Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

The effect of nodal connectivity and strut density within stochastic titanium scaffolds on osteogenesis

Modern orthopaedic implants use lattice structures that act as 3D scaffolds to enhance bone growth into and around implants. Stochastic scaffolds are of particular interest as they mimic the architecture of trabecular bone and can combine isotropic properties and adjustable structure. The existing research mainly concentrates on controlling the mechanical and biological performance of periodic lattices by adjusting pore size and shape. Still, less is known on how we can control the performance of stochastic lattices through their design parameters: nodal connectivity, strut density and strut thickness. To elucidate this, four lattice structures were evaluated with varied strut densities and connectivity, hence different local geometry and mechanical properties: low apparent modulus, high apparent modulus, and two with near-identical modulus. Pre-osteoblast murine cells were seeded on scaffolds and cultured in vitro for 28 days. Cell adhesion, proliferation and differentiation were evaluated. Additionally, the expression levels of key osteogenic biomarkers were used to assess the effect of each design parameter on the quality of newly formed tissue. The main finding was that increasing connectivity increased the rate of osteoblast maturation, tissue formation and mineralisation. In detail, doubling the connectivity, over fixed strut density, increased collagen type-I by 140%, increased osteopontin by 130% and osteocalcin by 110%. This was attributed to the increased number of acute angles formed by the numerous connected struts, which facilitated the organization of cells and accelerated the cell cycle. Overall, increasing connectivity and adjusting strut density is a novel technique to design stochastic structures which combine a broad range of biomimetic properties and rapid ossification.

Cortical and trabecular morphometric properties of the human calvarium

There is currently a gap in the literature that quantitatively describes the complex bone microarchitecture within the diploë (trabecular bone) and cortical layers of the human calvarium. The purpose of this study was to determine the morphometric properties of the diploë and cortical tables of the human calvarium in which key interacting factors of sex, location on the calvarium, and layers of the sandwich structure were considered. Micro-computed tomography (micro-CT) was utilized to capture images at 18 μm resolution of male (n = 26) and female (n = 24) embalmed calvarium specimens in the frontal and parietal regions (N = 50). All images were post-processed and analyzed using vendor bundled CT-Analyzer software to determine the morphometric properties of the diploë and cortical layers. A two-way mixed (repeated measures) analysis of variance (ANOVA) was used to determine diploë morphometric properties accounting for factors of sex and location. A three-way mixed ANOVA was performed to determine cortical morphometric properties accounting for factors of cortical layer (inner and outer table), sex, and location. The study revealed no two-way interaction effects between sex and location on the diploë morphometry except for fractal dimension. Trabecular thickness and separation in the diploë were significantly greater in the male specimens; however, females showed a greater number of trabeculae and fractal dimension on average. Parietal specimens revealed a greater porosity, trabecular separation, and deviation from an ideal plate structure, but a lesser number of trabeculae and connectivity compared to the frontal location. Additionally, the study observed a lower density and greater porosity in the inner cortical layer than the outer which may be due to clear distinctions between each layer's physiological environment. The study provides valuable insight into the quantitative morphometry of the calvarium in which finite element modelers of the skull can refer to when designing detailed heterogenous or subject-specific skull models to effectively predict injury. Furthermore, this study contributes towards the recent developments on physical surrogate models of the skull which require approximate measures of calvarium bone architecture in order to effectively fabricate a model and then accurately simulate a traumatic head impact event.

