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Spinal fusion is a standard surgical treatment for patients suffering from low back pain attributed to disc degeneration. However, results are somewhat variable and unpredictable. With fusion the kinematic behaviour of the spine is altered. Fusion and/or stabilizing implants carrying considerable load and prevent rotation of the fused segments. Associated with these changes, a risk for accelerated disc degeneration at the adjacent levels to fusion has been demonstrated. However, there is yet no method to predict the effect of fusion surgery on the adjacent tissue levels, i.e. bone and disc. The aim of this study was to develop a coupled and patient-specific mechanoregulated model to predict disc generation and changes in bone density after spinal fusion and to validate the results relative to patient follow-up data. To do so, a multiscale disc mechanoregulation adaptation framework was developed and coupled with a previously developed bone remodelling algorithm. This made it possible to determine extra cellular matrix changes in the intervertebral disc and bone density changes simultaneously based on changes in loading due to fusion surgery. It was shown that for 10 cases the predicted change in bone density and degeneration grade conforms reasonable well to clinical follow-up data. This approach helps us to understand the effect of surgical intervention on the adjacent tissue remodelling. Thereby, providing the first insight for a spine surgeon as to which patient could potentially be treated successfully by spinal fusion and in which patient has a high risk for adjacent tissue changes., Competing Interests: The authors have declared that no competing interests exist.

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.

A bone loading estimation algorithm was previously developed that provides in vivo loading conditions required for in vivo bone remodelling simulations. The algorithm derives a bone's loading history from its microstructure as assessed by high-resolution (HR) computed tomography (CT). This reverse engineering approach showed accurate and realistic results based on micro-CT and HR-peripheral quantitative CT images. However, its voxel size dependency, reproducibility and sensitivity still need to be investigated, which is the purpose of this study. Voxel size dependency was tested on cadaveric distal radii with micro-CT images scanned at 25 µm and downscaled to 50, 61, 75, 82, 100, 125 and 150 µm. Reproducibility was calculated with repeated in vitro as well as in vivo HR-pQCT measurements at 82 µm. Sensitivity was defined using HR-pQCT images from women with fracture versus non-fracture, and low versus high bone volume fraction, expecting similar and different loading histories, respectively. Our results indicate that the algorithm is voxel size independent within an average (maximum) error of 8.2% (32.9%) at 61 µm, but that the dependency increases considerably at voxel sizes bigger than 82 µm. In vitro and in vivo reproducibility are up to 4.5% and 10.2%, respectively, which is comparable to other in vitro studies and slightly higher than in other in vivo studies. Subjects with different bone volume fraction were clearly distinguished but not subjects with and without fracture. This is in agreement with bone adapting to customary loading but not to fall loads. We conclude that the in vivo bone loading estimation algorithm provides reproducible, sensitive and fairly voxel size independent results at up to 82 µm, but that smaller voxel sizes would be advantageous., (© 2016 The Author(s).)

Low trauma fractures are amongst the most frequently encountered problems in the clinical assessment and treatment of bones, with dramatic health consequences for individuals and high financial costs for health systems. Consequently, significant research efforts have been dedicated to the development of accurate computational models of bone biomechanics and strength. However, the estimation of the fabric tensors, which describe the microarchitecture of the bone, has proven to be challenging using in vivo imaging. On the other hand, existing research has shown that isotropic models do not produce accurate predictions of stress states within the bone, as the material properties of the trabecular bone are anisotropic. In this paper, we present the first biomechanical study that uses statistically-derived fabric tensors for the estimation of bone strength in order to obtain patient-specific results. We integrate a statistical predictive model of trabecular bone microarchitecture previously constructed from a sample of ex vivo micro-CT datasets within a biomechanical simulation workflow. We assess the accuracy and flexibility of the statistical approach by estimating fracture load for two different databases and bone sites, i.e., for the femur and the T12 vertebra. The results obtained demonstrate good agreement between the statistically-driven and micro-CT-based estimates, with concordance coefficients of 98.6 and 95.5% for the femur and vertebra datasets, respectively.

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.

It is well known that bone adapts its microstructure in response to loading. Based on this form-follows-function relationship, we previously developed a reverse approach to derive joint loads from bone microstructure as acquired with micro-computed tomography. Here, we challenge this approach by calculating hip-joint loading patterns for human and dog, two species exhibiting different locomotion, and comparing them to in vivo measurements. As a proof of concept to use the approach also for extinct taxa, we applied it to a cave lion fossil bone. Calculations were in close agreement with in vivo measurements during walking for extant species, showing distinguished patterns for bipedalism and quadrupedalism. The cave lion calculations clearly revealed its quadrupedal locomotion and suggested a more diverse behaviour compared to the dog, which is in agreement with extant felids. This indicates that our novel approach is potentially useful for making inferences about locomotion in living as well as extinct mammals and to study evolutionary joint development.

