Three-dimensional-line skeleton graph analysis of high-resolution magnetic resonance images: a validation study from 34-microm-resolution microcomputed tomography

Three-dimensional morphometric properties of rod- and plate-like trabeculae in adolescent cancellous bone

Background/Objective

Despite many researches have been carried out on the three-dimensional microarchitecture of cancellous bone, the morphometric properties of rod and plate trabeculae in adolescent cancellous bone have not yet been investigated. This study aimed to investigate three-dimensional morphometric properties of rod- and plate-like trabeculae in normal adolescent cancellous bone, and to compare them with adult cancellous bones to reveal morphometric changes from adolescence to adult life to obtain more insight into the subchondral bone adaptations during development and growth.

Methods

This study included 23 normal human proximal tibiae. These tibiae were divided into three groups: adolescents (9–17 years, n = 6), young adults (18–24 years, n = 9), and adults (25–30 years, n = 8). From each tibia, six cubic cancellous bone samples (dimensions 8 × 8 × 8 mm³) were sawed from each medial and lateral condyle, yielding a total of 276 samples. These samples were scanned using micro computed tomography leading to three-dimensional cubic voxel sizes of 10.5 × 10.5 × 10.5 μm³. The morphometric parameters of individual rod- and plate-like trabeculae were calculated and compared among three age groups.

Results

Significant differences in some morphometric parameters were revealed. The mean longitudinal length of rods was significantly greater in the adolescents than in the young adults. Plate volume density showed an increasing trend with age, although not significant. Trabeculae were more plate-like in adolescents in the medial condyle of adolescents than in the lateral condyle, and changed towards more plate-like trabeculae in the adults. The single best predictor for the mechanical properties was apparent density. Apparent density alone explained 59% variations in Young’s modulus, 77% in ultimate stress and 34% in failure energy, respectively (all p < 0.01). Morphometric parameters might improve this prediction.

Conclusion

In conclusion, this study has reported for the first time the morphometric parameters of rod- and plate-like trabeculae in adolescent proximal tibial cancellous bone, which will improve our understanding of morphometric changes in individual trabeculae during development and growth. Furthermore, separate analysis of individual rods and plates may also help reveal disease-related morphometric changes beyond bone mineral density.

The translational potential of this article

A thorough quantification of individual trabeculae during development and growth may help understand disease-related 3-D morphometric changes beyond bone mineral density.

Digital Topology and Geometry in Medical Imaging: A Survey

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

Morphology analysis of vertebral trabecular bone under dynamic loading based on multi-scale theory

Trabecular bone has a complicated porous microstructure and consists of interconnected plates and rods known as trabeculae. The microarchitecture of the trabeculae contributes to load distribution capacity and, particularly, the optimal bone strength. Many previous studies have shown that morphological parameters are used to characterize the microarchitecture of trabecular bone, but little is known about the mechanical role of trabecular morphology in the context of load-bearing behavior. Therefore, this study proposes a new segmentation method for examining the morphology of trabecular structure foci of load-bearing capability. A micro-finite element model of trabecular bone was obtained from the fourth lumbar vertebra on the basis of a three-dimensionally reconstructed micro-computed tomography (CT) image. We used an asymptotic homogenization method to determine microscopic stress by applying three unidirectional compressive loads in the vertical, anteroposterior, and right-left axes of two trabecular bone volumes. We then classified the complicated trabecular microstructure into three segments: primary and secondary trabeculae and trabeculae of no contribution. Next, a dynamic analysis was conducted by applying a force impulse load. The result indicated that 1/3 of the trabecular volume functions as primary trabecula. The morphology of the trabecular network could be visualized successfully highlighting the percolation of the stress wave in the primary trabecular segment. Further, we found that the role of the plate-like structures was that of a hub in the trabecular network system.

Noninvasive imaging of bone microarchitecture

The noninvasive quantification of peripheral compartment-specific bone microarchitecture is feasible with high-resolution peripheral quantitative computed tomography (HR-pQCT) and high-resolution magnetic resonance imaging (HR-MRI). In addition to classic morphometric indices, both techniques provide a suitable basis for virtual biomechanical testing using finite element (FE) analyses. Methodical limitations, morphometric parameter definition, and motion artifacts have to be considered to achieve optimal data interpretation from imaging studies. With increasing availability of in vivo high-resolution bone imaging techniques, special emphasis should be put on quality control including multicenter, cross-site validations. Importantly, conclusions from interventional studies investigating the effects of antiosteoporotic drugs on bone microarchitecture should be drawn with care, ideally involving imaging scientists, translational researchers, and clinicians.

3D shape-dependent thinning method for trabecular bone characterization

PURPOSE

Curve and surface thinning are widely-used skeletonization techniques for modeling objects in three dimensions. In the case of trabecular bone analysis, however, neither curve nor surface thinning is really efficient since the internal geometry of the object is usually composed of both rod and plate shapes. The purpose of this paper is to propose an original method called hybrid skeleton which better matches the geometry of the data compared to curve and surface skeletons. In the hybrid skeleton algorithm, 1D curves represent rod-shaped zones whereas 2D surfaces represent plate-shaped elements.

