Adaptive changes in micromechanical environments of cancellous and cortical bone in response to in vivo loading and disuse

Combining anabolic loading and raloxifene improves bone quantity and some quality measures in a mouse model of osteogenesis imperfecta

Osteogenesis imperfecta (OI) increases fracture risk due to changes in bone quantity and quality caused by mutations in collagen and its processing proteins. Current therapeutics improve bone quantity, but do not treat the underlying quality deficiencies. Male and female G610C+/- mice, a murine model of OI, were treated with a combination of raloxifene and in vivo axial tibial compressive loading starting at 10 weeks of age and continuing for 6 weeks to improve bone quantity and quality. Bone geometry and mechanical properties were measured to determine whole bone and tissue-level material properties. A colocalized Raman/nanoindentation system was used to measure chemical composition and nanomechanical properties in newly formed bone compared to old bone to determine if bone formed during the treatment regimen differed in quality compared to bone formed prior to treatment. Lastly, lacunar geometry and osteocyte apoptosis were assessed. OI mice were able to build bone in response to the loading, but this response was less robust than in control mice. Raloxifene improved some bone material properties in female but not male OI mice. Raloxifene did not alter nanomechanical properties, but loading did. Lacunar geometry was largely unchanged with raloxifene and loading. However, osteocyte apoptosis was increased with loading in raloxifene treated female mice. Overall, combination treatment with raloxifene and loading resulted in positive but subtle changes to bone quality.

Porosity and surface curvature effects on the permeability and wall shear stress of trabecular bone: Guidelines for biomimetic scaffolds for bone repair

Scaffolds are an essential component of bone tissue engineering to provide support and create a physiological environment for cells. Biomimetic scaffolds are a promising approach to fulfill the requirements. Bone allografts are widely used scaffolds due to their mechanical and structural characteristics. The scaffold geometry is well known to be an important determinant of induced mechanical stimulation felt by the cells. However, the impact of allograft geometry on permeability and wall shear stress distribution is not well understood. This information is essential for designing biomimetic scaffolds that provide a suitable environment for cells to proliferate and differentiate. The present study investigates the effect of geometry on the permeability and wall shear stress of bone allografts at both macroscopic and microscopic scales. Our results concluded that the wall shear stress was strongly correlated with the porosity of the allograft. The level of wall shear stress at a local scale was also determined by the surface curvature characteristics. The results of this study can serve as a guideline for future biomimetic scaffold designs that provide a mechanical environment favorable for osteogenesis and bone repair.

Cortical and Trabecular Bone Modeling and Implications for Bone Functional Adaptation in the Mammalian Tibia

Bone modeling involves the addition of bone material through osteoblast-mediated deposition or the removal of bone material via osteoclast-mediated resorption in response to perceived changes in loads by osteocytes. This process is characterized by the independent occurrence of deposition and resorption, which can take place simultaneously at different locations within the bone due to variations in stress levels across its different regions. The principle of bone functional adaptation states that cortical and trabecular bone tissues will respond to mechanical stimuli by adjusting (i.e., bone modeling) their morphology and architecture to mechanically improve their mechanical function in line with the habitual in vivo loading direction. This principle is relevant to various research areas, such as the development of improved orthopedic implants, preventative medicine for osteopenic elderly patients, and the investigation of locomotion behavior in extinct species. In the present review, the mammalian tibia is used as an example to explore cortical and trabecular bone modeling and to examine its implications for the functional adaptation of bones. Following a short introduction and an exposition on characteristics of mechanical stimuli that influence bone modeling, a detailed critical appraisal of the literature on cortical and trabecular bone modeling and bone functional adaptation is given. By synthesizing key findings from studies involving small mammals (rodents), large mammals, and humans, it is shown that examining both cortical and trabecular bone structures is essential for understanding bone functional adaptation. A combined approach can provide a more comprehensive understanding of this significant physiological phenomenon, as each structure contributes uniquely to the phenomenon.

