Finite element (FE) models of long bones constructed from computed-tomography (CT) data are emerging as an invaluable tool in the field of bone biomechanics. However, the performance of such FE models is highly dependent on the accurate capture of geometry and appropriate assignment of material properties. In this study, a combined numerical-experimental study is performed comparing FE-predicted surface strains with strain-gauge measurements. Thirty-six major, cadaveric, long bones (humerus, radius, femur and tibia), which cover a wide range of bone sizes, were tested under three-point bending and torsion. The FE models were constructed from trans-axial volumetric CT scans, and the segmented bone images were corrected for partial-volume effects. The material properties (Young's modulus for cortex, density-modulus relationship for trabecular bone and Poisson's ratio) were calibrated by minimizing the error between experiments and simulations among all bones. The R(2) values of the measured strains versus load under three-point bending and torsion were 0.96-0.99 and 0.61-0.99, respectively, for all bones in our dataset. The errors of the calculated FE strains in comparison to those measured using strain gauges in the mechanical tests ranged from -6% to 7% under bending and from -37% to 19% under torsion. The observation of comparatively low errors and high correlations between the FE-predicted strains and the experimental strains, across the various types of bones and loading conditions (bending and torsion), validates our approach to bone segmentation and our choice of material properties.

In computed tomography (CT), the representation of edges between objects of different densities is influenced by the limited spatial resolution of the scanner. This results in the misrepresentation of density of narrow objects, leading to errors of up to 70% and more. Our interest is in the imaging and measurement of narrow bone structures, and the issues are the same for imaging with clinical CT scanners, peripheral quantitative CT scanners or micro CT scanners. Mathematical models, phantoms and tests with patient data led to the following procedures: (i) extract density profiles at one-degree increments from the CT images at right angles to the bone boundary; (ii) consider the outer and inner edge of each profile separately due to different adjacent soft tissues; (iii) measure the width of each profile based on a threshold at fixed percentage of the difference between the soft-tissue value and a first approximated bone value; (iv) correct the underlying material density of bone for each profile based on the measured width with the help of the density-versus-width curve obtained from computer simulations and phantom measurements. This latter curve is specific to a certain scanner and is not dependent on the densities of the tissues within the range seen in patients. This procedure allows the calculation of the material density of bone. Based on phantom measurements, we estimate the density error to be below 2% relative to the density of normal bone and the bone-width error about one tenth of a pixel size.

Summary New models describing anthropometrically adjusted normal values of bone mineral density and content in children have been created for the various measurement sites. The inclusion of multiple explanatory variables in the models provides the opportunity to calculate Z-scores that are adjusted with respect to the relevant anthropometric parameters. Introduction Previous descriptions of children’s bone mineral measurements by age have focused on segmenting diverse populations by race and sex without adjusting for anthropometric variables or have included the effects of a single anthropometric variable. Methods We applied multivariate semi-metric smoothing to the various pediatric bone-measurement sites using data from the Bone Mineral Density in Childhood Study to evaluate which of sex, race, age, height, weight, percent body fat, and sexual maturity explain variations in the population’s bone mineral values. By balancing high adjusted R2 values with clinical needs, two models are examined. Results At the spine, whole body, whole body sub head, total hip, hip neck, and forearm sites, models were created using sex, race, age, height, and weight as well as an additional set of models containing these anthropometric variables and percent body fat. For bone mineral density, weight is more important than percent body fat, which is more important than height. For bone mineral content, the order varied by site with body fat being the weakest component. Including more anthropometrics in the model reduces the overlap of the critical groups, identified as those individuals with a Z-score below −2, from the standard sex, race, and age model. Conclusions If body fat is not available, the simpler model including height and weight should be used. The inclusion of multiple explanatory variables in the models provides the opportunity to calculate Z-scores that are adjusted with respect to the relevant anthropometric parameters.

Summary-A new model describing normal values of bone mineral density in children has been evaluated, which includes not only the traditional parameters of age, gender, and race, but also weight, height, percent body fat, and sexual maturity. This model may constitute a better comparative norm for a specific child with given anthropometric values.Introduction-Previous descriptions of children's bone mineral density (BMD) by age have focused on segmenting diverse populations by race and gender without adjusting for anthropometric variables or have included the effects of anthropometric variables over a relatively homogeneous population.