Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties

Tough Cortical Bone-Inspired Tubular Architected Cement-Based Material with Disorder

Cortical bone is a tough biological material composed of tube-like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in-plane crack deflection around osteons due to cement line-crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D-printing/casting) process, the study engineers architected tubular cement-based materials with the stepwise cracking toughening mechanism, that enables a non-brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6-fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack-tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance-curves (R-curve). "Disorder" curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate "periodicity" classification and misperceived disorder parameters (perturbation and Voronoi tessellation methods).

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.

Fluid-structure interaction (FSI) modeling of bone marrow through trabecular bone structure under compression

The present study has sought to investigate the fluid characteristic and mechanical properties of trabecular bone using fluid-structure interaction (FSI) approach under different trabecular bone orientations. This method imposed on trabecular bone structure at both longitudinal and transverse orientations to identify effects on shear stress, permeability, stiffness and stress regarded to the trabeculae. Sixteen FSI models were performed on different range trabecular cubes of 27 mm³ with eight models developed for each longitudinal and transverse direction. Results show that there was a moderate correlation between permeability and porosity, and surface area in the longitudinal and transverse orientations. For the longitudinal orientation, the permeability values varied between 3.66 × 10^-8 and 1.9 × 10^-7 and the sheer stress values varied between 0.05 and 1.8 Pa, whilst for the transverse orientation, the permeability values varied between 5.95 × 10^-10 and 1.78 × 10^-8 and the shear stress values varied between 0.04 and 3.1 Pa. Here, transverse orientation limits the fluid flow from passing through the trabeculae due to high shear stress disturbance generated within the trabecular bone region. Compared to physiological loading direction (longitudinal orientation), permeability is higher within the range known to trigger a response in bone cells. Additionally, shear stresses also increase with bone surface area. This study suggests the shear stress within bone marrow in real trabecular architecture could provide the mechanical signal to marrow cells that leads to bone anabolism and can depend on trabecular orientation.

Pelvic Construct Prediction of Trabecular and Cortical Bone Structural Architecture

The pelvic construct is an important part of the body as it facilitates the transfer of upper body weight to the lower limbs and protects a number of organs and vessels in the lower abdomen. In addition, the importance of the pelvis is highlighted by the high mortality rates associated with pelvic trauma. This study presents a mesoscale structural model of the pelvic construct and the joints and ligaments associated with it. Shell elements were used to model cortical bone, while truss elements were used to model trabecular bone and the ligaments and joints. The finite element (FE) model was subjected to an iterative optimization process based on a strain-driven bone adaptation algorithm. The bone model was adapted to a number of common daily living activities (walking, stair ascent, stair descent, sit-to-stand, and stand-to-sit) by applying onto it joint and muscle loads derived using a musculoskeletal modeling framework. The cortical thickness distribution and the trabecular architecture of the adapted model were compared qualitatively with computed tomography (CT) scans and models developed in previous studies, showing good agreement. The sensitivity of the model to changes in material properties of the ligaments and joint cartilage and changes in parameters related to the adaptation algorithm was assessed. Changes to the target strain had the largest effect on predicted total bone volumes. The model showed low sensitivity to changes in all other parameters. The minimum and maximum principal strains predicted by the structural model compared to a continuum CT-derived model in response to a common test loading scenario showed good agreement with correlation coefficients of 0.813 and 0.809, respectively. The developed structural model enables a number of applications such as fracture modeling, design, and additive manufacturing of frangible surrogates.

Thin Lamina Cribrosa Beams Have Different Collagen Microstructure Than Thick Beams

Purpose

To compare the collagen microstructural crimp characteristics between thin and thick lamina cribrosa (LC) beams.

Methods

Seven eyes from four sheep were fixed at 5 mm Hg IOP in 10% formalin. For each eye, one to three coronal cryosections through the LC were imaged with polarized light microscopy and analyzed to visualize the LC and determine collagen fiber microstructure. For every beam, we measured its width and three characteristics of the crimp of its collagen fibers: waviness, tortuosity, and amplitude. Linear mixed effects models were used to test whether crimp characteristics were associated with the LC beam width.