METHODS

The proposed hybrid skeleton algorithm is based on a combination of three methods. (1) A new variant of the method proposed by Bonnassie et al. for the classification of voxels as belonging to plate-like or rod-like structures, where the medial axis (MA) algorithm is replaced by a fast and connected skeletonization algorithm. In addition, the reversibility of the MA algorithm is replaced by an isotropic region-growth method to spread the rod and plate labels back to the original object. (2) A well chosen surface thinning method applied on the plate voxels set. (3) A well chosen curve skeleton thinning method applied on the rod voxels set. The efficiency and the robustness of the proposed algorithm were evaluated using synthesis test vectors. A clinical study was led on micro-CT (computed tomography) images of two different populations of osteoarthritic and osteoporotic trabecular bone samples. The morphological and topological characteristics of the two populations were evaluated using the proposed hybrid skeleton as well as the classification algorithm.

RESULTS

When evaluated on test vectors and compared to Bonnassie's algorithm, the proposed classification algorithm gives a slightly better rate of classification. The hybrid skeleton preserves the shape information of the processed objects. Interesting morphological and topological features as well as volumetric ones were extracted from the skeleton and from the classified volumes, respectively. The extracted features enable the two populations of osteoarthritic and osteoporotic trabecular bone samples to be distinguished.

CONCLUSIONS

Compared to curve-based or surface-based skeletons, the hybrid skeleton better matches the geometry of the data. Each rod is represented by a one-voxel-thick arc and each plate is represented by a one-voxel-thick surface. The hybrid skeleton as well as the proposed classification algorithm introduce relevant parameters linked to the presence of plates in the trabecular bone data, showing that rods and plates contain independent information about trabeculae. The hybrid skeleton offers a new opportunity for precise studies of porous media such as trabecular bone.

Effect of subvoxel processes on non-destructive characterization of β-tricalcium phosphate bone graft substitutes

The geometric features of bone graft substitutes, such as the pore and pore interconnection sizes, are of paramount importance for their biological performance. Such features are generally characterized by micro-computed tomography (μCT). Unfortunately, the resolution of μCT is often too limited. The aim of this study was to look at the effect of μCT resolution on the geometric characterization of four different bone graft substitutes. An attempt was also made to improve the characterization of these materials by applying a subvoxelization algorithm. The results revealed that both approaches increased the accuracy of the geometric characterization. They also showed that the interconnection size in particular was affected. Comparing the results obtained from the scanned and numerical subvoxelization datasets revealed a minor difference of less than 2.5% for the porosity values. The difference for the pore sizes was up to 10%. Considerable differences of up to 35-50% were found for the interconnection sizes. The present study demonstrates how complex geometric characterization is and how important it is for biomaterial researchers to be aware of the impact of μCT resolution on the pore and pore interconnection sizes.

Local plate/rod descriptors of 3D trabecular bone micro-CT images from medial axis topologic analysis

PURPOSE

Trabecular bone microarchitecture is made of a complex network of plate and rod structures evolving with age and disease. The purpose of this article is to propose a new 3D local analysis method for the quantitative assessment of parameters related to the geometry of trabecular bone microarchitecture.

METHODS

The method is based on the topologic classification of the medial axis of the 3D image into branches, rods, and plates. Thanks to the reversibility of the medial axis, the classification is next extended to the whole 3D image. Finally, the percentages of rods and plates as well as their mean thicknesses are calculated. The method was applied both to simulated test images and 3D micro-CT images of human trabecular bone.

RESULTS

The classification of simulated phantoms made of plates and rods shows that the maximum error in the quantitative percentages of plate and rods is less than 6% and smaller than with the structure model index (SMI). Micro-CT images of human femoral bone taken in osteoporosis and early or advanced osteoarthritis were analyzed. Despite the large physiological variability, the present method avoids the underestimation of rods observed with other local methods. The relative percentages of rods and plates were not significantly different between osteoarthritis and osteoporotic groups, whereas their absolute percentages were in relation to an increase of rod and plate thicknesses in advanced osteoarthritis with also higher relative and absolute number of nodes.

CONCLUSIONS

The proposed method is model-independent, robust to surface irregularities, and enables geometrical characterization of not only skeletal structures but entire 3D images. Its application provided more accurate results than the standard SMI on simple simulated phantoms, but the discrepancy observed on the advanced osteoarthritis group raises questions that will require further investigations. The systematic use of such a local method in the characterization of trabecular bone samples could provide new insight in bone microarchitecture changes related to bone diseases or to those induced by drugs or therapy.