The Novel Role of PGC1α in Bone Metabolism

Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC1α) is a protein that promotes transcription of numerous genes, particularly those responsible for the regulation of mitochondrial biogenesis. Evidence for a key role of PGC1α in bone metabolism is very recent. In vivo studies showed that PGC1α deletion negatively affects cortical thickness, trabecular organization and resistance to flexion, resulting in increased risk of fracture. Furthermore, in a mouse model of bone disease, PGC1α activation stimulates osteoblastic gene expression and inhibits atrogene transcription. PGC1α overexpression positively affects the activity of Sirtuin 3, a mitochondrial nicotinammide adenina dinucleotide (NAD)-dependent deacetylase, on osteoblastic differentiation. In vitro, PGC1α overexpression prevents the reduction of mitochondrial density, membrane potential and alkaline phosphatase activity caused by Sirtuin 3 knockdown in osteoblasts. Moreover, PGC1α influences the commitment of skeletal stem cells towards an osteogenic lineage, while negatively affects marrow adipose tissue accumulation. In this review, we will focus on recent findings about PGC1α action on bone metabolism, in vivo and in vitro, and in pathologies that cause bone loss, such as osteoporosis and type 2 diabetes.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Nonlinear voxel-based finite element model for strength assessment of healthy and metastatic proximal femurs

Nonlinear finite element (FE) models can accurately quantify bone strength in healthy and metastatic femurs. However, their use in clinical practice is limited since state-of-the-art implementations using tetrahedral meshes involve a lot of manual work for which specific modelling software and engineering knowledge are required. Voxel-based meshes could enable the transition since they are robust and can be highly automated. Therefore, the aim of this work was to bridge the modelling gap between the tetrahedral and voxel-based approach. Specifically, we validated a nonlinear voxel-based FE method relative to experimental data from 20 femurs with and without artificial metastases that had been mechanically loaded until failure. CT scans of the femurs were segmented and automatically converted into a voxel-based mesh with hexahedral elements. Nonlinear material properties were implemented in an open-source linear voxel-based FE solver by adding an additional loop to the routine such that the material properties could be adapted after each increment. Bone strength, quantified as the maximum force in the force-displacement curve, was evaluated. The results were compared to a previously established nonlinear tetrahedral FE approach as well as to the experimentally measured bone strength. The voxel-based FE model predicted the experimental bone strength very well both for healthy (R² = 0.90, RMSE = 0.88 kN) and metastatic femurs (R² = 0.93, RMSE = 0.64 kN). The model precision and accuracy were very similar to the ones obtained with the tetrahedral model (R² = 0.90/0.93, RMSE = 0.90/0.64 kN for intact/metastatic respectively). The more intuitive voxel-based meshes thus quantified macroscale femoral strength equally well as state-of-the-art tetrahedral models. The robustness, high level of automation and time-efficiency (< 30 min) of the implemented workflow offer great potential for developing FE models to improve fracture risk prediction in clinical practice.

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A nonlinear voxel-based FE model was evaluated to assess femoral bone strength

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Both healthy and metastatic femurs were evaluated

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The FE models predicted bone strength with high accuracy and precision

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Voxel-based and tetrahedral FE models showed similar accuracy and precision

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An iterative routine enabled material nonlinearity in a linear FE solver

Deletion of the Transcription Factor PGC-1α in Mice Negatively Regulates Bone Mass

Peroxisome proliferator-activated receptor-gamma coactivator (PGC1α) is a transcription coactivator that interacts with a broad range of transcription factors involved in several biological responses. Here, we show that PGC1α plays a role in skeletal homeostasis since aged PGC1α-deficient mice (PGC1α^-/-) display impaired bone structure. Micro-CT of the tibial mid-shaft showed a marked decrease of cortical thickness in PGC1α^-/- (- 11.9%, p < 0.05) mice compared to wild-type littermate. Trabecular bone was also impaired in knock out mice which displayed lower trabecular thickness (Tb.Th) (- 5.9% vs PGC1α^+/+, p < 0.05), whereas trabecular number (Tb.N) was higher than wild-type mice (+ 72% vs PGC1α^+/+, p < 0.05), thus resulting in increased (+ 31.7% vs PGC1α^+/+, p < 0.05) degree of anisotropy (DA), despite unchanged bone volume fraction (BV/TV). Notably, these impairments of cortical and trabecular bone led to a dramatic ~ 48.4% decrease in bending strength (p < 0.01). These changes in PGC1α^-/- mice were paralleled by a significant increase in osteoclast number at the cortical bone surface and in serum level of the bone resorption marker, namely, C-terminal cross-linked telopeptides of type I collagen (CTX-I). We also found that in cortical bone, there was lower expression of mRNA codifying for the key bone-building protein Osteocalcin (Ocn). Interestingly, Collagen I mRNA expression was reduced in mesenchymal stem cells from bone marrow of PGC1α^-/-, thus indicating that differentiation of osteoblast lineage is downregulated. Overall, results presented herein suggest that PGC1α may play a key role in bone metabolism.

