Three-dimensional methods for quantification of cancellous bone architecture

High-resolution three-dimensional micro-computed tomography detects bone loss and changes in trabecular architecture early: comparison with DEXA and bone histomorphometry in a rat model of disuse osteoporosis

RATIONALE AND OBJECTIVES

The ability of three-dimensional micro-computed tomography (3D-microCT) to detect changes in a rat model of disuse osteoporosis was evaluated and compared with two reference techniques: dual x-ray absorptiometry (DEXA) for bone mass, and bone histomorphometry (BHM) for bone mass and trabecular micro-architecture.

METHODS

Forty-two rats were divided into controls or were hindlimb unloaded for 7, 13, and 23 days. DEXA bone mineral density measurements were performed on right tibiae. Then, after plastic embedding, bone volume (BV/TV) and trabecular (Tb)-derived parameters of trabecular bone architecture (Tb Th, thickness; Tb N, number) were measured with BHM. 3D-microCT measurements of BV/TV, Tb Th, and Tb N were carried out on left tibiae.

RESULTS

Unloaded rats lost bone in a time-dependent manner. DEXA and 3D-microCT detected bone loss earlier than BHM. The decreases in Tb Th and Tb N were observed at day 13 only with 3D-microCT (P < 0.05 and P < 0.01, respectively). All bone mass and architectural parameters measured with the three techniques correlated significantly (0.59, 0.89, P < 0.001), except Tb Th.

CONCLUSIONS

3D-microCT is a valid technique for bone mass and micro-architecture measurements in this rat model of disuse osteoporosis.

The skeletal structure of insulin-like growth factor I-deficient mice

The importance of insulin-like growth factor I (IGF-I) for growth is well established. However, the lack of IGF-I on the skeleton has not been examined thoroughly. Therefore, we analyzed the structural properties of bone from mice rendered IGF-I deficient by homologous recombination (knockout [k/o]) using histomorphometry, peripheral quantitative computerized tomography (pQCT), and microcomputerized tomography (muCT). The k/o mice were 24% the size of their wild-type littermates at the time of study (4 months). The k/o tibias were 28% and L1 vertebrae were 26% the size of wild-type bones. Bone formation rates (BFR) of k/o tibias were 27% that of the wild-type littermates. The k/o bones responded normally to growth hormone (GH; 1.7-fold increase) and supranormally to IGF-I (5.2-fold increase) with respect to BFR. Cortical thickness of the proximal tibia was reduced 17% in the k/o mouse. However, trabecular bone volume (bone volume/total volume [BV/TV]) was increased 23% (male mice) and 88% (female mice) in the k/o mice compared with wild-type controls as a result of increased connectivity, increased number, and decreased spacing of the trabeculae. These changes were either less or not found in L1. Thus, lack of IGF-I leads to the development of a bone structure, which, although smaller, appears more compact.

Effects of daily treatment with parathyroid hormone on bone microarchitecture and turnover in patients with osteoporosis: a paired biopsy study

We examined paired iliac crest bone biopsy specimens from patients with osteoporosis before and after treatment with daily injections of 400 U of recombinant, human parathyroid hormone 1-34 [PTH(1-34)]. Two groups of patients were studied. The first group was comprised of 8 men with an average age 49 years. They were treated with PTH for 18 months. The second group was comprised of 8 postmenopausal women with an average age 54 years. They were treated with PTH for 36 months. The women had been and were maintained on hormone replacement therapy for the duration of PTH treatment. Patients were supplemented to obtain an average daily intake of 1500 mg of elemental calcium and 100 IU of vitamin D. The biopsy specimens were subjected to routine histomorphometric analysis and microcomputed tomography (CT). Cancellous bone area was maintained in both groups. Cortical width was maintained in men and significantly increased in women. There was no increase in cortical porosity. There was a significant increase in the width of bone packets on the inner aspect of the cortex in both men and women. This was accompanied by a significant decrease in eroded perimeter on this surface in both groups. Micro-CT confirmed the foregoing changes and, in addition, revealed an increase in connectivity density, a three dimensional (3D) measure of trabecular connectivity in the majority of patients. These findings indicate that daily PTH treatment exerts anabolic action on cortical bone in patients with osteoporosis and also can improve cancellous bone microarchitecture. The results provide a structural basis for the recent demonstration that PTH treatment reduces the incidence of osteoporosis-related fractures.

Three-dimensional analysis of nonhuman primate trabecular architecture using micro-computed tomography

Until recently, detailed analyses of the architecture of nonhuman primate cancellous bone have not been possible due to a combination of methodological constraints, including poor resolution imaging or destructive protocols. The development of micro-computed tomography (microCT) and morphometric methods associated with this imaging modality offers anthropologists a new means to study the comparative architecture of cancellous bone. Specifically, microCT will allow anthropologists to investigate the relationship between locomotor behavior and trabecular structure. We conducted a preliminary study on the trabecular patterns in the proximal humerus and femur of Hylobates lar, Ateles paniscus, Macaca mulatta, and Papio anubis to investigate the quantitative differences in their trabecular architecture and evaluate the potential of microCT in anthropological inquiry. MicroCT allows the researcher to evaluate variables beyond simple two-dimensional orientations and radiographic densities. For example, this methodology facilitates the study of trabecular thickness and bone volume fraction using three-dimensional data. Results suggest that density-related parameters do not reliably differentiate suspensory-climbing species from quadrupedal species. However, preliminary results indicate that measurements of the degree of anisotropy, a measure of trabecular orientation uniformity, do distinguish suspensory-climbing taxa from more quadrupedal species. The microCT method is an advance over conventional radiography and medical CT because it can accurately resolve micron-sized struts that make up cancellous bone, and from these images a wide array of parameters that have been demonstrated to be related to cancellous bone mechanical properties can be measured. Methodological problems pertinent to any comparative microCT study of primate trabecular architecture are discussed.