Experimental bone biopsies using two bone biopsy needles: quantitative micro-CT analysis of bone specimens

RATIONALE AND OBJECTIVES

The aim of this study was to investigate whether samples obtained using two kinds of small trephines, 2.4 and 1.8 mm in inner diameter, are sufficient for the quantitative evaluation of metabolic bone disease using micro-computed tomographic (CT) three-dimensional parameter data sets.

MATERIALS AND METHODS

A total of 19 porcine lumbar vertebrae prior to biopsy and biopsy samples from the use of 2.4- and 1.8-mm trephines were examined using micro-CT imaging. For quantitative analysis, seven three-dimensional structural parameters, including trabecular bone volume, trabecular number, trabecular thickness, trabecular separation, the structure model index, the degree of anisotropy, and the trabecular bone pattern factor, were measured using CtAn software. The difference and agreement between the biopsy samples and the baseline vertebrae specimens before biopsy were assessed using paired t tests and Bland-Altman analysis, respectively.

RESULTS

There were no significant differences between the 2.4-mm samples and the baseline vertebrae specimens for trabecular bone volume, trabecular thickness, and trabecular number, with mean differences of -0.9%, 2.3%, and -3.1%, respectively; there was no significant difference between the 1.8-mm samples and the baseline vertebrae specimens only for trabecular thickness, with a mean difference of 1.9%.

CONCLUSION

Samples taken from the use of the 2.4-mm trephine were better for quantitative analysis than those from the use of the 1.8-mm trephine and were acceptable for the quantitative evaluation of trabecular bone volume, trabecular thickness, and trabecular number.

Fuzzy logic structure analysis of trabecular bone of the calcaneus to estimate proximal femur fracture load and discriminate subjects with and without vertebral fractures using high-resolution magnetic resonance imaging at 1.5 T and 3 T

Newly developed fuzzy logic-derived structural parameters were used to characterize trabecular bone architecture in high-resolution magnetic resonance imaging (HR-MRI) of human cadaver calcaneus specimens. These parameters were compared to standard histomorphological structural measures and analyzed concerning performance in discriminating vertebral fracture status and estimating proximal femur fracture load. Sets of 60 sagittal 1.5 T and 3.0 T HR-MRI images of the calcaneus were obtained in 39 cadavers using a fast gradient recalled echo sequence. Structural parameters equivalent to bone histomorphometry and fuzzy logic-derived parameters were calculated using two chosen regions of interest. Calcaneal, spine, and hip bone mineral density (BMD) measurements were also obtained. Fracture status of the thoracic and lumbar spine was assessed on lateral radiographs. Finally, mechanical strength testing of the proximal femur was performed. Diagnostic performance in discriminating vertebral fracture status and estimating femoral fracture load was calculated using regression analyses, two-tailed t-tests of significance, and receiver operating characteristic (ROC) analyses. Significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters (r up to 0.92). Correlations between histomorphological or fuzzy logic parameters and calcaneal BMD were mostly significant (r up to 0.78). ROC analyses demonstrated that standard structural parameters were able to differentiate persons with and without vertebral fractures (area under the curve [A(Z)] up to 0.73). However, none of the parameters obtained in the 1.5-T images and none of the fuzzy logic parameters discriminated persons with and without vertebral fractures. Significant correlations were found between fuzzy or structural parameters and femoral fracture load. Using multiple regression analysis, none of the structural or fuzzy parameters were found to add discriminative value to BMD alone. In summary significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters. However, fuzzy logic-based calcaneal parameters were not well suited for vertebral fracture discrimination. Although significant correlations were found between fuzzy or structural parameters and femoral fracture load, multiple regression analysis showed limited improvement for estimating femoral failure load in addition to femoral BMD alone. Local femoral measurements are still needed to estimate femoral bone strength. Overall, parameters obtained at 3.0 T performed better than those at 1.5 T.

Structural and functional assessment of trabecular and cortical bone by micro magnetic resonance imaging

Osteoporosis is a multifactorial disorder of bone mineral homeostasis affecting the elderly. It is a major public health issue with significant socioeconomic consequences. Recent findings suggest that bone loss-the key manifestation of the disease-is accompanied by architectural deterioration, both affecting the bone's mechanical competence and susceptibility to fracture. This article reviews the potential of quantitative micro MRI (mu-MRI), including a discussion of the technical requirements for image acquisition, processing, and analysis for assessing the architectural implications of osteoporosis and as a means to monitor the response to treatment. With current technology, the resolution achievable in clinically acceptable scan times and necessary signal-to-noise ratio (SNR) is comparable to trabecular thickness. This limited spatial resolution regime demands processing and analysis algorithms designed to operate under such limiting conditions. It is shown that three different classes of structural parameters can be distinguished, characterizing scale, topology, and orientation. There is considerable evidence that osteoporotic bone loss affects all three classes but that topological changes, resulting from conversion of trabecular plates to rods, with the latter's eventual disconnection, are particularly prominent. Clinical applications discussed can be divided into those dealing with assessment of osteoporotic fracture risk as opposed to the study of the effect of disease progression and regression in response to treatment. Current data suggest that noninvasive assessment of cortical and trabecular bone (TB) architecture by mu-MRI may provide new surrogate endpoints to assess the efficacy of intervention in osteoporosis treatment and prevention.

