Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law

Phase diagrams of bone remodeling using a 3D stochastic cellular automaton

We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states: Formation, Quiescence, Resorption, and Environment. We simulate the Resorption and Formation processes on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment.

Mapping the Spatial Evolution of Proximal Femur Osteoporosis: A Retrospective Cross-Sectional Study Based on CT Scans

Purpose

The purpose of this study was to quantify the modifications occurring in osteoporosis at the level of the human proximal femur throughout the trabecular structure, along with the identification of certain anatomic regions preferentially affected by osteoporosis. Another goal was to map the evolution of the radiodensity of the trabecular bone as osteoporosis progresses to an advanced stage.

Methods

The study included CT scans (right femur) from 51 patients, out of which 40 had various degrees of osteoporosis, but no other local pathology. Ten regions of interest in two orthogonal slices have been identified and the differences in radiodensity as well as their evolution have been statistically analyzed in terms of relative and absolute changes.

Results

A detailed spatial map showing the evolution of osteoporosis was obtained. As osteoporosis evolved, the relative decrease in radiodensity was inversely correlated to the radiodensity of the healthy bone. In particular, the region covering the Ward triangle decreased the most, by an average 61-62% in osteopenia and 101-106% in advanced osteoporosis, while the principal compressive group was affected the least, showing a decrease by an average 14-15% in osteopenia and 29-32% in advanced osteoporosis. The absolute decrease in radiodensity was not correlated to the radiodensity of the healthy bone and was shifted to the inferior-posterior edge of the femur. Inside the femoral head, the upper region was affected the most in absolute terms, while the greater trochanter was less affected than the femoral neck. The maximum metaphyseal cortical bone density was unaffected by the progression of osteoporosis.

Conclusion

Significant differences were noticed in terms of the absolute and relative osteoporotic changes in radiodensity related to different anatomical regions of the human femoral bone. These differences become more pronounced as the disease progresses.

Artificial Intelligence-Based 3D Printing Strategies for Bone Scaffold Fabrication and Its Application in Preclinical and Clinical Investigations

3D printing has become increasingly popular in the field of bone tissue engineering. However, the mechanical properties, biocompatibility, and porosity of the 3D printed bone scaffolds are major requirements for tissue regeneration and implantation as well. Designing the scaffold architecture in accordance with the need to create better mechanical and biological stimuli is necessary to achieve unique scaffold properties. To accomplish this, different 3D designing strategies can be utilized with the help of the scaffold design library and artificial intelligence (AI). The implementation of AI to assist the 3D printing process can enable it to predict, adapt, and control the parameters on its own, which lowers the risk of errors. This Review emphasizes 3D design and fabrication of bone scaffold using different materials and the use of AI-aided 3D printing strategies. Also, the adaption of AI to 3D printing helps to develop patient-specific scaffolds based on different requirements, thus providing feedback and adequate data for reproducibility, which can be improvised in the future. These printed scaffolds can also serve as an alternative to preclinical animal test models to cut costs and prevent immunological interference.

Trabecula-level mechanoadaptation: Numerical analysis of morphological changes

BACKGROUND

Bone is a living material that, unlike man-made ones, demonstrates continuous adaptation of its structure and mechanical properties to resist the imposed mechanical loading. Adaptation in trabecular bone is characterised by improvement of its stiffness in the loading direction and respective realignment of trabecular load-bearing architecture. Considerable experimental and simulation evidence of trabecular bone adaptation to its mechanical environment at the tissue- and organ-levels was obtained, while little attention was given to the trabecula-level of this process. This study aims to describe and classify load-driven morphological changes at the level of individual trabeculae and to propose their drivers.

METHOD

For this purpose, a well-established mechanoregulation-based numerical model of bone adaptation was implemented in a user-defined subroutine that changed the structural and mechanical properties of trabeculae based on the magnitude of a mechanical stimulus. This subroutine was used in conjunction with finite-element models of variously shaped structures representing trabeculae loaded in compression or shear.

RESULTS

In all analysed cases, trabeculae underwent morphological evolution under applied compressive or shear loading. Among twelve cases analysed, six main mechanisms of morphological evolution were established: reorientation, splitting, merging, full resorption, thinning, and thickening. Moreover, all simulated cases presented the ability to reduce the mean value of von Mises stress while increasing their ability to resist compressive/shear loading during adaptation.

CONCLUSION

This study evaluated morphological and mechanical changes in trabeculae of different shapes in response to compressive or shear loadings and compared them based on the analysis of von Mises stress distribution as well as profiles of normal and shear stresses in the trabeculae at different stages of their adaptation.

A Superior Corrosion Protection of Mg Alloy via Smart Nontoxic Hybrid Inhibitor-Containing Coatings

The increase of corrosion resistance of magnesium and its alloys by forming the smart self-healing hybrid coatings was achieved in this work in two steps. In the first step, using the plasma electrolytic oxidation (PEO) treatment, a ceramic-like bioactive coating was synthesized on the surface of biodegradable MA8 magnesium alloy. During the second step, the formed porous PEO layer was impregnated with a corrosion inhibitor 8-hydroxyquinoline (8-HQ) and bioresorbable polymer polycaprolactone (PCL) in different variations to enhance the protective properties of the coating. The composition, anticorrosion, and antifriction properties of the formed coatings were studied. 8-HQ allows controlling the rate of material degradation due to the self-healing effect of the smart coating. PCL treatment of the inhibitor-containing layer significantly improves the corrosion and wear resistance and retains an inhibitor in the pores of the PEO layer. It was revealed that the corrosion inhibitor incorporation method (including the number of steps, impregnation, and the type of solvent) significantly matters to the self-healing mechanism. The hybrid coatings obtained by a 1-step treatment in a dichloromethane solution containing 6 wt.% polycaprolactone and 15 g/L of 8-HQ are characterized by the best corrosion resistance. This coating demonstrates the lowest value of corrosion current density (3.02 × 10−7 A cm−2). The formation of the hybrid coating results in the corrosion rate decrease by 18 times (0.007 mm year−1) as compared to the blank PEO layer (0.128 mm year−1). An inhibitor efficiency was established to be 83.9%. The mechanism of corrosion protection of Mg alloy via smart hybrid coating was revealed.