Continuum finite element (FE) models of bones and bone-implant configurations are usually based on clinical CT scans. In virtually all of these models, material properties assigned to the bone elements are chosen as isotropic. It has been shown, however, that cancellous bone can be highly anisotropic and that its elastic behavior is best described as orthotropic. Material models have been proposed to derive the orthotropic elastic constants from measurements of density and a fabric tensor. The use of such relationships in FE models derived from CT scans, however, is hampered by the fact that the measurement of such a fabric tensor is not possible from clinical CT images since the resolution of such images is not good enough to resolve the trabecular micro-architecture. In this study, we explore an alternative approach that is based on the paradigm that bone adapts its micro-architecture to the loading conditions, hence that fabric and stress tensors should be aligned and correlated. With this approach, the eigenvectors and eigenvalues of the element continuum-level stress tensor are used as an estimate of the element fabric tensor, from which the orthotropic material properties then are derived. Using an iterative procedure, element orthotropic material properties and fabric tensors are updated until a converged situation is reached. The goals of this study were to investigate the feasibility and accuracy of such an iterative approach to derive orthotropic material properties for a human proximal femur and to investigate whether models derived in this way can provide more accurate results than isotropic models. Results were compared to those obtained from models of the same femurs for which the fabric was measured from micro-CT scans. It was found that the iterative approach could well estimate the orientation of the fabric principal directions. When comparing the stress/damage values in the models with material properties based on estimated and measured fabric tensors, the differences were not significant, suggesting that the material properties based on the estimated fabric tensor well reflected those based on the measured fabric tensor. Errors were less than those obtained when using isotropic models. It is concluded that this novel approach can provide a reasonable estimate of anisotropic material properties of cancellous bone. We expect that this approach can lead to more accurate results in particular for models used to study implants, which are usually anchored in highly anisotropic cancellous bone regions.

Bone is a dynamic and hierarchical porous material whose spatial and temporal mechanical properties can vary considerably due to differences in its microstructure and due to remodeling. Hence, a multiscale analytical approach, which combines bone structural information at multiple scales to the remodeling cellular activities, could form an efficient, accurate and beneficial framework for the prognosis of changes in bone properties due to, e.g., bone diseases. In this study, an analytical formulation of bone remodeling integrated with multiscale micromechanical models is proposed to investigate the effects of structural changes at the nanometer level (collagen scale) on those at higher levels (tissue scale). Specific goals of this study are to derive a mechanical stimulus sensed by the osteocytes using a multiscale framework, to test the accuracy of the multiscale model for the prediction of bone density, and to demonstrate its multiscale capabilities by predicting changes in bone density due to changes occurring at the molecular level. At each different level, the bone composition was modeled as a two-phase material which made it possible to: (1) find a closed-form solution for the energy-based mechanical stimulus sensed by the osteocytes and (2) describe the anisotropic elastic properties at higher levels as a function of the stiffness of the elementary components (collagen, hydroxyapatite and water) at lower levels. The accuracy of the proposed multiscale model of bone remodeling was tested first by comparing the analytical bone volume fraction predictions to those obtained from the corresponding μFE-based computational model. Differences between analytical and numerical predictions were less than 1% while the computational time was drastically reduced, namely by a factor of 1 million. In a further analysis, the effects of changes in collagen and hydroxyapatite volume fractions on the bone remodeling process were simulated, and it was found that such changes considerably affect the bone density at the millimeter scale. In fact, smaller tissue density induces remodeling activities leading to finally higher overall bone density. The multiscale analytical model proposed in this study potentially provides an accurate and efficient tool for simulating patient-specific bone remodeling, which might be of importance in particular for the hip and spine, where an accurate assessment of bone micro-architecture is not possible., (Copyright © 2014 Elsevier Inc. All rights reserved.)