Results

For each eye and over all the eyes, LC beam width was positively associated with crimp waviness and tortuosity, and negatively associated with crimp amplitude (P's < 0.0001). Thin beams, average width 13.11 μm, had average (SD) waviness, tortuosity, and amplitude of 0.27 (0.17) radians, 1.017 (0.028) and 1.88 (1.41) μm, respectively. For thick beams, average width 26.10 μm, these characteristics were 0.33 (0.18) radians, 1.025 (0.037) and 1.58 (1.36) μm, respectively.

Conclusions

Our results suggest heterogeneity in LC beam mechanical properties. Thin beams were less wavy than their thicker counterparts, suggesting that thin beams may stiffen at lower IOP than thick beams. This difference may allow thin beams to support similar amounts of IOP-induced force as thicker beams, thus providing a similar level of structural support to the axons at physiologic IOP, despite the differences in width. Measurements of beam-level mechanical properties are needed to confirm these predictions.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

Patient-specific in silico models can quantify primary implant stability in elderly human bone

Secure implant fixation is challenging in osteoporotic bone. Due to the high variability in inter- and intra-patient bone quality, ex vivo mechanical testing of implants in bone is very material- and time-consuming. Alternatively, in silico models could substantially reduce costs and speed up the design of novel implants if they had the capability to capture the intricate bone microstructure. Therefore, the aim of this study was to validate a micro-finite element model of a multi-screw fracture fixation system. Eight human cadaveric humerii were scanned using micro-CT and mechanically tested to quantify bone stiffness. Osteotomy and fracture fixation were performed, followed by mechanical testing to quantify displacements at 12 different locations on the instrumented bone. For each experimental case, a micro-finite element model was created. From the micro-finite element analyses of the intact model, the patient-specific bone tissue modulus was determined such that the simulated apparent stiffness matched the measured stiffness of the intact bone. Similarly, the tissue modulus of a small damage region around each screw was determined for the instrumented bone. For validation, all in silico models were rerun using averaged material properties, resulting in an average coefficient of determination of 0.89 ± 0.04 with a slope of 0.93 ± 0.19 and a mean absolute error of 43 ± 10 μm when correlating in silico marker displacements with the ex vivo test. In conclusion, we validated a patient-specific computer model of an entire organ bone-implant system at the tissue-level at high resolution with excellent overall accuracy. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:954-962, 2018.

The Effect of Mechanical Varus on Anterior Cruciate Ligament and Lateral Collateral Ligament Stress: Finite Element Analyses

The current study analyzed changes in anterior cruciate ligament (ACL) and lateral collateral ligament stress as a result of mechanical varus. In an exploratory pilot study, progressive mechanical varus was introduced to a male finite element model of the lower limb at different knee flexion angles. Nine situations were analyzed (combinations of 0°, 30°, and 60° knee flexion and 0°, 5°, and 10° varus). The ACL stress was measured via changes in section force, von Mises stress, and fiber stress. Lateral collateral ligament stress was measured via changes in section force. For all 3 measures of the ACL, maximum stress values were found in extension, stress decreased with flexion, and the effect of varus introduction was most significant at 30° flexion. With 60° flexion, varus introduction produced a decrease in section force and von Mises stress and a small increase in fiber stress. In all situations and stress measures except fiber stress at 60° flexion, stress was concentrated at the posterolateral bundle. For the lateral collateral ligament, the introduction of 5° and 10° varus caused an increase in section force at all degrees of flexion. Stress in the ligament decreased with flexion. Mechanical varus of less than 10° was responsible for increased ACL stress, particularly at 0° and 30° knee flexion, and for increased lateral collateral ligament stress at all degrees of flexion. Stress was mostly concentrated on the posterolateral bundle of the ACL. [Orthopedics. 2016; 39(4):e729-e736.].

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.

Permeability study of cancellous bone and its idealised structures

Artificial bone is a suitable alternative to autografts and allografts, however their use is still limited. Though there were numerous reports on their structural properties, permeability studies of artificial bones were comparably scarce. This study focused on the development of idealised, structured models of artificial cancellous bone and compared their permeability values with bone surface area and porosity. Cancellous bones from fresh bovine femur were extracted and cleaned following an established protocol. The samples were scanned using micro-computed tomography (μCT) and three-dimensional models of the cancellous bones were reconstructed for morphology study. Seven idealised and structured cancellous bone models were then developed and fabricated via rapid prototyping technique. A test-rig was developed and permeability tests were performed on the artificial and real cancellous bones. The results showed a linear correlation between the permeability and the porosity as well as the bone surface area. The plate-like idealised structure showed a similar value of permeability to the real cancellous bones.