Bionic reconstruction of tension trabeculae in short-stem hip arthroplasty: a finite element analysis

BACKGROUND

Short-stem hip arthroplasty (SHA) is characterized by metaphyseal load transfer that effectively preserves the bone stock, but still suffers from stress shielding in the proximal femur. We designed a tension screw to mimic tension trabeculae in the new bionic collum femoris preserving (BCFP) short stem for bionic reconstruction, aiming to restore the biomechanics of hip joint.

METHODS

Native femur finite element model was constructed to investigate the biomechanics of hip joint based on computed tomography (CT) data. The maximum absolute principal stress/strain cloud chart allowed the direction of stress/strain to be assessed. Six BCFP models with different screw angles (5°, 10°, 15°, 20°, 25°, and 30°) and the Corail model were created. The stress/strain distribution and overall stiffness were compared between each of the BCFP and Corail implanted models.

RESULTS

The native model visualized the transfer pathways of tensile and compressive stress. The BCFP stems showed significantly higher stress and strain distribution in the greater trochanteric region compared to conventional total hip arthroplasty (THA). In particular, the BCFP-5° stem demonstrated the highest average strain in both medial and lateral regions and the overall stiffness was closest to the intact femur.

CONCLUSIONS

Stress transfer pathways of trabecular architecture provide biomechanical insight that serves as the basis for bionic reconstruction. The tension screw improves load transfer pattern in the proximal femur and prevents stress reduction in the greater trochanteric region. The BCFP-5° stem minimizes the stress shielding effect and presents a more bionic mechanical performance.

Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Framework of sampling the subject-specific static loads from the gait cycle of interindividual variation

BACKGROUND AND OBJECTIVE

Numerous techniques for bone remodeling simulation have been developed based on Wolff's law. However, most studies have been conducted with empirically determined static loads, which cannot reflect subject-specific characteristics. We recently proposed a new concept of representative static loads (RSLs) to efficiently consider the effect of cyclically repeated dynamic loads on bone remodeling simulation. Based on this concept, the goal of this study is to sample the subject-specific static loads (SSL) from a general gait cycle of interindividual variation.

METHODS

A total of 15 gait cycles (ten normal and five abnormal cycles) obtained from the public database were used in this study. Each gait cycle was applied to a femur FE model constructed from the clinical CT scan data to evaluate the strain energy distribution as a reference. Then, a natural coordinate was introduced to maintain the predefined locations of extreme points (i.e., two peaks and one valley) for both normal and abnormal gait cycles. To determine the RSLs in the natural coordinate, five out of ten normal gait cycles were used. Through an inverse transformation for each gait cycle, the RSLs in the natural coordinate were converted to the SSLs in the original coordinate. Topology optimization results with the proposed SSLs were compared with those with a single full gait cycle (reference). For comparison, topology optimization was also conducted with empirically determined loads (EDLs) which have been widely used in the literature.

RESULTS

For normal gait cycles, the proposed SSLs reduced the average computing cost by 95.86% while suppressing the errors of bone mass distribution and apparent stiffness below maximum 4.24% and 1.72%, respectively. Even for abnormal gait cycles, the errors of bone mass distribution and apparent stiffness were suppressed below maximum 9.49% and 2.12%, respectively. Conversely, the conventional EDLs (peak loads selected in this study) showed significantly larger errors of maximum 47.28% and 30.31% in bone mass distribution and apparent stiffness for normal gait cycles.

CONCLUSION

By virtue of using the coordinate transformation for each gait cycle, the proposed SSLs achieved a higher accuracy in the bone mass distribution and apparent stiffness than the previous RSLs and EDLs. Furthermore, this approach can be used for abnormal gait cycles which have higher interindividual variation.

Mechanoregulated trabecular bone adaptation: Progress report on in silico approaches

Adaptation is the process by which bone responds to changes in loading environment and modulates its properties and spatial organization to meet the mechanical demands. Adaptation in trabecular bone is achieved through increase in bone mass and alignment of trabecular-bone morphology along the loading direction. This transformation of internal microstructure is governed by mechanical stimuli sensed by mechanosensory cells in the bone matrix. Realisation of adaptation in the form of local bone-resorption and -formation activities as a function of mechanical stimuli is still debated. In silico modelling is a useful tool for simulation of various scenarios that cannot be investigated in vivo and particularly well suited for prediction of trabecular bone adaptation. This progress report presents the recent advances in in silico modelling of mechanoregulated adaptation at the scale of trabecular bone tissue. Four well-established bone-adaptation models are reviewed in terms of their recent improvements and validation. They consider various mechanical factors: (i) strain energy density, (ii) strain and damage, (iii) stress nonuniformity and (iv) daily stress. Contradictions of these models are discussed and their ability to describe adequately a real-life mechanoregulation process in bone is compared.

Optimizing femur symmetry judgment using three-dimensional data correction scheme in fractures of the proximal femur

BACKGROUND

The application of the 3D printing mirror image model is based on the symmetry of the limbs. Different from image fusion to judge the similarity, based on the commonality of the limb morphology of the same organism and the isotropic of the long bone cross-section, the symmetry of the femur has been determined by calculating the dimension difference of the corresponding cross-section of the non-fractured area. However, the previous version used equidistant cross-sections for measurement and two-dimensional data correction, and there were problems with insufficient reliability and data failure. The purpose of this study is to achieve a more accurate and universal symmetry verification scheme for bilateral tubular bones through an improved method.

METHODS

Forty-five imaging data of proximal femoral fracture and osteopathy were selected from October 2015 to September 2017. 10%, 30%, and 50% of the full-length of the bilateral femur is sliced to judge the similarity between paired femurs. Long and short axes of the bilateral femoral cross-sections on the two-dimensional slices were measured and compared. A stylized trigonometric were used to correct the measured axes lengths such that they more closely match with measurements taken from slices perpendicular to femoral shaft axis.

