Discovering 3D hidden elasticity in isotropic and transversely isotropic materials with physics-informed UNets.

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. STATEMENT OF SIGNIFICANCE: Elasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity-the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

A Noninvasive Clinical Method to Measure in Vivo Mechanical Strains of the Lamina Cribrosa by OCT.

Objective: To measure mechanical strain of the lamina cribrosa (LC) after intraocular pressure (IOP) change produced 1 week after a change in glaucoma medication. Design: Cohort study. Participants: Adult glaucoma patients (23 eyes, 15 patients) prescribed a change in IOP-lowering medication. Intervention: Noninvasive OCT imaging of the eye. Main Outcome Measures: Deformation calculated by digital volume correlation of OCT scans of the LC before and after IOP lowering by medication. Results: Among 23 eyes, 17 eyes of 12 persons had IOP lowering ≥ 3 mmHg (reduced IOP group) with tensile anterior-posterior Ezz strain = 1.0% ± 1.1% (P = 0.003) and compressive radial strain (Err) = -0.3% ± 0.5% (P = 0.012; random effects models accounting inclusion of both eyes in some persons). Maximum in-plane principal (tensile) strain and maximum shear strain in the reduced-IOP group were as follows: Emax = 1.7% ± 1.0% and Γmax = 1.4% ± 0.7%, respectively (both P < 0.0001 vs. zero). Reduced-IOP group strains Emax and Γmax were significantly larger with greater % IOP decrease (P < 0.0001 and P < 0.0001, respectively). The compliances of the Ezz, Emax, and Γmax strain responses, defined as strain normalized by the IOP decrease, were larger with more abnormal perimetric mean deviation or visual field index values (all P ≤ 0.02). Strains were unrelated to age (all P ≥ 0.088). In reduced-IOP eyes, mean LC anterior border posterior movement was only 2.05 µm posteriorly (P = 0.052) and not related to % IOP change (P = 0.94, random effects models). Only Err was significantly related to anterior lamina depth change, becoming more negative with greater posterior LC border change (P = 0.015). Conclusions: Lamina cribrosa mechanical strains can be effectively measured by changes in eye drop medication using OCT and are related to degree of visual function loss in glaucoma. Financial Disclosures: Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Full-field strain distribution in hierarchical electrospun nanofibrous poly-L(lactic) acid/collagen scaffolds for tendon and ligament regeneration: A multiscale study.

Regeneration of injured tendons and ligaments (T/L) is a worldwide need. In this study electrospun hierarchical scaffolds made of a poly-L (lactic) acid/collagen blend were developed reproducing all the multiscale levels of aggregation of these tissues. Scanning electron microscopy, microCT and tensile mechanical tests were carried out, including a multiscale digital volume correlation analysis to measure the full-field strain distribution of electrospun structures. The principal strains (εp1 and εp3) described the pattern of strains caused by the nanofibers rearrangement, while the deviatoric strains (εD) revealed the related internal sliding of nanofibers and bundles. The results of this study confirmed the biomimicry of such electrospun hierarchical scaffolds, paving the way to further tissue engineering and clinical applications.

Experimental Study on the Localized Deformation and Damage Behavior of Polymer-Bonded Explosive Simulant under Cyclic Compression.

Uniaxial cyclic compression tests were performed to investigate the compression deformation and damage of polymer-bonded explosive (PBX) simulant, particularly shear localization. The macroscopic mechanical behavior and mesoscale failure mechanisms of the PBX simulant were analyzed by optical observation and SEM scanning methods. After each cyclic compression, the specimen was scanned by X-ray computed tomography (CT), and the internal 3D deformation of the specimen was calculated using the digital volume correlation (DVC) method. The results show that the stress-strain curve of the PBX simulant exhibits five stages and coincides with the morphological changes on the surface of the specimen. The mesoscale failure mechanism is dominated by particle interface debonding and binder tearing, accompanied by a small amount of particle breakage. There are three bifurcation points (T1, T2, and T3) in the curves of the normal and shear strain components with compression strain. It was found that these bifurcation points can reflect the full progression of the specimen from inconspicuous damage to uniformly distributed damage, shear localization, and eventual macroscopic fracture. The strain invariant I1 can quantitatively and completely characterize the deformation and damage processes of the PBX simulant under cyclic compression.

