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J Kabel

Publications and source records attributed to J Kabel.

10 recordsLinked to original sources
PubMed2000

Properties of growing trabecular ovine bone. Part II: architectural and mechanical properties.

We aimed to highlight the relationship between age and the architectural properties of trabecular bone, to outline the patterns in which the variations in these properties take place, and to investigate the influence of the architecture on the mechanical properties of trabecular bone in growing animals. We studied 30 lambs in three age groups and 20 sheep in two age groups. Cubes of subchondral bone were cut from the proximal tibia according to a standardised protocol. They were serially sectioned and their architectural properties were determined. Similar cubes were obtained from the identical anatomical position of the contralateral tibia and their compressive mechanical properties measured. The values obtained from the skeletally immature and mature individuals were compared. Multiple regression analyses were performed between the architectural and the mechanical properties. The bone volume fraction, the mean trabecular volume, the architectural and the mechanical anisotropy, the elastic modulus, the bone strength, the energy absorption to failure, and the elastic energy correlated positively with increasing age whereas the connectivity density, the bone surface density, the ultimate strain, the absorption of viscoelastic energy and the relative loss of energy correlated inversely. The values of all variables were significantly different in the skeletally mature and immature groups. We determined the patterns in which the variations took place. The bone volume fraction of the trabecular bone tissue was found to be the major predictor of its compressive mechanical properties. Together with the mean trabecular volume and the bone surface density, it explained 81% of the variations in the compressive elastic modulus of specimens obtained from the contralateral tibiae.

Age Factors↗
PubMed1999

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone.

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.

Animals↗
PubMed1999

Connectivity and the elastic properties of cancellous bone.

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14-91 years and a wide range of trabecular architecture was found. Each specimen was three-dimensionally reconstructed with a voxel size of either 20 or 25 microm. Using the detailed three-dimensional reconstructions as input for microstructural finite-element models, the complete elastic properties of the trabecular architecture were obtained and maximum and mean stiffness could be calculated. Volume fraction and true three-dimensional architectural measurements of connectivity density and surface density were determined. Connectivity density was determined in an unbiased manner by the Euler number, which is a topological property. Using multiple regression analysis it was found that volume fraction explained by far the greatest part (84%-94%) of the variation in both mean and maximum stiffness. When connectivity density and surface density were included, the correlations increased marginally to 89%-95%. Noticeably negative regression coefficients were found for connectivity density. The results suggest that, in normal cancellous bone, the connectivity density has very limited value for assessment of elastic properties by morphological variables, but if a relation exists then stiffness decreases with increasing connectivity.

Adolescent↗
PubMed1999

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture.

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.

Adolescent↗
PubMed1998

Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions.

It would be advantageous if the mechanical properties of trabecular bone could be directly inferred from stereomorphometric parameters. For that purpose, apparent density and mean intercept length, as measures of bone mass and directionality (fabric), are commonly correlated with the elastic characteristics of bone samples, as determined in compression tests. However, complete and accurate relationships have not yet been established in this way. This may be due not only to the occurrence of artifacts in both the stereomorphometric and the mechanical assessments but also to an inherent inadequacy of mean intercept length in characterizing the full mechanical significance of bone architecture or nonhomogeneities in trabecular tissue properties not accounted for in stereomorphometry. In this study, we introduce a computer modeling approach allowing these biases to be eliminated. With use of high-resolution three-dimensional computer reconstructions of trabecular bone specimens for stereomorphometry and for microstructural finite element models to simulate mechanical tests, unbiased comparisons become feasible. The purpose was to investigate if accurate and complete relationships can be established in this way. Four different fabric measures were considered: mean intercept length and three volume-based ones. Compliance matrices were calculated from fabric tensors, with use of the mathematical relationship proposed by Cowin for 29 vertebral whale-bone specimens. These were correlated with the compliance constants determined directly from the microstructural finite element model simulation. The nine orthotropic elastic constants of all 29 specimens were well predicted from their stereomorphometric fabric and volume fraction values, with correlation coefficients ranging from R2adj = 0.9934 to 0.9963. When individual compliance components were considered (1/Ei, 1/Gij, or -v[ij]/Ei), correlation coefficients ranged from R2adj = 0.924 to 0.982. All four fabric measures performed equally well. It is concluded that volume fraction and fabric measures correlate highly with the apparent elastic properties of bone samples, provided that anisotropy and nonhomogeneity in the elastic properties of the trabecular tissue itself have negligible effects on the apparent properties. Whether this is true for bone in general remains to be seen, as only a subset was analyzed here. These methods, however, can be valuable in similar assessments of other subsets.

Animals↗
PubMed1997

Fabric and elastic principal directions of cancellous bone are closely related.

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.

Animals↗
PubMed1997

Age variations in the properties of human tibial trabecular bone.

We tested in compression specimens of human proximal tibial trabecular bone from 31 normal donors aged from 16 to 83 years and determined the mechanical properties, density and mineral and collagen content. Young's modulus and ultimate stress were highest between 40 and 50 years, whereas ultimate strain and failure energy showed maxima at younger ages. These age-related variations (except for failure energy) were non-linear. Tissue density and mineral concentration were constant throughout life, whereas apparent density (the amount of bone) varied with ultimate stress. Collagen density (the amount of collagen) varied with failure energy. Collagen concentration was maximal at younger ages but varied little with age. Our results suggest that the decrease in mechanical properties of trabecular bone such as Young's modulus and ultimate stress is mainly a consequence of the loss of trabecular bone substance, rather than a decrease in the quality of the substance itself. Linear regression analysis showed that collagen density was consistently the single best predictor of failure energy, and collagen concentration was the only predictor of ultimate strain.

Adolescent↗
PubMed1996

Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture.

A method is presented to find orthotropic elastic symmetries and constants directly from the elastic coefficients in the overall stiffness matrix of trabecular bone test specimens. Contrary to earlier developed techniques, this method does not require pure orthotropic behavior or additional fabric measurements. The method uses high-resolution computer reconstructions of trabecular bone specimens as input for large-scale FE-analyses to determine all the 21 elastic coefficients in the overall stiffness matrix of the specimen, using a direct mechanics approach. An optimization procedure is then used to find the coordinate transformation that yields the best orthotropic representation of this matrix. The method is illustrated here relative to two trabecular bone specimens. The techniques developed here can be used to obtain a complete characterization of the mechanical properties of trabecular architecture. With the development of in vivo reconstruction techniques, even in vivo measurements will be possible.

Algorithms↗
PubMedDate not supplied

The anisotropic Hooke's law for cancellous bone and wood.

A method of data analysis for a set of elastic constant measurements is applied to data bases for wood and cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to hardwoods and softwoods, and to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke's law for cancellous bone and a bulk density dependent one for hardwoods and softwoods.

Anisotropy↗