The loading direction dramatically affects the mechanical properties of the mouse tibia.

Introduction: The in vivo tibial loading mouse model has been extensively used to evaluate bone adaptation in the tibia after mechanical loading treatment. However, there is a prevailing assumption that the load is applied axially to the tibia. The aim of this in silico study was to evaluate how much the apparent mechanical properties of the mouse tibia are affected by the loading direction, by using a validated micro-finite element (micro-FE) model of mice which have been ovariectomized and exposed to external mechanical loading over a two-week period. Methods: Longitudinal micro-computed tomography (micro-CT) images were taken of the tibiae of eleven ovariectomized mice at ages 18 and 20 weeks. Six of the mice underwent a mechanical loading treatment at age 19 weeks. Micro-FE models were generated, based on the segmented micro-CT images. Three models using unitary loads were linearly combined to simulate a range of loading directions, generated as a function of the angle from the inferior-superior axis (θ, 0°-30° range, 5° steps) and the angle from the anterior-posterior axis (ϕ, 0°: anterior axis, positive anticlockwise, 0°-355° range, 5° steps). The minimum principal strain was calculated and used to estimate the failure load, by linearly scaling the strain until 10% of the nodes reached the critical strain level of -14,420 µÎµ. The apparent bone stiffness was calculated as the ratio between the axial applied force and the average displacement along the longitudinal direction, for the loaded nodes. Results: The results demonstrated a high sensitivity of the mouse tibia to the loading direction across all groups and time points. Higher failure loads were found for several loading directions (θ = 10°, ϕ 205°-210°) than for the nominal axial case (θ = 0°, ϕ = 0°), highlighting adaptation of the bone for loading directions far from the nominal axial one. Conclusion: These results suggest that in studies which use mouse tibia, the loading direction can significantly impact the failure load. Thus, the magnitude and direction of the applied load should be well controlled during the experiments.

Bone turnover and mineralisation kinetics control trabecular BMDD and apparent bone density: insights from a discrete statistical bone remodelling model.

The mechanical quality of trabecular bone is influenced by its mineral content and spatial distribution, which is controlled by bone remodelling and mineralisation. Mineralisation kinetics occur in two phases: a fast primary mineralisation and a secondary mineralisation that can last from several months to years. Variations in bone turnover and mineralisation kinetics can be observed in the bone mineral density distribution (BMDD). Here, we propose a statistical spatio-temporal bone remodelling model to study the effects of bone turnover (associated with the activation frequency Ac . f ) and mineralisation kinetics (associated with secondary mineralisation T sec ) on BMDD. In this model, individual basic multicellular units (BMUs) are activated discretely on trabecular surfaces that undergo typical bone remodelling periods. Our results highlight that trabecular BMDD is strongly regulated by Ac . f and T sec in a coupled way. Ca wt% increases with lower Ac . f and short T sec . For example, a Ac . f = 4 BMU/year/mm 3 and T sec = 8 years result in a mean Ca wt% of 25, which is in accordance with Ca wt% values reported in quantitative backscattered electron imaging (qBEI) experiments. However, for lower Ac . f and shorter T sec (from 0.5 to 4 years) one obtains a high Ca wt% and a very narrow skew BMDD to the right. This close link between Ac . f and T sec highlights the importance of considering both characteristics to draw meaningful conclusion about bone quality. Overall, this model represents a new approach to modelling healthy and diseased bone and can aid in developing deeper insights into disease states like osteoporosis.

Cortical bone adaptation response is region specific, but not peak load dependent: insights from µ CT image analysis and mechanostat simulations of the mouse tibia loading model.

