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

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.

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 με. 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.

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.

Large scale analysis of osteocyte lacunae in klotho hypomorphic mice using high-resolution micro-computed tomography

BACKGROUND

Osteocytes are the most abundant cell type in adult bone, and the morphological characteristics of osteocytes and their lacunae appear to influence bone mass and fragility. Although conventional computed tomography (CT) has contributed greatly to advances in bone morphometry, capturing details of the entire hierarchical assembly, e.g., osteocyte lacuna parameters, has been limited by the analytical performance of CT (> 1 µm resolution).

METHODS

We used high-resolution (700 nm) micro-CT to evaluate and compare the osteocyte lacuna parameters over a large scale, i.e., in a maximum of about 45,700 lacunae (average), in tibial metaphyseal cortical bones of wild-type (WT) and αKlotho-hypomorphic (kl/kl) mice, the latter a model that exhibits osteopenia and aberrant osteocytes.

RESULTS

Of osteocyte lacuna parameters, lacunar surface per lacunar volume were significantly lower and lacuna diameter were significantly larger in kl/kl mice compared to WT mice. By analysis of individual osteocyte lacunae, we found that lacunar sphericity in kl/kl mice was higher than that in WT mice, and the diameters in the major and the minor axes were respectively lower and higher in kl/kl mice, especially at the proximal site of the region of interest.

CONCLUSION

We successfully assessed osteocyte lacuna parameters on the largest scale in mice reported to date and found that the shape of osteocyte lacunae of kl/kl mice are significantly different from those of WT mice. Although the mechanisms underlying the lacunar shape differences observed are not yet clear, changes in lacunar geometry are known to affect the transitions of strains to the osteocyte microenvironment and likely local osteocyte response(s). Thus, the fact that the differences are limited to the mesial region near the primary spongiosa suggests the likelihood of site-specific anomalies in mechanosensitive effects in kl/kl osteocytes with consequent site-specific effects bone metabolism and function.

Using Finite Element Modeling in Bone Mechanoadaptation

PURPOSE OF THE REVIEW

Bone adapts structure and material properties in response to its mechanical environment, a process called mechanoadpatation. For the past 50 years, finite element modeling has been used to investigate the relationships between bone geometry, material properties, and mechanical loading conditions. This review examines how we use finite element modeling in the context of bone mechanoadpatation.

RECENT FINDINGS

Finite element models estimate complex mechanical stimuli at the tissue and cellular levels, help explain experimental results, and inform the design of loading protocols and prosthetics. FE modeling is a powerful tool to study bone adaptation as it complements experimental approaches. Before using FE models, researchers should determine whether simulation results will provide complementary information to experimental or clinical observations and should establish the level of complexity required. As imaging technics and computational capacity continue increasing, we expect FE models to help in designing treatments of bone pathologies that take advantage of mechanoadaptation of bone.

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.

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.