Intravoxel bone micromechanics for microCT-based finite element simulations

A statistical analysis of human talar shape and bone density distribution

The shape of the talus, its internal structure, and its mechanical properties are important in determining talar behavior during loading, which may be significant for the design of surgical tools and implants. Although recent studies using statistical shape modeling have described quantitative talar external shape variation, no similar quantitative study exists to describe the density distribution of internal talar structure. The goal of this study is to quantify statistical variation in talar shape and density to benefit the design of talar implants. To this end, weight-bearing computed tomography (CT) scans of the ankle were collected in neutral, bilateral standing posture, and three-dimensional models were generated for each talus. Local density derived from the Hounsfield unit of each CT voxel was extracted. A weighted spherical harmonic analysis was performed to quantify the talar external shape. One hundred and seventy-nine volumes of interest were placed in the same relative position within each talus to quantify the talar density. Additionally, a finite element analysis (FEA) was conducted on a talus with both heterogeneous and homogeneous material properties to observe the effect of these properties on the stress and strain response. Significant differences were found in the talar density in sex and age, as well as in the stress and strain response between homogeneous and heterogeneous FEA. These differences show the importance of considering heterogeneity when examining the load response of tarsal bones.

Effect of trabecular architectures on the mechanical response in osteoporotic and healthy human bone

Research at the mesoscale bone trabeculae arrangement yields intriguing results that, due to their clinical resolution, can be applied in clinical field, contributing significantly to the diagnosis of bone-related diseases. While the literature offers quantitative morphometric parameters for a thorough characterization of the mesoscale bone network, there is a gap in understanding relationships among them, particularly in the context of various bone pathologies. This research aims to bridge these gaps by offering a quantitative evaluation of the interplay among morphometric parameters and mechanical response at mesoscale in osteoporotic and non-osteoporotic bones. Bone mechanical response, dependent on trabecular arrangement, is defined by apparent stiffness, computationally calculated using the Gibson-Ashby model. Key findings indicate that: (i) in addition to bone density, measured using X-ray absorptiometry, trabecular connectivity density, trabecular spacing and degree of anisotropy are crucial parameters for characterize osteoporosis state; (ii) apparent stiffness values exhibit strong correlations with bone density and connectivity density; (iii) connectivity density and degree of anisotropy result the best predictors of mechanical response. Despite the inherent heterogeneity in bone structure, suggesting the potential benefit of a larger sample size in the future, this approach presents a valuable method to enhance discrimination between osteoporotic and non-osteoporotic samples.

Stress reduction through cortical bone thickening improves bone mechanical behavior in adult female Beclin-1+/- mice

Fragility fractures, which are more prevalent in women, may be significantly influenced by autophagy due to altered bone turnover. As an essential mediator of autophagy, Beclin-1 modulates bone homeostasis by regulating osteoclast and chondrocyte differentiation, however, the alteration in the local bone mechanical environment in female Beclin-1+/- mice remains unclear. In this study, our aim is to investigate the biomechanical behavior of femurs from seven-month-old female wild-type (WT) and Beclin-1+/- mice under peak physiological load, using finite element analysis on micro-CT images. Micro-CT imaging analyses revealed femoral cortical thickening in Beclin-1+/- female mice compared to WT. Three-point bending test demonstrated a 63.94% increase in whole-bone strength and a 61.18% increase in stiffness for female Beclin-1+/- murine femurs, indicating improved biomechanical integrity. After conducting finite element analysis, Beclin-1+/- mice exhibited a 26.99% reduction in von Mises stress and a 31.62% reduction in maximum principal strain in the femoral midshaft, as well as a 36.64% decrease of von Mises stress in the distal femurs, compared to WT mice. Subsequently, the strength-safety factor was determined using an empirical formula, revealing that Beclin-1+/- mice exhibited significantly higher minimum safety factors in both the midshaft and distal regions compared to WT mice. In summary, considering the increased response of bone adaptation to mechanical loading in female Beclin-1+/- mice, our findings indicate that increasing cortical bone thickness significantly improves bone biomechanical behavior by effectively reducing stress and strain within the femoral shaft.

Mechanoregulation may drive osteolysis during bone metastasis: A finite element analysis of the mechanical environment within bone tissue during bone metastasis and osteolytic resorption

Metastatic bone disease occurs in 70-80% of advanced breast cancer patients and bone tissue is accepted to have attractive physical properties that facilitate cancer cell attraction, adhesion, and invasion. Bone cells also facilitate tumour invasion by biochemical signalling and through resorption of the bone matrix (osteolysis), which releases factors that further stimulate tumour cell activity. The evolving mechanical environment during tumour invasion might play an important role in these processes, as the activity of both bone and cancer cells is regulated by mechanical cues. In particular bone loss and altered mineralisation have been reported, yet how these alter the mechanical environment local to bone and tumour cells is unknown. The objective of this study is to quantify changes in the mechanical environment within bone tissue, during bone metastasis and osteolytic resorption, using finite element analysis (FEA) models reconstructed from high-resolution μCT images of metastatic mouse bone. In particular, we quantify time-dependent changes in mechanical stimuli, local to and distant from an invading tumour mass, to investigate putative mechanobiological cues for osteolysis during bone metastasis. We report here that in early metastasis (3 weeks after tumour inoculation), there was a decrease in strain distribution within the proximal femur trabecular and distal cortical bone tissue. These changes in the mechanical environment preceded extensive osteolytic destruction, but coincided with the onset of early osteolysis, cortical thickening and mineralisation of proximal and distal femur bone. We propose that early changes in the mechanical environment within bone tissue may activate resorption by osteoclast cells and thereby contribute to the extensive osteolytic bone loss at later stage (6 weeks) bone metastasis.