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models. A DB of 33 human proximal femurs was generated from micro-CT scans with a nominal isotropic resolution of 82 µm. Continuum FE models were generated from the images using a pre-defined mesh template in combination with an iso-anatomic mesh morphing tool. Each element within the mesh template is at a specific anatomical location. For each element within the cancellous bone, a spherical region around the element centroid with a radius of 2mm was defined. Bone volume fraction and the mean-intercept-length fabric tensor were analyzed for that region. Ten femurs were used as test cases. For each test femur, four different models were generated: (1) an orthotropic model based on micro-CT fabric measurements (gold standard), (2) an orthotropic model based on the fabric derived from the best-matched database model, (3) an isotropic-I model in which the fabric tensor was set to the identity tensor, and (4) a second isotropic-II model with its total bone stiffness fitted to the gold standard. An elastic-plastic damage model was used to simulate failure and post failure behavior during a fall to the side. The results show that all models produce a similar stress distribution. However, compared to the gold standard, both isotropic-I and II models underestimated the stress/damage distributions significantly. We found no significant difference between DB-derived and gold standard models. Compared to the gold standard, the isotropic-I models further underestimated whole bone stiffness by 26.3% and ultimate load by 14.5%, while these differences for the DB-derived orthotropic models were only 4.9% and 3.1% respectively. The results indicate that the concept of using a DB to estimate patient-specific anisotropic material properties can considerably improve the results. We expect that this approach can lead to more accurate results in particular for cases where bone anisotropy plays an important role, such as in osteoporotic patients and around implants., (© 2013 Elsevier Ltd. All rights reserved.)

Objective: Osteoarthritis (OA) is characterized by loss of cartilage and alterations in subchondral bone architecture. Changes in cartilage and bone tissue occur simultaneously and are spatially correlated, indicating that they are probably related. We investigated two hypotheses regarding this relationship. According to the first hypothesis, both wear and tear changes in cartilage, and remodeling changes in bone are a result of abnormal loading conditions. According to the second hypothesis, loss of cartilage and changes in bone architecture result from endochondral ossification., Design: With an established bone adaptation model, we simulated adaptation to high load and endochondral ossification, and investigated whether alterations in bone architecture between these conditions were different. In addition, we analyzed bone structure differences between human bone samples with increasing degrees of OA, and compared these data to the simulation results., Results: The simulation of endochondral ossification led to a more refined structure, with a higher number of trabeculae in agreement with the finding of a higher trabecular number in osteochondral plugs with severe OA. Furthermore, endochondral ossification could explain the presence of a "double subchondral plate" which we found in some human bone samples. However, endochondral ossification could not explain the increase in bone volume fraction that we observed, whereas adaptation to high loading could., Conclusion: Based on the simulation and experimental data, we postulate that both endochondral ossification and adaptation to high load may contribute to OA bone structural changes, while both wear and tear and the replacement of mineralized cartilage with bone tissue may contribute cartilage thinning., (Copyright © 2012 Osteoarthritis Research Society International. Published by Elsevier Ltd. All rights reserved.)

Continuum finite element (FE) models of bones are commonly generated based on CT scans. Element material properties in such models are usually derived from bone density values using some empirical relationships. However, many different empirical relationships have been proposed. Most of these will provide isotropic material properties but relationships that can provide a full orthotropic elastic stiffness tensor have been proposed as well. Presently it is not clear which of these relationships best describes the material behavior of bone in continuum models, nor is it clear to what extent anisotropic models can improve upon isotropic models. The best way to determine the accuracy of such relationships for continuum analyses would be by quantifying the accuracy of the calculated stress/strain distribution, but this requires an accurate reference distribution that does not depend on such empirical relationships. In the present study, we propose a novel approach to generate such a reference stress distribution. With this approach, stress results obtained from a micro-FE model of a whole bone, that can represent the bone trabecular architecture in detail, are homogenized and the homogenized stresses are then used as a reference for stress results obtained from continuum models. The goal of the present study was to demonstrate this new approach and to provide examples of comparing continuum models with anisotropic versus isotropic material properties. Continuum models that implemented isotropic and orthotropic material definitions were generated for two proximal femurs for which micro-FE results were available as well, one representing a healthy and the other an osteoporotic femur. It was found that the continuum FE stress distributions calculated for the healthy femur compared well to the homogenized results of the micro-FE although slightly better for the orthotropic model (r=0.83) than for the isotropic model (r=0.79). For the osteoporotic bone also, the orthotropic model did better (r=0.83) than the isotropic model (r=0.77). We propose that this approach will enable a more relevant and accurate validation of different material models than experimental methods used so far., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

We previously developed a load-adaptive bone modelling and remodelling simulation model that can predict changes in the bone micro-architecture as a result of changes in mechanical loading or cell activity. In combination with a novel algorithm to estimate loading conditions, this offers the possibility for patient-specific predictions of bone modelling and remodelling. Based on such models, the underlying mechanisms of bone diseases and/or the effects of certain drugs and their influence on the bone micro-architecture can be investigated. In the present study we test the ability of this approach to predict changes in bone micro-architecture during hypoparathyroidism (HypoPT), as an illustrative example. We hypothesize that, apart from reducing bone turnover, HypoPT must also lead to increased osteocyte mechanosensitivity in order to explain the changes in bone mass seen in patients. Healthy human iliac crest biopsies were used as the starting point for the simulations that mimic HypoPT conditions and the resultant micro-architectures were compared to age-matched clinical HypoPT biopsies. Simulation results were in good agreement with the clinical data when osteocyte mechanosensitivity was increased by 40%. In conclusion, the results confirm our hypothesis, and also demonstrate that patient-specific bone modelling and remodelling simulations are feasible., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 mum had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.