Finite element study on the micromechanics of cement-augmented proximal femoral nail anti-rotation (PFNA) for intertrochanteric fracture treatment

Blade cut-out is a common complication when using proximal femoral nail anti-rotation (PFNA) for the treatment of intertrochanteric fractures. Although cement augmentation has been introduced to overcome the cut-out effect, the micromechanics of this approach remain to be clarified. While previous studies have developed finite element (FE) models based on lab-prepared or cadaveric samples to study the cement-trabeculae interface, their demanding nature and inherent disadvantages limit their application. The aim of this study was to develop a novel 'one-step forming' method for creating a cement-trabeculae interface FE model to investigate its micromechanics in relation to PFNA with cement augmentation. A human femoral head was scanned using micro-computed tomography, and four volume of interest (VOI) trabeculae were segmented. The VOI trabeculae were enclosed within a box to represent the encapsulated region of bone cement using ANSYS software. Tetrahedral meshing was performed with Hypermesh software based on Boolean operation. Finally, four cement-trabeculae interface FE models comprising four interdigitated depths and five FE models comprising different volume fraction were established after element removal. The effects of friction contact, frictionless contact, and bond contact properties between the bone and cement were identified. The maximum micromotion and stress in the interdigitated and loading bones were quantified and compared between the pre- and post-augmentation situations. The differences in micromotion and stress with the three contact methods were minimal. Micromotion and stress decreased as the interdigitation depth increased. Stress in the proximal interdigitated bone showed a correlation with the bone volume fraction (R2 = 0.70); both micromotion (R2 = 0.61) and stress (R2 = 0.93) at the most proximal loading region exhibited a similar correlation tendency. When comparing the post- and pre-augmentation situations, micromotion reduction in the interdigitated bone was more effective than stress reduction, particularly near the cement border. The cementation resulted in a significant reduction in micromotion within the loading bone, while the decrease in stress was minimal. Noticeable gradients of displacement and stress reduction can be observed in models with lower bone volume fraction (BV/TV). In summary, cement augmentation is more effective at reducing micromotion rather than stress. Furthermore, the reinforcing impact of bone cement is particularly prominent in cases with a low BV/TV. The utilization of bone cement may contribute to the stabilization of trabecular bone and PFNA primarily by constraining micromotion and partially shielding stress.

Meta-analysis of the Relationship Between Zinc and Copper in Patients with Osteoarthritis

This study aims to explore the relationship between osteoarthritis and the trace elements zinc and copper and to provide a theoretical basis for research on the related mechanisms for the prevention, diagnosis, and treatment of osteoarthritis. We searched all the literature indexed in Web Of Science, Embase, and PubMed as of January 10, 2024, summarized the zinc and copper detection indexes in patients with osteoarthritis, obtained clinical data through literature screening, quality assessment, and data extraction, and analyzed the data using Revman 5.4. A total of 13 papers were included in this study, totaling 7983 study subjects. These were divided into osteoarthritis and healthy control groups. The results from the meta-analysis showed that in patients with osteoarthritis, circulating copper levels, but not zinc levels, were significantly higher compared to healthy individuals. The level of copper in the blood of patients with osteoarthritis is significantly higher than that of healthy people.

Studying trabecular bone samples demonstrates a power law relation between deteriorated structure and mechanical properties - a study combining 3D printing with the finite element method

Introduction

The bone volume fraction (BV/TV) significantly contributes to the mechanical properties of trabecular bone. However, when studies compare normal trabeculae against osteoporotic trabeculae (in terms of BV/TV decrease), only an "average" mechanical result has been determined because of the limitation that no two trabecular structures are the same and that each unique trabecular structure can be mechanically tested only once. The mathematic relation between individual structural deterioration and mechanical properties during aging or the osteoporosis process has yet to be further clarified. Three-dimensional (3D) printing and micro-CT-based finite element method (μFEM) can assist in overcoming this issue.

Methods

In this study, we 3D printed structural-identical but BV/TV value-attenuated trabecular bones (scaled up ×20) from the distal femur of healthy and ovariectomized rats and performed compression mechanical tests. Corresponding μFEM models were also established for simulations. The tissue modulus and strength of 3D printed trabecular bones as well as the effective tissue modulus (denoted as Ez) derived from μFEM models were finally corrected by the side-artifact correction factor.

Results

The results showed that the tissue modulus _corrected, strength _corrected and Ez _corrected exhibited a significant power law function of BV/TV in structural-identical but BV/TV value-attenuated trabecular samples.