Computational modeling for osteogenic potential assessment of physical exercises based on loading-induced mechanobiological environments in cortical bone remodeling

Osteoporosis and disuse can cause bone loss which reduces the weight-bearing strength of long bones. Physical exercise or mechanical loading prevents bone loss as it promotes bone modeling through osteogenesis, i.e., new bone formation. Several studies have observed distinct bone remodeling responses to physical exercises; nevertheless, the underlying mechanism behind such responses is not well established. Loading-induced pore-pressure and fluid motion act as mechanobiological stimuli to bone cells namely osteocytes which further initiate osteoactivities. The shape of loading waveforms also affects the poromechanical environment of bone. Accordingly, the present study hypothesizes that loading waveforms associated with physiological exercises may expose the bone to different mechanobiological stimuli resulting in distinct bone remodeling. A poromechanical finite element model is developed to compute pore-pressure and interstitial fluid velocity in femoral cortical bone tissue (healthy and osteoporotic) subjected to loading waveforms of three physiological exercises namely walking, running, and jumping. The model also computes the mechanobiological stimulus as a function of fluid velocity. The outcomes indicate that pore-pressure and fluid velocity decrease significantly in osteoporotic bone tissue in comparison with healthy tissue. Jumping and running both improve pore-pressure and fluid velocity in healthy and osteoporotic tissues, whereas running significantly enhances mechanobiological stimulus in both the tissues which indicates a possible explanation for distinct bone remodeling to different physical exercises. The present work also suggests that running may be recommended as a potential biomechanical therapeutic to prevent bone loss. Overall, the present work contributes to the area of orthopedic research to develop effective designs of prophylactic exercises to improve bone health.

Towards mechanobiologically optimized mandible reconstruction: CAD/CAM miniplates vs. reconstruction plates for fibula free flap fixation: A finite element study

Due to their advantages in applicability, patient-specific (CAD/CAM) reconstruction plates are increasingly used in fibula free flap mandible reconstruction. In addition, recently, CAD/CAM miniplates, with further advantages in postoperative management, have been introduced. However, biomechanical conditions induced by CAD/CAM systems remain partially unknown. This study aimed to evaluate the primary fixation stability of CAD/CAM fixators. For a patient-specific scenario, the biomechanical conditions induced in a one segmental fibula free flap stabilized using either a CAD/CAM reconstruction plate or CAD/CAM miniplates were determined using finite element analysis. The main output parameters were the strains between intersegmental bone surfaces and stresses in the fixation systems due to different biting scenarios. CAD/CAM miniplates resulted in higher mechanical strains in the mesial interosseous gap, whereas CAD/CAM reconstruction plate fixation resulted in higher strains in the distal interosseous gap. For all investigated fixation systems, stresses in the fixation systems were below the material yield stress and thus material failure would not be expected. While the use of CAD/CAM miniplates resulted in strain values considered adequate to promote bone healing in the mesial interosseous gap, in the distal interosseous gap CAD/CAM reconstruction plate fixation might result in more beneficial tissue straining. A mechanical failure of the fixation systems would not be expected.

Mechanical metric for skeletal biomechanics derived from spectral analysis of stiffness matrix

A new metric for the quantitative and qualitative evaluation of bone stiffness is introduced. It is based on the spectral decomposition of stiffness matrix computed with finite element method. The here proposed metric is defined as an amplitude rescaled eigenvalues of stiffness matrix. The metric contains unique information on the principal stiffness of bone and reflects both bone shape and material properties. The metric was compared with anthropometrical measures and was tested for sex sensitivity on pelvis bone. Further, the smallest stiffness of pelvis was computed under a certain loading condition and analyzed with respect to sex and direction. The metric complements anthropometrical measures and provides a unique information about the smallest bone stiffness independent from the loading configuration and can be easily computed by state-of-the-art subject specified finite element algorithms.

