Heterogeneous linear elastic trabecular bone modelling using micro-CT attenuation data and experimentally measured heterogeneous tissue properties

Characterization of mechanical stiffness using additive manufacturing and finite element analysis: potential tool for bone health assessment

BACKGROUND

Bone health and fracture risk are known to be correlated with stiffness. Both micro-finite element analysis (μFEA) and mechanical testing of additive manufactured phantoms are useful approaches for estimating mechanical properties of trabecular bone-like structures. However, it is unclear if measurements from the two approaches are consistent. The purpose of this work is to evaluate the agreement between stiffness measurements obtained from mechanical testing of additive manufactured trabecular bone phantoms and μFEA modeling. Agreement between the two methods would suggest 3D printing is a viable method for validation of μFEA modeling.

METHODS

A set of 20 lumbar vertebrae regions of interests were segmented and the corresponding trabecular bone phantoms were produced using selective laser sintering. The phantoms were mechanically tested in uniaxial compression to derive their stiffness values. The stiffness values were also derived from in silico simulation, where linear elastic μFEA was applied to simulate the same compression and boundary conditions. Bland-Altman analysis was used to evaluate agreement between the mechanical testing and μFEA simulation values. Additionally, we evaluated the fidelity of the 3D printed phantoms as well as the repeatability of the 3D printing and mechanical testing process.

RESULTS

We observed good agreement between the mechanically tested stiffness and μFEA stiffness, with R2 of 0.84 and normalized root mean square deviation of 8.1%. We demonstrate that the overall trabecular bone structures are printed in high fidelity (Dice score of 0.97 (95% CI, [0.96,0.98]) and that mechanical testing is repeatable (coefficient of variation less than 5% for stiffness values from testing of duplicated phantoms). However, we noticed some defects in the resin microstructure of the 3D printed phantoms, which may account for the discrepancy between the stiffness values from simulation and mechanical testing.

CONCLUSION

Overall, the level of agreement achieved between the mechanical stiffness and μFEA indicates that our μFEA methods may be acceptable for assessing bone mechanics of complex trabecular structures as part of an analysis of overall bone health.

Effect of radiation-induced damage of trabecular bone tissue evaluated using indentation and digital volume correlation

Exposure to X-ray radiation for an extended amount of time can cause damage to the bone tissue and therefore affect its mechanical properties. Specifically, high-resolution X-ray Computed Tomography (XCT), in both synchrotron and lab-based systems, has been employed extensively for evaluating bone micro-to-nano architecture. However, to date, it is still unclear how long exposures to X-ray radiation affect the mechanical properties of trabecular bone, particularly in relation to lab-XCT systems. Indentation has been widely used to identify local mechanical properties such as hardness and elastic modulus of bone and other biological tissues. The purpose of this study is therefore, to use indentation and XCT-based investigative tools such as digital volume correlation (DVC) to assess the microdamage induced by long exposure of trabecular bone tissue to X-ray radiation and how this affects its local mechanical properties. Trabecular bone specimens were indented before and after X-ray exposures of 33 and 66 h, where variation of elastic modulus was evaluated at every stage. The resulting elastic modulus was decreased, and micro-cracks appeared in the specimens after the first long X-ray exposure and crack formation increased after the second exposure. High strain concentration around the damaged tissue exceeding 1% was also observed from DVC analysis. The outcomes of this study show the importance of designing appropriate XCT-based experiments in lab systems to avoid degradation of the bone tissue mechanical properties due to radiation and these results will help to inform future studies that require long X-ray exposure for in situ experiments or generation of reliable subject-specific computational models.

Nonlinear micro finite element models based on digital volume correlation measurements predict early microdamage in newly formed bone

Bone regeneration in critical-sized defects is a clinical challenge, with biomaterials under constant development aiming at enhancing the natural bone healing process. The delivery of bone morphogenetic proteins (BMPs) in appropriate carriers represents a promising strategy for bone defect treatment but optimisation of the spatial-temporal release is still needed for the regeneration of bone with biological, structural, and mechanical properties comparable to the native tissue. Nonlinear micro finite element (μFE) models can address some of these challenges by providing a tool able to predict the biomechanical strength and microdamage onset in newly formed bone when subjected to physiological or supraphysiological loads. Yet, these models need to be validated against experimental data. In this study, experimental local displacements in newly formed bone induced by osteoinductive biomaterials subjected to in situ X-ray computed tomography compression in the apparent elastic regime and measured using digital volume correlation (DVC) were used to validate μFE models. Displacement predictions from homogeneous linear μFE models were highly correlated to DVC-measured local displacements, while tissue heterogeneity capturing mineralisation differences showed negligible effects. Nonlinear μFE models improved the correlation and showed that tissue microdamage occurs at low apparent strains. Microdamage seemed to occur next to large cavities or in biomaterial-induced thin trabeculae, independent of the mineralisation. While localisation of plastic strain accumulation was similar, the amount of damage accumulated in these locations was slightly higher when including material heterogeneity. These results demonstrate the ability of the nonlinear μFE model to capture local microdamage in newly formed bone tissue and can be exploited to improve the current understanding of healing bone and mechanical competence. This will ultimately aid the development of BMPs delivery systems for bone defect treatment able to regenerate bone with optimal biological, mechanical, and structural properties.