Trabecular bone strength is marked not only by the onset of local yielding, but also by post-yield behavior. To study and predict trabecular bone elastic and yield properties, micro-finite element (micro-FE) models were successfully applied. However, trabecular bone strength predictions require micro-FE models incorporating post-yield behavior of trabecular bone tissue. Due to experimental difficulties, such data is currently not available. Here we used micro-FE modeling to determine failure behavior of trabecular bone tissue indirectly, by iteratively fitting FE simulation to experimental results. Failure parameters were fitted to an isotropic plasticity model based on Hill's yield function, using materially and geometrically nonlinear micro-FE models of seven bovine trabecular bone specimens. The predictive value of the averaged effective tissue properties was subsequently tested. The results showed that compression softening had to be included on the tissue level in order to accurately describe the apparent-level behavior of the bone specimens. A sensitivity study revealed that the simulated response was less sensitive to variations in the post-yield properties of the bone tissue than variations in the elastic and yield properties. Due to fitting of the tissue properties, apparent-level behavior could be accurately reproduced for each specimen separately. Predictions based on the averaged and fixed tissue properties were less accurate, due to inter-specimen variations in the tissue properties.

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density-modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.

From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.

It is widely believed that mechanical forces affect trabecular bone structure and orientation. The cellular mechanisms involved in this relationship, however, are poorly understood. In earlier work we developed a theoretical, computational framework, coupling bone-cell metabolic expressions to the local mechanical effects of external bone loading. This theory is based on the assumption that osteocytes within the bone tissue control the recruitment of bone-resorbing osteoclasts and bone-forming osteoblasts, by sending strain-energy-density (SED) related signals to trabecular surfaces through the osteocytic, canalicular network. The theory explains the known morphological effects of external bone-loading variations in magnitude and frequency. It also explains the development of osteoporosis, as an effect of increased osteoclast resorption due to estrogen deficiency in postmenopausal women, and to reduced physical activity levels in general. However, the theory uses lumped variables to represent the mechanisms of osteocyte mechano-sensing and signaling. The question is whether these mechanisms could not be specified in a more realistic way. On the one hand, anabolic osteocyte signals might be triggered by the local mechanical loading variables they experience directly, as we assumed in our original theory. On the other hand, osteocyte signals might be triggered by fluid flow in the osteocytic network at large, as was suggested by others. For that purpose we compared the effects of SED, maximal principal strain and volumetric strain as representing local loading variables, to their spatial gradients on the morphological predictions of our computational model. We found that, in concept, they all produced reasonable trabecular structures. However, the predicted trabecular morphologies based on SED as the triggering variable were more realistic in dimensions and relevant metabolic parameters.

A three-dimensional digital image correlation technique is presented for strain measurements in open-cell structures such as trabecular bone. The technique uses high-resolution computed tomography images for displacement measurements in the solid structure. In order to determine the local strain-state within single trabeculae, a tetrahedronization method is used to fill the solid structure with tetrahedrae. Displacements are calculated at the nodes of the tetrahedrae. The displacement data is subsequently converted to a deformation tensor in each of the tetrahedral element centers with a least-squares estimation method. Because the trabeculae are represented by a mesh, it is possible to deform this mesh according to the deformation tensor and, at the same time, visualize the calculated local strain in the deformed mesh with a finite element post-processing tool. In this way, the deformation of a single trabecula from an aluminum foam sample was determined and validated with rendered images of the three-dimensional sample. A precision analysis showed that a rigid translation or rotation does not affect the accuracy. Typical values for the standard deviation in the displacement and strain components are 2.0 microm and 0.01, respectively. Presently, the precision limits the technique to strain measurements beyond the yield strain.

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-Line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone.

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.

