Digital Topology on Adaptive Octree Grids

The theory of digital topology is used in many different image processing and computer graphics algorithms. Most of the existing theories apply to uniform cartesian grids, and they are not readily extensible to new algorithms targeting at adaptive cartesian grids. This article provides a rigorous extension of the classical digital topology framework for adaptive octree grids, including the characterization of adjacency, connected components, and simple points. Motivating examples, proofs of the major propositions, and algorithm pseudocodes are provided.

Dynamic simulation of three dimensional architectural and mechanical alterations in human trabecular bone during menopause

A three dimensional (3D) computational simulation of dynamic process of trabecular bone remodeling was developed with all the parameters derived from physiological and clinical data. Contributions of the microstructural bone formation deficits: trabecular plate perforations, trabecular rod breakages, and isolated bone fragments, to the rapid bone loss and disruption of trabecular microarchitecture during menopause were studied. Eighteen human trabecular bone samples from femoral neck (FN) and spine were scanned using a micro computed tomography (microCT) system. Bone resorption and formation were simulated as a computational cycle corresponding to 40-day resorption/160-day formation. Resorption cavities were randomly created over the bone surface according to the activation frequency, which was strictly based on clinical data. Every resorption cavity was refilled during formation unless it caused trabecular plate perforation, trabecular rod breakage or isolated fragments. A 20-year-period starting 5 years before and ending 15 years after menopause was simulated for each specimen. Elastic moduli, standard and individual trabeculae segmentation (ITS)-based morphological parameters were evaluated for each simulated 3D image. For both spine and FN groups, the time courses of predicted bone loss pattern by microstructural bone formation deficits were fairly consistent with the clinical measurements. The percentage of bone loss due to trabecular plate perforation, trabecular rod breakage, and isolated bone fragments were 73.2%, 18.9% and 7.9% at the simulated 15 years after menopause. The ITS-based plate fraction (pBV/BV), mean plate surface area (pTb.S), plate number density (pTb.N), and mean rod thickness (rTb.Th) decreased while rod fraction (rBV/BV) and rod number density (rTb.N) increased after the simulated menopause. The dynamic bone remodeling simulation based on microstructural bone formation deficits predicted the time course of menopausal bone loss pattern of spine and FN. Microstructural plate perforation could be the primary cause of menopausal trabecular bone loss. The combined effect of trabeculae perforation, breakage, and isolated fragments resulted in fewer and smaller trabecular plates and more but thinner trabecular rods.

Adaptations in trabecular bone microarchitecture in Olympic athletes determined by 7T MRI

PURPOSE

To produce in vivo high-resolution images of the knee and to determine the feasibility of using 7T MR to detect changes in trabecular bone microarchitecture in elite athletes (Olympic fencers) who undergo high impact activity.

MATERIALS AND METHODS

The dominant knees of four males from the U.S. Olympic Fencing Team and three matched healthy male controls were scanned in a 7T whole-body scanner using a quadrature knee coil with three-dimensional (3D) fast low angle shot (FLASH): 50 axial images at the distal femur (0.156 mm x 0.156 mm) and 80 axial images at the knee joint (0.195 mm x 0.195 mm). Bone volume fraction (BVF) and marrow volume fraction (MVF) images were computed and fuzzy distance transform (FDT) and digital topological analysis (DTA) were applied to determine: trabecular number (Tb.N), trabecular thickness (Tb.Th), and trabecular separation (Tb.Sp); BVF (BV/TV); trabecular and marrow space surface-to-curve ratio (SC, marker of plate to rod ratio); and trabecular and marrow space erosion index (EI, inverse marker for network connectivity). Quadriceps muscle volume (MV) was calculated as well. We calculated group means and performed two-tailed t-tests to determine statistical significance.

RESULTS

Compared to controls, fencers had: decreased Tb.Sp (P = 0.0082 at femur, P = 0.051 at joint); increased Tb.N (P < 0.05 at both femur and joint) and BV/TV (P < 0.001 at both femur and joint); increased trabecular SC and decreased marrow space SC (P < 0.01 at both femur and joint); decreased trabecular EI and increased marrow space EI (P < 0.01 at both femur and joint); and increased MV (P = 0.038). There was no difference in Tb.Th at the distal femur (P = 0.92) or joint (P = 0.71) between groups.

CONCLUSION

To our knowledge, this is the first study to perform 7T MRI of the knee in vivo. Elite athletes who undergo high impact activity have increased MV and improved trabecular bone structure compared to controls.