Effect of voxel size on 3D micro-CT analysis of cortical bone porosity

This study examines the impact of voxel size on 3D micro-CT analysis of human cortical bone porosity. The study is based on computed microtomography scans of 10 human anterior femoral midshaft specimens acquired at 5, 10, and 15 microm voxel sizes. Artificial voxel sizes (10, 20, and 40 microm) were generated from the smallest scan voxel size (5 microm) in order to compare actual scanning with artificial degradation, a method employed in other similar studies. Canal volume fraction (CaV/TV), canal surface to volume ratio (CaS/CaV), mean canal diameter (CaDm), mean canal separation (CaSp), canal number (CaN), degree of anisotropy (DA), and canal connectivity density (CaConnD) were calculated from matching volumes of interest for all datasets. Qualitatively, the clarity of the actual scan datasets deteriorated rapidly as voxel size increased. In contrast, within the artificially generated datasets, the clarity of cortical pores was better maintained until the largest voxel size (40 microm). Mean absolute percent error values, correlation coefficients, and paired t-tests revealed a pattern of increasing, and generally significant, differences between the smallest and progressively larger voxel sizes (both scanned and artificial). Relative to the actual scans, however, the artificial datasets were less sensitive to changing voxel size. These findings indicated that subtle changes in voxel size, within the range examined, have a considerable effect on human cortical porosity structural parameters. Additionally, the use of artificially increased voxel sizes should be viewed with caution as they may not reflect what can actually be obtained by scanning.

Estimating structural properties of trabecular bone from gray-level low-resolution images

In this paper the relationship between three-dimensional histomorphometric parameters derived from microCT and MRI images of distal radius trabecular bone samples is studied. microFE analysis of the trabecular samples is performed and Young's modulus for cranio-caudal direction is calculated. Most of the MRI and microCT parameters correlate significantly with, respectively, MRI and microCT estimates of bone volume fraction. For some of the parameters strong correlation between microCT and MRI results is also observed. However, in these cases there simultaneously exists correlation between: microCT parameter and microCT bone volume fraction; microCT and MRI bone volume fraction; MRI bone volume fraction and MRI parameter. It is found that, comparing to bone volume fraction, histomorphometric information derived from binarized MRI images does not improve estimation of the Young's modulus of trabecular bone samples (calculated for "gold standard" microCT data). Thus a novel method of "optimal paths" analysis of gray-level MRI images is introduced. "Optimal paths" parameters improve estimation of the Young's modulus of trabecular bone samples. They also provide surrogate, gray-level image-based measure of trabecular thickness.

Quantitative MRI for the assessment of bone structure and function

Osteoporosis is the most common degenerative disease in the elderly. It is characterized by low bone mass and structural deterioration of bone tissue, leading to morbidity and increased fracture risk in the hip, spine and wrist-all sites of predominantly trabecular bone. Bone densitometry, currently the standard methodology for diagnosis and treatment monitoring, has significant limitations in that it cannot provide information on the structural manifestations of the disease. Recent advances in imaging, in particular MRI, can now provide detailed insight into the architectural consequences of disease progression and regression in response to treatment. The focus of this review is on the emerging methodology of quantitative MRI for the assessment of structure and function of trabecular bone. During the past 10 years, various approaches have been explored for obtaining image-based quantitative information on trabecular architecture. Indirect methods that do not require resolution on the scale of individual trabeculae and therefore can be practiced at any skeletal location, make use of the induced magnetic fields in the intertrabecular space. These fields, which have their origin in the greater diamagnetism of bone relative to surrounding marrow, can be measured in various ways, most typically in the form of R2', the recoverable component of the total transverse relaxation rate. Alternatively, the trabecular network can be quantified by high-resolution MRI (micro-MRI), which requires resolution adequate to at least partially resolve individual trabeculae. Micro-MRI-based structure analysis is therefore technically demanding in terms of image acquisition and algorithms needed to extract the structural information under conditions of limited signal-to-noise ratio and resolution. Other requirements that must be met include motion correction and image registration, both critical for achieving the reproducibility needed in repeat studies. Key clinical applications targeted involve fracture risk prediction and evaluation of the effect of therapeutic intervention.