Metabolic bone diseases such as osteoporosis usually cause a decrease in bone mass and a deterioration of bone microarchitecture leading to a decline in bone strength. Methods to predict bone strength in patients are currently based on bone mass only. It has been suggested that an improved prediction of bone strength might be possible if structural changes are taken into account as well. In this study we evaluated which structural parameters (other than bone mass) are the best predictors for changes in bone mechanical properties of the human radius after different bone atrophy scenarios and whether the original strength of the affected bone can be recovered if bone loss is restored by thickening of the remaining structures. To answer these questions, a human radius was measured with a microcomputer tomography scanner to extract the full three-dimensional architecture of the distal radius at an isotropic resolution of 80 microm. Eight models with modified bone architecture were created and the mechanical variations due to these modifications were studied using microfinite element (micro-FE) simulations. In four models mass was lowered by 20%, either by reducing cortical thickness, trabecular thickness, or number of trabeculae or by overall thinning of structures. In the other four models bone mass was restored to the original value using a trabecular bone thickening procedure. The micro-FE analyses revealed that most load was carried by the cortical bone. For this reason, bone strength was affected most in the reduced cortical thickness model. For the same reason, the trabecular bone atrophy scenarios, all of which affected bone strength in a very similar way, resulted in less dramatic bone strength reduction. The restoration of bone mass did not recover the original bone strength. These findings demonstrate that the importance of different parameters for the prediction of bone strength also depends on the mechanical loading. This could explain why results of earlier studies on the importance of structural parameters can be inconsistent and site-dependent.

Results of both clinical and animal studies show that meniscectomy often leads to osteoarthritic degenerative changes in articular cartilage. It is generally assumed that this process of cartilage degeneration is due to changes in mechanical loading after meniscectomy. It is, however, not known why and where this cartilage degeneration starts. Load induced cartilage damage is characterized as either type (1)--damage without disruption of the underlying bone or calcified cartilage layer--or type (2), subchondral fracture with or without damage to the overlying cartilage. We asked the question whether cartilage degeneration after meniscectomy is likely to be initiated by type (1) and/or type (2) cartilage damage. To investigate that we applied an axisymmetric biphasic finite element analysis model of the knee joint. In this model the articular cartilage layers of the tibial and the femoral condyles, the meniscus and the bone underlying the articular cartilage of the tibia plateau were included. The model was validated with data from clinical studies, in which the effects of meniscectomy on contact areas and pressures were measured. It was found that both the maximal values and the distributions of the shear stress in the articular cartilage changed after meniscectomy, and that these changes could lead to both type (1) and type (2) cartilage damage. Hence it likely that the cartilage degeneration seen after meniscectomy is initiated by both type (1) and type (2) cartilage damage.

Mechanical loading of trabecular bone affects the bone architecture. Bone mass is correlated to the magnitude of the external load and trabeculae are aligned to the loading direction. Physical exercise increases bone mass while disuse or microgravity decreases it. In previous work we have presented a mathematical model of bone metabolism that could explain the emergence, maintenance and adaptation of trabecular bone under influence of the load imposed, using a 2-dimensional computer model (Huiskes et al., Nature 404 (2000), 704-706). This model was based on hypothetical mathematical descriptions of bone formation by osteoblastic cells, and resorption by osteoclastic cells, both as governed by mechanical stimuli. In order to quantitatively compare the behavior of the proposed regulation mechanism to real trabecular bone metabolism we present a 3-dimensional computer simulation model. The first 3-dimensional simulation results show that the regulatory rules proposed earlier mimic trabecular bone metabolism in a robust way.

Trabecular bone structure may complement bone volume/total volume fraction (BV/TV) in the prediction of the mechanical properties. Nonetheless, the direct in vivo use of information pertaining to trabecular bone structure necessitates some predictive analytical model linking structure measures to mechanical properties. In this context, the purpose of this study was to combine BV/TV and topological parameters so as to better estimate the mechanical properties of trabecular bone. Thirteen trabecular bone mid-sagittal sections were imaged by magnetic resonance (MR) imaging at the resolution of 117 x 117x 300 microm(3). Topological parameters were evaluated in applying the 3D-line skeleton graph analysis (LSGA) technique to the binary MR images. The same images were used to estimate the elastic moduli by finite element analysis (FEA). In addition to the mid-sagittal section, two cylindrical samples were cored from each vertebra along vertical and horizontal directions. Monotonic compression tests were applied to these samples to measure both vertical and horizontal ultimate stresses. BV/TV was found as a strong predictor of the mechanical properties, accounting for 89-94% of the variability of the elastic moduli and for 69-86% of the variability of the ultimate stresses. Topological parameters and BV/TV were combined following two analytical formulations, based on: (1) the normalization of the topological parameters; and on (2) an exponential fit-model. The normalized parameters accounted for 96-98% of the variability of the elastic moduli, and the exponential model accounted for 80-95% of the variability of the ultimate stresses. Such formulations could potentially be used to increase the prediction of the mechanical properties of trabecular bone.