Full-Field Strain Measurements of the Muscle-Tendon Junction Using X-ray Computed Tomography and Digital Volume Correlation.

We report, for the first time, the full-field 3D strain distribution of the muscle-tendon junction (MTJ). Understanding the strain distribution at the junction is crucial for the treatment of injuries and to predict tear formation at this location. Three-dimensional full-field strain distribution of mouse MTJ was measured using X-ray computer tomography (XCT) combined with digital volume correlation (DVC) with the aim of understanding the mechanical behavior of the junction under tensile loading. The interface between the Achilles tendon and the gastrocnemius muscle was harvested from adult mice and stained using 1% phosphotungstic acid in 70% ethanol. In situ XCT combined with DVC was used to image and compute strain distribution at the MTJ under a tensile load (2.4 N). High strain measuring 120,000 µÎµ, 160,000 µÎµ, and 120,000 µÎµ for the first principal stain (εp1), shear strain (γ), and von Mises strain (εVM), respectively, was measured at the MTJ and these values reduced into the body of the muscle or into the tendon. Strain is concentrated at the MTJ, which is at risk of being damaged in activities associated with excessive physical activity.

Long-term Remodeling Response in the Lamina Cribrosa Years after Intraocular Pressure Lowering by Suturelysis after Trabeculectomy.

OBJECTIVE: To measure the remodeling of the lamina cribrosa (LC) years after intraocular pressure (IOP) lowering by suturelysis. DESIGN: Cohort study. PARTICIPANTS: Glaucoma patients were imaged 20 minutes after laser suturelysis after trabeculectomy surgery and at their follow-up appointment 1 to 4 years later (16 image pairs; 15 persons). INTERVENTION: Noninvasive OCT imaging of the eye. MAIN OUTCOME MEASURES: Deformation calculated by correlating OCT scans of the LC immediately after IOP lowering by suturelysis and those acquired years later (defined as remodeling strain). RESULTS: The LC anterior border moved 60.9 ± 54.6 µm into the eye (P = 0.0007), and the LC exhibited regions of large local stretch in the anterior-posterior direction on long-term, maintained IOP lowering, resulting in a mean anterior-posterior remodeling strain of 14.0% ± 21.3% (P = 0.02). This strain and the LC border movement was 14 times and 124 times larger, respectively, than the direct response to IOP lowering by suturelysis. A larger anterior LC border movement was associated with greater mean anterior-posterior remodeling strain (P = 0.004). A thinner retinal nerve fiber layer at suturelysis was also associated with greater mean anterior-posterior remodeling strain at follow-up (P = 0.05). Worsening visual field indexes during follow-up were associated with a greater mean circumferential remodeling strain (P = 0.02), due to regions of large local circumferential stretch of the LC. Eyes with a more compliant LC torsional shear strain response at lysis were associated with worse mean deviation at follow-up (P = 0.03). CONCLUSIONS: Strains and LC border position changes measured years after IOP lowering are far larger than the immediate response to IOP lowering and indicate dramatic remodeling of the LC anatomical structure caused by IOP lowering and glaucoma progression. The remodeling strains indicate substantial local stretch in the anterior-posterior direction and are associated with movement of the LC anterior border into the eye. Eyes with greater direct strain response to IOP lowering, greater glaucoma damage at suturelysis, and greater worsening of visual field at follow-up experienced greater remodeling. TRIAL REGISTRATION: ClinicalTrials.gov Identifier: NCT03267849. FINANCIAL DISCLOSURE(S): Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

In vivo strain measurements in the human buttock during sitting using MR-based digital volume correlation.

