http://repub.eur.nl/res/aut/18106/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/15373/ 2004-07-01T00:00:00Z The purpose of this study was to examine the effect of mineralization on the mechanical properties of embryonic bone rudiments. For this purpose, four-point bending experiments were performed on unmineralized and mineralized embryonic mouse ribs at 16 and 17 days of gestational age. Young's modulus was calculated using force-displacement data from the experiment in combination with finite element analysis (FEA). For the unmineralized specimens, a calculated average for the Young's modulus of 1.11 (+/- 0.62) MPa was established after corrections for sticking to the four-point bending device and aspect ratio, which is the ratio between the length of the bone and its diameter. For the mineralized specimens, the value was 117 (+/- 62) MPa after corrections. Hence, Young's moduli of embryonic bone rudiments increase by two orders of magnitude within 1 day, during endochondral ossification. As an effect, the hypertrophic chondrocytes in the calcifying cartilage experience a significant change in their mechanical environment. The chondrocytes are effectively stress shielded, which means that they do not carry stresses since stresses are supported by the stiffest parts of the tissue, which are in this case the diaphyseal cortex and the calcified matrix. The deformability of the hypertrophic chondrocytes is, therefore, severely reduced. Since the transition is so sudden and enormous, it can be seen as a process of 'catastrophic' proportion for the hypertrophic chondrocytes. The subsequent resorption of calcified cartilage and the expansion of the marrow cavity could be consequential to stress shielding. http://repub.eur.nl/res/pub/15372/ 2004-03-01T00:00:00Z Osteoporotic vertebral fractures typically have a gradual onset, frequently remain clinically undetected, and do not seem to be related to traumatic events. The osteoporotic vertebrae may therefore be expected to display a less "optimal" bone architecture, leading to an uneven load distribution over the bone material. We evaluated the trabecular load distribution in an osteoporotic and a healthy vertebra under normal daily loading by combining three recent innovations: high resolution computed tomography (microCT) of entire bones, microfinite element analyses (microFEA), and parallel supercomputers. Much to our surprise, the number of highly loaded trabeculae was not higher in the osteoporotic vertebra than in the healthy one under normal daily loads (8% and 9%, respectively). The osteoporotic trabeculae were more oriented in the longitudinal direction, compensating for effects of bone loss and ensuring adequate stiffness for normal daily loading. The increased orientation did, however, make the osteoporotic structure less resistant against collateral "error" loads. In this case, the number of overloaded trabeculae in the osteoporotic vertebra was higher than in the healthy one (13% and 4%, respectively). These results strengthen the paradigm of a strong relationship between bone morphology and external loads applied during normal daily life. They also indicate that vertebral fractures result from actions like forward flexion or lifting, loads that may not be "daily" but are normally not traumatic either. If future clinical imaging techniques would enable such high-resolution images to be obtained in vivo, the combination of microCT and microFEA would produce a powerful tool to diagnose osteoporosis. http://repub.eur.nl/res/pub/15371/ 2003-10-01T00:00:00Z Osteoporosis is a progressive systemic skeletal condition characterized by low bone mass and microarchitectural deterioration, with a consequent increase in susceptibility to fracture. Hence, osteoporosis would be best diagnosed by in vivo measurements of bone strength. As this is not clinically feasible, our goal is to estimate bone strength through the assessment of elastic properties, which are highly correlated to strength. Previously established relations between morphological parameters (volume fraction and fabric) and elastic constants could be applied to estimate cancellous bone stiffness in vivo. However, these relations were determined for normal cancellous bone. Cancellous bone from osteoporotic patients may require different relations. In this study we set out to answer two questions. First, can the elastic properties of osteoporotic cancellous bone be estimated from morphological parameters? Second, do the relations between morphological parameters and elastic constants, determined for normal bone, apply to osteoporotic bone as well? To answer these questions we used cancellous bone cubes from femoral heads of patients with (n=26) and without (n=32) hip fractures. The elastic properties of the cubes were determined using micro-finite element analysis, assuming