The two major aims of the present study were: (i) quantify localised cortical bone adaptation at the surface level using contralateral endpoint imaging data and image analysis techniques, and (ii) investigate whether cortical bone adaptation responses are universal or region specific and dependent on the respective peak load. For this purpose, we re-analyse previously published µ CT data of the mouse tibia loading model that investigated bone adaptation in response to sciatic neurectomy and various peak load magnitudes (F = 0, 2, 4, 6, 8, 10, 12 N). A beam theory-based approach was developed to simulate cortical bone adaptation in different sections of the tibia, using longitudinal strains as the adaptive stimuli. We developed four mechanostat models: universal, surface-based, strain directional-based, and combined surface and strain direction-based. Rates of bone adaptation in these mechanostat models were computed using an optimisation procedure (131,606 total simulations), performed on a single load case (F = 10 N). Subsequently, the models were validated against the remaining six peak loads. Our findings indicate that local bone adaptation responses are quasi-linear and bone region specific. The mechanostat model which accounted for differences in endosteal and periosteal regions and strain directions (i.e. tensile versus compressive) produced the lowest root mean squared error between simulated and experimental data for all loads, with a combined prediction accuracy of 76.6, 55.0 and 80.7% for periosteal, endosteal, and cortical thickness measurements (in the midshaft of the tibia). The largest root mean squared errors were observed in the transitional loads, i.e. F = 2 to 6 N, where inter-animal variability was highest. Finally, while endpoint imaging studies provide great insights into organ level bone adaptation responses, the between animal and loaded versus control limb variability make simulations of local surface-based adaptation responses challenging.

Cortical thickness adaptation to combined mechanical loading and parathyroid hormone treatments is site specific and synergistic in the mouse tibia model.

In this study, we aimed to quantify the localised effects of mechanical loading (ML), low (20 µg/kg/day), moderate (40 µg/kg/day) or high (80 µg/kg/day) dosages of parathyroid hormone (PTH), and combined (PTHML) treatments on cortical bone adaptation in healthy 19-week old female C57BL/6 mice. To this end, we utilise a previously reported image analysis algorithm on µCT data of the mouse tibia published by Sugiyama et al. (2008) to measure changes in cortical area, marrow cavity area and local cortical thickness measures (ΔCt.Ar, ΔMa.Ar, ΔCt.Th respectively), evaluated at two cross-sections within the mouse tibia (proximal-middle (37 %) and middle (50 %)), and are compared to a superposed summation (P + M) of individual treatments to determine the effectiveness of combining treatments in vivo. ΔCt.Ar analysis revealed a non-linear, synergistic interactions between PTH and ML in the 37 % cross-section that saturates at higher PTH dosages, whereas the 50 % cross-section experiences an approximately linear, additive adaptation response. This coincided with an increase in ΔMa.Ar (indicating resorption of the endosteal surface), which was only counteracted by combined high dose PTH with ML in the middle cross-section. Regional analysis of ΔCt.Th changes reveal localised cortical thinning in response to low dose PTH treatment in the posteromedial region of the middle cross-section, signifying that PTH does not provide a homogeneous adaptation response around the cortical perimeter. We observe a synergistic response in the proximal-middle cross-section, with regions of compressive strain experiencing the greatest adaptation response to PTHML treatments, (peak ΔCt.Th of 189.32, 213.78 and 239.30 µm for low, moderate and high PTHML groups respectively). In contrast, PTHML treatments in the middle cross-section show a similar response to the superposed P + M group, with the exception of the combined high dose PTHML treatment which shows a synergistic interaction. These analyses suggest that, in mice, adding mechanical loading to PTH treatments leads to region specific bone responses; synergism of PTHML is only achieved in some regions experiencing high loading, while other regions respond additively to this combined treatment.

An automated parametric ear model to improve frugal 3D scanning methods for the advanced manufacturing of high-quality prosthetic ears.

Ear prostheses are commonly used for restoring aesthetics to those suffering missing or malformed external ears. Traditional fabrication of these prostheses is labour intensive and requires expert skill from a prosthetist. Advanced manufacturing including 3D scanning, modelling and 3D printing has the potential to improve this process, although more work is required before it is ready for routine clinical use. In this paper, we introduce a parametric modelling technique capable of producing high quality 3D models of the human ear from low-fidelity, frugal, patient scans; significantly reducing time, complexity and cost. Our ear model can be tuned to fit the frugal low-fidelity 3D scan through; (a) manual tuning, or (b) our automated particle filter approach. This potentially enables low-cost smartphone photogrammetry-based 3D scanning for high quality personalised 3D printed ear prosthesis. In comparison to standard photogrammetry, our parametric model improves completeness, from (81 ± 5)% to (87 ± 4)%, with only a modest reduction in accuracy, with root mean square error (RMSE) increasing from (1.0 ± 0.2) mm to (1.5 ± 0.2) mm (relative to metrology rated reference 3D scans, n = 14). Despite this reduction in the RMS accuracy, our parametric model improves the overall quality, realism, and smoothness. Our automated particle filter method differs only modestly compared to manual adjustments. Overall, our parametric ear model can significantly improve quality, smoothness and completeness of 3D models produced from 30-photograph photogrammetry. This enables frugal high-quality 3D ear models to be produced for use in the advanced manufacturing of ear prostheses.