There is increasing evidence that, in addition to bone mass, bone microarchitecture and its mechanical load distribution are important factors for the determination of bone strength. Recently, it has been shown that new high-resolution imaging techniques in combination with new modeling algorithms based on the finite element (FE) method can account for these additional factors. Such models thus could provide more relevant information for the estimation of bone failure load. The purpose of the present study was to determine whether results of whole-bone micro-FE (microFE) analyses with models based on three-dimensional peripheral quantitative computer tomography (3D-pQCT) images (isotropic voxel resolution of 165 microm) could predict the failure load of the human radius more accurately than results with dual-energy X-ray absorptiometry (DXA) or bone morphology measurements. For this purpose, microFE models were created using 54 embalmed cadaver arms. It was assumed that bone failure would be initiated if a certain percentage of the bone tissue (varied from 1% to 7%) would be strained beyond the tissue yield strain. The external force that produced this tissue strain was calculated from the FE analyses. These predictions were correlated with results of real compression testing on the same cadaver arms. The results of these compression tests were also correlated with results of DXA and structural measurements of these arms. The compression tests produced Colles-type fractures in the distal 4 cm of the radius. The predicted failure loads calculated from the FE analysis agreed well with those measured in the experiments (R(2) = 0.75 p < 0.001). Lower correlations were found with bone mass (R(2) = 0.48, p < 0.001) and bone structural parameters (R(2) = 0.57 p < 0.001). We conclude that application of the techniques investigated here can lead to a better prediction of the bone failure load for bone in vivo than is possible from DXA measurements, structural parameters, or a combination thereof.

Micro-finite element (microFE) models based on high-resolution images have enabled the calculation of elastic properties of trabecular bone in vitro. Recently, techniques have been developed to image trabecular bone structure in vivo, albeit at a lesser resolution. The present work studies the usefulness of such in-vivo images for microFE analyses, by comparing their microFE results to those of models based on high-resolution micro-CT (microCT) images. Fifteen specimens obtained from human femoral heads were imaged first with a 3D-pQCT scanner at 165 microns resolution and a second time with a microCT scanner at 56 microns resolution. A third set of images with a resolution of 165 microns was created by downscaling the microCT measurements. The microFE models were created directly from these images. Orthotropic elastic properties and the average tissue von Mises stress of the specimens were calculated from six FE-analyses per specimen. The results of the 165 microns models were compared to those of the 56 microns model, which was taken as the reference model. The results calculated from the pQCT-based models, correlated excellent with those calculated from the reference model for both moduli (R2 > 0.95) and for the average tissue von Mises stress (R2 > 0.83). Results calculated from the downscaled micro-CT models correlated even better with those of the reference models (R2 > 0.99 for the moduli and R2 > 0.96 for the average von Mises stress). In the case of the 3D-pQCT based models, however, the slopes of the regression lines were less than one and had to be corrected. The prediction of the Poisson's ratios was less accurate (R2 > 0.45 and R2 > 0.67) for the models based on 3D-pQCT and downscaled microCT images respectively). The fact that the results from the downscaled and original microCT images were nearly identical indicates that the need for a correction in the case of the 3D-pQCT measurements was not due to the voxel size of the images but due to a higher noise level and a lower contrast in these images, in combination with the application of a filtering procedure at 165 micron images. In summary: the results of microFE models based on in-vivo images of the 3D-pQCT can closely resemble those obtained from microFE models based on higher resolution microCT system.

The hypothesis that trabecular morphology can predict the elastic properties of cancellous bone has only partly been verified and no predictive analytical model is currently available. Such models are becoming increasingly relevant as the resolution levels of three-dimensional scanning techniques approach the size of trabeculae. This study took advantage of micro-finite-element methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. Numerical analysis was based on high-resolution three-dimensional computer reconstructions of cancellous bone specimens from which the complete elastic characteristics and trabecular morphology, represented by three different fabric measures (the mean intercept length and two volume-based ones), were calculated. Each fabric measure was analyzed individually using the tensorial relationships derived by Cowin (Mech Mater 4:137-147; 1985). Models for both stiffness and compliance entries were developed. The models based on stiffness entries could explain 93.4%-95.6% of the variance, whereas those based on compliance entries could explain 89.2%-89.4%. When using the former model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star volume distribution), with 23% less remaining variance. The high correlations found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtain considerably better estimates of bone quality in vivo compared with the rough two-dimensional density measurements used today.