Advancements in systems for prevention and management of pressure ulcers require a more detailed understanding of the complex response of soft tissues to compressive loads. This study aimed at quantifying the progressive deformation of the buttock based on 3D measurements of soft tissue displacements from MR scans of 10 healthy subjects in a semi-recumbent position. Measurements were obtained using digital volume correlation (DVC) and released as a public dataset. A first parametric optimisation of the global registration step aimed at aligning skeletal elements showed acceptable values of Dice coefficient (around 80%). A second parametric optimisation on the deformable registration method showed errors of 0.99mm and 1.78mm against two simulated fields with magnitude 7.30±3.15mm and 19.37±9.58mm, respectively, generated with a finite element model of the buttock under sitting loads. Measurements allowed the quantification of the slide of the gluteus maximus away from the ischial tuberosity (IT, average 13.74 mm) that was only qualitatively identified in the literature, highlighting the importance of the ischial bursa in allowing sliding. Spatial evolution of the maximus shear strain on a path from the IT to the seating interface showed a peak of compression in the fat, close to the interface with the muscle. Obtained peak values were above the proposed damage threshold in the literature. Results in the study showed the complexity of the deformation of the soft tissues in the buttock and the need for further investigations aimed at isolating factors such as tissue geometry, duration and extent of load, sitting posture and tissue properties.

Comparison of two contrast-enhancing staining agents for use in X-ray imaging and digital volume correlation measurements across the cartilage-bone interface.

OBJECTIVE: The pathogenesis of osteoarthritis (OA) is associated with subchondral bone changes, which is linked to abnormal strain distribution in the overlying articular cartilage. This highlights the importance of understanding mechanical interaction at the cartilage-bone interface. The aim of this study is to compare solutions of two contrast-enhancing staining agents (CESA) for combining high-resolution Contrast-Enhanced X-ray microfocus Computed Tomography (CECT) with Digital Volume Correlation (DVC) for full-field strain measurements at the cartilage-bone interface. DESIGN: Bovine osteochondral plugs were stained with phosphotungstic acid (PTA) in 70% ethanol or 1:2 hafnium-substituted Wells-Dawson polyoxometalate (Hf-WD POM) in PBS. Mechanical properties were assessed using micromechanical probing and nanoindentation. Strain uncertainties (from CECT data) were evaluated following two consecutive unloaded scans. Residual strains were computed following unconfined compression (ex situ) testing. RESULTS: PTA and Hf-WD POM enabled the visualisation of structural features in cartilage, allowing DVC computation on the CECT data. Residual strains up to ∼10,000 µÉ› were detected up to the tidemark. Nanoindentation showed that PTA-staining caused an average ∼6-fold increase in articular cartilage stiffness, a ∼19-fold increase in reduced modulus and ∼7-fold increase in hardness, whereas Hf-WD POM-stained specimens had mechanical properties similar to pre-stain tissue. Micromechanical probing showed a 77% increase in cartilage surface stiffness after PTA-staining, in comparison to a 16% increase in stiffness after staining with Hf-WD POM. CONCLUSION: Hf-WD POM is a more suitable CESA solution compared to PTA for CECT imaging combined with DVC as it allowed visualisation of structural features in the cartilage tissue whilst more closely maintaining tissue mechanical properties.

Quantifying the immediate post-implantation strain field of cadaveric tibiae implanted with cementless tibial trays: A time-elapsed micro-CT and digital volume correlation analysis during stair descent.

Primary stability, the mechanical fixation between implant and bone prior to osseointegration, is crucial for the long-term success of cementless tibial trays. However, little is known about the mechanical interplay between the implant and bone internally, as experimental studies quantifying internal strain are limited. This study employed digital volume correlation (DVC) to quantify the immediate post-implantation strain field of five cadaveric tibiae implanted with a commercially available cementless titanium tibial tray (Attune, DePuy Synthes). The tibiae were subjected to a five-step loading sequence (0-2.5 bodyweight, BW) replicating stair descent, with concomitant time-elapsed micro-CT imaging. With progressive loads, increased compression of trabecular bone was quantified, with the highest strains directly under the posterior region of the tibial tray implant, dissipating with increasing distance from the bone-implant interface. After load removal of the last load step (2.5BW), residual strains were observed in all of the five tibiae, with residual strains confined within 3.14 mm from the bone-implant interface. The residual strain is reflective of the observed initial migration of cementless tibial trays reported in clinical studies. The presence of strains above the yield strain of bone accepted in literature suggests that inelastic properties should be included within finite element models of the initial mechanical environment. This study provides a means to experimentally quantify the internal strain distribution of human tibia with cementless trays, increasing the understanding of the mechanical interaction between bone and implant.