Does mechanical stimulation really protect the architecture of trabecular bone? A simulation study

Although it is beyond doubt that mechanical stimulation is crucial to maintain bone mass, its role in preserving bone architecture is much less clear. Commonly, it is assumed that mechanics helps to conserve the trabecular network since an "accidental" thinning of a trabecula due to a resorption event would result in a local increase of load, thereby activating bone deposition there. However, considering that the thin trabecula is part of a network, it is not evident that load concentration happens locally on the weakened trabecula. The aim of this work was to clarify whether mechanical load has a protective role for preserving the trabecular network during remodeling. Trabecular bone is made dynamic by a remodeling algorithm, which results in a thickening/thinning of trabeculae with high/low strain energy density. Our simulations show that larger deviations from a regular cubic lattice result in a greater loss of trabeculae. Around lost trabeculae, the remaining trabeculae are on average thinner. More generally, thin trabeculae are more likely to have thin trabeculae in their neighborhood. The plausible consideration that a thin trabecula concentrates a higher amount of strain energy within itself is therefore only true when considering a single isolated trabecula. Mechano-regulated remodeling within a network-like architecture leads to local concentrations of thin trabeculae.

Change of mechanical vertebrae properties due to progressive osteoporosis: combined biomechanical and finite-element analysis within a rat model

For assessing mechanical properties of osteoporotic bone, biomechanical testing combined with in silico modeling plays a key role. The present study focuses on microscopic mechanical bone properties in a rat model of postmenopausal osteoporosis. Female Sprague-Dawley rats were (1) euthanized without prior interventions, (2) sham-operated, and (3) subjected to ovariectomy combined with a multi-deficiencies diet. Rat vertebrae (corpora vertebrae) were imaged by micro-CT, their stiffness was determined by compression tests, and load-induced stress states as well as property changes due to the treatment were analyzed by finite-element modeling. By comparing vertebra stiffness measurements with finite-element calculations of stiffness, an overall microscopic Young's modulus of the bone was determined. Macroscopic vertebra stiffness as well as the microscopic modulus diminish with progression of osteoporosis by about 70 %. After strong initial changes of bone morphology, further decrease in macroscopic stiffness is largely due to decreasing microscopic Young's modulus. The micromechanical stress calculations reveal particularly loaded vertebra regions prone to failure. Osteoporosis-induced changes of the microscopic Young's modulus alter the fracture behavior of bone, may influence bone remodeling, and should be considered in the design of implant materials.

Limitations of global morphometry in predicting trabecular bone failure

Efforts in finding independent measures for accurate and reliable prediction of trabecular bone failure have led to the development of a number of morphometric indices characterizing trabecular bone microstructure. Generally, these indices assume a high homogeneity within the bone specimen. However, in the present study we found that the variance in bone volume fraction (BV/TV) in a single bone specimen can be relatively large (CV = 9.07% to 28.23%). To assess the limitations of morphometric indices in the prediction of bone failure for specimens in which the assumption of homogeneity is not met, we harvested 13 cadaveric samples from a single human spine. We tested these cylindrical samples using image-guided failure assessment (IGFA), a technique combining stepwise microcompression and time-lapsed micro-computed tomography (µCT). Additionally, we computed morphometric indices for the entire sample as well as for 10 equal subregions along the anatomical axis. We found that ultimate strength was equally well predicted by BV/TV of the entire sample (R(2)  = 0.55) and BV/TV of the weakest subregion (R(2)  = 0.57). Investigating three-dimensional animations of structural bone failure, we showed that two main failure mechanisms determine the competence of trabecular bone samples; in homogeneous, isotropic trabecular bone samples, competence is determined by a whole set of trabecular elements, whereas in inhomogeneous, anisotropic bone samples a single or a missing trabeculae may induce catastrophic failure. The latter failure mechanism cannot be described by conventional morphometry, indicating the need for novel morphometric indices also applicable to the prediction of failure in inhomogeneous bone samples.

