less collagen damage when compared to the bone irradiated at room temperature. Additionally, Cornu et al. [32] showed that ultimate strength, stiffness and work to failure were not reduced significantly on trabecular bone irradiated under dry ice. In the field of high-resolution X-ray imaging of biological samples, protection against radiation damage is also essential to preserve their integrity. Cryofixation methods have been demonstrated to protect biological samples from visible structural damage and have enabled cryo-soft X-ray tomography (cryo-SXT) to become the only imaging modality able to provide nanoscale 3D information of whole cells in a near-native state [35–37]. However, soft X-rays (~0.1–1 keV) are not able to penetrate bone tissue, nor can they be accommodated for in situ mechanics protocols. Furthermore, cryotechniques involve freeze-drying of the specimens at −150 ◦C and have been shown to induce microdamage and significantly reduce torsional strength, compressive yield stress and compressive modulus of cortical bone [32,38–40]. Hence, low temperatures positively influence bone preservation during irradiation. However, mechanical testing of bone in such conditions, below the freezing temperature of water, cannot be conducted, as the mechanical properties of bone would be affected. In fact, due to the large water content of bone, ice crystals may cause structural damage to the tissue [23].

Therefore, it is essential to define some guidelines in order to preserve bone tissue integrity and mechanics during in situ SR-microCT experiments. Very recently, DVC applied to SR-microCT images of trabecular bone was used to investigate the influence of SR irradiation-induced microdamage on the bone's apparent mechanics [14]. Microcracks were detected in the bone tissue after long exposures to SR radiation, despite the apparent elastic properties remaining unaltered. Also, high local strain levels were observed that corresponded to the microdamaged areas. However, reducing the total exposure to SR X-ray radiation was able to preserve bone integrity and plasticity. The results of that study [14] provided important information on bone degradation and residual strain accumulation resulting from SR X-ray exposure, but the study had some limitations. Firstly, bone specimens were subjected to cyclic mechanical loading during SR-microCT imaging; thus, the full-field strain measurements were not entirely due to SR irradiation but also to the mechanics. In fact, DVC results showed that even at reduced exposures to SR radiation, there were some regions of high strain concentration, which may have been induced by the mechanical load and further enhanced by the irradiation. Secondly, reducing the total exposure by decreasing the exposure time per projection during SR-microCT acquisition notably decreased image quality and, consequently, DVC performance. Hence, further evaluation and optimisation of the imaging setup is needed in order to preserve bone integrity while maximising image quality for reliable DVC-computed full-field measurement within the bone tissue.

In this context, there is a clear need to define experimental protocols for in situ SR-microCT mechanics able to preserve bone tissue integrity against SR X-ray radiation-induced damage, exploiting the research conducted in different fields. The aim of this study is, therefore, to propose a novel proof-of-concept methodology to retain bone tissue integrity, based on residual strain determination via DVC, by decreasing the environmental temperature during SR-microCT testing.

#### **2. Materials and Methods**

## *2.1. Specimen Preparation*

Samples were obtained from a fresh bovine femur. A section (20 mm in thickness) was cut with a hacksaw from the proximal diaphysis of the femur and a diamond-coated core drill was used to extract 4 mm cylindrical compact (n = 2) and 6 mm trabecular (n = 2) bone specimens under constant water irrigation. The ends of the cores were trimmed to achieve a 12 mm length for the compact and a 16 mm length for the trabecular bone specimens. Brass endcaps were used to embed the ends of the specimens (~2 mm), ensuring perpendicularity between the bone cores and the endcap bases. Samples were kept frozen at −20 ◦C and thawed for approximately 2 h in saline solution at room temperature before imaging.

## *2.2. SR-MicroCT Imaging*

SR-microCT was performed at the Diamond-Manchester Imaging Branchline I13-2 (Figure 1a) of Diamond Light Source (DLS), Oxfordshire, UK. A partially coherent polychromatic 'pink' beam (5–35 keV) of parallel geometry was generated by an undulator from an electron storage ring of 3.0 GeV. The undulator gap was set to 5 mm for data collection and, to limit bone damage, 11 mm for low-dose alignment. The beam was reflected from the platinum stripe of a grazing-incidence focusing mirror and high-pass filtered with 1.4 mm pyrolytic graphite, 3.2 mm aluminium and 50 μm steel. The propagation (sample-to-scintillator) distance was approximately 40 mm. Images were recorded by a sCMOS (2560 × 2160 pixels) pco.edge 5.5 (PCO AG, Kelheim, Germany) detector which was coupled to a 500 μm-thick CdWO4 scintillator and a visual light microscope with a 4× objective lens, providing a total magnification of 8×. This resulted in an effective voxel size of 0.81 μm and a field of view of 2.1 × 1.8 mm2. A total of 1801 projection images were collected over 180◦ of continuous rotation ('fly-scan'), with an exposure time of 512 ms per projection (11 ms overhead per exposure), adopting the imaging conditions reported in [14]. The total scanning time was approximately 15 min. The projection images were flat-field- and dark-field-corrected prior to image reconstruction using SAVU [41], which incorporated ring artefact suppression and optical distortion correction [42]. Each specimen underwent five full consecutive tomographic data collections.