High-accuracy optical coherence elastography digital volume correlation methods to measure depth regions with low correlation.

The decreasing correlation of optical coherence tomography (OCT) images with depth is an unavoidable problem for the depth measurement of the digital volume correlation (DVC) based optical coherence elastography (OCE) method. We propose an OCE-DVC method to characterize biological tissue deformation in deeper regions. The method proposes a strategy based on reliability layer guided displacement tracking to achieve the OCE-DVC method for the deformation measurement in deep regions of OCT images. Parallel computing solves the computational burden associated with the OCE-DVC method. The layer-by-layer adaptive data reading methods are used to guarantee the parallel computing of high-resolution OCT images. The proposed method shown in this study nearly doubles the depth of quantitative characterization of displacement and strain. At this depth, the standard deviation of displacement and strain measurements is reduced by nearly 78%. Under nonuniform deformation field, OCE-DVC method tracked the displacement with large strain gradient in depth region.

3D strain pattern in additively manufactured AlSi10Mg from digital volume correlation.

Although much research has focused on AlSi10Mg processed via laser-based powder bed fusion, the material deformation mechanisms at the microscale are still unclear. To improve the current understanding, 3D measurements of the strain field at the microstructural scale are needed to complement surface-based SEM observations. This work demonstrates that X-ray tomography combined with digital volume correlation can be used to measure the strain in the bulk of AlSi10Mg using the Si-rich particles contained in the heat-treated microstructure as markers. The method allows for measuring strains larger than 0.5 % with a spatial resolution of 35 µm and it can thus be used to study the impact of factors like porosity distribution or crystallographic texture on the material deformation and damage mechanisms.

A Comprehensive Mechanical Characterization of Subject-Specific 3D Printed Scaffolds Mimicking Trabecular Bone Architecture Biomechanics.

This study presents a polymeric scaffold designed and manufactured to mimic the structure and mechanical compressive characteristics of trabecular bone. The morphological parameters and mechanical behavior of the scaffold were studied and compared with trabecular bone from bovine iliac crest. Its mechanical properties, such as modulus of elasticity and yield strength, were studied under a three-step monotonic compressive test. Results showed that the elastic modulus of the scaffold was 329 MPa, and the one for trabecular bone reached 336 MPa. A stepwise dynamic compressive test was used to assess the behavior of samples under various loading regimes. With microcomputed tomography (µCT), a three-dimensional reconstruction of the samples was obtained, and their porosity was estimated as 80% for the polymeric scaffold and 88% for trabecular bone. The full-field strain distribution of the samples was measured using in situ µCT mechanics and digital volume correlation (DVC). This provided information on the local microdeformation mechanism of the scaffolds when compared to that of the tissue. The comprehensive results illustrate the potential of the fabricated scaffolds as biomechanical templates for in vitro studies. Furthermore, there is potential for extending this structure and fabrication methodology to incorporate suitable biocompatible materials for both in vitro and in vivo clinical applications.

Quantifying internal intervertebral disc strains to assess nucleus replacement device designs: a digital volume correlation and ultra-high-resolution MRI study.