RESULTS

540 valid data items from the long axis and short axis of the bilateral side of the distal femur were obtained, and 192 of these were corrected. There were no significant differences between the left and right of the long and short axis of each cross-section in paired cases (P>0.05).

CONCLUSIONS

This study have demonstrated symmetricity of the left and right femurs. The availability of CT data at any position of the patient's lower limbs is realized through replacing the previous "two-dimensional data correction" with "three-dimensional data correction".

Integration of mechanics and biology in computer simulation of bone remodeling

Bone remodeling is a complex physiological process that spans across multiple spatial and temporal scales and is regulated by both mechanical and hormonal cues. An imbalance between bone resorption and bone formation in the process of bone remodeling may lead to various bone pathologies. One powerful and non-invasive approach to gain new insights into mechano-adaptive bone remodeling is computer modeling and simulation. Recent findings in bone physiology and advances in computer modeling have provided a unique opportunity to study the integration of mechanics and biology in bone remodeling. Our objective in this review is to critically appraise recent advances and developments and discuss future research opportunities in computational bone remodeling approaches that enable integration of mechanics and cellular and molecular pathways. Based on the critical appraisal of the relevant recent published literature, we conclude that multiscale in silico integration of personalized bone mechanics and mechanobiology combined with data science and analytics techniques offer the potential to deepen our knowledge of bone remodeling and provide ample opportunities for future research.

Maintaining Bone Health in the Lumbar Spine: Routine Activities Alone Are Not Enough

Public health organisations typically recommend a minimum amount of moderate intensity activities such as walking or cycling for two and a half hours a week, combined with some more demanding physical activity on at least 2 days a week to maintain a healthy musculoskeletal condition. For populations at risk of bone loss in the lumbar spine, these guidelines are particularly relevant. However, an understanding of how these different activities are influential in maintaining vertebral bone health is lacking. A predictive structural finite element modelling approach using a strain-driven algorithm was developed to study mechanical stimulus and bone adaptation in the lumbar spine under various physiological loading conditions. These loading conditions were obtained with a previously developed full-body musculoskeletal model for a range of daily living activities representative of a healthy lifestyle. Activities of interest for the simulations include moderate intensity activities involving limited spine movements in all directions such as, walking, stair ascent and descent, sitting down and standing up, and more demanding activities with large spine movements during reaching and lifting tasks. For a combination of moderate and more demanding activities, the finite element model predicted a trabecular and cortical bone architecture representative of a healthy vertebra. When more demanding activities were removed from the simulations, areas at risk of bone degradation were observed at all lumbar levels in the anterior part of the vertebral body, the transverse processes and the spinous process. Moderate intensity activities alone were found to be insufficient in providing a mechanical stimulus to prevent bone degradation. More demanding physical activities are essential to maintain bone health in the lumbar spine.

The effect of functionally graded materials on bone remodeling around osseointegrated trans-femoral prostheses

Osseointegrated trans-femoral fixations have been used as alternatives for conventional sockets in recent years. Despite numerous advantages, the dissimilarity of the mechanical properties between bone and implant has led to issues in periprosthetic bone adaptation. This study aims to address these issues by proposing fixations made of functionally graded materials (FGMs). The computational study of bone remodeling was performed by linking a bone remodeling algorithm to the finite element analysis. The 3D model of the femur was created by computerized tomography (CT) scan images, and a Titanium fixture, along with nine Titanium/Hydroxyapatite FGM fixtures, were modeled. The analyses revealed evident advantages for the FGM fixtures over the conventionally used Titanium fixtures. Furthermore, it was shown that the gradation direction considerably affects the bone adaptation procedure. The results showed that using a radial FGM with low-stiffness material in the outer layer and less metal composition significantly improves the bone remodeling behavior.

Determination of the representative static loads for cyclically repeated dynamic loads: a case study of bone remodeling simulation with gait loads

BACKGROUND AND OBJECTIVE

Bone has the self-optimizing capability to adjust its structure in order to efficiently support external loads. Bone remodeling simulations have been developed to reflect the above characteristics in a more effective way. In most studies, however, only a set of static loads have been empirically determined although both static and dynamic loads affect bone remodeling phenomenon. The goal of this study is to determine the representative static loads (RSLs) to efficiently consider the statically equivalent effect of cyclically repeated dynamic loads on bone remodeling simulation.

METHODS

Based on the concept of two-scale approach, the RSLs for the gait cycles are determined from five subjects. First, the gait profiles at the hip joint are selected from the public database and then are preprocessed. The finite element model of the proximal femur is constructed from the clinical CT scan data to determine the strain energy distribution during the gait cycles. An optimization problem is formulated to determine the candidate static loads that minimize the errors of the spatial strain energy distribution for five gait profiles. Then, all candidate static loads from five gait profiles are partitioned into multiple clusters. The RSLs and the corresponding coefficients can be determined at the center of the densest cluster. For verification, topology optimization is separately conducted with the whole gait cycle (reference), empirically determined loads (conventional), and the RSLs (proposed). The strain energy density-based bone remodeling simulation is also conducted for another comparison.

RESULTS

For the gait loads, the use of the RSLs enables a 99% reduction of the function calls with negligible errors in the bone spatial distribution (6.75% for two representative static loads and 6.24% for three representative static loads) and apparent stiffness (4.84% for two representative static loads and 4.47% for three representative static loads), compared with the use of a whole gait cycle as reference.

CONCLUSION

This study shows the feasibility of the RSLs and provides a theoretical foundation for investigating the relationship between static and dynamic loads in the aspect of bone remodeling simulation.