Beam theory for rapid strain estimation in the mouse tibia compression model.

The mouse tibia compression model is a leading model for studying bone's mechanoadaptive response to load. In studying this mechanoadaptive response, (FE) modelling is often used to determine the stress/strain within the tibia. The development of such models can be challenging and computationally expensive. An alternate approach is to use continuum mechanics based analytical theories, such as beam theory (BT). However, applying BT to the mouse tibia requires the fibula be neglected, introducing error in the stress/strain distribution. While several studies have applied BT to the mouse tibia, no study has explored the accuracy of this approach. To address these questions, this work investigates the use of BT in determining stress/strain within the mouse tibia. By comparing BT against FE modelling, it was found that BT can accurately predict tibial stress/strain if correction factors are applied to account for the effect of the fibula. The 25, 37, 50 and 75% cross sections are studied. Focusing on the 37% cross section, without correction, BT can have errors of approximately 21.6%. With correction, this is reduced to 6.6%. Such correction factors are presented. The developed BT model is applicable in the diaphysis and distal metaphysis, where the assumptions of BT are valid. This work verifies BT for determining localised strains in a mouse tibia compression model. This is anticipated to provide efficiency dividends, allowing for high throughput modelling of the mouse tibia, advancing study of bone's mechanoadaptive response.

Treatment with a long-acting chimeric CSF1 molecule enhances fracture healing of healthy and osteoporotic bones.

Macrophage-targeted therapies, including macrophage colony-stimulating factor 1 (CSF1), have been shown to have pro-repair impacts post-fracture. Preclinical/clinical applications of CSF1 have been expedited by development of chimeric CSF1-Fc which has extended circulating half-life. Here, we used mouse models to investigate the bone regenerative potential of CSF1-Fc in healthy and osteoporotic fracture. We also explored whether combination of CSF1-Fc with interleukin (IL)-4 provided additional fracture healing benefit in osteopenic bone. Micro-computed tomography, in situ histomorphometry, and bone mechanical parameters were used to assess systemic impacts of CSF1-Fc therapy in naive mice (male and female young, adult and geriatric). An intermittent CSF1-Fc regimen was optimized to mitigate undesirable impacts on bone resorption and hepatosplenomegaly, irrespective of age or gender. The intermittent CSF1-Fc regimen was tested in a mid-diaphyseal femoral fracture model in healthy bones with treatment initiated 1-day post-fracture. Weekly CSF1-Fc did not impact osteoclasts but increased osteal macrophages and improved fracture strength. Importantly, this treatment regimen also improved fracture union and strength in an ovariectomy-model of delayed fracture repair. Combining CSF1-Fc with IL-4 initiated 1-week post-fracture reduced the efficacy of CSF1-Fc. This study describes a novel strategy to specifically achieve bone regenerative actions of CSF1-Fc that has the potential to alleviate fragility fracture morbidity and mortality.

Cortical Thickness Adaptive Response to Mechanical Loading Depends on Periosteal Position and Varies Linearly With Loading Magnitude.