Microstructure Determines Apparent-Level Mechanics Despite Tissue-Level Anisotropy and Heterogeneity of Individual Plates and Rods in Normal Human Trabecular Bone

Trabecular plates and rods determine apparent elastic modulus and yield strength of trabecular bone, serving as important indicators of bone's mechanical integrity in health and disease. Although trabecular bone's apparent-level mechanical properties have been widely reported, tissue mechanical properties of individual trabeculae have not been fully characterized. We systematically measured tissue mineral density (TMD)-dependent elastic modulus of individual trabeculae using microindentation and characterized its anisotropy as a function of trabecular type (plate or rod), trabecular orientation in the global coordinate (longitudinal, oblique, or transverse along the anatomic loading axis), and indentation direction along the local trabecular coordinate (axial or lateral). Human trabecular bone samples were scanned by micro-computed tomography for TMD and microstructural measurements. Individual trabecula segmentation was used to decompose trabecular network into individual trabeculae, where trabecular type and orientation were determined. We performed precise, selective indentation of trabeculae in each category using a custom-built, microscope-coupled microindentation device. Co-localization of TMD at each indentation site was performed to obtain TMD-to-modulus correlations. We found significantly higher TMD and tissue modulus in trabecular plates than rods. Regardless of trabecular type and orientation, axial tissue modulus was consistently higher than lateral tissue modulus, with ratios ranging from 1.13 to 1.41. Correlations between TMD and tissue modulus measured from axial and lateral indentations were strong but distinct: axial correlation predicted higher tissue modulus than lateral correlation at the same TMD level. To assess the contribution of experimentally measured anisotropic tissue properties of individual trabeculae to apparent-level mechanics, we constructed non-linear micro-finite element models using a new set of trabecular bone samples and compared model predictions to mechanical testing measurements. Heterogeneous anisotropic models accurately predicted apparent elastic modulus but were no better than a simple homogeneous isotropic model. Variances in tissue-level properties may therefore contribute nominally to apparent-level mechanics in normal human trabecular bone. © 2021 American Society for Bone and Mineral Research (ASBMR).

Loss of longitudinal superiority marks the microarchitecture deterioration of osteoporotic cancellous bones

Osteoporosis (OP), a skeletal disease making bone mechanically deteriorate and easily fracture, is a global public health issue due to its high prevalence. It has been well recognized that besides bone loss, microarchitecture degradation plays a crucial role in the mechanical deterioration of OP bones, but the specific role of microarchitecture in OP has not been well clarified and quantified from mechanics perspective. Here, we successfully decoupled and identified the specific roles of microarchitecture, bone mass and tissue property in the failure properties of cancellous bones, through μCT-based digital modeling and finite element method simulations on bone samples from healthy and ovariectomy-induced osteoporotic mice. The results show that the microarchitecture of healthy bones exhibits longitudinal superiority in mechanical properties such as the effective stiffness, strength and toughness, which fits them well to bearing loads along their longitudinal direction. OP does not only reduce bone mass but also impair the microarchitecture topology. The former is mainly responsible for the mechanical degradation of bones in magnitude, wherever the latter accounts for the breakdown of their function-favorable anisotropy, the longitudinal superiority. Hence, we identified the microarchitecture-deterioration-induced directional mismatch between material and loading as a hazardous feature of OP and defined a longitudinal superiority index as measurement of the health status of bone microarchitecture. These findings provide useful insights and guidelines for OP diagnosis and treat assessment.