Introduction: Nucleus replacement has been proposed as a treatment to restore biomechanics and relieve pain in degenerate intervertebral discs (IVDs). Multiple nucleus replacement devices (NRDs) have been developed, however, none are currently used routinely in clinic. A better understanding of the interactions between NRDs and surrounding tissues may provide insight into the causes of implant failure and provide target properties for future NRD designs. The aim of this study was to non-invasively quantify 3D strains within the IVD through three stages of nucleus replacement surgery: intact, post-nuclectomy, and post-treatment. Methods: Digital volume correlation (DVC) combined with 9.4T MRI was used to measure strains in seven human cadaveric specimens (42 ± 18 years) when axially compressed to 1 kN. Nucleus material was removed from each specimen creating a cavity that was filled with a hydrogel-based NRD. Results: Nucleus removal led to loss of disc height (12.6 ± 4.4%, p = 0.004) which was restored post-treatment (within 5.3 ± 3.1% of the intact state, p > 0.05). Nuclectomy led to increased circumferential strains in the lateral annulus region compared to the intact state (-4.0 ± 3.4% vs. 1.7 ± 6.0%, p = 0.013), and increased maximum shear strains in the posterior annulus region (14.6 ± 1.7% vs. 19.4 ± 2.6%, p = 0.021). In both cases, the NRD was able to restore these strain values to their intact levels (p ≥ 0.192). Discussion: The ability of the NRD to restore IVD biomechanics and some strain types to intact state levels supports nucleus replacement surgery as a viable treatment option. The DVC-MRI method used in the present study could serve as a useful tool to assess future NRD designs to help improve performance in future clinical trials.

Damage Detection in a Polymer Matrix Composite from 4D Displacement Field Measurements.

Standard Digital Volume Correlation (DVC) approaches enable quantitative analyses of specimen deformation to be performed by measuring displacement fields between discrete states. Such frameworks are thus limited by the number of scans (due to acquisition duration). Considering only one projection per loading step, Projection-based Digital Volume Correlation (P-DVC) allows 4D (i.e., space and time) full-field measurements to be carried out over entire loading histories. The sought displacement field is decomposed over a basis of separated variables, namely, temporal and spatial modes. In the present work, the spatial modes are constructed via scan-wise DVC, and only the temporal amplitudes are sought via P-DVC. The proposed method is applied to a glass fiber mat reinforced polymer specimen containing a machined notch, subjected to in situ cyclic tension and imaged via X-ray Computed Tomography. The P-DVC enhanced DVC method employed herein enables for the quantification of damage growth over the entire loading history up to failure.

Development of a method to investigate strain distribution across the cartilage-bone interface in guinea pig model of spontaneous osteoarthritis using lab-based contrast enhanced X-ray-computed tomography and digital volume correlation.

OBJECTIVE: Strain changes at the cartilage-bone interface play a crucial role in osteoarthritis (OA) development. Contrast-Enhanced X-ray Computed Tomography (CECT) and Digital Volume Correlation (DVC) can measure 3D strain changes at the osteochondral interface. Using lab-based CT systems it is often difficult to visualise soft tissues such as articular cartilage without staining to enhance contrast. Contrast-Enhancing Staining Agents (CESAs), such as Phosphotungstic Acid (PTA) in 70% ethanol, can cause tissue shrinkage and alter tissue mechanics. The aims of this study were, firstly, to assess changes to the mechanical properties of osteochondral tissue after staining with a PTA/PBS solution, and secondly, to visualise articular cartilage during loading and with CECT imaging in order to compare strain across the interface in both healthy and OA joints using DVC. DESIGN: Nanoindentation was used to assess changes to mechanical properties in articular cartilage and subchondral bone before and after staining. Hindlimbs from Dunkin-Hartley guinea pigs were stained with 1% PTA/PBS at room temperature for 6 days. Two consecutive CECT datasets were acquired for DVC error analysis. In-situ compression with a load corresponding to 2x body weight was applied, the specimen was re-imaged, and DVC was performed between the pre- and post-load tomograms. RESULTS: Nanoindentation before and after PTA/PBS staining showed similar cartilage stiffness (p < 0.05), however, staining significantly decreased the stiffness of subchondral bone (∼9-fold; p = 0.0012). In severe OA specimens, third principal/compressive (εp3) strain was 141.7% higher and shear strain (γ) was 98.2% higher in tibial articular cartilage compared to non-OA (2 - month) specimens. A 23.1% increase in third principal stain strain and a 54.5% significant increase in the shear (γ) strain (p = 0.0027) was transferred into the mineralised regions of calcified cartilage and subchondral bone in severe OA specimens. CONCLUSIONS: These results indicate the suitability of PTA in PBS as a contrast agent for the visualisation of cartilage during CECT imaging and allowed DVC computation of strain across the cartilage-bone interface. However, further research is needed to address the reduction in stiffness of subchondral bone after incubation in PBS.