Complete volumetric decomposition of individual trabecular plates and rods and its morphological correlations with anisotropic elastic moduli in human trabecular bone

Trabecular plates and rods are important microarchitectural features in determining mechanical properties of trabecular bone. A complete volumetric decomposition of individual trabecular plates and rods was used to assess the orientation and morphology of 71 human trabecular bone samples. The ITS-based morphological analyses better characterize microarchitecture and help predict anisotropic mechanical properties of trabecular bone.

INTRODUCTION

Standard morphological analyses of trabecular architecture lack explicit segmentations of individual trabecular plates and rods. In this study, a complete volumetric decomposition technique was developed to segment trabecular bone microstructure into individual plates and rods. Contributions of trabecular type-associated morphological parameters to the anisotropic elastic moduli of trabecular bone were studied.

MATERIALS AND METHODS

Seventy-one human trabecular bone samples from the femoral neck (FN), tibia, and vertebral body (VB) were imaged using muCT or serial milling. Complete volumetric decomposition was applied to segment trabecular bone microstructure into individual plates and rods. The orientation of each individual trabecula was determined, and the axial bone volume fractions (aBV/TV), axially aligned bone volume fraction along each orthotropic axis, were correlated with the elastic moduli. The microstructural type-associated morphological parameters were derived and compared with standard morphological parameters. Their contributions to the anisotropic elastic moduli, calculated by finite element analysis (FEA), were evaluated and compared.

RESULTS

The distribution of trabecular orientation suggested that longitudinal plates and transverse rods dominate at all three anatomic sites. aBV/TV along each axis, in general, showed a better correlation with the axial elastic modulus (r(2) = 0.95 approximately 0.99) compared with BV/TV (r(2) = 0.93 approximately 0.94). The plate-associated morphological parameters generally showed higher correlations with the corresponding standard morphological parameters than the rod-associated parameters. Multiple linear regression models of six elastic moduli with individual trabeculae segmentation (ITS)-based morphological parameters (adjusted r(2) = 0.95 approximately 0.98) performed equally well as those with standard morphological parameters (adjusted r(2) = 0.94 approximately 0.97) but revealed specific contributions from individual trabecular plates or rods.

CONCLUSIONS

The ITS-based morphological analyses provide a better characterization of the morphology and trabecular orientation of trabecular bone. The axial loading of trabecular bone is mainly sustained by the axially aligned trabecular bone volume. Results suggest that trabecular plates dominate the overall elastic properties of trabecular bone.

Quantification of the roles of trabecular microarchitecture and trabecular type in determining the elastic modulus of human trabecular bone

The roles of microarchitecture and types of trabeculae in determining elastic modulus of trabecular bone have been studied in microCT images of 29 trabecular bone samples by comparing their Young's moduli calculated by finite element analysis (FEA) with different trabecular type-specific reconstructions. The results suggest that trabecular plates play an essential role in determining elastic properties of trabecular bone.

INTRODUCTION

Osteoporosis is an age-related disease characterized by low bone mass and architectural deterioration. Other than bone volume fraction (BV/TV), microarchitecture of bone is also believed to be important in governing mechanical properties of trabecular bone. We quantitatively examined the role of microarchitecture and relative contribution of trabecular types of individual trabecula in determining the elastic property of trabecular bone.

MATERIALS AND METHODS

Twenty-nine human cadaveric trabecular bone samples were scanned at 21-mum resolution using a microCT system. Digital topological analysis (DTA) consisting of skeletonization and classification was combined with a trabecular type-specific reconstruction technique to extract the skeleton and identify topological type of trabeculae of the original trabecular bone image. Four different microCT-based finite element (FE) models were constructed for each specimen: (1) original full voxel; (2) skeletal voxel; (3) rod-reconstructed, preserving rod volume and plate skeleton; and (4) plate-reconstructed, preserving plate volume and rod skeleton. For each model, the elastic moduli were calculated under compression along each of three image-coordinate axis directions. Plate and rod tissue fractions directly measured from DTA-based topological classification were correlated with the elastic moduli computed from full voxel model.

RESULTS

The elastic moduli of skeleton models were significantly correlated with those of full voxel models along all three coordinate axes (r(2) = 0.38 approximately 0.53). The rod-reconstructed model contained 21.3% of original bone mass and restored 1.5% of elastic moduli, whereas the plate-reconstructed model contained 90.3% of bone mass and restored 53.2% of elastic moduli. Plate tissue fraction showed a significantly positive correlation (r(2) = 0.49) with elastic modulus by a power law, whereas rod tissue fraction showed a significantly negative correlation (r(2) = 0.42).

CONCLUSIONS

These results quantitatively show that the microarchitecture alone affects elastic moduli of trabecular bone and trabecular plates make a far greater contribution than rods to the bone's elastic behavior.