Evaluating a theoretical and an empirical model of "side effects" in cancellous bone

Accurate measurement of cancellous bone's apparent elastic modulus, E, is confounded by the experimental artefacts created when trabeculae are severed during specimen preparation. Although standardized axial testing protocols have been developed to deal with the so-called "end effects" caused by severed trabeculae at the loading surfaces, much less attention has been given to the "side effects" around the periphery and the specimen size dependence they create. Two models (one theoretical, one empirical) have been proposed in the literature to predict the reduction in E with decreasing specimen diameter. The current study used finite element method (FEM) modelling to analyze bovine cancellous bone from five different anatomic sites and quantify the changes in E that occurred with specimen diameter. The two models were adapted so that they could predict E based on diameter and architectural parameters (BV/TV, DA, Tb.Sp) alone, without requiring that a "true" modulus be known a priori. Both models fit the data equally well; however, the empirical model gives simpler estimations as a function of trabecular separation (Tb.Sp). A minimum diameter of 5-8 Tb.Sp is recommended.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53-0.65, average error of 13-17%). A lower correlation was found for failure load (R2 = 0.21-0.48, average error of 9-15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75-0.80 for stiffness, R2 = 0.55-0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Prediction of mechanical properties of trabecular bone in patients with type 2 diabetes using damage based finite element method

Type-2 diabetic (T2D) and osteoporosis (OP) suffered patients are more prone to fragile fracture though the nature of alteration in areal bone mineral density (aBMD) in these two cases are completely different. Therefore, it becomes crucial to compare the effect of T2D and OP on alteration in mechanical and structural properties of femoral trabecular bone. This study investigated the effect of T2D, OP, and osteopenia on bone structural and mechanical properties using micro-CT, nanoindentation and compression test. Further, a nanoscale finite element model (FEM) was developed to predict the cause of alteration in mechanical properties. Finally, a damage-based FEM was proposed to predict the pathological related alteration of bone's mechanical response. The obtained results demonstrated that the T2D group had lower volume fraction (-18.25%, p = 0.023), young's modulus (-23.47%, p = 0.124), apparent modulus (-37.15%, p = 0.02), and toughness (-40%, p = 0.001) than the osteoporosis group. The damage-based FE results were found in good agreement with the compression experiment results for all three pathological conditions. Also, nanoscale FEM results demonstrated that the elastic and failure properties of mineralised collagen fibril decreases with increase in crystal size. This study reveals that T2D patients are more prone to fragile fracture in comparison to OP and osteopenia patients. Also, the proposed damage-based FEM can help to predict the risk of fragility fracture for different pathological conditions.

Bone remodeling analysis for a swine skull at continuous scale based on the smoothed finite element method

In order to study bone response during chewing, bone remodeling analysis at a continuous scale is performed to a swine skull obtained using μCT. The smoothed finite element method (S-FEM) is utilized to replace the finite element method (FEM) in bone remodeling as it is solving the "overly-stiff" problem in FEM by introducing strain smoothing technology to soften the stiffness matrix. Three S-FEM models with different levels of softening effects are developed, including node-based, edge-based, and face-based, which leads to various bone remodeling results for a better understanding of the remodeling process. During the remodeling process, the strain energy density is used as the mechanical stimulus, and the surface elements or smoothing domains are regarded as cortical bone. Under the action of mechanical stimuli, cortical bone and cancellous bone have been remodeled. In remodeling progress, ES-FEM shows close results as compared with the experimental μCT in nodal bone density distribution, FEM and FS-FEM are close to the μCT experimental model in average nodal density. In summary, the combined use of several methods provides more angles for the description of bone remodeling.

A comparison of density-modulus relationships used in finite element modeling of the shoulder

Subject- and site-specific modeling techniques greatly improve the accuracy of computational models derived from clinical-resolution quantitative computed tomography (QCT) data. The majority of shoulder finite element (FE) studies use density-modulus relationships developed for alternative anatomical locations. As such, the objectives of this study were to compare the six most commonly used density-modulus relationships in shoulder finite element (FE) studies. To achieve this, ninety-eight (98) virtual trabecular bone cores were extracted from uCT scans of scapulae from 14 cadaveric specimens (7 male; 7 female). Homogeneous tissue moduli of 20 GPa, and heterogeneous tissue moduli scaled by CT-intensity were considered. Micro finite element models (µ-FEMs) of each virtual core were compressively loaded to 0.5% apparent strain and apparent strain energy density (SED_app) was collected. Each uCT virtual core was then co-registered to clinical QCT images, QCT-FEMs created, and each of the 6 density-modulus relationships applied (6 × 98 = 588 QCT-FEMs). The loading and boundary conditions were replicated and SED_app was collected and compared to µ-FEM SED_app. When a homogeneous tissue modulus was considered in the µ-FEMs, SED_app was best predicted in QCT-FEMs with the density-modulus relationship developed from pooled anatomical locations (QCT-FEM SED_app = 0.979µ-FEM SED_app + 0.0066, r² = 0.933). A different density-modulus relationship best predicted SED_app (QCT-FEM SED_app = 1.014µ-FEM SED_app + 0.0034, r² = 0.935) when a heterogeneous tissue modulus was considered. This study compared density-modulus relationships used in shoulder FE studies using an independent computational methodology for comparing these relationships.