Cylinders or walls? A new computational model to estimate the MR transverse relaxation rate dependence on trabecular bone architecture

OBJECTIVE

Bone density is distributed in a complex network of interconnecting trabecular plates and rods that are interspersed with bone marrow. A computational model to assess the dependence of the relaxation rate on the geometry of bone can consider the distribution of bone material in the form of two components: cylinders and open walls (walls with gaps). We investigate whether the experimentally known dependence of the transverse relaxation rate on the trabecular bone structure can be usefully interpreted in terms of these two components.

MATERIALS AND METHODS

We established a computer model based on an elementary computational cell. The model includes a variable number of open walls and infinitely long cylinders as well as multiple geometric parameters. The transverse relaxation rate is computed as a function of these parameters. Within the model, increasing the trabecular spacing with a fixed trabecular radius is equivalent to thinning the trabeculae while maintaining constant spacing.

RESULTS

Increasing the number of cylinder and wall gap elements beyond their nearest neighbors does not change the transverse relaxation rate. Although the absolute contribution to the relaxation due to open walls is on average more important than that due to cylinders, the latter drops off rapidly. The change on transverse relaxation rate is larger for changing cylinder geometry than for changing wall geometry, as it can be seen from the effect on the relaxation rate when trabecular spacing is varied, compared to varying the size of wall gaps.

CONCLUSION

Our results provide strong evidence that trabecular thinning, which is associated with increasing age, decreases the relaxation rates. The effect of thinning plates and rods on the transverse relaxation can be understood in terms of simple cylinders and open walls. A reduction in the relaxation rate can be seen as an indication of thinning cylinders, corresponding to reduced bone stability and ultimately, osteoporosis.

Fast trabecular bone strength predictions of HR-pQCT and individual trabeculae segmentation-based plate and rod finite element model discriminate postmenopausal vertebral fractures

Although high-resolution peripheral quantitative computed tomography (HR-pQCT) has advanced clinical assessment of trabecular bone microstructure, nonlinear microstructural finite element (µFE) prediction of yield strength using a HR-pQCT voxel model is impractical for clinical use due to its prohibitively high computational costs. The goal of this study was to develop an efficient HR-pQCT-based plate and rod (PR) modeling technique to fill the unmet clinical need for fast bone strength estimation. By using an individual trabecula segmentation (ITS) technique to segment the trabecular structure into individual plates and rods, a patient-specific PR model was implemented by modeling each trabecular plate with multiple shell elements and each rod with a beam element. To validate this modeling technique, predictions by HR-pQCT PR model were compared with those of the registered high-resolution micro-computed tomography (HR-µCT) voxel model of 19 trabecular subvolumes from human cadaveric tibia samples. Both the Young's modulus and yield strength of HR-pQCT PR models strongly correlated with those of µCT voxel models (r²  = 0.91 and 0.86). Notably, the HR-pQCT PR models achieved major reductions in element number (>40-fold) and computer central processing unit (CPU) time (>1200-fold). Then, we applied PR model µFE analysis to HR-pQCT images of 60 postmenopausal women with (n = 30) and without (n = 30) a history of vertebral fracture. HR-pQCT PR model revealed significantly lower Young's modulus and yield strength at the radius and tibia in fracture subjects compared to controls. Moreover, these mechanical measurements remained significantly lower in fracture subjects at both sites after adjustment for areal bone mineral density (aBMD) T-score at the ultradistal radius or total hip. In conclusion, we validated a novel HR-pQCT PR model of human trabecular bone against µCT voxel models and demonstrated its ability to discriminate vertebral fracture status in postmenopausal women. This accurate nonlinear µFE prediction of the HR-pQCT PR model, which requires only seconds of desktop computer time, has tremendous promise for clinical assessment of bone strength.