Discussion

Using 3D printed bones, this study confirms the long-known relationship measured in trabecular tissue with varying volume fractions. In the future, 3D printing may help us attain better bone strength evaluations and even personal fracture risk assessments for patients who suffer from osteoporosis.

A New Microarchitecture-Based Parameter to Predict the Micromechanical Properties of Bone Allografts

Scaffolds are an essential component of bone tissue engineering. They provide support and create a physiological environment for cells to proliferate and differentiate. Bone allografts extracted from human donors are promising scaffolds due to their mechanical and structural characteristics. Bone microarchitecture is well known to be an important determinant of macroscopic mechanical properties, but its role at the microscopic, i.e., the trabeculae level is still poorly understood. The present study investigated linear correlations between microarchitectural parameters obtained from X-ray computed tomography (micro-CT) images of bone allografts, such as bone volume fraction (BV/TV), degree of anisotropy (DA), or ellipsoid factor (EF), and micromechanical parameters derived from micro-finite element calculations, such as mean axial strain (ε_z) and strain energy density (W_e). DAEF, a new parameter based on a linear combination of the two microarchitectural parameters DA and EF, showed a strong linear correlation with the bone mechanical characteristics at the microscopic scale. Our results concluded that the spatial distribution and the plate-and-rod structure of trabecular bone are the main determinants of the mechanical properties of bone at the microscopic level. The DAEF parameter could, therefore, be used as a tool to predict the level of mechanical stimulation at the local scale, a key parameter to better understand and optimize the mechanism of osteogenesis in bone tissue engineering.

Osteocyte Estrogen Receptor β (Ot-ERβ) Regulates Bone Turnover and Skeletal Adaptive Response to Mechanical Loading Differently in Male and Female Growing and Adult Mice

Age-related bone loss is a failure of balanced bone turnover and diminished skeletal mechanoadaptation. Estrogen receptors, ERα and ERβ, play critical roles in osteoprotective regulation activated by estrogen and mechanical signals. Previous studies mainly focused on ERα and showed that osteocyte-ERα (Ot-ERα) regulated trabecular, but not cortical bone, and played a minor role in load-induced cortical adaptation. However, the role of Ot-ERβ in bone mass regulation remains unrevealed. To address this issue, we characterized bone (re)modeling and gene expression in male and female mice with Ot-ERβ deletion (ERβ-dOT) and littermate control (LC) at 10 weeks (young) or 28 weeks (adult) of age, as well as their responses to in vivo tibial compressive loading. Increased cancellous bone mass appeared in the L4 vertebral body of young male ERβ-dOT mice. At the same time, femoral cortical bone gene expression showed signs consistent with elevated osteoblast and osteoclast activities (type-I collagen, Cat K, RANKL). Upregulated androgen receptor (AR) expression was observed in young male ERβ-dOT mice relative to LC, suggesting a compensatory effect of testosterone on male bone protection. In contrast, bone mass in L4 decreased in adult male ERβ-dOT mice, attributed to potentially increased bone resorption activity (Cat K) with no change in bone formation. There was no effect of ERβ-dOT on bone mass or gene expression in female mice. Sex-dependent regulation of Ot-ERβ also appeared in load-induced cortical responsiveness. Young female ERβ-dOT mice showed an enhanced tibial cortical anabolic adaptation compared with LC. In contrast, an attenuated cortical anabolic response presented at the proximal tibia in male ERβ-dOT mice at both ages. For the first time, our findings suggest that Ot-ERβ regulates bone (re)modeling and the response to mechanical signals through different mechanisms in males and females. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

Improve biomechanical stability using intramedullary nails with femoral neck protection in femoral shaft fractures

BACKGROUND AND OBJECTIVE

Elderly patients treated for femoral shaft fractures have a higher risk of hip fracture. We hypothesized that intramedullary nails protecting the femoral neck can improve mechanical strength and reduce the risk of subsequent hip fracture. This study aims to analyze the biomechanical stability using intramedullary nails with or without femoral neck protection through finite element analysis.

METHODS

Thirty finite element models (FEMs) were established, including five different conditions of femoral shaft fracture: Fracture healing, Proximal fractures (Transverse and oblique), Distal fractures (Transverse and oblique), and five different fixation methods. Femoral neck protection groups: cephalomedullary nail (CN), reconstruction nail (RN); No femoral neck protection groups: type-1 of antegrade intramedullary nail (AIN-1), type-2 of antegrade intramedullary nail (AIN-2), and retrograde intramedullary nail (RIN). The maximum stress of bone and internal fixation in the femoral neck region for all type of fixation were calculated to evaluate the biomechanical stability.