The Effect of Material Heterogeneity, Element Type, and Down-Sampling on Trabecular Stiffness in Micro Finite Element Models

Preclinical and clinical bone strength predictions can be elucidated by understanding bone mechanics at a variety of hierarchical levels. As such, down-sampled micro-CT images are often used to make comparisons across image resolutions or used to reduce computational resources in micro finite element models (µFEMs). Therefore, the objectives of this study were to compare trabecular apparent modulus among (i) hexahedral and tetrahedral µFEMs, (ii) µFEMs generated from 32, 64, and 64 µm down-sampled from 32 µm µCT scans, and (iii) µFEMs with homogeneous and heterogeneous tissue moduli. Trabecular µFEMs were generated from scans at the three spatial resolutions taken from the glenoid vault of 14 cadaveric specimens. Simulated unconstrained compression was performed and used to calculate and compare the apparent modulus of each µFEM. It was found that models derived from high-resolution images that account for material heterogeneity are nearly equivalent whether hexahedral or tetrahedral elements are used. However, translation of stiffness from down-sampled scans are not equivalent to scans performed at the down-sampled resolution, or that account for trabecular material heterogeneity. Material heterogeneity is most representative of in vivo trabecular bone and to accurately model trabecular mechanical properties, material heterogeneity should be considered in future µFEM development.

Young's modulus of trabecular bone at the tissue level: A review

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties.

STATEMENT OF SIGNIFICANCE

The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Estimating the Effective Elastic Parameters of Nodular Cast Iron from Micro-Tomographic Imaging and Multiscale Finite Elements: Comparison between Numerical and Experimental Results

Herein, we describe in detail a methodology to estimate the effective elastic parameters of nodular cast iron, using micro-tomography in conjunction with multiscale finite elements. We discuss the adjustment of the image acquisition parameters, address the issue of the representative-volume choice, and present a brief discussion on image segmentation. In addition, the finite-element computational implementation developed to estimate the effective elastic parameters from segmented microstructural images is described, indicating the corresponding computational costs. We applied the proposed methodology to a nodular cast iron, and estimated the graphite elastic parameters through a comparison between the numerical and experimental results.

Knockdown Indian Hedgehog (Ihh) does not delay Fibular Fracture Healing in genetic deleted Ihh mice and pharmaceutical inhibited Ihh Mice

The objective of this study was to determine if Ihh is required for fracture healing. Fibular fracture was created in adult Col2a1-CreER^T2; Ihh^fl/fl mice. Ihh^fl/fl mice received Tamoxifen (TM) to delete Ihh. WT mice received Cyclopamine to inhibit Hh pathway. Callus tissue properties and Ihh pathway were analyzed at 1, 2, and 3 weeks post-fracture by X-ray, micro-CT, mechanical test, RT-PCR and immunohistochemistry. Deleted Ihh was evidenced by the occurrence of growth plate closure in the Ihh^fl/fl mice by X-ray 3 weeks after TM treatment. All mice showed fracture healing at 3 weeks post-operation. Histology analysis indicated that, compared to the control, cartilage area was less in fracture sites from Ihh deficient animals by either genetic deletion or drug inhibition at 1 and 2 weeks post-fracture. Ihh immunostaining and its mRNA level were diminished in the fracture callus in Ihh reduced mice. There was no significant difference in BV/TV, BMD and mechanical test. Interruption to Ihh pathway by either genetic or pharmaceutical approach didn’t affect fibular fracture healing in these mice. This surprised finding implicates that the deleted Ihh does not affect fracture healing in this model.

Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level

OBJECTIVE OF THE STUDY

The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue.

PATIENTS

Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study.

MATERIALS AND METHODS

Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan^® software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2^® software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone.

RESULTS

In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress.

CONCLUSION

Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters.

Chronic alcohol abuse in men alters bone mechanical properties by affecting both tissue mechanical properties and microarchitectural parameters

OBJECTIVE OF THE STUDY

Alcohol-induced secondary osteoporosis in men has been characterized by higher fracture prevalence and a modification of bone microarchitecture. Chronic alcohol consumption impairs bone cell activity and results in an increased fragility. A few studies highlighted effects of heavy alcohol consumption on some microarchitectural parameters of trabecular bone. But to date and to our knowledge, micro- and macro-mechanical properties of bone of alcoholic subjects have not been investigated.

PATIENTS

In the present study, mechanical properties and microarchitecture of trabecular bone samples from the iliac crest of alcoholic male patients (n=15) were analyzed and compared to a control group (n=8).