Accuracy of individual trabecula segmentation based plate and rod finite element models in idealized trabecular bone microstructure

Currently, specimen-specific micro finite element (μFE) analysis based micro computed tomography (μCT) images have become a major computational tool for the assessment of the mechanical properties of human trabecular bone. Despite the fine characterization of the three-dimensional (3D) trabecular microstructure based on high-resolution μCT images, conventional μFE models with each voxel converted to an element are not efficient in predicting the nonlinear failure behavior of bone due to a prohibitive computational cost. Recently, a highly efficient individual trabecula segmentation (ITS)-based plate and rod (PR) modeling technique has been developed by substituting individual plates and rods with shell and beam elements, respectively. In this technical brief, the accuracy of novel PR μFE models was examined in idealized microstructure models over a broad range of trabecular thicknesses. The Young's modulus and yield strength predicted by simplified PR models strongly correlated with those of voxel models at various voxel sizes. The conversion from voxel models to PR models resulted in an ∼762-fold reduction in the largest model size and significantly accelerated the nonlinear FE analysis. The excellent predictive power of the PR μFE models, demonstrated in an idealized trabecular microstructure, provided a quantitative mechanical basis for this promising tool for an accurate and efficient assessment of trabecular bone mechanics and fracture risk.

The relationship between trabecular bone structure modeling methods and the elastic modulus as calculated by FEM

Trabecular bone cores were collected from the femoral head at the time of surgery (hip arthroplasty). Investigated were 42 specimens, from patients with osteoporosis and coxarthrosis. The cores were scanned used computer microtomography (microCT) system at an isotropic spatial resolution of 36 microns. Image stacks were converted to finite element models via a bone voxel-to-element algorithm. The apparent modulus was calculated based on the assumptions that for the elastic properties, E = 10 MPa and ν = 0.3. The compressive deformation as calculated by finite elements (FE) analysis was 0.8%. The models were coarsened to effectively change the resolution or voxel size (from 72 microns to 288 microns or from 72 microns to 1080 microns). The aim of our study is to determine how an increase in the distance between scans changes the elastic properties as calculated by FE models. We tried to find a border value voxel size at which the module values were possible to calculate. As the voxel size increased, the mean voxel volume increased and the FEA-derived apparent modulus decreased. The slope of voxel size versus modulus relationship correlated with several architectural indices of trabecular bone.

Multi-scale modelling of elastic moduli of trabecular bone

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results.

3D shape-dependent thinning method for trabecular bone characterization

PURPOSE

Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of trabecular bone analysis, however, neither curve nor surface thinning is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. The purpose of this paper is to propose an original method called hybrid skeleton which better matches the geometry of the data compared to curve and surface skeletons. In the hybrid skeleton algorithm, 1D curves represent rod-shaped zones whereas 2D surfaces represent plate-shaped elements.

METHODS

The proposed hybrid skeleton algorithm is based on a combination of three methods. (1) A new variant of the method proposed by Bonnassie et al. for the classification of voxels as belonging to plate-like or rod-like structures, where the medial axis (MA) algorithm is replaced by a fast and connected skeletonization algorithm. In addition, the reversibility of the MA algorithm is replaced by an isotropic region-growth method to spread the rod and plate labels back to the original object. (2) A well chosen surface thinning method applied on the plate voxels set. (3) A well chosen curve skeleton thinning method applied on the rod voxels set. The efficiency and the robustness of the proposed algorithm were evaluated using synthesis test vectors. A clinical study was led on micro-CT (computed tomography) images of two different populations of osteoarthritic and osteoporotic trabecular bone samples. The morphological and topological characteristics of the two populations were evaluated using the proposed hybrid skeleton as well as the classification algorithm.

RESULTS

When evaluated on test vectors and compared to Bonnassie's algorithm, the proposed classification algorithm gives a slightly better rate of classification. The hybrid skeleton preserves the shape information of the processed objects. Interesting morphological and topological features as well as volumetric ones were extracted from the skeleton and from the classified volumes, respectively. The extracted features enable the two populations of osteoarthritic and osteoporotic trabecular bone samples to be distinguished.

CONCLUSIONS

Compared to curve-based or surface-based skeletons, the hybrid skeleton better matches the geometry of the data. Each rod is represented by a one-voxel-thick arc and each plate is represented by a one-voxel-thick surface. The hybrid skeleton as well as the proposed classification algorithm introduce relevant parameters linked to the presence of plates in the trabecular bone data, showing that rods and plates contain independent information about trabeculae. The hybrid skeleton offers a new opportunity for precise studies of porous media such as trabecular bone.