Modeling of bending and torsional stiffnesses of bone at sub-microscale: Effect of curved mineral lamellae

Recent transmission electron microscopy images of transverse sections of human cortical bone showed that mineral lamellae (polycrystalline sheets of apatite crystals) form arcuate multi-radius patterns around collagen fibrils. The 3-6 nm thick mineral lamellae are arranged in stacks of 3-20 layers and curve around individual fibrils, few fibrils, and higher numbers of collagen fibrils. We evaluate the effect of these stacked mineral lamellae with various radius of curvature patterns on the elastic bending and torsional responses of bone at the sub-microscale using a finite element method. We find that the curved multi-radius stack patterns increased the bending and torsional stiffnesses by 7% and 23%, respectively, compared to when the stacks of mineral lamellae only encircle individual fibrils for the idealized geometric models considered. This study provides new insights into the structure-property relations for the bone ultrastructure.

Finite element analysis of femoral neck strains during stair ascent and descent

For older population, a better understanding of the hip joint loading environment is needed for the prevention of hip pain, and the reduction of the stress fractures and fall risks. Using the motion analysis and inverse dynamics methods, combined with musculoskeletal modelling, static optimization, and finite element (FE) femur model, the difference of femoral neck strains between stair ascent vs. descent, young vs. older populations was compared. A two-way repeated-measures MANOVA was applied to test the effect of age and stair direction on the femoral neck strains. The strains at the femoral neck cross-section were greater for stair descent than ascent for both age groups (mostly P = 0.001 to 0006) but there was no difference between age groups. In this study, femoral neck strains represented bone loading environment in more direct ways than joint reaction forces/moments or joint contact forces, the risk of hip pain, falls and stress fractures might be greater during stair descent than ascent. Possible preventative methods to reduce these risks should be developed in the future studies.

Maximum effect of the heterogeneity of tissue mineralization on the effective cortical bone elastic properties

The mineralization level is heterogeneous in cortical bone extracellular matrix as a consequence of remodeling. Models of the effective elastic properties at the millimeter scale have been developed based on idealizations of the vascular pore network and matrix properties. Some popular models do not take into account the heterogeneity of the matrix. However, the errors on the predicted elasticity when the difference in elastic properties between osteonal and interstitial tissues is not modeled have not been quantified. This work provides an estimation of the maximum error. We compare the effective elasticity of a representative volume element (RVE) assuming (1) different elastic properties in osteonal and interstitial tissues vs. (2) average matrix properties. In order to account for the variability of bone microstructure, we use a collection of high resolution images of the pore network to build RVEs. In each RVE we assumed a constant osteonal wall thickness and we artificially varied this thickness between 35 and 140 [Formula: see text]m to create RVEs with different amounts of osteonal tissue. The homogenization problem was solved with a fast Fourier transform (FFT)-based numerical scheme. We found that the error depends on pore volume fraction and varies on average from 1 to [Formula: see text] depending on the assumed diameter of the osteons. The results suggest that matrix heterogeneity may be disregarded in cortical bone models in most practical cases.

Biomechanical design prognosis of two extramedullary fixation devices for subtrochanteric femur fracture: a finite element study

The design rationale of extramedullary fixation for femur fracture has remained a matter of debate in the orthopaedic community. The present work provides a comparative preclinical assessment between two standard fracture fixation techniques: dynamic hip screw (DHS) and proximal femoral locking plate (PFLP), by employing finite element (FE)-based in silico models. The study attempts to evaluate and compare the two implants on following biomechanical behaviours: (1) stress variation on the femur and implant, (2) axial displacement of the fixated femur constructs, (3) postoperative stress shielding and longer term external remodelling of the host bone. We hypothesised that, of the two implants, PFLP has better biomechanical characteristics when used for subtrochanteric femoral fracture (SFF) fixation considering long-term adaptation. A comminuted fracture, simulated as two-part fracture gap of 20 mm, was created in the subtrochanteric region of a femur CAD model. Non-uniform physiological load cases were considered. External bone adaptation was modelled mathematically using stress analysis coupled with a growth model, in which strain energy density (SED) acted as feedback control variable. The computational results predicted lower stress shielding (by ~ 6%) and relatively less cortical thinning beneath the plate for PFLP as compared to DHS. DHS-fixated femur, on the other hand, predicted superior postoperative rigidity. Graphical Abstract FE-based comparative assessment between two extramedullary femur fixation devices-dynamic hip screw (DHS) and proximal femoral locking plate (PFLP).

A mathematical biomechanical model for bone remodeling integrated with a radial point interpolating meshless method

Bone remodeling is a highly complex process, in which bone cells interact and regulate bone's apparent density as a response to several external and internal stimuli. In this work, this process is numerically described using a novel 2D biomechanical model. Some of the new features in this model are (i) the mathematical parameters used to determine bone's apparent density and cellular density; (ii) an automatic boundary recognition step to spatially control bone remodeling and (iii) an approach to mimic the mechanical transduction to osteoclasts and osteoblasts. Moreover, this model is combined with a meshless approach - the Radial Point Interpolation Method (RPIM). The use of RPIM is an asset for this application, especially in the construction of the boundary maps. This work studies bone's adaptation to a certain loading regime through bone resorption. The signaling pathways of bone cells are dependent on the level of strain energy density (SED) in bone. So, when SED changes, bone cells' functioning is affected, causing also changes on bone's apparent density. With this model, bone is able to achieve an equilibrium state, optimizing its structure to withstand the applied loads. Results suggest that this model has the potential to provide high quality solutions while being a simpler alternative to more complex bone remodeling models in the literature.