MATERIALS AND METHODS

Nanoindentation tests were performed to determine the tissue's micromechanical properties, micro-computed tomography was used to measure microarchitectural parameters, and numerical simulations provided the apparent mechanical properties of the samples.

RESULTS

Compared to controls, bone tissue from alcoholic patients exhibited an increase of micromechanical properties at tissue scale, a significant decrease of apparent mechanical properties at sample scale, and significant changes in several microarchitectural parameters. In particular, a crucial role of structure model index (SMI) on mechanical properties was identified.

CONCLUSIONS

3D microarchitectural parameters are at least as important as bone volume fraction to predict bone fracture risk in the case of alcoholic patients.

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

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

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

As in clinical studies, finite element analysis (FEA) developed from computed tomography (CT) images of bones are useful in pre-clinical rodent studies assessing treatment effects on vertebral body (VB) strength. Since strength predictions from microCT-derived FEAs (μFEA) have not been validated against experimental measurements of mouse VB strength, a parametric analysis exploring material and failure definitions was performed to determine whether elastic μFEAs with linear failure criteria could reasonably assess VB strength in two studies, treatment and genetic, with differences in bone volume fraction between the control and the experimental groups. VBs were scanned with a 12-μm voxel size, and voxels were directly converted to 8-node, hexahedral elements. The coefficient of determination or R (2) between predicted VB strength and experimental VB strength, as determined from compression tests, was 62.3% for the treatment study and 85.3% for the genetic study when using a homogenous tissue modulus (E t) of 18 GPa for all elements, a failure volume of 2%, and an equivalent failure strain of 0.007. The difference between prediction and measurement (that is, error) increased when lowering the failure volume to 0.1% or increasing it to 4%. Using inhomogeneous tissue density-specific moduli improved the R (2) between predicted and experimental strength when compared with uniform E t=18 GPa. Also, the optimum failure volume is higher for the inhomogeneous than for the homogeneous material definition. Regardless of model assumptions, μFEA can assess differences in murine VB strength between experimental groups when the expected difference in strength is at least 20%.

Experimentally-based multiscale model of the elastic moduli of bovine trabecular bone and its constituents

The elastic moduli of trabecular bone were modeled using an analytical multiscale approach. Trabecular bone was represented as a porous nanocomposite material with a hierarchical structure spanning from the collagen-mineral level to the trabecular architecture level. In parallel, compression testing was done on bovine femoral trabecular bone samples in two anatomical directions, parallel to the femoral neck axis and perpendicular to it, and the measured elastic moduli were compared with the corresponding theoretical results. To gain insights on the interaction of collagen and minerals at the nanoscale, bone samples were deproteinized or demineralized. After such processing, the treated samples remained as self-standing structures and were tested in compression. Micro-computed tomography was used to characterize the hierarchical structure of these three bone types and to quantify the amount of bone porosity. The obtained experimental data served as inputs to the multiscale model and guided us to represent bone as an interpenetrating composite material. Good agreement was found between the theory and experiments for the elastic moduli of the untreated, deproteinized, and demineralized trabecular bone.

Improving the finite element model accuracy of tissue engineering scaffolds produced by selective laser sintering

In bone tissue engineering, both geometrical and mechanical properties of a scaffold play a major part in the success of the treatment. The mechanical stresses and strains that act on cells on a scaffold in a physiological environment are a determining factor on the subsequent tissue formation. Computational models are often used to simulate the effect of changes of internal architectures and external loads applied to the scaffold in order to optimise the scaffold geometry for the prospective implantation site. Finite element analysis (FEA) based on computer models of the scaffold is a common technique, but would not take into account actual inaccuracies due to the manufacturing process. Image based FEA using CT scans of fabricated scaffolds can provide a more accurate analysis of the scaffold, and was used in this work in order to accurately simulate and predict the mechanical performance of bone tissue engineering scaffolds, fabricated using selective laser sintering (SLS), with a view to generating a methodology that could be used to optimise scaffold design. The present work revealed that an approach that assumes isotropic properties of SLS fabricated scaffolds will lead to inaccurate predictions of the FE model. However, a dependency of the grey value of the CT scans and the mechanical properties was discovered, which may ultimately lead to accurate FE models without the need of experimental validation.

Skin stem cell hypotheses and long term clone survival--explored using agent-based modelling

Epithelial renewal in skin is achieved by the constant turnover and differentiation of keratinocytes. Three popular hypotheses have been proposed to explain basal keratinocyte regeneration and epidermal homeostasis: 1) asymmetric division (stem-transit amplifying cell); 2) populational asymmetry (progenitor cell with stochastic fate); and 3) populational asymmetry with stem cells. In this study, we investigated lineage dynamics using these hypotheses with a 3D agent-based model of the epidermis. The model simulated the growth and maintenance of the epidermis over three years. The offspring of each proliferative cell was traced. While all lineages were preserved in asymmetric division, the vast majority were lost when assuming populational asymmetry. The third hypothesis provided the most reliable mechanism for self-renewal by preserving genetic heterogeneity in quiescent stem cells, and also inherent mechanisms for skin ageing and the accumulation of genetic mutation.