A quantitative assessment of bone tissue stresses and strains is essential for the understanding of failure mechanisms associated with osteoporosis, osteoarthritis, loosening of implants and cell- mediated adaptive bone-remodeling processes. According to Wolff's trajectorial hypothesis, the trabecular architecture is such that minimal tissue stresses are paired with minimal weight. This paradigm at least suggests that, normally, stresses and strains should be distributed rather evenly over the trabecular architecture. Although bone stresses at the apparent level were determined with finite element analysis (FEA), by assuming it to be continuous, there is no data available on trabecular tissue stresses or strains of bones in situ under physiological loading conditions. The objectives of this project were to supply reasonable estimates of these quantities for the canine femur, to compare trabecular-tissue to apparent stresses, and to test Wolff's hypothesis in a quantitative sense. For that purpose, the newly developed method of large-scale micro-FEA was applied in conjunction with micro-CT structural measurements. A three-dimensional high-resolution computer reconstruction of a proximal canine femur was made using a micro-CT scanner. This was converted to a large-scale FE-model with 7.6 million elements, adequately refined to represent individual trabeculae. Using a special-purpose FE-solver, analyses were conducted for three different orthogonal hip-joint loading cases, one of which represented the stance-phase of walking. By superimposing the results, the tissue stress and strain distributions could also be calculated for other force directions. Further analyses of results were concentrated on a trabecular volume of interest (VOI) located in the center of the head. For the stance phase of walking an average tissue principal strain in the VOI of 279 strain was found, with a standard deviation of 212 microstrain. The standard deviation depended not only on the hip-force magnitude, but also on its direction. In more than 95% of the tissue volume the principal stresses and strains were in a range from zero to three times the averages, for all hip-force directions. This indicates that no single load creates even stress or strain distributions in the trabecular architecture. Nevertheless, excessive values occurred at few locations only, and the maximum tissue stress was approximately half the value reported for the tissue fatigue strength. These results thus indicate that trabecular bone tissue has a safety factor of approximately two for hip-joint loads that occur during normal activities.

A quantitative assessment of bone tissue stresses and strains is essential for the understanding of failure mechanisms associated with osteoporosis, osteoarthritis, loosening of implants and cell-mediated adaptive bone-remodeling processes. According to Wolff's trajectorial hypothesis, the trabecular architecture is such that minimal tissue stresses are paired with minimal weight. This paradigm at least suggests that, normally, stresses and strains should be distributed rather evenly over the trabecular architecture. Although bone stresses at the apparent level were determined with finite element analysis (FEA), by assuming it to be continuous, there is no data available on trabecular tissue stresses or strains of bones in situ under physiological loading conditions. The objectives of this project were to supply reasonable estimates of these quantities for the canine femur, to compare trabecular-tissue to apparent stresses, and to test Wolff's hypothesis in a quantitative sense. For that purpose, the newly developed method of large-scale micro-FEA was applied in conjunction with micro-CT structural measurements. A three-dimensional high-resolution computer reconstruction of a proximal canine femur was made using a micro-CT scanner. This was converted to a large-scale FE-model with 7.6 million elements, adequately refined to represent individual trabeculae. Using a special-purpose FE-solver, analyses were conducted for three different orthogonal hip-joint loading cases, one of which represented the stance-phase of walking. By superimposing the results, the tissue stress and strain distributions could also be calculated for other force directions. Further analyses of results were concentrated on a trabecular volume of interest (VOI) located in the center of the head. For the stance phase of walking an average tissue principal strain in the VOI of 279 strain was found, with a standard deviation of 212 microstrain. The standard deviation depended not only on the hip-force magnitude, but also on its direction. In more than 95% of the tissue volume the principal stresses and strains were in a range from zero to three times the averages, for all hip-force directions. This indicates that no single load creates even stress or strain distributions in the trabecular architecture. Nevertheless, excessive values occurred at few locations only, and the maximum tissue stress was approximately half the value reported for the tissue fatigue strength. These results thus indicate that trabecular bone tissue has a safety factor of approximately two for hip-joint loads that occur during normal activities.