Multiscale finite element modeling of mechanical strains and fluid flow in osteocyte lacunocanalicular system

Osteocytes form over 90% of the bone cells and are postulated to be mechanosensors responsible for regulating the function of osteoclasts and osteoblasts in bone modeling and remodeling. Physical activity results in mechanical loading on the bones. Osteocytes are thought to be the main mechanosensory cells in bone. Upon load osteocytes secrete key factors initiating downstream signaling pathways that regulate skeletal metabolism including the Wnt/β-catenin signaling pathway. Osteocytes have dendritic structures and are housed in the lacunae and canaliculi within the bone matrix. Mechanical loading is known to have two primary effects, namely a mechanical strain (membrane disruption by stretching) on the lacunae/cells, and fluid flow, in the form of fluid flow shear stress (FFSS), in the space between the cell membranes and the lacuna-canalicular walls. In response, osteocytes get activated via a process called mechanotransduction in which mechanical signals are transduced to biological responses. The study of mechanotransduction is a complex subject involving principles of engineering mechanics as well as biological signaling pathway studies. Several length scales are involved as the mechanical loading on macro sized bones are converted to strain and FFSS responses at the micro-cellular level. Experimental measurements of strain and FFSS at the cellular level are very difficult and correlating them to specific biological activity makes this a very challenging task. One of the methods commonly adopted is a multi-scale approach that combines biological and mechanical experimentation with in silico numerical modeling of the engineering aspects of the problem. Finite element analysis along with fluid-structure interaction methodologies are used to compute the mechanical strain and FFSS. These types of analyses often involve a multi-length scale approach where models of both the macro bone structure and micro structure at the cellular length scale are used. Imaging modalities play a crucial role in the development of the models and present their own challenges. This paper reviews the efforts of various research groups in addressing this problem and presents the work in our research group. A clear understanding of how mechanical stimuli affect the lacunae and perilacunar tissue strains and shear stresses on the cellular membranes may ultimately lead to a better understanding of the process of osteocyte activation.

Mechanical regulation of bone formation and resorption around implants in a mouse model of osteopenic bone

Although mechanical stimulation is considered a promising approach to accelerate implant integration, our understanding of load-driven bone formation and resorption around implants is still limited. This lack of knowledge may delay the development of effective loading protocols to prevent implant loosening, especially in osteoporosis. In healthy bone, formation and resorption are mechanoregulated processes. In the intricate context of peri-implant bone regeneration, it is not clear whether bone (re)modelling can still be load-driven. Here, we investigated the mechanical control of peri-implant bone (re)modelling with a well-controlled mechanobiological experiment. We applied cyclic mechanical loading after implant insertion in tail vertebrae of oestrogen depleted mice and we monitored peri-implant bone response by in vivo micro-CT. Experimental data were combined with micro-finite element simulations to estimate local tissue strains in (re)modelling locations. We demonstrated that a substantial increase in bone mass around the implant could be obtained by loading the entire bone. This augmentation could be attributed to a large reduction in bone resorption rather than to an increase in bone formation. We also showed that following implantation, mechanical regulation of bone (re)modelling was transiently lost. Our findings should help to clarify the role of mechanical stimulation on the maintenance of peri-implant bone mass.

An exclusion approach for addressing partial volume artifacts with quantititive computed tomography-based finite element modeling of the proximal tibia

INTRODUCTION

Quantitative computed tomography based finite element modeling (QCT-FE) has potential to clarify the role of subchondral bone stiffness in osteoarthritis. The limited spatial resolution of clinical QCT systems, however, results in partial volume (PV) artifacts and low contrast between cortical and trabecular bone, which adversely affects the accuracy of QCT-FE models. The objective of this research was to evaluate the agreement between stiffness predictions offered by QCT-FE models of proximal tibial subchondral bone (constructed with and without a new voxel-exclusion algorithm) with experimentally-derived local subchondral bone structural stiffness.

METHODS

Thirteen proximal tibial compartments were obtained and imaged using QCT. Two types of QCT-FE models were developed: (1) standard model, which employed the standard procedure for QCT-FE modeling; and (2) "voxel exclusion (VE)" model, which addressed PV artifacts by excluding low density voxels during the material mapping stage of construction. We assessed agreement between QCT-FE stiffness estimates (using standard and VE approaches) with experimental stiffness by reporting predicted variance from linear regression and mean bias with 95% Limits of Agreement (LOA).

RESULTS

The standard and VE models explained 81% and 84% of the variance in experimentally measured stiffness, respectively. The standard model showed a mean bias of -268 N/mm (LOA -1210 to 679 N/mm); the VE model showed a mean bias of +59 N/mm (LOA -762 to 910 N/mm).

INTERPRETATION

The VE model explained more variance in subchondral bone stiffness with less bias. Our findings indicate that the VE method has potential to improve QCT-FE models of bone affected by PV artifacts.