The aim of the current study was to quantify the local effect of mechanical loading on cortical bone formation response at the periosteal surface using previously obtained µCT data from a mouse tibia mechanical loading study. A novel image analysis algorithm was developed to quantify local cortical thickness changes (ΔCt.Th) along the periosteal surface due to different peak loads (0N ≤ F ≤ 12N) applied to right-neurectomised mature female C57BL/6 mice. Furthermore, beam analysis was performed to analyse the local strain distribution including regions of tensile, compressive, and low strain magnitudes. Student's paired t-test showed that ΔCt.Th in the proximal (25%), proximal/middle (37%), and middle (50%) cross-sections (along the z-axis of tibia) is strongly associated with the peak applied loads. These changes are significant in a majority of periosteal positions, in particular those experiencing high compressive or tensile strains. No association between F and ΔCt.Th was found in regions around the neutral axis. For the most distal cross-section (75%), the association of loading magnitude and ΔCt.Th was not as pronounced as the more proximal cross-sections. Also, bone formation responses along the periosteum did not occur in regions of highest compressive and tensile strains predicted by beam theory. This could be due to complex experimental loading conditions which were not explicitly accounted for in the mechanical analysis. Our results show that the bone formation response depends on the load magnitude and the periosteal position. Bone resorption due to the neurectomy of the loaded tibia occurs throughout the entire cross-sectional region for all investigated cortical sections 25, 37, 50, and 75%. For peak applied loads higher than 4 N, compressive and tensile regions show bone formation; however, regions around the neutral axis show constant resorption. The 50% cross-section showed the most regular ΔCt.Th response with increased loading when compared to 25 and 37% cross-sections. Relative thickness gains of approximately 70, 60, and 55% were observed for F = 12 N in the 25, 37, and 50% cross-sections. ΔCt.Th at selected points of the periosteum follow a linear response with increased peak load; no lazy zone was observed at these positions.

Toward Patient Specific Models of Pediatric IVDs: A Parametric Study of IVD Mechanical Properties.

Patient specific finite element (FE) modeling of the pediatric spine is an important challenge which offers to revolutionize the treatment of pediatric spinal pathologies, for example adolescent idiopathic scoliosis (AIS). In particular, modeling of the intervertebral disc (IVD) is a unique challenge due to its structural and mechanical complexity. This is compounded by limited ability to non-invasively interrogate key mechanical parameters of a patient's IVD. In this work, we seek to better understand the link between mechanical properties and mechanical behavior of patient specific FE models of the pediatric lumbar spine. A parametric study of IVD parameter was conducted, coupled with insights from current knowledge of the pediatric IVD. In particular, the combined effects of parameters was investigated. Recommendations are made toward areas of importance in patient specific FE modeling of the pediatric IVD. In particular, collagen fiber bundles of the IVD are found to dominate IVD mechanical behavior and are thus recommended as an area of primary focus for patient specific FE models. In addition, areas requiring further experimental research are identified. This work provides a valuable building block toward the development of patient specific models of the pediatric spine.

Soot particle morphology and nanostructure with oxygenated fuels: A comparative study into cold-start and hot-start operation.

This study investigates the morphology and nanostructure of soot particles during cold-start and hot-start engine operation of a diesel engine using oxygenated fuels. The soot samples were analysed using transmission electron microscopy. The oxygen content in the fuel was varied between 0 and 12%. The results showed that the primary particles during cold-start have significantly smaller size when compared to hot-start engine operation. The addition of oxygenated fuels also resulted in smaller sized primary particles. Smaller radius of gyration and higher fractal dimension of soot aggregates during cold-start would mean smaller aggregate size with a more compact structure. Shorter fringes with a higher inter-fringe spacing for cold-start would mean lower graphitisation of soot particles that could be related to higher oxidation reactivity of soot particles.

Estimation of load conditions and strain distribution for in vivo murine tibia compression loading using experimentally informed finite element models.

The murine tibia compression model, is the gold standard for studying bone adaptation due to mechanical loading in vivo. Currently, a key limitation of the experimental protocol and associated finite element (FE) models is that the exact load transfer, and consequently the loading conditions on the tibial plateau, is unknown. Often in FE models, load is applied to the tibial plateau based on inferences from micro-computed tomography (µCT). Experimental models often use a single strain gauge to assess the three-dimensional (3D) loading state. However, a single strain gauge is insufficient to validate such FE models. To address this challenge, we develop an experimentally calibrated method for identifying the load application region on the tibial plateau based upon measurements from three strain gauges. To achieve this, axial compression was conducted on mouse tibiae (n=3), with strains gauges on three surfaces. FE simulations were performed to compute the strains at the gauge locations as a function of a variable load location. By minimising the error between experimental and FE strains, the precise load location was identified; this was found to vary between tibia specimens. It was further shown that commonly used FE loading conditions, found in literature, did not replicate the experimental strain distribution, highlighting the importance of load calibration. This work provides critical insights into how load is transferred to the tibial plateau. Importantly, this work develops an experimentally informed technique for loading the tibial plateau in FE models.