Mechanical and microarchitectural analyses of cancellous bone through experiment and computer simulation

The relationship between microarchitecture to the failure mechanism and mechanical properties can be assessed through experimental and computational methods. In this study, both methods were utilised using bovine cadavers. Twenty four samples of cancellous bone were extracted from fresh bovine and the samples were cleaned from excessive marrow. Uniaxial compression testing was performed with displacement control. After mechanical testing, each specimen was ashed in a furnace. Four of the samples were exemplarily scanned using micro-computed tomography (μCT) and three dimensional models of the cancellous bones were reconstructed for finite element simulation. The mechanical properties and the failure modes obtained from numerical simulations were then compared to the experiments. Correlations between microarchitectural parameters to the mechanical properties and failure modes were then made. The Young's modulus correlates well with the bone volume fraction with R² = 0.615 and P value 0.013. Three different types of failure modes of cancellous bone were observed: oblique fracture (21.7%), perpendicular global fracture (47.8%), and scattered localised fracture (30.4%). However, no correlations were found between the failure modes to the morphological parameters. The percentage of error between computer predictions and the actual experimental test was from 6 to 12%. These mechanical properties and information on failure modes can be used for the development of synthetic cancellous bone.

Fast and accurate specimen-specific simulation of trabecular bone elastic modulus using novel beam-shell finite element models

Elastic modulus and strength of trabecular bone are negatively affected by osteoporosis and other metabolic bone diseases. Micro-computed tomography-based beam models have been presented as a fast and accurate way to determine bone competence. However, these models are not accurate for trabecular bone specimens with a high number of plate-like trabeculae. Therefore, the aim of this study was to improve this promising methodology by representing plate-like trabeculae in a way that better reflects their mechanical behavior. Using an optimized skeletonization and meshing algorithm, voxel-based models of trabecular bone samples were simplified into a complex structure of rods and plates. Rod-like and plate-like trabeculae were modeled as beam and shell elements, respectively, using local histomorphometric characteristics. To validate our model, apparent elastic modulus was determined from simulated uniaxial elastic compression of 257 cubic samples of trabecular bone (4mm×4mm×4mm; 30μm voxel size; BIOMED I project) in three orthogonal directions using the beam-shell models and using large-scale voxel models that served as the gold standard. Excellent agreement (R(2)=0.97) was found between the two, with an average CPU-time reduction factor of 49 for the beam-shell models. In contrast to earlier skeleton-based beam models, the novel beam-shell models predicted elastic modulus values equally well for structures from different skeletal sites. It allows performing detailed parametric analyses that cover the entire spectrum of trabecular bone microstructures.

Local strain and damage mapping in single trabeculae during three-point bending tests

The use of bone mineral density as a surrogate to diagnose bone fracture risk in individuals is of limited value. However, there is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element analysis (FEA) applied to 3D image data of several mm-sized trabecular bone structures obtained from non-invasive imaging modalities for the prediction of apparent mechanical properties. However, there is a lack of FE damage models, based on solid experimental facts, which are needed to validate such approaches and to provide criteria marking elastic-plastic deformation transitions as well as microdamage initiation and accumulation. In this communication, we present a strategy that could elegantly lead to future damage models for FEA: direct measurements of local strains involved in microdamage initiation and plastic deformation in single trabeculae. We use digital image correlation to link stress whitening in bone, reported to be correlated to microdamage, to quantitative local strain values. Our results show that the whitening zones, i.e. damage formation, in the presented loading case of a three-point bending test correlate best with areas of elevated tensile strains oriented parallel to the long axis of the samples. The average local strains along this axis were determined to be (1.6±0.9)% at whitening onset and (12±4)% just prior to failure. Overall, our data suggest that damage initiation in trabecular bone is asymmetric in tension and compression, with failure originating and propagating over a large range of tensile strains.

Fast Tool for Evaluation of Iliac Crest Tissue Elastic Properties Using the Reduced-Basis Methods

Computationally expensive finite element (FE) methods are generally used for indirect evaluation of tissue mechanical properties of trabecular specimens, which is vital for fracture risk prediction in the elderly. This work presents the application of reduced-basis (RB) methods for rapid evaluation of simulation results. Three cylindrical transiliac crest specimens (diameter: 7.5 mm, length: 10–12 mm) were obtained from healthy subjects (20 year-old, 22 year-old, and 24 year-old females) and scanned using microcomputed tomography imaging. Cubic samples of dimensions 5×5×5 mm3 were extracted from the core of the cylindrical specimens for FE analysis. Subsequently, a FE solution library (test space) was constructed for each of the specimens by varying the material property parameters: tissue elastic modulus and Poisson’s ratio, to develop RB algorithms. The computational speed gain obtained by the RB methods and their accuracy relative to the FE analysis were evaluated. Speed gains greater than 4000 times, were obtained for all three specimens for a loss in accuracy of less than 1% in the maxima of von-Mises stress with respect to the FE-based value. The computational time decreased from more than 6 h to less than 18 s. RB algorithms can be successfully utilized for real-time reliable evaluation of trabecular bone elastic properties.