RESULTS

Maximum equivalent stress values of bone in the femoral neck region for five different conditions of femoral shaft fracture: AIN-2 (77.23 MPa) >RIN (77.15 MPa) > AIN-1 (76.71 MPa) > CN (60.74 MPa) > RN (57.66 MPa) for the fracture healing; RIN (80.05 MPa) > AIN-1 (79.15 MPa) > AIN-2(78.77 MPa) > RN (65.16 MPa) > CN (65.03 MPa) for the proximal transverse fracture; RIN (80.10 MPa) > AIN-2 (79.36 MPa) > AIN-1 (79.18 MPa) > RN (65.09 MPa) > CN (64.96 MPa) for the proximal oblique fracture; RIN (80.24 MPa) > AIN-2 (79.68 MPa) > AIN-1 (79.33 MPa) > CN (65.02 MPa) > RN (64.76 MPa) for the distal transverse fracture; RIN (80.23 MPa) > AIN-2 (79.61 MPa) > AIN-1 (79.35 MPa) > CN (65.06 MPa) > RN (64.76 MPa) for the distal oblique fracture. Maximum equivalent stress of internal fixation in the femoral neck region is greater than the maximum stress of bone and avoids stress concentration of bone for the femoral neck protection groups (CN and RN).

CONCLUSIONS

Intramedullary nails with femoral neck protection in the treatment of femoral shaft fractures improve mechanical strength and prevent secondary hip fractures and decrease the overall risk of reoperation postoperatively.

Medial tibial plateau sustaining higher physiological stress than the lateral plateau: based on 3D printing and finite element method

Background

Medial compartment knee osteoarthritis (KOA) accounts for most KOA cases, and increased trabecular bone volume fraction (BV/TV) is one of the pathological changes in the tibial plateau of KOA. How BV/TV changes before and after the menopause and its effects on medial compartment KOA are yet to be clarified.

Methods

Twenty femurs from twenty 12-week-old rats were included. The operated group underwent ovariectomy (to represent the osteoporosis condition), called the O group, and the non-operated group was the normal control, called the N group. Micro-CT scans of the femoral condyles were acquired 12 weeks after the surgery, and the volume of interest (VOI) of medial-, inter-, and lateral-condyle trabeculae were three-dimensional (3D) printed for uniaxial compression mechanical test and simulated by the finite element (FE) method.

Results

The results demonstrated that the O group indicated poorer trabecular architecture than the N group in three parts of the femoral condyle, especially in the intercondyle. Within the group, the BV/TV, trabecular thickness (Tb.Th), and trabecular number (Tb.N) ratios between the medial and lateral condyles were greater than 1 in both N and O groups. The medial condyle trabeculae's mechanical properties were higher than those of the lateral condyle, and this superiority appears to be broadened under osteoporotic conditions. FE modelling well reproduced these mechanical differentiations.

Conclusions

According to Wolff's law, the higher BV/TV and mechanical properties of the medial femoral condyle may be due to inherent imbalanced loading on the knee component. Alterations in BV/TV and their corresponding mechanical properties may accompany KOA.

Interactive effects of various loading parameters on the fluid dynamics within the lacunar-canalicular system for a single osteocyte

The osteocyte lacunar-canalicular system (LCS) serves as a mechanotransductive core where external loading applied to the skeleton is transduced into mechanical signals (e.g., fluid shear) that can be sensed by mechanosensors (osteocytes). The fluid velocity and shear stress within the LCS are affected by various loading parameters. However, the interactive effect of distinct loading parameters on the velocity and shear stress in the LCS remains unclear. To address this issue, we developed a multiscale modeling approach, combining a poroelastic finite element (FE) model with a single osteocytic LCS unit model to calculate the flow velocity and shear stress within the LCS. Next, a sensitivity analysis was performed to investigate individual and interactive effects of strain magnitude, strain rate, number of cycles, and intervening short rests between loading cycles on the velocity and shear stress around the osteocyte. Lastly, we developed a relatively simple regression model to predict those outcomes. Our results demonstrated that the strain magnitude or rate alone were the main factors affecting the velocity and shear stress; however, the combination of these two was not directly additive, and addition of a short rest between cycles could enhance the combination of these two related factors. These results show highly interactive effects of distinct loading parameters on fluid velocity and shear stress in the LCS. Specifically, our results suggest that an enhanced fluid dynamics environment in the LCS can be achieved with a brief number of load cycles combined with short rest insertion and high strain magnitude and rate.