The Curvature, Collagen Network Structure, and Their Relationship to the Pressure-Induced Strain Response of the Human Lamina Cribrosa in Normal and Glaucoma Eyes.

The lamina cribrosa (LC) is a connective tissue in the optic nerve head (ONH). The objective of this study was to measure the curvature and collagen microstructure of the human LC, compare the effects of glaucoma and glaucoma optic nerve damage, and investigate the relationship between the structure and pressure-induced strain response of the LC in glaucoma eyes. Previously, the posterior scleral cups of 10 normal eyes and 16 diagnosed glaucoma eyes were subjected to inflation testing with second harmonic generation (SHG) imaging of the LC and digital volume correlation (DVC) to calculate the strain field. In this study, we applied a custom microstructural analysis algorithm to the maximum intensity projection of SHG images to measure features of the LC beam and pore network. We also estimated the LC curvatures from the anterior surface of the DVC-correlated LC volume. Results showed that the LC in glaucoma eyes had larger curvatures p≤0.03), a smaller average pore area (p = 0.001), greater beam tortuosity (p < 0.0001), and more isotropic beam structure (p = 0.01) than in normal eyes. The difference measured between glaucoma and normal eyes may indicate remodeling of the LC with glaucoma or baseline differences that contribute to the development of glaucomatous axonal damage.

Mapping internal strain fields of fused filament fabrication metal filled polylactic acid structure using digital volume correlation.

With the advancement in Fused Filament Fabrication (FFF), its application is increasing widely across different industries such as aeronautical, biomedical, robotics, etc. The internal structure is becoming more complex and intricate with varying materials of reinforcement which are used to improve mechanical properties. Current measurement techniques like Digital Image Correlation (DIC) are non-destructive testing methods that do not provide enough information on the behaviour of internal microstructure for anisotropic FFF materials. Digital Volume Correlation (DVC) is non-destructive testing technique which provides full field internal 3D deformation and strain fields. Copper particle filled PLA samples manufactured using FFF method with 20, 40, 60 and 80 infill percentages were loaded in tension inside Micro-CT. X-rays were passed through the sample to get a volumetric dataset for different loadings. Using DVC method on the dataset, internal displacement and strain fields were generated for 20, 40, 60 and 80 infill percentage FFF sample.

In vivo evaluation of ankle kinematics and tibiotalar joint contact strains using digital volume correlation and 3 T clinical MRI.

BACKGROUND: In vivo evaluation of ankle joint biomechanics is key to investigating the effect of injuries on the mechanics of the joint and evaluating the effectiveness of treatments. The objectives of this study were to 1) investigate the kinematics and contact strains of the ankle joint and 2) to investigate the correlation between the tibiotalar joint contact strains and the prevalence of osteochondral lesions of the talus distribution. METHODS: Eight healthy human ankle joints were subjected to compressive load and 3 T MRIs were obtained before and after applying load. The MR images in combination with digital volume correlation enabled non-invasive measurement of ankle joint kinematics and tibiotalar joint contact strains in three dimensions. FINDINGS: The total translation of the calcaneus was smaller (0.48 ± 0.15 mm, p < 0.05) than the distal tibia (0.93 ± 0.16 mm) and the talus (1.03 ± 0.26 mm). These movements can produce compressive and shear joint contact strains (approaching 9%), which can cause development of lesions on joints. 87.5% of peak tensile, compressive, and shear strains in the tibiotalar joint took place in the medial and lateral zones. INTERPRETATION: The findings suggested that ankle bones translate independently from each other, and in some cases in opposite directions. These findings help explain the distribution of osteochondral lesions of the talus which have previously been observed to be in medial and lateral regions of the talar dome in 90% of cases. They also provide a reason for the central region of talar dome being less susceptible to developing osteochondral lesions.