Computer-based automatic classification of trabecular bone pattern can assist radiographic bone quality assessment at dental implant site

OBJECTIVE:

To develop and validate an automated classification method that determines the trabecular bone pattern at implant site based on three-dimensional bone morphometric parameters derived from CBCT images.

METHODS:

25 human cadaver mandibles were scanned using CBCT clinical scanning protocol. Volumes-of-interest comprising only the trabecular bone of the posterior regions were selected and segmented for three-dimensional morphometric parameters calculation. Three experts rated all bone regions into one of the three trabecular pattern classes (sparse, intermediate and dense) to generate a reference classification. Morphometric parameters were used to automatically classify the trabecular pattern with linear discriminant analysis statistical model. The discriminatory power of each morphometric parameter for automatic classification was indicated and the accuracy compared to the reference classification. Repeated-measures analysis of variances were used to statistically compare morphometric indices between the three classes. Finally, the outcome of the automatic classification was evaluated against a subjective classification performed independently by four different observers.

RESULTS:

The overall correct classification was 83% for quantity-, 86% for structure-related parameters and 84% for the parameters combined. Cross-validation showed a 79% model prediction accuracy. Bone volume fraction (BV/TV) had the most discriminatory power in the automatic classification. Trabecular bone patterns could be distinguished based on most morphometric parameters, except for trabecular thickness (Tb.Th) and degree of anisotropy (DA). The interobserver agreement between the subjective observers was fair (0.25), while the test-retest agreement was moderate (0.46). In comparison with the reference standard, the overall agreement was moderate (0.44).

CONCLUSION:

Automatic classification performed better than subjective classification with a prediction model comprising structure- and quantity-related morphometric parameters.

ADVANCES IN KNOWLEDGE:

Computer-aided trabecular bone pattern assessment based on morphometric parameters could assist objectivity in clinical bone quality classification.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

A novel in silico method to quantify primary stability of screws in trabecular bone

Insufficient primary stability of screws in bone leads to screw loosening and failure. Unlike conventional continuum finite-element models, micro-CT based finite-element analysis (micro-FE) is capable of capturing the patient-specific bone micro-architecture, providing accurate estimates of bone stiffness. However, such in silico models for screws in bone highly overestimate the apparent stiffness. We hypothesized that a more accurate prediction of primary implant stability of screws in bone is possible by considering insertion-related bone damage. We assessed two different screw types and loading scenarios in 20 trabecular bone specimens extracted from 12 cadaveric human femoral heads (N = 5 for each case). In the micro-FE model, we predicted specimen-specific Young's moduli of the peri-implant bone damage region based on morphometric parameters such that the apparent stiffness of each in silico model matched the experimentally measured stiffness of the corresponding in vitro specimen as closely as possible. The standard micro-FE models assuming perfectly intact peri-implant bone overestimated the stiffness by over 330%. The consideration of insertion related damaged peri-implant bone corrected the mean absolute percentage error down to 11.4% for both loading scenarios and screw types. Cross-validation revealed a mean absolute percentage error of 14.2%. We present the validation of a novel micro-FE modeling technique to quantify the apparent stiffness of screws in trabecular bone. While the standard micro-FE model overestimated the bone-implant stiffness, the consideration of insertion-related bone damage was crucial for an accurate stiffness prediction. This approach provides an important step toward more accurate specimen-specific micro-FE models. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2415-2424, 2017.

Microscale poroelastic metamodel for efficient mesoscale bone remodelling simulations

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

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

INTRODUCTION

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R²=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.