Predicting the elastic properties of selective laser sintered PCL/β-TCP bone scaffold materials using computational modelling

This study assesses the ability of finite element (FE) models to capture the mechanical behaviour of sintered orthopaedic scaffold materials. Individual scaffold struts were fabricated from a 50:50 wt% poly-ε-caprolactone (PCL)/β-tricalcium phosphate (β-TCP) blend, using selective laser sintering. The tensile elastic modulus of single struts was determined experimentally. High resolution FE models of single struts were generated from micro-CT scans (28.8 μm resolution) and an effective strut elastic modulus was calculated from tensile loading simulations. Three material assignment methods were employed: (1) homogeneous PCL elastic constants, (2) composite PCL/β-TCP elastic constants based on rule of mixtures, and (3) heterogeneous distribution of micromechanically-determined elastic constants. In comparison with experimental results, the use of homogeneous PCL properties gave a good estimate of strut modulus; however it is not sufficiently representative of the real material as it neglects the β-TCP phase. The rule of mixtures method significantly overestimated strut modulus, while there was no significant difference between strut modulus evaluated using the micromechanically-determined elastic constants and experimentally evaluated strut modulus. These results indicate that the multi-scale approach of linking micromechanical modelling of the sintered scaffold material with macroscale modelling gives an accurate prediction of the mechanical behaviour of the sintered structure.

Anterior and posterior variations in mechanical properties of human vertebrae measured by nanoindentation

Osteoporotic spinal fractures are a significant global public health issue affecting more than 200 million people. Local degradation of the mechanical properties of bone and changes in global spine curvature increase fracture risk. However, a gap in knowledge exists relating material properties of trabecular bone in different regions of the spine. The purpose of our project was to measure the intrinsic mechanical properties of the anterior and posterior regions of human vertebral bodies in the thoracic and lumbar spine. Nanoindentation was used to evaluate Young's modulus (E) and hardness (H) of anterior and posterior trabecular bone regions from each vertebra (T7, T8 and L4). One-way ANOVA and the Turkey-Kramer test were used to analyze significance between vertebrae and t-test was used to test for significance within vertebrae. There was no difference in (E) and (H) within vertebrae. Young's modulus in the anterior regions of T7 (19.8±1.3) and T8 (19.6±1.4) were statistically greater than that in L4 (17.6±0.5). There was no difference between the posterior regions of all the vertebrae. There was a statistical significant difference in hardness between the anterior regions of T7 and T8 compared to L4, while the posterior regions demonstrated no difference. The results presented in this study, for the first time, reveal the differences in bone properties between the kyphotic thoracic spine and lordotic lumbar spine regions. This information will be helpful in understanding vertebral body remodeling and adaption in different regions of the spine which may be associated with spinal curvature and loading conditions.

Finite element analysis of a micromechanical model of bone and a new 3D approach to validation

Finite Element Analysis (FEA) is now widely used to analyse the mechanical behaviour of bone structures. Ideally, simulations are validated against experimental data. To date, validation of Finite Element Models (FEMs) has been 2 Dimensional (2D) only, being based on comparison with surface-mounted strain gauge readings. In this study we present a novel 3-Dimensional (3D) approach to validation that allows comparison of modelled with experimental results between any two points in 3D space throughout the structure, providing magnitude and direction data for comparison, internally and externally. Specifically, we validate a FEM of a rat tibia, including trabecular network geometry, using a material testing stage housed within a microCT scanner. We further apply novel landmark based morphometric approaches to more effectively compare modelled and experimental results. 542 landmark points on the cortical and trabecular bone surfaces of the model were selected and validated in 3D against experimental data. This approach may hold considerable potential in fields wherein a better understanding of the mechanical behaviour of trabecular networks is important, e.g., the studies of osteoporosis and trabecular loss after orthopaedic implant insertion.

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.