In silico experiments of bone remodeling explore metabolic diseases and their drug treatment

Bone structure and function are maintained by well-regulated bone metabolism and remodeling. Although the underlying molecular and cellular mechanisms are now being understood, physiological and pathological states of bone are still difficult to predict due to the complexity of intercellular signaling. We have now developed a novel in silico experimental platform, V-Bone, to integratively explore bone remodeling by linking complex microscopic molecular/cellular interactions to macroscopic tissue/organ adaptations. Mechano-biochemical couplings modeled in V-Bone relate bone adaptation to mechanical loading and reproduce metabolic bone diseases such as osteoporosis and osteopetrosis. V-Bone also enables in silico perturbation on a specific signaling molecule to observe bone metabolic dynamics over time. We also demonstrate that this platform provides a powerful way to predict in silico therapeutic effects of drugs against metabolic bone diseases. We anticipate that these in silico experiments will substantially accelerate research into bone metabolism and remodeling.

Analysis of spinal stress analysis application in determining method for the pedicle screw placement under the guidance of X-Ray

OBJECTIVE

To evaluate the accuracy of a novel guidance method of pedicle screw implantation determined by spinal stress.

METHODS

We retrospectively analyzed patients underwent pedicle screw internal fixation between January 2015 and August 2018 in our hospital. Patients were divided into two groups according to the methods of pedicle screw implantation namely, the conventional nail placement and novel guidance method of pedicle screw implantation determined by spinal stress. Accuracy of spinal pedicle screw placements was evaluated using intraoperative and postoperative X-ray computed tomography (CT) examination and intraoperative touch of nerve root dissection pedicle bone. The success rate of intraoperative one-time screw placement was calculated according to Heary classification I.

RESULTS

A total of 785 patients underwent pedicle screw internal fixation were retrospectively analyzed. Among them 384 patients were treated using conventional nail placement (Group A) and 401 patients were treated using the technique according to analysis of spinal stress (Group B). There was no significant difference in terms of the characteristics between two groups. There were significant differences in terms of the success rate of total of screw placement (88.7% vs. 96.2%, P < 0.001) including thoracic screw placement (87.8% vs. 94.5%, P = 0.003) and lumbar screw placement (88.8% vs. 96.5%, P = 0.001) for Group A and Group B, respectively.

CONCLUSIONS

Using the novel guidance method of pedicle screw implantation determined by spinal stress might improve the accuracy of pedicle screw implantation.

Biomechanical investigation of extragraft bone formation influences on the operated motion segment after anterior cervical spinal discectomy and fusion

Although the clinical importance of extragraft bone formation (ExGBF) and bridging (ExGBB) has been reported, few studies have investigated the biomechanical influences of ExGBF on the motion segment. In this study, ExGBF was simulated at the C5-C6 motion segment after anterior cervical discectomy and fusion using a developed finite element model and a sequential bone-remodelling algorithm in flexion and extension. The computer simulation results showed that extragraft bone was primarily formed in the extension motion and grew to form ExGBB. A stepwise decrease in the intersegmental rotation angle, maximum von Mises stress and strain energy density on the trabecular bone with ExGBF were predicted in extension. When ExGBB was formed in the trabecular bone region, the intersegmental rotation angle slightly decreased with additional bone formation. However, the stress and strain energy density on the trabecular bone region decreased until ExGBB reached the peripheral cortical margin. The results offer a rationale supporting the hypothesis that mechanical stimuli influence ExGBF. ExGBF was helpful in increasing the stability of the motion segment and decreasing the fracture risk of trabecular bones, even in cases in which ExGBB was not formed. ExGBB can be classified as either soft or hard bridging based on a biomechanical point of view.

Numerical Simulation of Mandible Bone Remodeling under Tooth Loading: A Parametric Study

Bone adapts to the change of mechanical stimulus by bone remodeling activities. A number of numerical algorithms have been developed to model the adaptive bone remodeling under mechanical loads for orthopedic and dental applications. This paper examines the effects of several model parameters on the computed apparent bone density in mandible under normal chewing and biting forces. The density change rate was based on the strain energy density per unit mass. The algorithms used in this study containing an equilibrium zone (lazy zone) and saturated values of density change rate provides certain stability to result in convergence without discontinuous checkerboard patterns. The parametric study shows that when different boundary conditions were applied, the bone density distributions at convergence were very different, except in the vicinity of the applied loads. Compared with the effects of boundary conditions, the models are less sensitive to the choice of initial density values. Several models starting from different initial density values resulted in similar but not exactly the same bone density distribution at convergence. The results also show that higher reference value of mechanical stimulus resulted in lower average bone density at convergence. Moreover, the width of equilibrium zone did not substantially affect the average density at convergence. However, with increasing width, the areas with the highest and the lowest bone density areas were all reduced. The limitations of the models and challenges for future work were discussed for the better agreement between the computed results and the in vivo data.

Exploring conditions that make cortical bone geometry optimal for physiological loading

While physiological loading on lower long bones changes during bone development, the bone cross section either remains circular or slowly changes from nearly circular to other shapes such as oval and roughly triangular. Bone is said to be an optimal structure, where strength is maximized using the optimal distribution of bone mass (also called Wolff's law). One of the most appropriate mathematical validations of this law would be a structural optimization-based formulation where total strain energy is minimized against a mass and a space constraint. Assuming that the change in cross section during bone development and homeostasis after adulthood is direct result of the change in physiological loading, this work investigates what optimization problem formulation (collectively, design variables, objective function, constraints, loading conditions, etc.) results in mathematically optimal solutions that resemble bones under actual physiological loading. For this purpose, an advanced structural optimization-based computational model for cortical bone development and defect repair is presented. In the optimization problem, overall bone stiffness is maximized first against a mass constraint, and then also against a polar first moment of area constraint that simultaneously constrains both mass and space. The investigation is completed in two stages. The first stage is developmental stage when physiological loading on lower long bones (tibia) is a random combination of axial, bending and torsion. The topology optimization applied to this case with the area moment constraint results into circular and elliptical cross sections similar to that found in growing mouse or human. The second investigation stage is bone homeostasis reached in adulthood when the physiological loading has a fixed pattern. A drill hole defect is applied to the adult mouse bone, which would disrupt the homeostasis. The optimization applied after the defect interestingly brings the damaged section back to the original intact geometry. The results, however, show that cortical bone geometry is optimal for the physiological loading only when there is also a constraint on polar moment of area. Further numerical experiments show that application of torsion along with the gait-analysis-based physiological loading improves the results, which seems to indicate that the cortical bone geometry is optimal for some amount of torsion in addition to the gait-based physiological loading. This work has a potential to be extended to bone growth/development models and fracture healing models, where topology optimization and polar moment of area constraint have not been introduced earlier.