METHODS

Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R² and RMSE%.

RESULTS

The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%.

CONCLUSIONS

Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone

BACKGROUND

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface.

METHODS

Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness.

FINDINGS

Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm³ density.

INTERPRETATION

In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

BACKGROUND

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

RESULTS

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

CONCLUSIONS

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

Biomechanical Role of Bone Anisotropy Estimated on Clinical CT Scans by Image Registration

Image-based modeling is a popular approach to perform patient-specific biomechanical simulations. Accurate modeling is critical for orthopedic application to evaluate implant design and surgical planning. It has been shown that bone strength can be estimated from the bone mineral density (BMD) and trabecular bone architecture. However, these findings cannot be directly and fully transferred to patient-specific modeling since only BMD can be derived from clinical CT. Therefore, the objective of this study was to propose a method to predict the trabecular bone structure using a µCT atlas and an image registration technique. The approach has been evaluated on femurs and patellae under physiological loading. The displacement and ultimate force for femurs loaded in stance position were predicted with an error of 2.5% and 3.7%, respectively, while predictions obtained with an isotropic material resulted in errors of 7.3% and 6.9%. Similar results were obtained for the patella, where the strain predicted using the registration approach resulted in an improved mean squared error compared to the isotropic model. We conclude that the registration of anisotropic information from of a single template bone enables more accurate patient-specific simulations from clinical image datasets than isotropic model.

A Predictive Model of Vertebral Trabecular Anisotropy From Ex Vivo Micro-CT

Spine-related disorders are amongst the most frequently encountered problems in clinical medicine. For several applications such as 1) to improve the assessment of the strength of the spine, as well as 2) to optimize the personalization of spinal interventions, image-based biomechanical modeling of the vertebrae is expected to play an important predictive role. However, this requires the construction of computational models that are subject-specific and comprehensive. In particular, they need to incorporate information about the vertebral anisotropic micro-architecture, which plays a central role in the biomechanical function of the vertebrae. In practice, however, accurate personalization of the vertebral trabeculae has proven to be difficult as its imaging in vivo is currently infeasible. Consequently, this paper presents a statistical approach for accurate prediction of the vertebral fabric tensors based on a training sample of ex vivo micro-CT images. To the best of our knowledge, this is the first predictive model proposed and validated for vertebral datasets. The method combines features selection and partial least squares regression in order to derive optimal latent variables for the prediction of the fabric tensors based on the more easily extracted shape and density information. Detailed validation with 20 ex vivo T12 vertebrae demonstrates the accuracy and consistency of the approach for the personalization of trabecular anisotropy.

Clinical Use of Quantitative Computed Tomography-Based Finite Element Analysis of the Hip and Spine in the Management of Osteoporosis in Adults: the 2015 ISCD Official Positions-Part II

The International Society for Clinical Densitometry (ISCD) has developed new official positions for the clinical use of quantitative computed tomography (QCT)-based finite element analysis of the spine and hip. The ISCD task force for QCT reviewed the evidence for clinical applications and presented a report with recommendations at the 2015 ISCD Position Development Conference. Here we discuss the agreed upon ISCD official positions with supporting medical evidence, rationale, controversy, and suggestions for further study. Parts I and III address the clinical use of QCT of the hip, and the clinical feasibility of existing techniques for opportunistic screening of osteoporosis using CT scans obtained for other diagnosis such as colonography was addressed.

Multiphasic modelling of bone-cement injection into vertebral cancellous bone

Percutaneous vertebroplasty represents a current procedure to effectively reinforce osteoporotic bone via the injection of bone cement. This contribution considers a continuum-mechanically based modelling approach and simulation techniques to predict the cement distributions within a vertebra during injection. To do so, experimental investigations, imaging data and image processing techniques are combined and exploited to extract necessary data from high-resolution μCT image data. The multiphasic model is based on the Theory of Porous Media, providing the theoretical basis to describe within one set of coupled equations the interaction of an elastically deformable solid skeleton, of liquid bone cement and the displacement of liquid bone marrow. The simulation results are validated against an experiment, in which bone cement was injected into a human vertebra under realistic conditions. The major advantage of this comprehensive modelling approach is the fact that one can not only predict the complex cement flow within an entire vertebra but is also capable of taking into account solid deformations in a fully coupled manner. The presented work is the first step towards the ultimate and future goal of extending this framework to a clinical tool allowing for pre-operative cement distribution predictions by means of numerical simulations.