Sciatic neurectomy-related cortical bone loss exhibits delayed onset yet stabilises more rapidly than trabecular bone

Disuse osteoporosis occurs after extended periods of bed rest or nerve damage leading to increased risk of fracture. It remains to be established, however, whether the trajectory of bone loss is equivalent in bone's cortical and trabecular compartments following long-term periods of reduced loading. Herein, we evaluate sciatic neurectomy-related cortical and trabecular bone loss in the tibia by microCT. The right hind limb of seventeen 12 week-old female mice was subjected to sciatic neurectomy (right, SN; left, contralateral internal control) and the animals were sacrificed in four groups (n = 3-5/group) at 5, 35, 65 and 95 days thereafter. Cortical bone mass, geometry and mineral density were evaluated along almost the entire tibial length and trabecular bone was examined at the proximal metaphysis. We found that trabecular bone volume (BV/TV) and number were decreased within 5 days, with a trajectory of loss that only plateaued after 65 days post-SN. In contrast, decreases in cortical thickness, cross-sectional area, second moment of inertia along minor and major axes and predicted resistance to torsion were unmodified during the early 5 day period, attaining significance only after 35 days post-SN and, thereafter showed no further deterioration. Only cortical ellipticity and periosteal enclosed area, continued to change in the SN limbs (vs. contralateral) between 35 and 95 days along the tibia length. On the other hand, cortical tissue mineral density was unmodified by SN at any time point. These data indicate that SN-related cortical bone loss extends along almost the entire tibia, exhibits delayed onset and yet stabilises its architecture more rapidly than trabecular bone. These data suggest that the cortical and trabecular compartments behave as distinct modules in response to SN even within an individual bone.

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Responses to sciatic neurectomy (SN) in tibial trabecular bone are very protracted.

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Responses to SN in the cortices have delayed onset but stabilize more rapidly.

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Trabecular and cortical bone behave modularly in response to SN.

The plate-to-rod transition in trabecular bone loss is elusive

Changes in trabecular micro-architecture are key to our understanding of osteoporosis. Previous work focusing on structure model index (SMI) measurements have concluded that disease progression entails a shift from plates to rods in trabecular bone, but SMI is heavily biased by bone volume fraction. As an alternative to SMI, we proposed the ellipsoid factor (EF) as a continuous measure of local trabecular shape between plate-like and rod-like extremes. We investigated the relationship between EF distributions, SMI and bone volume fraction of the trabecular geometry in a murine model of disuse osteoporosis as well as from human vertebrae of differing bone volume fraction. We observed a moderate shift in EF median (at later disease stages in mouse tibia) and EF mode (in the vertebral samples with low bone volume fraction) towards a more rod-like geometry, but not in EF maximum and minimum. These results support the notion that the plate to rod transition does not coincide with the onset of bone loss and is considerably more moderate, when it does occur, than SMI suggests. A variety of local shapes not straightforward to categorize as rod or plate exist in all our trabecular bone samples.

Cancellous Bone May Have a Greater Adaptive Strain Threshold Than Cortical Bone

Strain magnitude has a controlling influence on bone adaptive response. However, questions remain as to how and if cancellous and cortical bone tissues respond differently to varied strain magnitudes, particularly at a molecular level. The goal of this study was to characterize the time‐dependent gene expression, bone formation, and structural response of the cancellous and cortical bone of female C57Bl/6 mice to mechanical loading by applying varying load levels (low: −3.5 N; medium: −5.2 N; high: −7 N) to the skeleton using a mouse tibia loading model. The loading experiment showed that cortical bone mass at the tibial midshaft was significantly enhanced following all load levels examined and bone formation activities were particularly elevated at the medium and high loads applied. In contrast, for the proximal metaphyseal cancellous bone, only the high load led to significant increases in bone mass and bone formation indices. Similarly, expression of genes associated with inhibition of bone formation (e.g., Sost) was altered in the diaphyseal cortical bone at all load levels, but in the metaphyseal cortico‐cancellous bone only by the high load. Finite element analysis determined that the peak tensile or compressive strains that were osteogenic for the proximal cancellous bone under the high load were significantly greater than those that were osteogenic for the midshaft cortical tissues under the low load. These results suggest that the magnitude of the strain stimulus regulating structural, cellular, and molecular responses of bone to loading may be greater for the cancellous tissues than for the cortical tissues. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Bone Geometry Is Altered by Follistatin-Induced Muscle Growth in Young Adult Male Mice