equal tissue moduli for all specimens. The morphological parameters were determined using microcomputed tomography. Our results showed that, for equal tissue properties, the elastic properties of cancellous bone from fracture patients could indeed be estimated from morphological parameters. The morphology-based relations used to estimate the elastic properties of cancellous bone are not different for women with or without fractures. http://repub.eur.nl/res/pub/15283/ 2002-05-01T00:00:00Z Osteoporosis is currently defined in terms of low bone mass. However, the source of fragility leading to fracture has not been adequately described. In particular, the contributions of bone tissue properties and architecture to the risk or incidence of fracture are poorly understood. In an earlier experimental study, it was found that the architectural anisotropy of cancellous bone from the femoral heads of fracture patients was significantly increased compared with age- and density-matched control material (Ciarelli et al., J Bone Miner Res 15:32-40; 2000). Using a combination of compression testing and micro-finite element analysis on a subset of cancellous bone specimens from that study, we calculated the hard tissue mechanical properties and the apparent (macroscopic) mechanical properties. The tissue modulus was 10.0 GPa (SD 2.2) for the control group and 10.8 GPa (SD 3.3) for the fracture group (not significant). There were no differences in either the apparent yield strains, percentages of highly strained tissue, or the relationship between apparent yield stress and apparent elastic modulus. Hence, a difference in the tissue yield properties is unlikely. At the apparent level, the fracture group had a significantly decreased transverse stiffness, resulting in increased mechanical anisotropy. These changes suggest that bone in the fracture group was "overadapted" to the primary load axis, at the cost of fragility in the transverse direction. We conclude that individuals with a history of osteoporotic fractures do not have weaker bone tissue. Architectural and mechanical anisotropy alone renders their bone weaker in the nonprimary loading direction. http://repub.eur.nl/res/pub/15368/ 2001-07-01T00:00:00Z STUDY DESIGN: A finite-element study to investigate the amount of trabecular bone at risk of fracture and the distribution of load between trabecular core and cortical shell, for healthy, osteopenic, and osteoporotic vertebrae. OBJECTIVES: To determine differences between health y, osteopenic, and osteoporotic vertebrae with regard to the risk of fracture and the load distribution. SUMMARY OF BACKGROUND DATA: The literature contains no reports on the effects of osteopenia and osteoporosis on load distribution in vertebral bodies, nor any reports on the amount of trabecular bone at risk of fracture. METHODS: Computed tomography data of vertebral bodies were used to construct patient-specific finite-element models. These models were then used in finite-element analyses to determine the physiologic stresses and strains in the vertebrae. RESULTS: For all three classes of vertebrae the contribution of the trabecular core to the total load transfer decreased from about 70% near the endplates to about 50% in the midtransverse region. The amount of trabecular bone that is at risk of fracture was about 1% for healthy vertebrae, about 3% for osteopenic vertebrae, and about 16% for osteoporotic vertebrae. CONCLUSIONS: Our finite-element models indicated that neither osteopenia nor osteoporosis had any effect on the contribution of the trabecular core to the total load placed on the vertebra. The trabecular core carried about half the load. Our finite-element models indicated that osteoporosis had a significant effect on the amount of trabecular bone at risk of fracture, which increased from about 1% in healthy vertebrae to about 16% for osteoporotic vertebrae. http://repub.eur.nl/res/pub/15366/ 2001-04-01T00:00:00Z In micro finite element analyses (microFEA) of cancellous bone, the 3D-imaging data that the FEA-models are based on, contain a range of gray-values. In the construction of the eventual FEA-model, these gray-values are commonly thresholded. Although thresholding is successful at small voxel sizes, at larger voxel sizes there is substantial loss of trabecular connectivity. We propose a new method: the gray-value method, where the microFEA-models use the information within the 3D-imaging data directly, without prior thresholding. Our question was twofold. First, how does the gray-value method compare to both plain and mass-compensated thresholding? Second, what is the effect of element size on the results obtained with the gray-value method? We used nine microCT-scans of human vertebral cancellous bone. These were degraded to represent different resolutions, and converted into microFEA-models