Effect of specimen conditioning on the microarchitectural parameters of trabecular bone assessed by micro-computed tomography

The best way to preserve the mechanical properties of bone specimens is hydration in NaCl, whereas the reference process in microCT analysis is defatting. However, for finite element modelling (FEM) it is necessary to use the same bone specimens for biomechanical testing and 3D imaging. This study aimed to evaluate the effect of sample conditioning on trabecular bone microarchitectural parameters. Trabecular bones were analysed by microCT under three successive conditions: first, the fatted samples were analysed immersed in NaCl (process N); second, they were hydrated for 24 h then imaged without immersion (process H); third, the samples were defatted before analysis (process D). The microarchitectural parameters bone volume/tissue volume (BV/TV), trabecular spacing (Tb.Sp), number (Tb.N) and thickness (Tb.Th) were calculated. Except for BV/TV, there was no significant difference between the processes N and D. In process H, BV/TV, Tb.Th and Tb.N were higher and BS/BV and Tb.Sp were lower than in process D. Results showed that the process D may be replaced by the process N. The process H induced significant differences in microarchitectural parameters when compared to process D. Nevertheless, this sample conditioning should be used to develop FEM when microCT images are to be acquired during compressive testing.

Characterization of trabecular bone structure from high-resolution magnetic resonance images using fuzzy logic

The purpose of this work was to apply fuzzy logic image processing techniques to characterize the trabecular bone structure with high-resolution magnetic resonance images. Fifteen ex vivo high-resolution magnetic resonance images of specimens of human radii at 1.5 T and 12 in vivo high-resolution magnetic resonance images of the calcanei of peri- and postmenopausal women at 3 T were obtained. Soft segmentation using fuzzy clustering was applied to MR data to obtain fuzzy bone volume fraction maps, which were then analyzed with three-dimensional (3D) fuzzy geometrical parameters and measures of fuzziness. Geometrical parameters included fuzzy perimeter and fuzzy compactness, while measures of fuzziness included linear index of fuzziness, quadratic index of fuzziness, logarithmic fuzzy entropy, and exponential fuzzy entropy. Fuzzy parameters were validated at 1.5 T with 3D structural parameters computed from microcomputed tomography images, which allow the observation of true trabecular bone structure and with apparent MR structural indexes at 1.5 T and 3 T. The validation was statistically performed with the Pearson correlation coefficient as well as with the Bland-Altman method. Bone volume fraction correlation values (r) were up to .99 (P<.001) with good agreements based on Bland-Altman analysis showing that fuzzy clustering is a valid technique to quantify this parameter. Measures of fuzziness also showed consistent correlations to trabecular number parameters (r>.85; P<.001) and good agreements based on Bland-Altman analysis, suggesting that the level of fuzziness in high-resolution magnetic resonance images could be related to the trabecular bone structure.

Optimal cut of trabecular network

It has been shown recently that failure of mechanically tested trabecular bone samples can be localized within a part of the volume of the samples. Bone volume fraction BV/TV of failure regions was found to be a better determinant of the mechanical competence of the specimens and was smaller than BV/TV of the whole samples. These results suggest that localization of a failure within a part of an inhomogeneous trabecular network can be related to the presence of a surface of minimal cut-a surface separating the analyzed trabecular sample into two disjoint parts in such a way, that the separation requires removal of minimal possible amount of bone material. Thus, to properly address the problem of mechanical competence of a trabecular bone sample, one must be able to detect and describe the surface of minimal cut. In this paper an algorithm localizing surfaces of minimal cut within 3D trabecular structures is introduced.

Advanced Imaging Assessment of Bone Quality

Noninvasive and/or nondestructive techniques can provide structural information about bone, beyond simple bone densitometry. While the latter provides important information about osteoporotic fracture risk, many studies indicate that bone mineral density (BMD) only partly explains bone strength. Quantitative assessment of macrostructural characteristics, such as geometry, and microstructural features, such as relative trabecular volume, trabecular spacing, and connectivity, may improve our ability to estimate bone strength. Methods for quantitatively assessing macrostructure include (besides conventional radiographs) dual X ray absorptiometry (DXA) and computed tomography (CT), particularly volumetric quantitative computed tomography (vQCT). Methods for assessing microstructure of trabecular bone noninvasively and/or nondestructively include high-resolution computed tomography (hrCT), microcomputed tomography (micro-CT), high-resolution magnetic resonance (hrMR), and micromagnetic resonance (micro-MR). vQCT, hrCT, and hrMR are generally applicable in vivo; micro-CT and micro-MR are principally applicable in vitro. Despite progress, problems remain. The important balances between spatial resolution and sampling size, or between signal-to-noise and radiation dose or acquisition time, need further consideration, as do the complexity and expense of the methods versus their availability and accessibility. Clinically, the challenges for bone imaging include balancing the advantages of simple bone densitometry versus the more complex architectural features of bone, or the deeper research requirements versus the broader clinical needs. The biological differences between the peripheral appendicular skeleton and the central axial skeleton must be further addressed. Finally, the relative merits of these sophisticated imaging techniques must be weighed with respect to their applications as diagnostic procedures, requiring high accuracy or reliability, versus their monitoring applications, requiring high precision or reproducibility.

