A. Odgaard
http://repub.eur.nl/ppl/18112/
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RePub, Erasmus University RepositoryParallel plate model for trabecular bone exhibits volume fraction-dependent bias
http://repub.eur.nl/pub/15365/
Wed, 01 Nov 2000 00:00:01 GMT<div>J.S. Day</div><div>M. Ding</div><div>A. Odgaard</div><div>D.R. Sumner</div><div>I. Hvid</div><div>H.H. Weinans</div>
Unbiased stereological methods were used in conjunction with microcomputed tomographic (micro-CT) scans of human and animal bone to investigate errors created when the parallel plate model was used to calculate morphometric parameters. Bone samples were obtained from the human proximal tibia, canine distal femur, rat tail, and pig spine and scanned in a micro-CT scanner. Trabecular thickness, trabecular spacing, and trabecular number were calculated using the parallel plate model. Direct thickness, and spacing and connectivity density were calculated using unbiased three-dimensional methods. Both thickness and spacing calculated using the plate model were well correlated to the direct three-dimensional measures (r(2) = 0. 77-0.92). The correlation between trabecular number and connectivity density varied greatly (r(2) = 0.41-0.94). Whereas trabecular thickness was consistently underestimated using the plate model, trabecular spacing was underestimated at low volume fractions and overestimated at high volume fractions. Use of the plate model resulted in a volume-dependent bias in measures of thickness and spacing (p < 0.001). This was a result of the fact that samples of low volume fraction were much more "rod-like" than those of the higher volume fraction. Our findings indicate that the plate model provides biased results, especially when populations with different volume fractions are compared. Therefore, we recommend direct thickness measures when three-dimensional data sets are available.A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models
http://repub.eur.nl/pub/15269/
Sun, 01 Jan 1995 00:00:01 GMT<div>R. van Rietbergen</div><div>H.H. Weinans</div><div>R. Huiskes</div><div>A. Odgaard</div>
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.