using plain thresholding, mass-compensated thresholding, and the gray-value method. The apparent elastic moduli of the specimens were determined using microFEA. The different methods were compared on the basis of the apparent elastic moduli, compared to those calculated for a 28 microm reference model. The results showed that the gray-value method greatly improves the results relative to other methods. The gray-value method gives accurate predictions of the apparent elastic moduli, for voxel sizes up to one trabecular thickness (Tb.Th.). For voxel sizes greater than one Tb.Th. the accuracy, although still better than for both thresholding methods, becomes increasingly worse. http://repub.eur.nl/res/pub/15304/ 1996-01-01T00:00:00Z FE-models for structural solid mechanics analyses can be readily generated from computer images via a 'voxel convesion' method, whereby voxels in a two- or three-dimesional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithm that can compensate for a large number of element. The solving methods described in this paper are based on an iterative solving algorithm in combination with a uniqueelement Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of 105 3-D brick elements on a workstation and on the order of 106 elements on a Cray computer. The methods are demonstrated for the Boussinesq problem and for FF models that represent a porous trabecular bone structure The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques. http://repub.eur.nl/res/pub/15269/ 1995-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/15379/ 1993-11-01T00:00:00Z Connective soft tissues at the interface between implants and bone, such as in human joint replacements, can endanger the stability of the implant fixation. The potential of an implant to generate interface bone resorption and form soft tissue depends on many variables, including mechanical ones. These mechanical factors can be expressed in terms of relative motions between bone and implant at the interface or deformation of the interfacial material. The purpose of this investigation was to determine if interface debonding and subsequent relative interface motions can be responsible for interface degradation and soft tissue interposition as seen in experiments and clinical results. A finite element computer program was augmented with a mathematical description of interface debonding, dependent on interface stress criteria, and soft tissue interface interposition, dependent on relative interface motions. Three simplified models of orthopaedic implants were constructed: a cortical bone screw for fracture fixation plates, a femoral resurfacing prosthesis and a straight stem model, cemented in a bone. The predicted computer configurations were compared with clinical observations. The computer results showed how interface disruption and fibrous tissue interposition interrelate and possibly enhance each other, whereby a progressive development of the soft tissue layer can occur. Around the cortical bone screw, the predicted resorption patterns were relatively large directly under the screw head and showed a pivot point in the opposite cortex. The resurfacing cup model predicted some fibrous tissue formation under the medial and lateral cup rim, whereby the medial layer developed first because of higher initial interface stresses. The straight stem model predicted initial interface failure at the proximal parts. After proximal resorption and fibrous tissue interposition, the medial interface was completely disrupted and developed an interface layer. The distal and mid lateral side maintained within the strength criterion. Although the applied models were relatively simple, the results showed reasonable qualitative agreement with resorption patterns found in clinical studies concerning bone screws and the resurfacing cup. The hypothesis that interface debonding and subsequent relative (micro)motions could be responsible for bone resorption and fibrous tissue propagation is thereby sustained by the results. http://repub.eur.nl/res/pub/15361/ 1992-12-01T00:00:00Z The process of adaptive bone remodeling can be described mathematically and simulated in a computer model, integrated with the finite element method. In the model discussed here, cortical and trabecular bone are described as continuous materials with variable density. The remodeling rule applied to simulate the remodeling process in each element individually is, in fact, an objective function for an optimization process, relative to the external load. Its purpose is to obtain a constant, preset value for the strain energy per unit bone mass, by adapting the density. If an element in the structure cannot achieve that, it either turns to its maximal density (cortical bone) or resorbs completely. It is found that the solution obtained in generally a discontinuous