Forceful mastication activates osteocytes and builds a stout jawbone

Bone undergoes a constant reconstruction process of resorption and formation called bone remodeling, so that it can endure mechanical loading. During food ingestion, masticatory muscles generate the required masticatory force. The magnitude of applied masticatory force has long been believed to be closely correlated with the shape of the jawbone. However, both the mechanism underlying this correlation and evidence of causation remain largely to be determined. Here, we established a novel mouse model of increased mastication in which mice were fed with a hard diet (HD) to elicit greater masticatory force. A novel in silico computer simulation indicated that the masticatory load onto the jawbone leads to the typical bone profile seen in the individuals with strong masticatory force, which was confirmed by in vivo micro-computed tomography (micro-CT) analyses. Mechanistically, increased mastication induced Insulin–like growth factor (IGF)-1 and suppressed sclerostin in osteocytes. IGF-1 enhanced osteoblastogenesis of the cells derived from tendon. Together, these findings indicate that the osteocytes balance the cytokine expression upon the mechanical loading of increased mastication, in order to enhance bone formation. This bone formation leads to morphological change in the jawbone, so that the bone adapts to the mechanical environment to which it is exposed.

Mathematical modeling of bone in-growth into undegradable porous periodic scaffolds under mechanical stimulus

Undegradable scaffolds, as a key element in bone tissue engineering, prevail in the present clinical applications, and the bone in-growth into such scaffolds under mechanical stimulus is an important issue to evaluate the bone-repair effect. This work aims to develop a mathematical framework to investigate the effect of mechanical stimulus on the bone in-growth into undegradable scaffolds. First, the osteoclast and osteoblast activities were coupled by their autocrine and paracrine effects. Second, the mechanical stimulus was empirically incorporated into the coupling cell activities on the basis of experimental observations. Third, the effect of mechanical stimulus including intensity and duration on the bone in-growth process was numerically studied; moreover, the homeostasis of scaffold–bone system under the mechanical stimulus was also treated. The results showed that the numbers of osteoblasts and osteoclasts in the scaffold–bone system tended to constants representing the system homeostasis. Both the mechanical intensity and duration optimized the final bone formation. The numerical results of the bone formation were comparable to the experimental results in rats. The findings from this modeling study could be used to explain many physiological phenomena and clinical observations. The developed model integrates both cell and tissue scales, which can be used as a platform to investigate bone remodeling under mechanical stimulus.

Cancellous bone and theropod dinosaur locomotion. Part I-an examination of cancellous bone architecture in the hindlimb bones of theropods

This paper is the first of a three-part series that investigates the architecture of cancellous ('spongy') bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and has previously been used to infer locomotor biomechanics in extinct tetrapod vertebrates, especially primates. Despite great promise, cancellous bone architecture has remained little utilized for investigating locomotion in many other extinct vertebrate groups, such as dinosaurs. Documentation and quantification of architectural patterns across a whole bone, and across multiple bones, can provide much information on cancellous bone architectural patterns and variation across species. Additionally, this also lends itself to analysis of the musculoskeletal biomechanical factors involved in a direct, mechanistic fashion. On this premise, computed tomographic and image analysis techniques were used to describe and analyse the three-dimensional architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs for the first time. A comprehensive survey across many extant and extinct species is produced, identifying several patterns of similarity and contrast between groups. For instance, more stemward non-avian theropods (e.g. ceratosaurs and tyrannosaurids) exhibit cancellous bone architectures more comparable to that present in humans, whereas species more closely related to birds (e.g. paravians) exhibit architectural patterns bearing greater similarity to those of extant birds. Many of the observed patterns may be linked to particular aspects of locomotor biomechanics, such as the degree of hip or knee flexion during stance and gait. A further important observation is the abundance of markedly oblique trabeculae in the diaphyses of the femur and tibia of birds, which in large species produces spiralling patterns along the endosteal surface. Not only do these observations provide new insight into theropod anatomy and behaviour, they also provide the foundation for mechanistic testing of locomotor hypotheses via musculoskeletal biomechanical modelling.

Cancellous bone and theropod dinosaur locomotion. Part II-a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single 'characteristic posture' for a given species-one in which bone continuum-level principal stresses best align with cancellous bone fabric-and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well.

Biomechanical bearing-based typing method for osteonecrosis of the femoral head: ABC typing

Type classification of osteonecrosis of the femoral head (ONFH) is important for collapse prediction in ONFH, which depends on a complexity of factors. At present, most typing is based on single factors, including the location or size of the necrosis, or the bone repair capacity after ONFH, and is therefore limited. The present study proposes an 'ABC' method for ONFH typing based on biomechanics and the stress distribution characteristics of the femoral head's bone trabeculae. In total, 132 ONFH patients (223 hips) were enrolled at Guanganmen Hospital (Beijing, China). Each of the hip joints included was subjected to computerized tomography and/or magnetic resonance imaging. The images with the maximum necrotic area in the coronal femoral head were selected, and the femoral head's maximum transverse diameter was divided into three pillars (A, B and C, from the outside to the inside) according to a 3:4:3 diameter ratio. ONFH was typed according to the number of pillars involved in the necrosis. Differences in the collapse rate of different ONFH types, and the correlation between the theoretical collapse risk and the observed collapse rate was analysed. The ONFH types significantly differed in their collapse rate (χ²=76.93, P<0.001) in the following order: A-C (88.6%)>AB (74.1%)>BC (52.4%)>A (50%)>B (9.5%)>C (0%). The collapse risk was significantly correlated with the collapse rate (correlation coefficient R=1). The types A-C and AB had high collapse rates/risks, whereas types B and C had a satisfactory prognosis. The ABC typing proposed in the present study is thus suitable for collapse risk prediction in ONFH. Type classification using this method may provide a valuable reference for selecting regimens for ONFH treatment.