Atypical Defect Motions in Brittle Layered Sodium Titanate Nanowires.

In situ tensile tests show atypical defect motions in the brittle Na2Ti3O7 (NTO) nanowire (NW) within the elastic deformation range. After brittle fracture, elastic recovery of the NTO NW is followed by reversible motion of the defects in a time-dependent manner. An in situ cyclic loading-unloading test shows that these mobile defects shift back and forth along the NW in accordance with the loading-unloading cycles and eventually restore their initial positions after the load is completely removed. The existence of the defects within the NTO NWs and their motions does not lead to plastic deformation of the NW. The atypical defect motion is speculated to be the result of the glidibility of the TiO6 layers, where weakly bonded cation layers are in between. Exploration of the above novel observation can establish new understandings of the deformation behavior of superlattice nanostructures.

Steered molecular dynamics characterization of the elastic modulus and deformation mechanisms of single natural tropocollagen molecules.

Collagen is a common structural protein, providing mechanical integrity for various vertebrate connective tissues such as cartilage and bone. The mechanical behaviours of these tissues under physical stimulations are controlled by the hierarchical structure of collagen and its interactions with other extracellular matrix molecules. However, the mechanical properties and deformation mechanisms of natural collagen under physiological loading rates at the molecular level are not fully understood. In this study, comprehensive steered molecular dynamics (SMD) simulations were performed on the 2nd intact overlap region (d2ol) and the 2nd intact D-period (d2olgp) of an in-situ characterized collagen molecule, under a large range of strain rates (6.5 × 106% s-1 to 1.3 × 1012% s-1). The results show that, depending on the applied strain rates, tropocollagen molecules unfold in different ways. Particularly, at high and intermediate strain rates, the number of inter-chain hydrogen bonds decreases rapidly even at small deformations, leading to a dramatic increase in the force. This results in an increase in the estimated Young's modulus of collagen triple helices as the deformation rate goes up, which, together with the nonlinear mechanical behaviour, explains the broad range of the Young's modulus for collagen model peptides reported in earlier SMD studies. Atomistic-level analyses indicate that the elastic modulus of single tropocollagen molecules decreases as the strain rate becomes smaller. However, for strain rates below 1.3 × 108% s-1, the tangent Young's modulus of d2ol (d2olgp) converges to approximately 3.2 GPa (3.4 GPa), at the strain of 10.5% (12%) when the segment is fully uncrimped. Furthermore, for strain rates under 1.3 × 108% s-1, d2ol and d2olgp show identical deformation mechanisms (unwinding, uncoiling and backbone stretching), but the corresponding strain ranges are different. This study will aid in future studies on characterizing the mechanical properties of collagen molecules and collagen-like peptides by indicating the proper pulling strain rates and how to determine the suitable strain range used for evaluating the elastic modulus.

In situ mechanical resonance behaviour of pristine and defective zinc blende GaAs nanowires.

The structural versatility of semiconducting gallium arsenide (GaAs) nanowires (NWs) provides an exciting direction for the engineering of their mechanical and dynamic properties. However, the dynamic behaviour of GaAs NWs remains unexplored. In this study, comprehensive in situ mechanical resonance tests were conducted to explore the dynamic behaviour of pristine and defective zinc blende GaAs NWs. The effects of stacking faults (SFs), amorphous shell, NW tapering and end-mass particles were investigated. The quality factors (QFs) of the GaAs NWs were found to be predominately governed by surface effects, which increased linearly with the volume to surface area ratio. Interestingly, SFs were found not to influence the QFs. To extract the mechanical properties, the Euler-Bernoulli beam theory was modified, to incorporate the core-shell model, NW tapering and end-mass particles. It was found that the core-shell model accurately predicts the mechanical properties of the pristine GaAs NWs, which exhibit significant stiffening at radii below 50 nm. Conversely, the mechanical properties of the defective NWs were influenced by the presence of SFs, causing a wide variance in the Young's modulus. Apart from establishing an understanding of the resonance behaviour of GaAs NWs, this research provides guidance for the design of NWs for their applications in dynamic nanomechanical devices with tailorable dynamic properties.