In situ synchrotron radiation µCT indentation of cortical bone: Anisotropic crack propagation, local deformation, and fracture.

The development of treatment strategies for skeletal diseases relies on the understanding of bone mechanical properties in relation to its structure at different length scales. At the microscale, indention techniques can be used to evaluate the elastic, plastic, and fracture behaviour of bone tissue. Here, we combined in situ high-resolution SRµCT indentation testing and digital volume correlation to elucidate the anisotropic crack propagation, deformation, and fracture of ovine cortical bone under Berkovich and spherical tips. Independently of the indenter type we observed significant dependence of the crack development due to the anisotropy ahead of the tip, with lower strains and smaller crack systems developing in samples indented in the transverse material direction, where the fibrillar bone ultrastructure is largely aligned perpendicular to the indentation direction. Such alignment allows to accommodate the strain energy, inhibiting crack propagation. Higher tensile hoop strains generally correlated with regions that display significant cracking radial to the indenter, indicating a predominant Mode I fracture. This was confirmed by the three-dimensional analysis of crack opening displacements and stress intensity factors along the crack front obtained for the first time from full displacement fields in bone tissue. The X-ray beam significantly influenced the relaxation behaviour independent of the tip. Raman analyses did not show significant changes in specimen composition after irradiation compared to non-irradiated tissue, suggesting an embrittlement process that may be linked to damage of the non-fibrillar organic matrix. This study highlights the importance of three-dimensional investigation of bone deformation and fracture behaviour to explore the mechanisms of bone failure in relation to structural changes due to ageing or disease. STATEMENT OF SIGNIFICANCE: Characterising the three-dimensional deformation and fracture behaviour of bone remains essential to decipher the interplay between structure, function, and composition with the aim to improve fracture prevention strategies. The experimental methodology presented here, combining high-resolution imaging, indentation testing and digital volume correlation, allows us to quantify the local deformation, crack propagation, and fracture modes of cortical bone tissue. Our results highlight the anisotropic behaviour of osteonal bone and the complex crack propagation patterns and fracture modes initiating by the intricate stress states beneath the indenter tip. This is of wide interest not only for the understanding of bone fracture but also to understand other architectured (bio)structures providing an effective way to quantify their toughening mechanisms in relation to their main mechanical function.

On the material dependency of peri-implant morphology and stability in healing bone.

The microstructural architecture of remodeled bone in the peri-implant region of screw implants plays a vital role in the distribution of strain energy and implant stability. We present a study in which screw implants made from titanium, polyetheretherketone and biodegradable magnesium-gadolinium alloys were implanted into rat tibia and subjected to a push-out test four, eight and twelve weeks after implantation. Screws were 4 mm in length and with an M2 thread. The loading experiment was accompanied by simultaneous three-dimensional imaging using synchrotron-radiation microcomputed tomography at 5 µm resolution. Bone deformation and strains were tracked by applying optical flow-based digital volume correlation to the recorded image sequences. Implant stabilities measured for screws of biodegradable alloys were comparable to pins whereas non-degradable biomaterials experienced additional mechanical stabilization. Peri-implant bone morphology and strain transfer from the loaded implant site depended heavily on the biomaterial utilized. Titanium implants stimulated rapid callus formation displaying a consistent monomodal strain profile whereas the bone volume fraction in the vicinity of magnesium-gadolinium alloys exhibited a minimum close to the interface of the implant and less ordered strain transfer. Correlations in our data suggest that implant stability benefits from disparate bone morphological properties depending on the biomaterial utilized. This leaves the choice of biomaterial as situational depending on local tissue properties.