Importance of Material Properties and Porosity of Bone on Mechanical Response of Articular Cartilage in Human Knee Joint—A Two-Dimensional Finite Element Study

Mechanical behavior of bone is determined by the structure and intrinsic, local material properties of the tissue. However, previously presented knee joint models for evaluation of stresses and strains in joints generally consider bones as rigid bodies or linearly elastic solid materials. The aim of this study was to estimate how different structural and mechanical properties of bone affect the mechanical response of articular cartilage within a knee joint. Based on a cadaver knee joint, a two-dimensional (2D) finite element (FE) model of a knee joint including bone, cartilage, and meniscus geometries was constructed. Six different computational models with varying properties for cortical, trabecular, and subchondral bone were created, while the biphasic fibril-reinforced properties of cartilage and menisci were kept unaltered. The simplest model included rigid bones, while the most complex model included specific mechanical properties for different bone structures and anatomically accurate trabecular structure. Models with different porosities of trabecular bone were also constructed. All models were exposed to axial loading of 1.9 times body weight within 0.2 s (mimicking typical maximum knee joint forces during gait) while free varus–valgus rotation was allowed and all other rotations and translations were fixed. As compared to results obtained with the rigid bone model, stresses, strains, and pore pressures observed in cartilage decreased depending on the implemented properties of trabecular bone. Greatest changes in these parameters (up to −51% in maximum principal stresses) were observed when the lowest modulus for trabecular bone (measured at the structural level) was used. By increasing the trabecular bone porosity, stresses and strains were reduced substantially in the lateral tibial cartilage, while they remained relatively constant in the medial tibial plateau. The present results highlight the importance of long bones, in particular, their mechanical properties and porosity, in altering and redistributing forces transmitted through the knee joint.

Full-Field Strain Measurement During Mechanical Testing of the Human Femur at Physiologically Relevant Strain Rates

Understanding the mechanical properties of human femora is of great importance for the development of a reliable fracture criterion aimed at assessing fracture risk. Earlier ex vivo studies have been conducted by measuring strains on a limited set of locations using strain gauges (SGs). Digital image correlation (DIC) could instead be used to reconstruct the full-field strain pattern over the surface of the femur. The objective of this study was to measure the full-field strain response of cadaver femora tested at a physiological strain rate up to fracture in a configuration resembling single stance. The three cadaver femora were cleaned from soft tissues, and a white background paint was applied with a random black speckle pattern over the anterior surface. The mechanical tests were conducted up to fracture at a constant displacement rate of 15 mm/s, and two cameras recorded the event at 3000 frames per second. DIC was performed to retrieve the full-field displacement map, from which strains were derived. A low-pass filter was applied over the measured displacements before the crack opened in order to reduce the noise level. The noise levels were assessed using a dedicated control plate. Conversely, no filtering was applied at the frames close to fracture to get the maximum resolution. The specimens showed a linear behavior of the principal strains with respect to the applied force up to fracture. The strain rate was comparable to the values available in literature from in vivo measurements during daily activities. The cracks opened and fully propagated in less than 1 ms, and small regions with high values of the major principal strains could be spotted just a few frames before the crack opened. This corroborates the hypothesis of a strain-driven fracture mechanism in human bone. The data represent a comprehensive collection of full-field strains, both at physiological load levels and up to fracture. About 10,000 points were tracked on each bone, providing superior spatial resolution compared to ∼15 measurements typically collected using SGs. These experimental data collection can be further used for validation of numerical models, and for experimental verification of bone constitutive laws and fracture criteria.