Scale and boundary conditions effects on the apparent elastic moduli of trabecular bone modeled as a periodic cellular solid

We study apparent elastic moduli of trabecular bone, which is represented, for simplicity, by a two- or three-dimensional periodic cellular network. The term "apparent" refers to the case when the region used in calculations (or specimen size) is smaller than a representative volume element and the moduli depend on the size of that region and boundary conditions. Both the bone tissue forming the network and the pores (represented by a very soft material) are assumed, for simplicity, as homogeneous, linear elastic, and isotropic. In order to investigate the effects of scale and boundary conditions on the moduli of these networks we vary the specimen size and apply four different boundary conditions: displacement, traction, mixed, and periodic. The analysis using periodic boundary conditions gives the effective moduli, while the displacement, traction, and mixed boundary conditions give apparent moduli. The apparent moduli calculated using displacement and traction boundary conditions bound the effective moduli from above and below, respectively. The larger is the size of the region used in our calculations, the closer are the bounds. Our choice of mixed boundary conditions gives results that are very close to those obtained using periodic boundary conditions. We conduct this analysis computationally using a finite element method. We also investigate the effect of mismatch in elastic moduli of bone tissue and soft fill, trabecular bone structure geometry, and bone tissue volume fraction on the apparent elastic moduli of idealized periodic models of trabecular bone. This study gives guidance on how the size of the specimen and boundary conditions (used in experiments or simulations) influence elastic moduli of cellular materials. This approach is applicable to heterogeneous materials in general.

Direct gene therapy for bone regeneration: gene delivery, animal models, and outcome measures

While various problems with bone healing remain, the greatest clinical change is the absence of an effective approach to manage large segmental defects in limbs and craniofacial bones caused by trauma or cancer. Thus, nontraditional forms of medicine, such as gene therapy, have been investigated as a potential solution. The use of osteogenic genes has shown great potential in bone regeneration and fracture healing. Several methods for gene delivery to the fracture site have been described. The majority of them include a cellular component as the carrying vector, an approach known as cell-mediated gene therapy. Yet, the complexity involved with cell isolation and culture emphasizes the advantages of direct gene delivery as an alternative strategy. Here we review the various approaches of direct gene delivery for bone repair, the choice of animal models, and the various outcome measures required to evaluate the efficiency and safety of each technique. Special emphasis is given to noninvasive, quantitative, in vivo monitoring of gene expression and biodistribution in live animals. Research efforts should aim at inducing a transient, localized osteogenic gene expression within a fracture site to generate an effective therapeutic approach that would eventually lead to clinical use.

Genetic algorithm and image processing for osteoporosis diagnosis

Osteoporosis is considered as a major public health threat. It is characterized by a decrease in the density of bone, decreasing its strength and leading to an increased risk of fracture. In this work, the morphological, topological and mechanical characteristics of 2 populations of arthritic and osteoporotic trabecular bone samples are evaluated using artificial intelligence and recently developed skeletonization algorithms. Results show that genetic algorithms associated with image processing tools can precisely separate the 2 populations.