Mineral heterogeneity has a minor influence on the apparent elastic properties of human cancellous bone: a SRμCT-based finite element study

At the tissue level, the local material properties of human cancellous bone are heterogeneous due to constant remodelling. Since standard high-resolution computed tomography scanning methods are unable to capture this heterogeneity in detail, local differences in mineralisation are normally not incorporated in computational models. To investigate the effects of heterogeneous mineral distribution on the apparent elastic properties, 40 cancellous bone samples from the human femoral neck were scanned by means of synchrotron radiation microcomputed tomography (SRμCT). SRμCT-based micromechanical finite element models that accounted for mineral heterogeneity were compared with homogeneous models. Evaluation of the apparent stiffness tensor of both model types revealed that homogeneous models led to a minor but significant (p < 0.05) overestimation of the elastic properties of heterogeneous models by 2.18 ± 1.89%. Variation of modelling parameters did not affect the overestimation to a great extent. It was concluded that the heterogeneous mineralisation has only a minor influence on the apparent elastic properties of human cancellous bone.

An approximate model for cancellous bone screw fixation

This paper presents a finite element (FE) model to identify parameters that affect the performance of an improved cancellous bone screw fixation technique, and hence potentially improve fracture treatment. In cancellous bone of low apparent density, it can be difficult to achieve adequate screw fixation and hence provide stable fracture fixation that enables bone healing. Data from predictive FE models indicate that cements can have a significant potential to improve screw holding power in cancellous bone. These FE models are used to demonstrate the key parameters that determine pull-out strength in a variety of screw, bone and cement set-ups, and to compare the effectiveness of different configurations. The paper concludes that significant advantages, up to an order of magnitude, in screw pull-out strength in cancellous bone might be gained by the appropriate use of a currently approved calcium phosphate cement.

Computational modelling of the natural hip: a review of finite element and multibody simulations

PRIMARY OBJECTIVE

The hip joint suffers from a high prevalence of degenerative conditions. Athough patient's well-being could be improved through early and more effective interventions, without a greater understanding of the mechanics of the hip, these developments cannot be attained. Thus, this review article summarises the current literature on this subject in order to provide a platform for future developments. To illustrate the influence computational simulations have had on the knowledge advancement in hip mechanics, we explored two methodological approaches: finite element (FE) analysis and multibody dynamics (MBD).

MAIN OUTCOMES AND RESULTS

Notwithstanding the unique capabilities of FE and MBD, the former generally offers the micromechanics of the articulating surfaces whereas the latter the macromechanics of the skeleton, these two methodologies also provide the bulk of the literature regarding computational modelling of the musculoskeletal system. Although FE has provided significant knowledge on contact pressures and the effects of musculoskeletal geometries, in particular cartilage and bone shapes, MBD has afforded a wealth of understanding on the influence of gait patterns and muscle attachment locations on force magnitudes.

CONCLUSIONS

These two computational techniques have, and will continue to, provide significant contributions towards the development of interventions. It is hoped that this article will help focus ongoing technological developments by highlighting areas of success, but also areas of under development.

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.

Effects of trabecular type and orientation on microdamage susceptibility in trabecular bone

Trabecular architecture becomes more rod-like and anisotropic in osteoporotic and aging trabecular bone. In order to address the effects of trabecular type and orientation on trabecular bone damage mechanics, microstructural finite element modeling was used to identify the yielded tissue in ten bovine tibial trabecular bone samples compressed to 1.2% on-axis apparent strain. The yielded tissue was mapped onto individual trabeculae identified by an Individual Trabeculae Segmentation (ITS) technique, and the distribution of the predicted yielding among trabecular types and orientations was compared to the experimentally measured microdamage. Although most of the predicted yielded tissue was found in longitudinal plates (73+/-11%), the measured microcrack density was positively correlated with the proportion of the yielded tissue in longitudinal rods (R(2)=0.52, p=0.02), but not in rods of other directions or plates. The overall fraction of rods and the fractions of rods along the longitudinal and transverse axes were also correlated with the measured microcrack density. In contrast, diffuse damage area did not correlate with any of these quantities. These results agree with the findings that both in vitro and in vivo microcrack densities are correlated with Structure Model Index (SMI), and are also consistent with decreased energy to failure in more rod-like trabecular bone. Together the results suggest that bending or buckling deformations of rod-like trabeculae may make trabecular structures more susceptible to microdamage formation. Moreover, while simple strain-based tissue yield criteria may account for macroscopic yielding, they may not be suitable for identifying damage.

