Using Nonlinear Response to Estimate the Strength of an Elastic Network

Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a network to static and periodic strain can be used to estimate its ultimate (or breaking) stress. Since bone fracture in older adults results from the weakening of porous bone, we discuss the possibility of using $\Gamma$ as a non-invasive diagnostic of osteoporotic bone.Comment: 4 pages, 4 figure

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method

Purpose: This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Materials and Methods: Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. Results: The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. Conclusion: The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm. ⓒ 2011 by Korean Academy of Oral and Maxillofacial Radiology

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Is Poorly Associated With Vertebral Strength.

Trabecular bone score (TBS) rests on the textural analysis of dual-energy X-ray absorptiometry (DXA) to reflect the decay in trabecular structure characterizing osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible because prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly owing to an unrealistic setup and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings were used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation ("full vertebra"); 2) via the classical endplate embedding ("vertebral body"); or 3) via a ball joint to induce anterior wedge failure ("vertebral section"). High-resolution peripheral quantitative computed tomography (HR-pQCT) scans acquired from prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (Fexp ) and apparent failure stress (σexp ) was assessed, and their relative contribution to a multilinear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with Fexp and σexp , except for the "vertebral body" case (r(2) = 0.396, p = 0.028). Aside from the "vertebra section" setup where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing setup, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk. © 2015 American Society for Bone and Mineral Research

A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform

BACKGROUND: The degree of anisotropy (DA) on radiographs is related to bone structure, we present a new index to assess DA. METHODS: In a region of interest from calcaneus radiographs, we applied a Fast Fourier Transform (FFT). All the FFT spectra involve the horizontal and vertical components corresponding respectively to longitudinal and transversal trabeculae. By visual inspection, we measured the spreading angles: Dispersion Longitudinal Index (DLI) and Dispersion Transverse Index (DTI) and calculated DA = 180/(DLI+DTI). To test the reliability of DA assessment, we synthesized images simulating radiological projections of periodic structures with elements more or less disoriented. RESULTS: Firstly, we tested synthetic images which comprised a large variety of structures from highly anisotropic structure to the almost isotropic, DA was ranging from 1.3 to 3.8 respectively. The analysis of the FFT spectra was performed by two observers, the Coefficients of Variation were 1.5% and 3.1 % for intra-and inter-observer reproducibility, respectively. In 22 post-menopausal women with osteoporotic fracture cases and 44 age-matched controls, DA values were respectively 1.87 ± 0.15 versus 1.72 ± 0.18 (p = 0.001). From the ROC analysis, the Area Under Curve (AUC) were respectively 0.65, 0.62, 0.64, 0.77 for lumbar spine, femoral neck, total femoral BMD and DA. CONCLUSION: The highest DA values in fracture cases suggest that the structure is more anisotropic in osteoporosis due to preferential deletion of trabeculae in some directions

A retrospective case-control study assessing the role of trabecular bone score in postmenopausal Caucasian women with osteopenia: analyzing the odds of vertebral fracture.

This case-control study assessed whether the trabecular bone score (TBS), determined from gray-level analysis of DXA images, might be of any diagnostic value, either alone or combined with bone mineral density (BMD), in the assessment of vertebral fracture risk among postmenopausal women with osteopenia. Of 243 postmenopausal Caucasian women, 50-80 years old, with BMD T-scores between -1.0 and -2.5, we identified 81 with osteoporosis-related vertebral fractures and compared them with 162 age-matched controls without fractures. Primary outcomes were BMD and TBS. For BMD, each incremental decrease in BMD was associated with an OR = 1.54 (95% CI = 1.17-2.03), and the AUC was 0.614 (0.550-0.676). For TBS, corresponding values were 2.53 (1.82-3.53) and 0.721 (0.660-0.777). The difference in the AUC for TBS vs. BMD was statistically significant (p = 0.020). The OR for (TBS + BMD) was 2.54 (1.86-3.47) and the AUC 0.732 (0.672-0.787). In conclusion, the TBS warrants a closer look to see whether it may be of clinical usefulness in the determination of fracture risk in postmenopausal osteopenic women

Micro-imagerie par résonance magnétique nucléaire : application à la structure trabéculaire osseuse

International audienceL'ostéoporose est une maladie caractérisée par une baisse de densité osseuse et une altération de la microarchitecture trabéculaire. Le but de ce travail est la validation d'une technique d'évaluation de l'architecture osseuse effectuée à partir de clichés radiographiques. Dans une première phase, nous avons mis en place un protocole expérimental permettant de reconstruire un modèle numérique 3D du tissu osseux à partir de la technique d'imagerie par résonance magnétique (IRM). Différents outils de caractérisation 3D, tant morphologiques que topologiques, ainsi qu'un outil de simulation numérique du processus radiographique ont été développés et appliqués sur ce modèle. Dans une deuxième phase, nous utiliserons ces outils afin de mettre en évidence des corrélations entre les caractéristiques 3D de la structure et celles de sa projection radiographique

Micro-imagerie par résonance magnétique nucléaire : application à la structure trabéculaire osseuse

L'ostéoporose est une maladie caractérisée par une baisse de densité osseuse et une altération de la microarchitecture trabéculaire. Le but de ce travail est la validation d'une technique d'évaluation de l'architecture osseuse effectuée à partir de clichés radiographiques. Dans une première phase, nous avons mis en place un protocole expérimental permettant de reconstruire un modèle numérique 3D du tissu osseux à partir de la technique d'imagerie par résonance magnétique (IRM). Différents outils de caractérisation 3D, tant morphologiques que topologiques, ainsi qu'un outil de simulation numérique du processus radiographique ont été développés et appliqués sur ce modèle. Dans une deuxième phase, nous utiliserons ces outils afin de mettre en évidence des corrélations entre les caractéristiques 3D de la structure et celles de sa projection radiographique

A new computational efficient approach for trabecular bone analysis using beam models generated with skeletonized graph technique

Micro-finite element (FE) analysis is a well established technique for the evaluation of the elasticproperties of trabecular bone, but is limited in its application due to the large number of elements that itrequires to represent the complex internal structure of the bone. In this paper, we present an alternative FE approach that makes use of a recently developed 3D-line Skeleton Graph Analysis (LSGA) technique to represent the complex internal structure of trabecular bone as a network of simple straight beam elements in which the beams are assigned geometrical properties of the trabeculae that they represent. Since an enormous reduction of cputime can be obtained with this beam modeling approach, ranging from approximately 1,200 to 3,600 for the problems investigated here, we think that the FE modeling technique that we introduced could potentially constitute an interesting alternative for the evaluation of the elastic mechanical properties of trabecular bone