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.

NUMERICAL SIMULATION OF APPARENT DENSITY EVOLUTION OF TRABECULAR BONE UNDER FATIGUE LOADING: EFFECT OF BONE INITIAL PROPERTIES

Bone remodeling is a physiological phenomenon coupling resorption and formation processes that are mainly mediated by osteoclasts and osteoblasts, in response to mechanical stimuli transduced by osteocytes to biochemical signals activating the bone multicellular unit. Under normal loading conditions, bone resorption and formation are balanced by a homeostasis process. When bone is subjected to overstress, microdamaging occurs, which induces a modification of the structural integrity and microarchitecture. This has drawn significant attention to the mechanical properties of bone. In this context, the current study has been carried out with the aim of numerically investigating the impact of the mechanical properties on the remodeling process of the trabecular bone under cyclic loading, highlighting the effects of different values of the mineral density and the Young’s modulus. This was performed using a mechanobiological model, coupling mechanical and biological approaches, allowing to numerically simulate the effect of the selected parameters for a 20-year-period of cyclic loading for 2D and 3D models of a human femur head. The current work is an explorative numerical study, and the obtained results revealed the changes in the overall stiffness of the bone according to the mechanical properties.

Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

The strong dependence between cortical bone elasticity at the millimetre-scale (mesoscale) and cortical porosity has been evidenced by previous studies. However, bone is an anisotropic composite material made by mineral, proteins and water assembled in a hierarchical structure. Whether the variations of structural and compositional properties of bone affect the different elastic coefficients at the mesoscale is not clear. Aiming to understand the relationships between bone elastic properties and compositions and microstructure, we applied state-of-the-art experimental modalities to assess these aspects of bone characteristics. All elastic coefficients (stiffness tensor of the transverse isotropic bone material), structure of the vascular pore network, collagen and mineral properties were measured in 52 specimens from the femoral diaphysis of 26 elderly donors. Statistical analyses and micromechanical modeling showed that vascular pore volume fraction and the degree of mineralization of bone are the most important determinants of cortical bone anisotropic mesoscopic elasticity. Though significant correlations were observed between collagen properties and elasticity, their effects in bone mesoscopic elasticity were minor in our data. This work also provides a unique set of data exhibiting a range of variations of compositional and microstructural cortical bone properties in the elderly and gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone. STATEMENT OF SIGNIFICANCE: This study reports the relationships between microstructure, composition and the mesoscale anisotropic elastic properties of human femoral cortical bone in elderly. For the first time, we provide data covering the complete anisotropic elastic tensor, the microstructure of cortical vascular porosity, mineral and collagen characteristics obtained from the same or adjacent samples in each donor. The results revealed that cortical vascular porosity and degree of mineralization of bone are the most important determinants of bone anisotropic stiffness at the mesoscale. The presented data gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone.

3D patient-specific finite element models of the proximal femur based on DXA towards the classification of fracture and non-fracture cases

Osteoporotic bone fractures reduce quality of life and drastically increase mortality. Minimally irradiating imaging techniques such as dual-energy X-ray absorptiometry (DXA) allow assessment of bone loss through the use of bone mineral density (BMD) as descriptor. Yet, the accuracy of fracture risk predictions remains limited. Recently, DXA-based 3D modelling algorithms were proposed to analyse the geometry and BMD spatial distribution of the proximal femur. This study hypothesizes that such approaches can benefit from finite element (FE)-based biomechanical analyses to improve fracture risk prediction. One hundred and eleven subjects were included in this study and stratified in two groups: (a) 62 fracture cases, and (b) 49 non-fracture controls. Side fall was simulated using a static peak load that depended on patient mass and height. Local mechanical fields were calculated based on relationships between tissue stiffness and BMD. The area under the curve (AUC) of the receiver operating characteristic method evaluated the ability of calculated biomechanical descriptors to discriminate fracture and control cases. The results showed that the major principal stress was better discriminator (AUC > 0.80) than the volumetric BMD (AUC ≤ 0.70). High discrimination capacity was achieved when the analysis was performed by bone type, zone of fracture and gender/sex (AUC of 0.91 for women, trabecular bone and trochanter area), and outcomes suggested that the trabecular bone is critical for fracture discrimination. In conclusion, 3D FE models derived from DXA scans might significantly improve the prediction of hip fracture risk; providing a new insight for clinicians to use FE simulations in clinical practice for osteoporosis management.