patchwork. For a two-dimensional proximal femur model this patchwork shows a good resemblance with the density distribution of a real proximal femur. It is shown that the discontinuous end configuration is dictated by the nature of the differential equations describing the remodeling process. This process can be considered as a nonlinear dynamical system with many degrees of freedom, which behaves divergent relative to the objective, leading to many possible solutions. The precise solution is dependent on the parameters in the remodeling rule, the load and the initial conditions. The feedback mechanism in the process is self-enhancing, denser bone attracts more strain energy, whereby the bone becomes even more dense. It is suggested that this positive feedback of the attractor state (the strain energy field) creates order in the end configuration. In addition, the process ensures that the discontinuous end configuration is a structure with a relatively low mass, perhaps a minimal-mass structure, although this is no explicit objective in the optimization process. It is hypothesized that trabecular bone is a chaotically ordered structure which can be considered as a fractal with characteristics of optimal mechanical resistance and minimal mass, of which the actual morphology depends on the local (internal) loading characteristics, the sensor-cell density and the degree of mineralization http://repub.eur.nl/res/pub/15381/ 1992-07-08T00:00:00Z For the purpose of studying bone remodeling around prostheses, a segmental replacement for the goat tibia was designed, using a conical, screw-threaded, hydroxyapatite-coated stem for fixation. Eight goats were provided with the implant, seven of which loosened within 10 days post-operatively, displaying progressive radiolucency and gross rotational motion. The eighth one also loosened radiographically, but developed a stabilizing callus bridge to prevent motion. A second design of similar shape and coating, but lacking the screw threads, was designed and also applied in eight animals. In this case, no loosening occurred in the first 6 weeks post-operatively. It is concluded that the application of screwed intramedullary stems for prosthetic fixation is not a viable concept, because the threads prevent the stem from subsiding and restabilizing when minor initial interface stress-relaxation and remodeling has occurred. http://repub.eur.nl/res/pub/15376/ 1992-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/15377/ 1990-11-05T00:00:00Z In the present study, the effects of a fibrous membrane between cement and bone in a femoral total hip replacement were investigated. The study involved the problem of modeling this fibrous membrane in finite-element analyses, and its global consequences for the load-transfer mechanism and its resulting stress patterns. A finite-element model was developed, suitable to describe nonlinear contact conditions in combination with nonlinear material properties of the fibrous membrane. The fibrous tissue layer was described as a highly compliant material with little resistance against tension and shear. The analysis showed that the load transfer mechanism from stem to bone changes drastically when such a membrane is present. These effects are predominantly caused by tensile loosening and slip at the interface, and are enhanced by the nonlinear membrane characteristics. Using parametric analysis, it was shown that these effects on the load-transfer mechanism cannot be described satisfactorily with linear elastic models. Most importantly, the fibrous tissue interposition causes excessive stress concentrations in bone and cement, and relatively high relative displacements between these materials. http://repub.eur.nl/res/pub/15267/ 1987-01-01T00:00:00Z The subject of this article is the development and application of computer-simulation methods to predict stress-related adaptive bone remodeling, in accordance with 'Wolff's Law'. These models are based on the Finite Element Method (FEM) in combination with numerical formulations of adaptive bone-remodeling theories. In the adaptive remodeling models presented, the Strain Energy Density (SED) is used as a feed-back control variable to determine shape or bone density adaptations to alternative functional requirements, whereby homeostatic SED distribution is assumed as the remodeling objective. These models are applied to investigate the relation between 'stress shielding' and bone resorption in the femoral cortex around intramedullary prostheses, such as used in Total Hip Arthroplasty (THA). It is shown that the amount of bone resorption depends mainly on the rigidity and the bonding characteristics of the implant. Homeostatic SED can be obtained when the resorption process occurs at the periosteal surface, rather than inside the cortex, provided that the stem is adequately flexible.