A three-dimensional microcomputed tomographic study of site-specific variation in trabecular microarchitecture in the human second metacarpal

Variation in trabecular microarchitecture is widely accepted as being regulated by both functional (mechanical loading) and genetic parameters, although the relative influence of each is unclear. Studies reporting inter-site differences in trabecular morphology (volume, number and structure) reveal a complex interaction at the gene-environment interface. We report inter- and intra-site variation in trabecular anatomy using a novel model of contralateral (left vs right) and ipsilateral (head vs base) comparisons for the human second metacarpal in a sample of n = 29 historically known 19th century EuroCanadians. Measures of bone volume fraction, structure model index, connectivity, trabecular number, spacing and thickness as well as degree of anisotropy were obtained from 5-mm volumes of interest using three-dimensional microcomputed tomography. We hypothesized that: (i) the more diverse loading environment of metacarpal heads should produce a more robust trabecular architecture than corresponding bases within sides and (ii) the ipsilateral differences between epiphyses will be larger on the right side than on the left side, as a function of handedness. Analysis of covariance (Side x Epiphysis) with Age as covariate revealed a clear dichotomy between labile and constrained architectures within and among anatomical sites. The predicted variation in loading was accommodated by changes in trabecular volume, whereas trabecular structure did not vary significantly by side or by epiphysis within sides. Age was a significant covariate only for females. We conclude that environmental and genetic regulation of bone adaptation may act through distinct pathways and local anatomies to ensure an integrated lattice of sufficient mass to meet normal functional demands.

Tissue modulus calculated from beam theory is biased by bone size and geometry: implications for the use of three-point bending tests to determine bone tissue modulus

Current practice to determine bone tissue modulus of murine cortical bone is to estimate it from three-point bending tests, using Euler-Bernoulli beam theory. However, murine femora are not perfect beams; hence, results can be inaccurate. Our aim was to assess the accuracy of beam theory, which we tested for two commonly used inbred strains of mice, C57BL/6 (B6) and C3H/He (C3H). We measured the three-dimensional structure of male and female B6 and C3H femora (N=20/group) by means of micro-computed tomography. For each femur five micro-finite element (micro-FE) models were created that simulated three-point bending tests with varying distances between the supports. Tissue modulus was calculated from beam theory using micro-FE results. The accuracy of beam theory was assessed by comparing the beam theory-derived moduli with the modulus as used in the micro-FE analyses. An additional set of fresh-frozen femora (10 B6 and 12 C3H) was biomechanically tested and subjected to the same micro-FE analyses. These combined experimental-computational analyses enabled an unbiased assessment of specimen-specific tissue modulus. We found that by using beam theory, tissue modulus was underestimated for all femora. Femoral geometry and size had strong effects on beam theory-derived tissue moduli. Owing to their relatively thin cortex, underestimation was markedly higher for B6 than for C3H. Underestimation was dependent on support width in a strain-specific manner. From our combined experimental-computational approach we calculated tissue moduli of 12.0+/-1.3 GPa and 13.4+/-2.1 GPa for B6 and C3H, respectively. We conclude that tissue moduli in murine femora are strongly underestimated when calculated from beam theory. Using image-based micro-FE analyses we could precisely quantify this underestimation. We showed that previously reported murine inbred strain-specific differences in tissue modulus are largely an effect of geometric differences, not accounted for by beam theory. We suggest a re-evaluation of the tissue properties obtained from three-point bending tests, especially in mouse genetics.

How can bone turnover modify bone strength independent of bone mass?

The amount of bone turnover in the skeleton has been identified as a predictor of fracture risk independent of areal bone mineral density (aBMD) and is increasingly cited as an explanation for discrepancies between areal bone mineral density and fracture risk. A number of mechanisms have been proposed to explain how bone turnover influences bone biomechanics, including regulation of tissue degree of mineralization, the disconnection or fenestration of individual trabeculae by remodeling cavities, and the ability of cavities formed during the remodeling process to act as stress risers. While these mechanisms can influence bone biomechanics, they also modify bone mass. If bone turnover is to explain any of the observed discrepancies between fracture risk and areal bone mineral density, however, it must not only modify bone strength, but must also modify bone strength in excess of what would be expected from the associated change in bone mass. This article summarizes biomechanical studies of how tissue mineralization, trabecular disconnection, and the presence of remodeling cavities might have an effect on cancellous bone strength independent of bone mass. Existing data support the idea that all of these factors may have a disproportionate effect on bone stiffness and/or strength, with the exception of average tissue degree of mineralization, which may not affect bone strength independent of aBMD. Disproportionate effects of mineral content on bone biomechanics may instead come from variation in tissue degree of mineralization at the micro-structural level. The biomechanical explanation for the relationship between bone turnover and fracture incidence remains to be determined, but must be examined not in terms of bone biomechanics, but in terms of bone biomechanics relative to bone mass.