#### *2.3. In Situ Testing and Temperature Control*

Specimens were placed within an in situ testing device (CT5000-TEC, Deben, Bury Saint Edmunds, UK) and kept in saline solution during image acquisition (Figure 1a). The device is equipped with a 5 kN load cell, Peltier heated and cooled jaws with a temperature range from −20 ◦C to +160 ◦C and an environmental chamber. A small preload (2–5 N) was first applied to ensure good end-contact and avoid motion artefacts during tomographic acquisition, after which the actuator was stopped, and the jaws' positions held throughout the test. Bone specimens (N = 1 compact and N = 1 trabecular) were imaged at room temperature (Troom ≈ 23 ◦C) and at ~0 ◦C (N = 1 compact andN=1 trabecular) by cooling and keeping the Peltier jaws at the target temperature. A thermocouple (Type K, RS Pro, RS Components, Corby, UK) was also attached to the surface of the bone samples and was used during the in situ test to monitor the temperature directly at the tissue during image acquisition and between tomographies. Temperature measurements and recordings were processed with a thermocouple data logger (USB TC-08, Pico Technology, St Neots, UK). For reliable temperature measurements, the thermocouple was calibrated prior to the experiment.

## *2.4. Image Post-Processing*

Five datasets were obtained for each specimen and further processed using Fiji platform [43]. After image reconstruction, each 3D dataset consisted of 2000 images (2400 × 2400 pixels) with 32-bit grey-levels. Images were converted to 8-bit greyscale and cropped to parallelepipeds (volume of interest (VOI)) with a cross-section of 1400 × 1400 pixels (1.134 × 1.134 mm2) and a height equal to 1800 pixels (1.46 mm) in the centre of the scanned volume (Figure 1b,c). Noise in the images was reduced by applying a nonlocal means filter [44], where the variance of the noise was automatically estimated for each dataset [45]. The five consecutive scans per specimen were first rigidly registered using the first acquired dataset as a reference. The 3D rigid registration was based on sum of squares differences as a similarity measurement between the reference and each target image. Finally, the filtered VOIs were masked by setting to zero-intensity the non-bony voxels (i.e., Haversian and Volkmann's canals in compact bone and bone marrow space in trabecular bone). A binary image (value of one for bone voxel and zero elsewhere) was first created using Otsu's threshold algorithm followed by a despeckling filter to remove 3D regions less than three voxels in volume both in white and black areas, which are mainly related to nonfiltered noise. Additionally, isolated pixels were removed, and small holes were filled by using a series of morphological operations as described in [16]. The quality of the binary images was checked by visual inspection. Masked images, with the original greyscale value in the bony voxels and zero elsewhere, were obtained by multiplying the filtered image with the final binary image (Figure 1d,e).

**Figure 1.** (**a**) Experimental setup at I13-2 beamline. The direction of the beam is indicated by the dashed-dotted line. Specimens were scanned within a loading device using a 4× lens objective. The temperature in the device was controlled with a circulating coolant and monitored on the tissue via an additional thermocouple attached to the surface of the specimens. SR-microCT reconstructed volume of interest (VOI) (1.13 × 1.13 × 1.46 mm3) analysed for (**b**) trabecular and (**c**) compact bones with an effective voxel size of 0.81 μm. Two-dimensional cross-section through the middle of the VOI after masking the bone marrow (**d**) from the trabecular bone and the Haversian and Volkmann's canals (**e**) from the compact bone.

#### *2.5. Digital Volume Correlation*

Digital volume correlation (DaVis v10.0, LaVision, Göttingen, Germany) was carried out to evaluate the residual strain in the bone tissue due to progressive damage induced by X-ray exposure to SR radiation during SR-microCT at different temperatures. DaVis software is based on a local approach of correlation, which has been widely used in bone mechanics [13,14,46]. Details on the operating principles of the software are reported elsewhere [16,47]. DVC was applied to the masked images to avoid large strain artefacts in regions with insufficient greyscale pattern (i.e., bone marrow) [16]. A different multi-pass scheme was used for the DVC computation on compact and trabecular specimens after an evaluation of the baseline strains in the first two consecutive tomograms for the four specimens, obtained in a nominal 'zero-strain' state, where the irradiation-induced damage was considered minimal (Supplementary Materials). A final subvolume of 32 voxels, reached via successive (predictor) passes using subvolumes of 112, 56, 48 and 40 voxels, was used for the compact bone, whereas, for the trabecular bone, a final subvolume of 64 voxels, reached via successive passes of 112, 88, 80 and 72 voxels, was adopted. Given the voxel size of the SR-microCT images, the final DVC measurement spatial resolution was 25.9 μm for compact and 51.8 μm for trabecular bones. Additionally, in both cases, subvolumes with a correlation coefficient below 0.6 were removed from the resultant displacement vectors to avoid artefacts due to poor correlation. The different processing schemes for both bone typologies mainly depended on the higher number of features (i.e., osteocyte lacunae) available in the compact bone specimens compared to the trabecular ones, which allowed a smaller subvolume size to be used for the former [11]. To evaluate the 3D full-field residual strain distribution in the bone tissue over time in relation to the damage induced by continuous X-ray exposure to SR radiation, DVC was performed by registering the reference image (first acquired tomogram) with each of the remaining tomograms. First (<sup>ε</sup>p1) and third (<sup>ε</sup>p3) principal strains and maximum shear ( γmax) strain were computed within the bone volume after a bicubic interpolation of the measured strain. Furthermore, in order to couple the initiation and propagation of microcracks in the tissue with the displacement and first principal strain directions, dedicated MATLAB (v2018a, MathWorks, Natick, MA, USA) scripts were developed. The MATLAB scripts allow for the representation of any set of orthogonal slices within the volume and for the computation of the displacement and first principal strain values and their corresponding direction for each subvolume.