The development of the musculoskeletal system and its maintenance depends on the reciprocal relationship between muscle and bone. The size of skeletal muscles and the forces generated during muscle contraction are potent sources of mechanical stress on the developing skeleton, and they shape bone structure during growth. This is particularly evident in hypermuscular global myostatin (Mstn)‐null mice, where larger muscles during development increase bone mass and alter bone shape. However, whether muscle hypertrophy can similarly influence the shape of bones after the embryonic and prepubertal period is unknown. To address this issue, bone structure was assessed after inducing muscle hypertrophy in the lower hindlimbs of young‐adult C57BL/6J male mice by administering intramuscular injections of recombinant adeno‐associated viral vectors expressing follistatin (FST), a potent antagonist of Mstn. Two FST isoforms were used: the full‐length 315 amino acid isoform (FST‐315) and a truncated 288 amino acid isoform (FST‐288). In both FST‐treated cohorts, muscle hypertrophy was observed, and the anterior crest of the tibia, adjacent to the tibialis anterior muscle, was lengthened. Hypertrophy of the muscles surrounding the tibia caused the adjacent cortical shell to recede inward toward the central axis: an event driven by bone resorption adjacent to the hypertrophic muscle. The findings reveal that inducing muscle hypertrophy in mice can confer changes in bone shape in early adulthood. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Murine Axial Compression Tibial Loading Model to Study Bone Mechanobiology: Implementing the Model and Reporting Results

In vivo, tibial loading in mice is increasingly used to study bone adaptation and mechanotransduction. To achieve standardized and defined experimental conditions, loading parameters and animal-related factors must be considered when performing in vivo loading studies. In this review, we discuss these loading and animal-related experimental conditions, present methods to assess bone adaptation, and suggest reporting guidelines. This review originated from presentations by each of the authors at the workshop "Developing Best Practices for Mouse Models of In Vivo Loading" during the Preclinical Models Section at the Orthopaedic Research Society Annual Meeting, San Diego, CA, March 2017. Following the meeting, the authors engaged in detailed discussions with consideration of relevant literature. The guidelines and recommendations in this review are provided to help researchers perform in vivo loading experiments in mice, and thus further our knowledge of bone adaptation and the mechanisms involved in mechanotransduction. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:233-252, 2020.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

A new method to monitor bone geometry changes at different spatial scales in the longitudinal in vivo μCT studies of mice bones

Longitudinal studies of bone adaptation in mice using in vivo micro-computed tomography (μCT) have been commonly used for pre-clinical evaluation of physical and pharmacological interventions. The main advantage of this approach is to use each mouse as its own control, reducing considerably the sample size required by statistical power analysis. To date, multi-scale estimation of bone adaptations become essential since the bone activity that takes place at different scales may be associated with different bone mechanisms. Measures of bone adaptations at different time scales have been attempted in a previous study. This paper extends quantification of bone activity at different spatial scales with a proposition of a novel framework. The method involves applying level-set method (LSM) to track the geometric changes from the longitudinal in vivo μCT scans of mice tibia. Bone low- and high-spatial frequency patterns are then estimated using multi-resolution analysis. The accuracy of the framework is quantified by applying it to two times separated scanned images with synthetically manipulated global and/or local activity. The Root Mean Square Deviation (RMSD) was approximately 1.5 voxels or 0.7 voxels for the global low-spatial frequency or local high-spatial frequency changes, respectively. The framework is further applied to the study of bone changes in longitudinal datasets of wild-type mice tibiae over time and space. The results demonstrate the ability for the spatio-temporal quantification and visualisation of bone activity at different spatial scales in longitudinal studies thus providing further insight into bone adaptation mechanisms.