Computational study of estimating 3D trabecular bone microstructure for the volume of interest from CT scan data

Inspired by the self-optimizing capabilities of bone, a new concept of bone microstructure reconstruction has been recently introduced by using 2D synthetic skeletal images. As a preliminary clinical study, this paper proposes a topology optimization-based method that can estimate 3D trabecular bone microstructure for the volume of interest (VOI) from 3D computed tomography (CT) scan data with enhanced computational efficiency and phenomenological accuracy. For this purpose, a localized finite element (FE) model is constructed by segmenting a target bone from CT scan data and determining the physiological local loads for the VOI. Then, topology optimization is conducted with multiresolution bone mineral density (BMD) deviation constraints to preserve the patient-specific spatial bone distribution obtained from the CT scan data. For the first time, to our knowledge, this study has demonstrated that 60-μm resolution trabecular bone images can be reconstructed from 600-μm resolution CT scan data (a 62-year-old woman with no metabolic bone disorder) for the 4 VOIs in the proximal femur. The reconstructed trabecular bone includes the characteristic trabecular patterns and has morphometric indices that are in good agreement with the anatomical data in the literature. As for computational efficiency, the localization for the VOI reduces the number of FEs by 99%, compared with that of the full FE model. Compared with the previous single-resolution BMD deviation constraint, the proposed multiresolution BMD deviation constraints enable at least 65% and 47% reductions in the number of iterations and computing time, respectively. These results demonstrate the clinical feasibility and potential of the proposed method.

Trabecular health of vertebrae based on anisotropy in trabecular architecture and collagen/apatite micro-arrangement after implantation of intervertebral fusion cages in the sheep spine

Healthy trabecular bone shows highly anisotropic trabecular architecture and the preferential orientation of collagen and apatite inside a trabecula, both of which are predominantly directed along the cephalocaudal axis. This makes trabecular bone stiff in the principally loaded direction (cephalocaudal axis). However, changes in these anisotropic trabecular characteristics after the insertion of implant devices remain unclear. We defined the trabecular architectural anisotropy and the preferential orientation of collagen and apatite as parameters of trabecular bone health. In the present study, we analyzed these parameters after the implantation of two types of intervertebral fusion cages, open and closed box-type cages, into sheep spines for 2 and 4months. Alteration and evolution of trabecular health around and inside the cages depended on the cage type and implantation duration. At the boundary region, the values of trabecular architectural anisotropy and apatite orientation for the closed-type cages were similar to those for isotropic conditions. In contrast, significantly larger anisotropy was found for open-type cages, indicating that the open-type cage tended to maintain trabecular anisotropy. Inside the open-type cage, trabecular architectural anisotropy and apatite orientation significantly increased with time after implantation. Assessing trabecular anisotropy might be useful for the evaluation of trabecular health and the validation and refinement of implant designs.

Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations

Bone functional tissue adaptation is a multiaspect physiological process driven by interrelated mechanical and biological stimuli which requires the combined activity of osteoclasts and osteoblasts. In previous work, the authors developed a phenomenological mesoscale structural modelling approach capable of predicting internal structure of the femur based on daily activity loading, which relied on the iterative update of the cross-sectional areas of truss and shell elements representative of trabecular and cortical bones, respectively. The objective of this study was to introduce trabecular reorientation in the phenomenological model at limited computational cost. To this aim, a metamodel derived from poroelastic microscale continuum simulations was used to predict the functional adaptation of a simplified proximal structural femur model. Clear smooth trabecular tracts are predicted to form in the regions corresponding to the main trabecular groups identified in literature, at minimal computational cost.

Numerical Method for the Design of Healing Chamber in Additive-Manufactured Dental Implants

The inclusion of a healing chamber in dental implants has been shown to promote biological healing. In this paper, a novel numerical approach to the design of the healing chamber for additive-manufactured dental implants is proposed. This study developed an algorithm for the modeling of bone growth and employed finite element method in ANSYS to facilitate the design of healing chambers with a highly complex configuration. The model was then applied to the design of dental implants for insertion into the posterior maxillary bones. Two types of ITI® solid cylindrical screwed implant with extra rectangular-shaped healing chamber as an initial design are adopted, with which to evaluate the proposed system. This resulted in several configurations for the healing chamber, which were then evaluated based on the corresponding volume fraction of healthy surrounding bone. The best of these implants resulted in a healing chamber surrounded by around 9.2% more healthy bone than that obtained from the original design. The optimal design increased the contact area between the bone and implant by around 52.9%, which is expected to have a significant effect on osseointegration. The proposed approach is highly efficient which typically completes the optimization of each implant within 3–5 days on an ordinary personal computer. It is also sufficiently general to permit extension to various loading conditions.

Voxel size dependency, reproducibility and sensitivity of an in vivo bone loading estimation algorithm

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous.

Estimation of Local Bone Loads for the Volume of Interest

Computational bone remodeling simulations have recently received significant attention with the aid of state-of-the-art high-resolution imaging modalities. They have been performed using localized finite element (FE) models rather than full FE models due to the excessive computational costs of full FE models. However, these localized bone remodeling simulations remain to be investigated in more depth. In particular, applying simplified loading conditions (e.g., uniform and unidirectional loads) to localized FE models have a severe limitation in a reliable subject-specific assessment. In order to effectively determine the physiological local bone loads for the volume of interest (VOI), this paper proposes a novel method of estimating the local loads when the global musculoskeletal loads are given. The proposed method is verified for the three VOI in a proximal femur in terms of force equilibrium, displacement field, and strain energy density (SED) distribution. The effect of the global load deviation on the local load estimation is also investigated by perturbing a hip joint contact force (HCF) in the femoral head. Deviation in force magnitude exhibits the greatest absolute changes in a SED distribution due to its own greatest deviation, whereas angular deviation perpendicular to a HCF provides the greatest relative change. With further in vivo force measurements and high-resolution clinical imaging modalities, the proposed method will contribute to the development of reliable patient-specific localized FE models, which can provide enhanced computational efficiency for iterative computing processes such as bone remodeling simulations.