Cancellous bone architecture and mechanics are intimately related. The trabecular architecture of cancellous bone is considered determined by its mechanical environment (Wolff's law), and the mechanical properties of cancellous bone are inversely determined by the trabecular architecture and material properties. Much effort has been spent in expressing these relations, but the techniques and variables necessary for this have not been fully identified. It is obvious, however, that some measure of architectural anisotropy (fabric) is needed. Within the last few years, volume-based measures of fabric have been introduced as alternatives to the mean intercept length method, which has some theoretical problems. This paper seeks to answer which of four different fabric measures best predicts finite element calculated mechanical anisotropy directions. Twenty-nine cancellous bone specimens were three-dimensionally reconstructed using the automated serial sectioning technique. A series of large-scale finite-element analyses were performed on each of the three-dimensional reconstructions to calculate the compliance matrix for each specimen, from which the mechanical principal directions were derived. The architectural anisotropy was determined in three-dimensional space for each specimen using mean intercept length (MIL), volume orientation (VO), star volume distribution (SVD) and star length distribution (SLD). Each of the architectural anisotropy results were expressed by a fabric tensor. Architectural main directions were determined from the fabric tensors and compared with the FE-calculated mechanical anisotropy directions. All architectural measures predicted the mechanical main directions rather well, which supports the assumption that mechanical anisotropy directions are aligned with fabric directions. MIL showed a significant, though very small (1.4 degrees), deviation from the primary mechanical direction. VO had difficulty in determining secondary and tertiary mechanical directions; its mean deviation was 8.9 degrees. SVD and SLD provided marginally better predictors of mechanical anisotropy directions than MIL and VO.

The apparent mechanical behavior of trabecular bone depends on properties at the tissue or trabecular level. Many investigators have attempted to determine trabecular tissue properties and loading. However, accuracy and applicability of all methods reported are limited. The small size of the trabeculae and a possible size effect are complicating factors when using traditional testing methods on single trabeculae. Other methods reported, using models that describe the trabecular structure, are of limited value because they consider bone as a repetitive structure in order to describe a reasonably large region of bone. The present study introduces a new finite-element method strategy that enables analysis of reasonably large regions of trabecular bone in full detail. The method uses three-dimensional serial reconstruction techniques to construct a large-scale FE model, by directly converting voxels to elements. A 5 mm cube of trabecular bone was modeled in this way, resulting in a FE model that consists of 296,679 elements. Special strategies were developed to solve the set of equations that results from the FE approach. Using this model in combination with experimental apparent data taken from the literature, the upper and lower boundaries for the tissue modulus were calculated to be 10.1 and 2.23 GPa, respectively. From the local stress and strain distributions it was concluded that the deformation mode of the trabeculae in the present cube was predominantly in bending. It was concluded that the method developed offers new perspectives for the study of trabecular bone.

Severe loss of bone related to stress-shielding is one problem threatening the long-term integrity of noncemented total hip arthroplasty. It is widely accepted that this phenomenon is caused by adaptive bone remodeling according to Wolff's law. Recently, quantitative bone-remodeling theories have been proposed, suitable for use in computer-simulation models in combination with finite-element codes, which can be applied to simulate the long-term effect of the remodeling process. In the present paper, the results of such a computer simulation are compared with those in an animal experiment. A three-dimensional finite-element model was constructed from an animal experimental configuration concerning the implantation of a fully coated femoral hip prosthesis in dogs. The simulation results of the adaptive bone-remodeling process (geometric adaptations at the periosteal surface and density adaptations within the cancellous bone) were compared with cross-sectional measurements of the canine femurs after 2 years of follow-up. The detailed comparison showed that long-term changes in the morphology of bone around femoral components of total hip replacements can be fully explained with the present quantitative adaptive bone-remodeling theory.

Bone resorption around hip stems is a disturbing phenomenon, although its clinical significance and its eventual effects on replacement longevity are as yet uncertain. The relationship between implant flexibility and the extent of bone loss, frequently established in clinical patient series and animal experiments, does suggest that the changes in bone morphology are an effect of stress shielding and a subsequent adaptive remodeling process. This relationship was investigated using strain-adaptive bone-remodeling theory in combination with finite element models to simulate the bone remodeling process. The effects of stem material flexibility, bone flexibility, and bone reactivity on the process and its eventual outcome were studied. Stem flexibility was also related to proximal implant/bone interface stresses. The results sustain the hypothesis that the resorptive processes are an effect of bone adaptation to stress shielding. The effects of stem flexibility are confirmed by the simulation analysis. It was also established that individual differences in bone reactivity and mechanical bone quality (density and stiffness) may account for the individual variations found in patients and animal experiments. Flexible stems reduce stress shielding and bone resorption. However, they increase proximal interface stresses. Hence, the cure against bone resorption they represent may develop into increased loosening rates because of interface debonding and micromotion. The methods presented in this paper can be used to establish optimal stem-design characteristics or check the adequacy of designs in preclinical testing procedures.