A novel technique with reduced computed tomography exposure to predict vertebral compression fracture: a finite element study based on rat vertebrae

Vertebral compression fractures are a significant clinical issue with an annual incidence of approximately 750,000 cases in the USA alone. Mechanical properties of vertebrae are successfully evaluated through finite element (FE) models based on vertebrae CT. However, clinical drawbacks associated to radiation transmission encouraged to explore the possibility to use selected or reduced portions of the vertebra. The objective of our study was to develop a new procedure to predict vertebral compression fracture from sub-volumes. We reconstructed rat vertebras from micro-CT of thoracic and lumbar groups. Each vertebra was partitioned into three sub-volumes of different axial thickness. FE simulating compression tests were performed on each model to evaluate their failure load and stiffness. Using a power function, a high correlation was found for stiffness and strength. The sub-volume with three fifths thickness had a failure load of 180.7 ± 19.2 N for thoracic and of 209.5 ± 27.4 N for the lumbar vertebra. These values were not significantly different from the values found for the entire vertebra (p > 0.05). Based on our findings, failure loads and stiffnesses obtained with reduced CT scans can be successfully used to predict full vertebral failure. This sub-region analysis and power relationship suggests that one can limit radiation exposure to patients when bone characterization is needed. Graphical abstract Estimated mechanical properties in relation to the extent of the computed tomography reconstruction.

X-ray physics-based CT-to-composition conversion applied to a tissue engineering scaffold, enabling multiscale simulation of its elastic behavior

Nowadays, the assessment of the mechanical competence of tissue engineering scaffolds based on computer simulations is a well-accepted technology. Typically, such simulations are performed by means of the Finite Element (FE) method, with the underlying structural model being created based on micro-computed tomography (microCT). Here, this analysis modality is applied to a new, ternary composite, consisting of PHBV, i.e. poly(3-hydroxybutyrate-co-3-hydroxyvalerate), PLGA, i.e. poly(lactic-co-glycolide), as well as of TCP, i.e. tricalcium phosphate hydrate. The studied scaffold structure is made up by fibers of this new composite material, manufactured by means of the rapid prototyping method. The data collected from microCT is utilized for adequately defining the mechanical properties of the FE model. In particular, the three-dimensional field of grey values is interpreted in terms of the underlying field of attenuation coefficients, taking into account the photon energy employed in microCT imaging, eventually allowing for calculation of the three-dimensionally distributed, voxel-specific composition of the studied material. For the sake of keeping the FE simulations as efficient as possible, groups of voxels are combined into one finite element; the grey value of the latter is obtained by volume averaging. Employing a two-step micromechanical homogenization scheme, the experimentally accessible stiffness of the three constituents (PHBV, PLGA, and TCP) is then, finite element by finite element, upscaled to the composition-dependent stiffness of the composite material. The plausibility and adequacy of the FE model is demonstrated by simulating the effects of uniaxial compression on the scaffold structure, in terms of resulting stress and strain fields, highlighting the importance of the fiber junctions (as they are the mechanically most stressed regions), and that neglecting the material heterogeneity would lead to a potentially significant underestimation of stresses and strains. Finally, a comparison is made of the employed analysis modality of microCT data with a previously pursued, simplified analysis strategy, highlighting the conceptual superiority of the former, and pointing out the application limits of the latter.

A Lower Limb-Pelvis Finite Element Model with 3D Active Muscles

A lower limb-pelvis finite element (FE) model with active three-dimensional (3D) muscles was developed in this study for biomechanical analysis of human body. The model geometry was mainly reconstructed from a male volunteer close to the anthropometry of a 50th percentile Chinese male. Tissue materials and structural features were established based on the literature and new implemented experimental tests. In particular, the muscle was modeled with a combination of truss and hexahedral elements to define its passive and active properties as well as to follow the detailed anatomy structure. Both passive and active properties of the model were validated against the experiments of Post-Mortem Human Surrogate (PMHS) and volunteers, respectively. The model was then used to simulate driver's emergency braking during frontal crashes and investigate Knee-Thigh-Hip (KTH) injury mechanisms and tolerances of the human body. A significant force and bending moment variance was noted for the driver's femur due to the effects of active muscle forces during emergency braking. In summary, the present lower limb-pelvis model can be applied in various research fields to support expensive and complex physical tests or corresponding device design.

Biomechanical study on surgical fixation methods for minimally invasive treatment of hallux valgus

Hallux valgus (HV) was one of the most frequent female foot deformities. The aim of this study was to evaluate mechanical responses and stabilities of the Kirschner, bandage and fiberglass fixations after the distal metatarsal osteotomy in HV treatment. Surface traction of different forefoot regions in bandage fixation and the biomechanical behavior of fiberglass bandage material were measured by a pressure sensor device and a mechanical testing, respectively. A three-dimensional foot finite element (FE) model was developed to simulate the three fixation methods (Kirschner, bandage and fiberglass fixations) in weight bearing. The model included 28 bones, sesamoids, ligaments, plantar fascia, cartilages and soft tissue. The peak Von Mises stress (MS) and compression stress (CS) of the distal fragment were predicted from the three fixation methods: Kirschner fixation (MS=6.71MPa, CS=1.232MPa); Bandage fixation (MS=14.90MPa, CS=9.642MPa); Fiberglass fixation (MS=15.83MPa, CS=19.70MPa). Compared with the Kirschner and bandage fixation, the fiberglass fixation reduced the relative movement of osteotomy fragments and obtained the maximum CS. We concluded that fiberglass fixation in HV treatment was helpful to the bone healing of distal fragment. The findings were expected to guide further therapeutic planning of HV patient.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics

While in clinical settings, bone mineral density measured by computed tomography (CT) remains the key indicator for bone fracture risk, there is an ongoing quest for more engineering mechanics-based approaches for safety analyses of the skeleton. This calls for determination of suitable material properties from respective CT data, where the traditional approach consists of regression analyses between attenuation-related grey values and mechanical properties. We here present a physics-oriented approach, considering that elasticity and strength of bone tissue originate from the material microstructure and the mechanical properties of its elementary components. Firstly, we reconstruct the linear relation between the clinically accessible grey values making up a CT, and the X-ray attenuation coefficients quantifying the intensity losses from which the image is actually reconstructed. Therefore, we combine X-ray attenuation averaging at different length scales and over different tissues, with recently identified 'universal' composition characteristics of the latter. This gives access to both the normally non-disclosed X-ray energy employed in the CT-device and to in vivo patient-specific and location-specific bone composition variables, such as voxel-specific mass density, as well as collagen and mineral contents. The latter feed an experimentally validated multiscale elastoplastic model based on the hierarchical organization of bone. Corresponding elasticity maps across the organ enter a finite element simulation of a typical load case, and the resulting stress states are increased in a proportional fashion, so as to check the safety against ultimate material failure. In the young patient investigated, even normal physiological loading is probable to already imply plastic events associated with the hydrated mineral crystals in the bone ultrastructure, while the safety factor against failure is still as high as five. Copyright © 2016 John Wiley & Sons, Ltd.

Contribution of fluid in bone extravascular matrix to strain-rate dependent stiffening of bone tissue - A poroelastic study

Osteoporotic fractures represent an increasing cost to society, and its diagnosis methods based on bone density still lack accuracy in identifying risk of fracture. This is why a better understanding of mechanical behavior of bone tissue is of importance, especially when it comes to relating experimental observations to realistic physiological fall loading conditions. This study aims at exploring the stiffening effect of pore fluid in bone extravascular matrix subject to high strain rate loading that is more realistic to simulate a physiological fall. A computational approach is used, where bone tissue microstructure extracted from micro-CT images is modeled using finite elements. The solid phase of bone tissue is modeled as a poroelastic material, a porous matrix filled with fluid. When the extravascular matrix experiences certain volumetric deformation, the fluid in pores presents load carrying capacity, which consequently varies the apparent stiffness of bone tissue. It is shown that effects of fluid stiffening in bone can be significant, depending on the chosen material properties, the amount of volumetric strain in tissue and the loading rate with respect to hydraulic conductivity and drainage conditions. It is also shown that such stiffening effect is influenced by bone microstructure, and is more significant in cortical bone than in trabecular bone.

Patient-specific geometrical modeling of orthopedic structures with high efficiency and accuracy for finite element modeling and 3D printing

We improved the geometrical modeling procedure for fast and accurate reconstruction of orthopedic structures. This procedure consists of medical image segmentation, three-dimensional geometrical reconstruction, and assignment of material properties. The patient-specific orthopedic structures reconstructed by this improved procedure can be used in the virtual surgical planning, 3D printing of real orthopedic structures and finite element analysis. A conventional modeling consists of: image segmentation, geometrical reconstruction, mesh generation, and assignment of material properties. The present study modified the conventional method to enhance software operating procedures. Patient's CT images of different bones were acquired and subsequently reconstructed to give models. The reconstruction procedures were three-dimensional image segmentation, modification of the edge length and quantity of meshes, and the assignment of material properties according to the intensity of gravy value. We compared the performance of our procedures to the conventional procedures modeling in terms of software operating time, success rate and mesh quality. Our proposed framework has the following improvements in the geometrical modeling: (1) processing time: (femur: 87.16 ± 5.90 %; pelvis: 80.16 ± 7.67 %; thoracic vertebra: 17.81 ± 4.36 %; P < 0.05); (2) least volume reduction (femur: 0.26 ± 0.06 %; pelvis: 0.70 ± 0.47, thoracic vertebra: 3.70 ± 1.75 %; P < 0.01) and (3) mesh quality in terms of aspect ratio (femur: 8.00 ± 7.38 %; pelvis: 17.70 ± 9.82 %; thoracic vertebra: 13.93 ± 9.79 %; P < 0.05) and maximum angle (femur: 4.90 ± 5.28 %; pelvis: 17.20 ± 19.29 %; thoracic vertebra: 3.86 ± 3.82 %; P < 0.05). Our proposed patient-specific geometrical modeling requires less operating time and workload, but the orthopedic structures were generated at a higher rate of success as compared with the conventional method. It is expected to benefit the surgical planning of orthopedic structures with less operating time and high accuracy of modeling.

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.