Inverse finite element modeling for characterization of local elastic properties in image-guided failure assessment of human trabecular bone

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone's material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur's volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.

Informing phenomenological structural bone remodelling with a mechanistic poroelastic model

Studies suggest that fluid motion in the extracellular space may be involved in the cellular mechanosensitivity at play in the bone tissue adaptation process. Previously, the authors developed a mesoscale predictive structural model of the femur using truss elements to represent trabecular bone, relying on a phenomenological strain-based bone adaptation algorithm. In order to introduce a response to bending and shear, the authors considered the use of beam elements, requiring a new formulation of the bone adaptation drivers. The primary goal of the study presented here was to isolate phenomenological drivers based on the results of a mechanistic approach to be used with a beam element representation of trabecular bone in mesoscale structural modelling. A single-beam model and a microscale poroelastic model of a single trabecula were developed. A mechanistic iterative adaptation algorithm was implemented based on fluid motion velocity through the bone matrix pores to predict the remodelled geometries of the poroelastic trabecula under 42 different loading scenarios. Regression analyses were used to correlate the changes in poroelastic trabecula thickness and orientation to the initial strain outputs of the beam model. Linear (R(2) > 0.998) and third-order polynomial (R(2) > 0.98) relationships were found between change in cross section and axial strain at the central axis, and between beam reorientation and ratio of bending strain to axial strain, respectively. Implementing these relationships into the phenomenological predictive algorithm for the mesoscale structural femur has the potential to produce a model combining biofidelic structure and mechanical behaviour with computational efficiency.

Peri-implant stress correlates with bone and cement morphology: Micro-FE modeling of implanted cadaveric glenoids

Aseptic loosening of cemented joint replacements is a complex biological and mechanical process, and remains a clinical concern especially in patients with poor bone quality. Utilizing high resolution finite element analysis of a series of implanted cadaver glenoids, the objective of this study was to quantify relationships between construct morphology and resulting mechanical stresses in cement and trabeculae. Eight glenoid cadavers were implanted with a cemented central peg implant. Specimens were imaged by micro-CT, and subject-specific finite element models were developed. Bone volume fraction, glenoid width, implant-cortex distance, cement volume, cement-cortex contact, and cement-bone interface area were measured. Axial loading was applied to the implant of each model and stress distributions were characterized. Correlation analysis was completed across all specimens for pairs of morphological and mechanical variables. The amount of trabecular bone with high stress was strongly negatively correlated with both cement volume and contact between the cement and cortex (r = -0.85 and -0.84, p < 0.05). Bone with high stress was also correlated with both glenoid width and implant-cortex distance. Contact between the cement and underlying cortex may dramatically reduce trabecular bone stresses surrounding the cement, and this contact depends on bone shape, cement amount, and implant positioning.

Computational modelling of bone augmentation in the spine

Computational models are gaining importance not only for basic science, but also for the analysis of clinical interventions and to support clinicians prior to intervention. Vertebroplasty has been used to stabilise compression fractures in the spine for years, yet there are still diverging ideas on the ideal deposition location, volume, and augmentation material. In particular, little is known about the long-term effects of the intervention on the surrounding biological tissue. This review aims to investigate computational efforts made in the field of vertebroplasty, from the augmentation procedure to strength prediction and long-term in silico bone biology in augmented human vertebrae. While there is ample work on simulating the augmentation procedure and strength prediction, simulations predicting long-term effects are lacking. Recent developments in bone remodelling simulations have the potential to show adaptation to cement augmentation and, thus, close this gap.

Oldest pathology in a tetrapod bone illuminates the origin of terrestrial vertebrates

The origin of terrestrial tetrapods was a key event in vertebrate evolution, yet how and when it occurred remains obscure, due to scarce fossil evidence. Here, we show that the study of palaeopathologies, such as broken and healed bones, can help elucidate poorly understood behavioural transitions such as this. Using high-resolution finite element analysis, we demonstrate that the oldest known broken tetrapod bone, a radius of the primitive stem tetrapod Ossinodus pueri from the mid-Viséan (333 million years ago) of Australia, fractured under a high-force, impact-type loading scenario. The nature of the fracture suggests that it most plausibly occurred during a fall on land. Augmenting this are new osteological observations, including a preferred directionality to the trabecular architecture of cancellous bone. Together, these results suggest that Ossinodus, one of the first large (>2m length) tetrapods, spent a significant proportion of its life on land. Our findings have important implications for understanding the temporal, biogeographical and physiological contexts under which terrestriality in vertebrates evolved. They push the date for the origin of terrestrial tetrapods further back into the Carboniferous by at least two million years. Moreover, they raise the possibility that terrestriality in vertebrates first evolved in large tetrapods in Gondwana rather than in small European forms, warranting a re-evaluation of this important evolutionary event.

Trabecular orientation in the human femur and tibia and the relationship with lower-limb alignment for patients with osteoarthritis of the knee

Wolff׳s Law suggests that the orientation of trabeculae in human bone changes in response to altered loading patterns. The aim of this study was to investigate trabecular orientation in both the femur and tibia and to compare this with the mechanical axis of the leg. The study involved analysis of radiographs from patients with osteoarthritis of the knee (n=91). For each patient, the trabecular orientation in both the distal femur and proximal tibia was measured from a standard anteroposterior radiograph of the knee and the mechanical axis of the leg was calculated from a long leg view taken while weight bearing. There was a significant correlation between the mechanical axis and the trabecular orientation in each of the regions considered in the femur (r=-0.41, -0.30, 0.52, and 0.23) and tibia (r=-0.27 and 0.31). Multiple regression analysis, with mechanical axis as the dependent variable, produced an R(2) of 0.62. Greater trabecular anisotropy (i.e. greater alignment) was observed in the medial femur and tibia compared to the lateral side (p<0.01). The results give an insight into the trabecular changes that may take place during development of osteoarthritis and following surgery. In particular, we propose that the orientation of the trabeculae in both the distal femur and proximal tibia will reflect the angle of mechanical loading through the knee.