High-resolution peripheral quantitative computed tomography can assess microstructural and mechanical properties of human distal tibial bone

High-resolution peripheral quantitative computed tomography (HR-pQCT) is a newly developed in vivo clinical imaging modality. It can assess the 3D microstructure of cortical and trabecular bone at the distal radius and tibia and is suitable as an input for microstructural finite element (microFE) analysis to evaluate bone's mechanical competence. In order for microstructural and image-based microFE analyses to become standard clinical tools, validation with a current gold standard, namely, high-resolution micro-computed tomography (microCT), is required. Microstructural measurements of 19 human cadaveric distal tibiae were performed for the registered HR-pQCT and microCT images, respectively. Next, whole bone stiffness, trabecular bone stiffness, and elastic moduli of cubic subvolumes of trabecular bone in both HR-pQCT and microCT images were determined by microFE analysis. The standard HR-pQCT patient protocol measurements, derived bone volume fraction (BV/TV(d)), trabecular number (Tb.N*), trabecular thickness (Tb.Th), trabecular spacing (Tb.Sp), and cortical thickness (Ct.Th), as well as the voxel-based direct measurements, BV/TV, Tb.N*, Tb.Th*, Tb.Sp*, Ct.Th, bone surface-to-volume ratio (BS/BV), structure model index (SMI), and connectivity density (Conn.D), correlated well with their respective gold standards, and both contributed to microFE-predicted mechanical properties in either single or multiple linear regressions. The mechanical measurements, although overestimated by HR-pQCT, correlated highly with their gold standards. Moreover, elastic moduli of cubic subvolumes of trabecular bone predicted whole bone or trabecular bone stiffness in distal tibia. We conclude that microstructural measurements and mechanical parameters of distal tibia can be efficiently derived from HR-pQCT images and provide additional information regarding bone fragility.

Comparison of trabecular bone behavior in core and whole bone samples using high-resolution modeling of a vertebral body

Computational analysis of trabecular bone normally involves the modeling of (experimental tests of) cored samples. However, the lack of constraint on the sides of the extracted trabecular bone samples limits the information that can be inferred regarding true in situ behavior. Here, the element-by-element voxel-based finite element method was applied via, a custom-written software suite (FEEBE), to a 72 microm resolution model of an ovine vertebra. The difference between the apparent modulus of eight concentric core cylinders when modeled as part of the whole bone (containing 84 x 10(6) degrees of freedom) and independent of the whole bone was investigated. The results showed that cored trabecular bone apparent modulus depended significantly on the core diameter when modeled as an extracted core (r (2) = 0.975) and as part of a whole bone (r (2) = 0.986). The cause of this result was separated into the side-artifact effect and bone volume fraction (BV/TV) effect. For the independently modeled cores, the apparent modulus of an inner core region of interest varied with increasing thickness of the outer annulus. This was attributed to the side-artifact effect, given that the BV/TV of the core region was constant. Within the whole trabecular structure, the side artifact was eliminated as the entire bone structure was modeled. However, a BV/TV effect influenced the apparent modulus depending on the size of the core selected for determining apparent modulus. Changing the size of the core varied the overall BV/TV of the core, and this significantly (r (2) = 0.999) influences the apparent modulus. Therefore, determining a 'true' apparent modulus for trabecular bone was not achievable. The independently modeled cores consistently under-predict the in vivo apparent modulus. It is recommended that if a 'true' apparent modulus is required, the BV/TV at which it is required needs to be first determined. Apparent modeling of entire bones at microscale resolution allowed regions of low and high tissue strains to be identified, consistent with patterns of trabecular bone remodeling and resorption reported in literature. The basivertebral vein cavity underwent the highest strains within the entire vertebral body, suggesting that failure might initiate here, despite containing visibly thicker struts and plate trabeculae. Although computationally expensive, analysis of the entire vertebral body provided a full picture of in situ trabecular bone deformation.

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.

Effects of loading orientation on the morphology of the predicted yielded regions in trabecular bone

While the effects of bone mineral density and architecture in osteoporotic bone have been studied extensively, the micromechanics of yielding and failure have received less attention. However, understanding architectural features associated with failure should provide insight into assessing bone quality. In this study, microstructural finite element models were used to compute regions of tissue level yielding in ten bovine tibial trabecular bone samples. The morphology, number, and mean volume of the yielded regions were quantified for four apparent strains under two loading conditions. For on-axis loading, the mean aspect ratio of the tissue that yielded due to compressive strain increased with increasing apparent strain, expanding along the principal trabecular orientation. This suggests that tissue level yielding progresses along vertical trabeculae when a specimen is loaded on-axis. The number, but not the volume, of the regions yielded due to tensile strain increased with increasing applied load, consistent with relaxation and redistribution of stresses around the yielded regions. When the specimens were compressed perpendicular to the principal axis, the aspect ratio of the yielded regions was close to one, while the number, mean volume, and mean thickness of the yielded regions increased. This indicates that localized high strains consistent with bending rather than axial deformation of struts occur at the tissue level. Overall, the results provide new insight into trabecular bone failure, which is relevant to assessing diagnostic tests for fracture risk or evaluating osteoporosis treatments.