Importance of individual rods and plates in the assessment of bone quality and their contribution to bone stiffness

Local morphometry based on the assessment of individual rods and plates was applied to 42 human vertebral trabecular bone samples. Results showed that multiple linear regression models based on local morphometry as a measure for bone microstructure helped improving our understanding of the role of local structural changes in the determination of bone stiffness as assessed from direct and computational biomechanics.

INTRODUCTION

In a recent study, we proposed a method for local morphometry of trabecular bone, i.e., morphometry as applied to individual rods and plates. In this study, we used this method to study the relative importance of local morphometry in the assessment of bone architecture and its relative contribution to the stiffness of human vertebral bone.

MATERIALS AND METHODS

We extracted 42 human trabecular bone autopsies from nine intact spinal columns. The cylindrical samples were imaged with muCT to assess bone microstructure. From these images, global and local morphometric indices were derived and related to Young's modulus as assessed by experimental uniaxial compression testing (Emeas) and computational finite element analysis (EFE).

RESULTS

We found the best single predictor for Young's modulus to be apparent bone volume density (BV/TV), which explained 89% of the variance in EFE when fitted with a power law. A multiple linear regression model combining mean trabecular spacing (Tb.Sp), mean slenderness of the rods (<Ro.Sl>), and the relative amount of rod volume to total bone volume (Ro.BV/BV) was able to explain 90% of the variance in EFE. This model could not be improved by adding BV/TV as an independent variable. Furthermore, we found that mean trabecular thickness of the rods was significantly related to EFE (r2 = 0.42), whereas mean trabecular thickness of plates had no correlation to Young's modulus. Because the globally determined trabecular thickness does not discriminate between rods and plates, this index had only a poor predictive power for EFE (r2 = 0.09), showing the importance of local analysis of individual rods and plates.

CONCLUSIONS

From these results, we conclude that models based on local morphometry help improving our understanding of the relative importance of local structural changes in the determination of the stiffness of bone. Separate analysis of individual rods and plates may help to better predict age and disease-related fractures as well as to shed new light on the effect of pharmaceutical intervention in the prevention of such fractures beyond BMD.

Volumetric spatial decomposition of trabecular bone into rods and plates--a new method for local bone morphometry

Bone microarchitecture is believed to play a key role in determining bone quality. We therefore present a new method for the volumetric spatial decomposition of trabecular bone samples into its basic elements (rods and plates). This new method is a framework for the element based description of bone microarchitecture. First, the newly developed algorithm was validated on computer-generated models. Then, it was applied to 328 human trabecular bone samples harvested from 70 donors at five different anatomical sites (calcaneus, femoral head, iliac crest, lumbar spine 2 and 4), which were previously scanned by microcomputed tomography. Standard three-dimensional morphometric algorithms were used to analyze the trabeculae on an individual basis with respect to their volume, surface, and thickness. The results were statistically compared for the five sites. In this study, it was possible for the first time to spatially decompose trabecular bone structures in its volumetric elements; rods and plates. The size of the largest element in the structures showed significant differences for the five compared sites. In samples from femoral head, we found that basically one "major element" was spanning through the whole structure whereas in lumbar spine and calcaneus, smaller elements dominate. From this, we suggest that the strength of strong, dense plate-like structures is determined by the major elements whereas in looser rod-like structures the strength is given by the arrangement, quality, and shape of a whole set of elements. Furthermore, we found that globally determined structural indices such as the mean curvature of the bone surface (<H>) or related to this the structure model index (SMI) are almost exclusively explained by the arrangement of the plates. This also suggests that rods hold independent information characterizing trabecular bone quality, especially in the spine. These findings may improve the understanding of the site-specific role of bone microarchitecture in determining bone quality and in future studies the competence of bone.

Site-matched assessment of structural and tissue properties of cortical bone using scanning acoustic microscopy and synchrotron radiation μCT

200 MHz scanning acoustic microscopy (SAM) and synchrotron radiation muCT (SR-muCT) were used to assess microstructural parameters and tissue properties in site-matched regions of interest in cortical bone. Anterior and postero-lateral regions of ten cross sections from human cortical radius were explored. Structural parameters, including diameter and number of Haversian canals per cortical area (Ca.Dm, N.Ca/Ar) and porosity Po were assessed with both methods using a custom-developed image fusion and analysis software. Acoustic impedance Z and degree of mineralization of bone DMB were extracted separately for osteonal and interstitial tissues from the fused images. Structural parameter estimations obtained from radiographic and acoustic images were almost identical. DMB and impedance values were in the range between 0.77 and 1.28 g cm(-3) and 5.13 and 12.1 Mrayl, respectively. Interindividual and regional variations were observed, whereas the strongest difference was found between osteonal and interstitial tissues (Z: 7.2 +/- 1.1 Mrayl versus 9.3 +/- 1.0 Mrayl, DMB: 1.06 +/- 0.07 g cm(-3) versus 1.16 +/- 0.05 g cm(-3), paired t-test, p < 0.05). Weak, but significant correlations between DMB and Z were obtained for the osteonal (R(2) = 0.174, p < 10(-4)) and for the pooled (osteonal and interstitial) data. The regression of the pooled osteonal and interstitial tissue data follows a second-order polynomial (R(2) = 0.39, p < 10(-4)). Both modalities fulfil the requirement for a simultaneous evaluation of cortical bone microstructure and material properties at the tissue level. While SAM inspection is limited to the evaluation of carefully prepared sample surfaces, SR-muCT provides volumetric information on the tissue without substantial preparation requirements. However, SAM provides a quantitative estimate of elastic properties at the tissue level that cannot be captured by SR-muCT.