From histology to micro-CT: Measuring and modeling resorption cavities and their relation to bone competence

The process of bone remodelling plays an essential role in the emergence and maintenance of bone geometry and its internal structure. Osteoclasts are one of the three main bone cell types that play a crucial role in the bone remodelling cycle. At the microstructural level, osteoclasts create bone deficits by eroding resorption cavities. Understanding how these cavities impair the mechanical quality of the bone is not only relevant in quantifying the impact of resorption cavities in healthy bone and normal aging, but maybe even more so in quantifying their role in metabolic bone diseases. Metabolic bone diseases and their treatment are both known to affect the bone remodelling cycle; hence, the bone mechanical competence can and will be affected. However, the current knowledge of the precise dimensions of these cavities and their effect on bone competence is rather limited. This is not surprising considering the difficulties in deriving three-dimensional (3D) properties from two-dimensional (2D) histological sections. The measurement difficulties are reflected in the evaluation of how resorption cavities affect bone competence. Although detailed 3D models are generally being used to quantify the mechanical impact of the cavities, the representation of the cavities themselves has basically been limited to simplified shapes and averaged cavity properties. Qualitatively, these models indicate that cavity size and location are important, and that the effect of cavities is larger than can be expected from simple bone loss. In summary, the dimensions of osteoclast resorption cavities were until recently estimated from 2D measures; hence, a careful interpretation of resorption cavity dimensions is necessary. More effort needs to go into correctly quantifying resorption cavities using modern 3D imaging techniques like micro-computed tomography (micro-CT) and synchrotron radiation CT. Osteoclast resorption cavities affect bone competence. The structure-function relationships have been analysed using computational models that, on one hand, provide rather detailed information on trabecular bone structure, but on the other incorporate rather crude assumptions on cavity dimensions. The use of high-resolution representations and parametric descriptions could be potential routes to improve the quantitative fidelity of these models.

A comparative study of orthotropic and isotropic bone adaptation in the femur

Functional adaptation of the femur has been studied extensively by embedding remodelling algorithms in finite element models, with bone commonly assumed to have isotropic material properties for computational efficiency. However, isotropy is insufficient in predicting the directionality of bone's observed microstructure. A novel iterative orthotropic 3D adaptation algorithm is proposed and applied to a finite element model of the whole femur. Bone was modelled as an optimised strain-driven adaptive continuum with local orthotropic symmetry. Each element's material orientations were aligned with the local principal stress directions and their corresponding directional Young's moduli updated proportionally to the associated strain stimuli. The converged predicted density distributions for a coronal section of the whole femur were qualitatively and quantitatively compared with the results obtained by the commonly used isotropic approach to bone adaptation and with ex vivo imaging data. The orthotropic assumption was shown to improve the prediction of bone density distribution when compared with the more commonly used isotropic approach, whilst producing lower comparative mass, structurally optimised models. It was also shown that the orthotropic approach can provide additional directional information on the material properties distributions for the whole femur, an advantage over isotropic bone adaptation. Orthotropic bone models can help in improving research areas in biomechanics where local structure and mechanical properties are of key importance, such as fracture prediction and implant assessment.

Connecting mechanics and bone cell activities in the bone remodeling process: an integrated finite element modeling

Bone adaptation occurs as a response to external loadings and involves bone resorption by osteoclasts followed by the formation of new bone by osteoblasts. It is directly triggered by the transduction phase by osteocytes embedded within the bone matrix. The bone remodeling process is governed by the interactions between osteoblasts and osteoclasts through the expression of several autocrine and paracrine factors that control bone cell populations and their relative rate of differentiation and proliferation. A review of the literature shows that despite the progress in bone remodeling simulation using the finite element (FE) method, there is still a lack of predictive models that explicitly consider the interaction between osteoblasts and osteoclasts combined with the mechanical response of bone. The current study attempts to develop an FE model to describe the bone remodeling process, taking into consideration the activities of osteoclasts and osteoblasts. The mechanical behavior of bone is described by taking into account the bone material fatigue damage accumulation and mineralization. A coupled strain-damage stimulus function is proposed, which controls the level of autocrine and paracrine factors. The cellular behavior is based on Komarova et al.'s (2003) dynamic law, which describes the autocrine and paracrine interactions between osteoblasts and osteoclasts and computes cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Therefore, when an external mechanical stress is applied, bone formation and resorption is governed by cells dynamic rather than adaptive elasticity approaches. The proposed FE model has been implemented in the FE code Abaqus (UMAT routine). An example of human proximal femur is investigated using the model developed. The model was able to predict final human proximal femur adaptation similar to the patterns observed in a human proximal femur. The results obtained reveal complex spatio-temporal bone adaptation. The proposed FEM model gives insight into how bone cells adapt their architecture to the mechanical and biological environment.

An Analytical Approach to Investigate the Evolution of Bone Volume Fraction in Bone Remodeling Simulation at the Tissue and Cell Level

Simulation of bone remodeling at the bone cell level can predict changes in bone microarchitecture and density due to bone diseases and drug treatment. Their clinical application, however, is limited since bone microarchitecture can only be measured in the peripheral skeleton of patients and since the simulations are very time consuming. To overcome these issues, we have developed an analytical model to predict bone density adaptation at the organ level, in agreement with our earlier developed bone remodeling theory at the cellular level. Assuming a generalized geometrical model at the microlevel, the original theory was reformulated into an analytical equation that describes the evolution of bone density as a function of parameters that describe cell activity, mechanotransduction and mechanical loading. It was found that this analytical model can predict changes in bone density due to changes in these cell-level parameters that are in good agreement with those predicted by the earlier numerical model that implemented a detailed micro-finite element (FE) model to represent the bone architecture and loading, at only a fraction of the computational costs. The good agreement between analytical and numerical density evolutions indicates that the analytical model presented in this study can predict well bone functional adaptation and, eventually, provide an efficient tool for simulating patient-specific bone remodeling and for better prognosis of bone fracture risk.