The effect of in situ/in vitro three-dimensional quantitative computed tomography image voxel size on the finite element model of human vertebral cancellous bone

Quantitative computed tomography–based finite element modeling technique is a promising clinical tool for the prediction of bone strength. However, quantitative computed tomography–based finite element models were created from image datasets with different image voxel sizes. The aim of this study was to investigate whether there is an influence of image voxel size on the finite element models. In all 12 thoracolumbar vertebrae were scanned prior to autopsy (in situ) using two different quantitative computed tomography scan protocols, which resulted in image datasets with two different voxel sizes (0.29 × 0.29 × 1.3 mm3 vs 0.18 × 0.18 × 0.6 mm3). Eight of them were scanned after autopsy (in vitro) and the datasets were reconstructed with two voxel sizes (0.32 × 0.32 × 0.6 mm3 vs. 0.18 × 0.18 × 0.3 mm3). Finite element models with cuboid volume of interest extracted from the vertebral cancellous part were created and inhomogeneous bilinear bone properties were defined. Axial compression was simulated. No effect of voxel size was detected on the apparent bone mineral density for both the in situ and in vitro cases. However, the apparent modulus and yield strength showed significant differences in the two voxel size group pairs (in situ and in vitro). In conclusion, the image voxel size may have to be considered when the finite element voxel modeling technique is used in clinical applications.

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone". The underlying representative volume element of the macroscopic bone material contains two types of phases: a spherical, impermeable extracellular bone matrix phase interacts with interpenetrating cylindrical pore channel phases that are oriented in all different space directions. This type of interaction is modeled by means of a self-consistent homogenization scheme. While the permeability of the bone matrix equals to zero, the permeability of the pore phase is found through expressing the classical Hagen-Poiseuille law for laminar flow in the format of a "micro-Darcy law". The upscaling scheme contains pore size and porosity as geometrical input variables; however, they can be related to each other, based on well-known relations between porosity and specific bone surface. As two key results, validated through comprehensive experimental data, it appears (i) that the famous Kozeny-Carman constant (which relates bone permeability to the cube of the porosity, the square of the specific surface, as well as to the bone fluid viscosity) needs to be replaced by an again porosity-dependent rational function, and (ii) that the overall bone permeability is strongly affected by the pore fluid viscosity, which, in case of polarized fluids, is strongly increased due to the presence of electrically charged pore walls.

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.

The role of endplate poromechanical properties on the nutrient availability in the intervertebral disc

OBJECTIVE

To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP).

METHODS

50 micro-models of different BEP samples were generated from μCTs of lumbar vertebrae and allowed direct determination of porosity values. Permeability values were calculated by using the micro-models, through the simulation of permeation via computational fluid dynamics. These educated ranges of porosity and permeability values were used as inputs for mechano-transport simulations to assess their effect on both the distributions of metabolites within an IVD model and the poromechanical calculations within the cartilaginous part of the endplate i.e., the cartilage endplate (CEP).

RESULTS

BEP effective permeability was highly correlated to local variations of porosity (R(2) ≈ 0.88). Universal patterns between bone volume fraction and permeability arose from these results and from other experimental data in the literature. These variations in BEP permeability and porosity had negligible effects on the distributions of metabolites within the disc. In the CEP, the variability of the poromechanical properties of the BEP did not affect the predicted consolidation but induced higher fluid velocities.

CONCLUSIONS

The present paper provides the first sets of thoroughly identified BEP parameter values that can be further used in patient-specific poromechanical studies. Representing BEP structural changes through variations in poromechanical properties did not affect the diffusion of metabolites. However, attention might be paid to alterations in fluid velocities and cell mechano-sensing within the CEP.

Hyperlipidemia affects multiscale structure and strength of murine femur

To improve bone strength prediction beyond limitations of assessment founded solely on the bone mineral component, we investigated the effect of hyperlipidemia, present in more than 40% of osteoporotic patients, on multiscale structure of murine bone. Our overarching purpose is to estimate bone strength accurately, to facilitate mitigating fracture morbidity and mortality in patients. Because (i) orientation of collagen type I affects, independently of degree of mineralization, cortical bone׳s micro-structural strength; and, (ii) hyperlipidemia affects collagen orientation and μCT volumetric tissue mineral density (vTMD) in murine cortical bone, we have constructed the first multiscale finite element (mFE), mouse-specific femoral model to study the effect of collagen orientation and vTMD on strength in Ldlr(-/-), a mouse model of hyperlipidemia, and its control wild type, on either high fat diet or normal diet. Each µCT scan-based mFE model included either element-specific elastic orthotropic properties calculated from collagen orientation and vTMD (collagen-density model) by experimentally validated formulation, or usual element-specific elastic isotropic material properties dependent on vTMD-only (density-only model). We found that collagen orientation, assessed by circularly polarized light and confocal microscopies, and vTMD, differed among groups and that microindentation results strongly correlate with elastic modulus of collagen-density models (r(2)=0.85, p=10(-5)). Collagen-density models yielded (1) larger strains, and therefore lower strength, in simulations of 3-point bending and physiological loading; and (2) higher correlation between mFE-predicted strength and 3-point bending experimental strength, than density-only models. This novel method supports ongoing translational research to achieve the as yet elusive goal of accurate bone strength prediction.