Novel algorithm detecting trabecular termini in muCT and MRI images

In this paper, a novel algorithm detecting trabecular termini in three-dimensional images of trabecular bone is introduced. The algorithm is applied to the analysis of muCT and MRI images of distal radius trabecular bone samples. In muCT images, the volume of the trabecular termini constitutes at most 2.1% of the bone volume fraction BV/TV and is typically smaller than 1% of BV/TV. Isolated trabeculae are not observed in the interior of the trabecular bone samples. Trabecular bone structure assessed with muCT appears thus highly optimized. The volume and the number of the trabecular termini do not correlate with BV/TV. These quantities do not correlate also with apparent Young's modulus of the samples. In contrast in MRI images, segmented with the dual reference limit method, the volume of the trabecular termini and the volume of isolated parts constitute even up to 14% of the apparent bone volume fraction App.BV/TV. For MRI images, the volume of the trabecular termini increases significantly with decreasing App.BV/TV. The volume and the number of the trabecular termini, derived from MRI images do not correlate with Young's modulus. There is also no correlation between the number and the volume of the trabecular termini, estimated from MRI and muCT images. The volume of the trabecular termini is overestimated 15 times in MRI images. App.BV/TV correlates strongly with BV/TV. Young's modulus derived from MRI images correlates strongly with Young's modulus found for muCT data. It is shown that the diagnostic significance of latter result is highly limited.

An orientation distribution function for trabecular bone

We describe a new method for quantifying the orientation of trabecular bone from three-dimensional images. Trabecular lattices from five human vertebrae were decomposed into individual trabecular elements, and the orientation, mass, and thickness of each element were recorded. Continuous functions that described the total mass (M(phi,theta)) and mean thickness (tau(phi,theta)) of all trabeculae as a function of orientation were derived. The results were compared with experimental measurements of the elastic modulus in three principal anatomic directions. A power law scaling relationship between the anisotropies in mass and elastic modulus was observed; the scaling exponent was 1.41 (R2=0.88). As expected, the preponderance of trabecular mass was oriented along the cranial-caudal direction; on average, there was 3.4 times more mass oriented vertically than horizontally. Moreover, the vertical trabeculae were 30% thicker, on average, than the horizontal trabeculae. The vertical trabecular thickness was inversely related to connectivity (R2=0.70; P=0.07), suggesting a possible organization into either few, thick trabeculae or many thin trabeculae. The method, which accounts for the mechanical connectedness of the lattice, provides a rapid way to both visualize and quantify the three-dimensional organization of trabecular bone.

Accuracy of 3D MR microscopy for trabecular bone assessment: a comparative study on calcaneus samples using 3D synchrotron radiation microtomography

Magnetic resonance (MR) imaging is attractive for a noninvasive and radiation-free assessment of in vivo trabecular bone architecture. However the quantitative evaluation of architectural parameters could be biased by the limited sensitivity of MR. The aim of this study was to determine the accuracy of trabecular bone architectural parameters obtained from 3D high-resolution MR images, by comparison to reference images obtained by high-resolution X-ray microtomography using synchrotron radiation, from 29 samples of human calcaneus. MR images were obtained with a 66 microm x 66 microm x 66 microm voxel size, using a 8.5 T MR microscope. Microtomography images were acquired with a 10 microm x 10 microm x 10 mum voxel size, from the same samples. 3D architectural parameters characterizing the morphometry, topology, anisotropy, and orientation were computed from both modalities and carefully compared. To avoid errors, an identical region of interest was selected in the two corresponding images, and the same algorithms were run at identical spatial resolution. Our results establish that network connectivity, orientation and anisotropy are reliable from the MR data. The bone volume fraction, and morphometric parameters measured from the MR data, were found to be biased with respect to their values from the microtomography data, although there was a significant correlation between the two modalities.

