D Ulrich

Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques

In this study, we investigate if finite element (FE) analyses of human trabecular bone architecture based on 168 microm images can provide relevant information about the bone mechanical characteristics. Three human trabecular bone samples, one taken from the femoral head, one from the iliac crest, and one from the lumbar spine, were imaged with micro-computed tomography (micro-CT) using a 28 microm resolution. After reconstruction the resolution was coarsened to 168 microm. First, all reconstructions were thresholded and directly converted to FE-models built of hexahedral elements. For the coarser resolutions of two samples, this resulted in a loss of trabecular connections and a subsequent loss of stiffness. To reduce this effect, a tetrahedral element meshing based on the marching cubes algorithm, as well as a modified hexahedron meshing, which thresholds the image such that load carrying bone mass is preserved, were employed. For each sample elastic moduli and tissue Von Mises stresses of the three different 168 microm models were compared to those from the hexahedron 28 microm model. For one sample the hexahedron meshing at 168 microm produced excellent results. For the other two samples the results obtained from the hexahedral models at 168 microm resolution were poor. Considerably better results were attained for these samples when using the mass-compensated or tetrahedron meshing techniques. We conclude that the accuracy of the FE-models at 168 microm strongly depends on the bone morphology, in particular its trabecular thickness. A substantial loss of trabecular connections during the hexahedron meshing process indicates that poor FE results will be obtained. In this case the tetrahedron or mass-compensated hexahedron meshing techniques can reduce the loss of connections and produce better results than the plain hexahedron meshing techniques.

Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions.

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 Wolffs 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 Wolffs 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.

Load transfer analysis of the distal radius from in-vivo high-resolution CT-imaging

Prevention of osteoporotic bone fractures requires accurate diagnostic methods to detect the increase in bone fragility at an early stage of osteoporosis. However, todays bone fracture risk prediction, primarily based on bone density measurement, is not sufficiently precise. There is increasing evidence that, in addition to bone density, also the bone microarchitecture and its mechanical loading conditions are important factors determining the fracture risk. Recently, it has been shown that new high-resolution imaging techniques in combination with new computer modeling techniques based on the finite-element (FE) method can account for these additional factors. These techniques might provide information that is more relevant for the prediction of bone fracture risk. So far, however, these new imaged-based FE techniques have not been feasible in-vivo. The objectives of this study were to quantify the load transfer through the trabecular network in a distal radius using a computer model based on in-vivo high-resolution images and to determine if common regions of fractures can be explained as a result of high tissue loading in these regions. The left distal radius and the two adjacent carpal bones of a healthy volunteer were imaged using a high-resolution three-dimensional CT system providing an isotropic resolution of 165 microm. The bone representation was converted into a FE-model that was used to calculate stresses and strains in the trabecular network. The two carpal bones were loaded using different load ratios (for each load case 1000 N in total) representing impact forces on the hand either in near-neutral position or ulnar/radial deviation. The load transfer through the trabecular network of the radius was characterized by the tissue strain energy density (SED) distribution for all load cases. It was found that the distribution of the tissue loading depends on the ratio of the forces acting on the carpal bones. For all load cases the higher SED values (on average: 0.02 +/- 0.08 (S.D.) N mm(-2)) are found in a 10 mm region adjacent to the articular surface which corresponds well with the region where Colles- or Chauffeur-fractures occur. We expect that, eventually, this new approach can lead to a better prediction of the fracture risk than methods based on bone density alone since it accounts for the bone microstructure as well as its loading conditions.

Bone structure as revealed by microtomography

The appearance of cancellous bone architecture is different for various skeletal sites and various disease states. In the iliac crest it is more plate-like, whereas in the spine rods dominate. During aging and disease plates are perforated and connecting rods are dissolved. There is a continuous shift from one structural type to the other. So traditional histomorphometric procedures, which are based on a fixed model type, will lead to questionable results. 3D microtomography allows to assess model independent structural parameters so that trabecular thickness, for example, can be determined directly. Not only mean thicknesses are available but also thickness histograms which are helpful to identify pathological states. Other features such as trabecular separation, degree of anisotropy and structural type index can be extracted from the 3D images and allow to characterize cancellous bone and its changes due to aging, disease and treatment. To fully exploit the significance of bone structure on bone strength large scale finite element (FE) analyses are performed. Hence microtomography, performed with a sufficiently fine isotropic spatial resolution, reveals information on the structural features of cancellous bone which were not available so far and which will, hopefully, lead to a better understanding of the pathogenesis of bone diseases and subsequently to improved treatment regimes.

First Results of a Multiple Fan-Beam Approach to Analyze Bone Structure in vivo

Multiple fan-beam CT combines the advantages of fan-beam and cone-beam CT, i.e. the precise reconstructions of the former and the fast (2D) data acquisition of the latter. Two systems had been realized: a 3D-Micro-CT for the examination of bone samples and small laboratory animals with a spatial resolution of 20 micrometer, and a 3D-pQCT system for the examination of patients with a spatial resolution of 120 micrometer. Both system are able to perform complete 3D examinations within two minutes. In this work we report on pilot studies performed with the 3D-pQCT on the distal radius of patients. First results of longitudinal examinations reveal surprising temporal changes of cortical as well as cancellous bone. Hence it is now possible to base the theoretical models on real data and to consider the consequences of structural changes on the mechanical competence of bone in individual patients.