Bone structure of the calcaneus: analysis with magnetic resonance imaging and correlation with histomorphometric study

The purpose of this study was to compare structural measurements obtained from MR images of the calcaneus with those obtained from conventional histomorphometry. Sagittal magnetic resonance (MR) images of the calcaneus of 24 fresh human cadaveric feet were obtained at a spatial resolution achievable in vivo. A three-dimensional gradient echo-sequence was used with a slice thickness of 700 microm and in plane resolution of 172 x 172 microm. Structural analysis (four histomorphometric parameters; seven connectivity parameters) was performed in the superior region of the calcaneus. Bone biopsy specimens were obtained in the same area and were sectioned for histomorphometric study. Most of the MR histomorphometric parameters were overestimated (by a factor ranging from 0.8 to 3), as compared with histomorphometry. However, significant ( P<0.05) correlations were found between MR imaging and histomorphometric measurements for bone volume/tissue volume, trabecular separation, trabecular number, star volume of the marrow space, node count and terminus count. MR histomorphometric parameters correlated much better with histomorphometry than connectivity parameters. This study suggests that structural parameters characterizing cancellous bone in the calcaneus can be derived from MR images in the limited spatial resolution regime applicable in vivo.

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 elastic properties of trabecular bone, but is limited in its application due to the large number of elements that it requires 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.

Analysis of 1H-NMR relaxation time distributions in L1 to L6 rat lumbar vertebrae

A better knowledge of the NMR relaxation behavior of bone tissue can improve the definition of imaging protocols to detect bone diseases like osteoporosis. The six rat lumbar vertebrae, from L1 to L6, were analyzed by means of both transverse (T(2)) and longitudinal (T(1)) relaxation of (1)H nuclei at 20 MHz and 30 degrees C. Distributions of relaxation times, computed using the multiexponential inversion software uniform penalty inversion, extend over decades for both T(2) and T(1) relaxation. In all samples, the free induction decay (FID) from an inversion-recovery (IR) T(1) measurement shows an approximately Gaussian (solid-like) component, exp[-1/2(t/T(GC))2], with T(GC) approximately 12 micros (GC for Gaussian component) and a liquid-like component (LLC) with initially simple-exponential decay. Averaging and smoothing procedures are adopted to obtain the ratio alpha between GC and LLC signals and to get separate T(1) distributions for GC and LLC. Distributions of T(1) for LLC show peaks centered at 300-500 ms and shoulders going down to 10 ms, whereas distributions of T(1) for GC are single broad peaks centered at roughly 100 ms. The T(2) distributions by Carr-Purcell-Meiboom-Gill at 600 micros echo spacing are very broad and extend from 1 ms to hundreds of ms. This long echo spacing does not allow one to see a peak in the region of hundreds of micros, which is better seen by single spin-echo T(2) measurements. Results of the relaxation analysis were then compared with densitometric data. From the study, a clear picture of the intratrabecular and intertrabecular (1)H signals emerges. In particular, the GC is presumed to be due to (1)H in collagen, LLC due to all the fluids in the bone including water and fat, and the very short T(2) peak due to the intratrabecular water. Overall, indications of some trends in composition and in pore-space distributions going from L1 to L6 appeared. Published results on rat vertebrae obtained by fitting the curves by discrete two-component models for both T(2) and T(1) are consistent with our results and can be better interpreted in light of the shown distributions of relaxation times.

Evaluation of 9.4-T MR microimaging in assessing normal and defective fetal bone development: comparison of MR imaging and histological findings

We evaluated 9.4-T magnetic resonance (MR) microimaging in assessing normal and defective bone development in mouse embryos. For this purpose, we performed 9.4-T MR microimaging on developing bones in normal embryos, and also in Runx2/Cbfa1-/- embryos with severely defective bone development. MR images were compared with the histological and histochemical features of these fetal bones. MR microimaging delineate successfully the normal long bone development in embryos. The T1- and T2-weighted MR microimaging demonstrated chondrocyte maturation in different regions of growing cartilage, such as epiphysis, physis, hypertrophic cartilage, and zone of provisional calcification. These developmental changes were detectable in as early as E14.5 embryos. The MR microimaging clearly demonstrated defective bone development in Runx2/Cbfa1-/- embryos. The femur from E18.5 homozygous Runx2/Cbfa1-/- embryos lacked MR signal intensity patterns including the hypertrophic cartilage, which are characteristic of the bone from the age-matched Runx2/Cbfa1+/+ embryos. Interestingly, however, the tibia from the same mutants was associated with MR signal patterns indicative of hypertrophic cartilage but not of the primary spongiosa and ossifying perichondrium, suggesting that bone development is differently regulated in these two long bones. On the other hand, the bones from heterozygous Runx2/Cbfa1+/- embryos exhibited an MR phenotype intermediate between the Runx2/Cbfa1+/+ and Runx2/Cbfa1-/- embryos; the primary spongiosa and ossifying perichondrium formation occurred normally even in the absence of preceding organized maturation of chondrocytes, a phenotype that was not detected by histological examinations. We concluded that MR microimaging is useful in assessing the bone development.