Trabecular structure assessment in lumbar vertebrae specimens using quantitative magnetic resonance imaging and relationship with mechanical competence

The purpose of this study was to use quantitative magnetic resonance imaging (MRI; high-resolution [HR] and relaxometry) to assess trabecular bone structure in lumbar vertebrae specimens and to compare these techniques with bone mineral density (BMD) in predicting stress values obtained from mechanical tests. Fourteen vertebral midsagittal sections from lumbar vertebrae L3 were obtained from cadavers (aged 22-76 years). HR images with a slice thickness of 300 microm and an in-plane spatial resolution of 117 microm2 x 117 microm2 were obtained. Transverse relaxation time T2' distribution was measured by using an asymmetric spin-echo (ASE) sequence. Traditional morphometric measures of bone structure such as apparent trabecular bone fraction (app. BV/TV), apparent trabecular bone number (app. Tb.N), apparent trabecular bone separation (app. Tb.Sp), and apparent trabecular bone thickness (app. Tb.Th) as well as the directional mean intercept length (MIL) were calculated. Additionally, BMD measurements of these sections were obtained by dual-energy X-ray absorptiometry (DXA) and biomechanical properties such as directional stress values (to fracture) were determined on adjacent specimens. With the exception of T2', all morphological parameters correlated very well with age, BMD, and stress values (R between 0.79 and 0.92). However, in the direction perpendicular to the magnetic field, T2' values enhanced the adjusted R2 correlation value with horizontal (M/L) stress values in addition to BMD from 0.70 to 0.91 (p < 0.05).

A three-dimensional simulation of age-related remodeling in trabecular bone

After peak bone mass has been reached, the bone remodeling process results in a decrease in bone mass and strength. The formation deficit, the deficit of bone formation compared with previous resorption, results in bone loss. Moreover, trabeculae disconnected by resorption cavities probably are not repaired. The contributions of these mechanisms to the total bone loss are unclear. To investigate these contributions and the concomitant changes in trabecular architecture and mechanical properties, we made a computer simulation model of bone remodeling using microcomputed tomography (micro-CT) scans of human vertebral trabecular bone specimens. Up to 50 years of physiological remodeling were simulated. Resorption cavities were created and refilled 3 months later. These cavities were not refilled completely, to simulate the formation deficit. Disconnected trabeculae were not repaired; loose fragments generated during the simulation were removed. Resorption depth, formation deficit, and remodeling space were based on biological data. The rate of bone loss varied between 0.3% and 1.1% per year. Stiffness anisotropy increased, and morphological anisotropy (mean intercept length [MIL]) was almost unaffected. Connectivity density increased or decreased, depending on the remodeling parameters. The formation deficit accounted for 69-95%, disconnected trabeculae for 1-21%, and loose fragments for 1-17% of the bone loss. Increasing formation deficit from 1.8% to 5.4% tripled bone loss but only doubled the decrease in stiffness. Increasing resorption depth from 28 to 56 microm slightly increased bone loss but drastically decreased stiffness. Decreasing the formation deficit helps to prevent bone loss, but reducing resorption depth is more effective in preventing loss of mechanical stiffness.

Mechanical consequences of bone loss in cancellous bone

The skeleton is continuously being renewed in the bone remodeling process. This prevents accumulation of damage and adapts the architecture to external loads. A side effect is a gradual decrease of bone mass, strength, and stiffness with age. We investigated the effects of bone loss on the load distribution and mechanical properties of cancellous bone using three-dimensional (3D) computer models. Several bone loss scenarios were simulated. Bone matrix was removed at locations of high strain, of low strain, and random throughout the architecture. Furthermore, resorption cavities and thinning of trabeculae were simulated. Removal of 7% of the bone mass at highly strained locations had deleterious effects on the mechanical properties, while up to 50% of the bone volume could be removed at locations of low strain. Thus, if remodeling would be initiated only at highly strained locations, where repair is likely needed, cancellous bone would be continuously at risk of fracture. Thinning of trabeculae resulted in relatively small decreases in stiffness; the same bone loss caused by resorption cavities caused large decreases in stiffness and high strain peaks at the bottom of the cavities. This explains that a reduction in the number and size of resorption cavities in antiresorptive drug treatment can result in large reductions in fracture risk, with small increases in bone mass. Strains in trabeculae surrounding a cavity increased by up to 1,000 microstrains, which could lead to bone apposition. These results give insight in the mechanical effects of bone remodeling and resorption at trabecular level.

Parallel plate model for trabecular bone exhibits volume fraction-dependent bias

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.

Estimation of wrist fracture load using phalangeal speed of sound: an in vitro study

This study aimed to evaluate the ability of speed of sound (SOS) measured at the phalanges to estimate simulated wrist fracture load and stress. SOS was measured along the proximal phalanges of the second, third and fourth fingers using an ultrasound (US) system operating in axial transmission mode. The bone mineral density (BMD) of the radius and the phalanges was also measured with quantitative computed tomography (QCT) and dual x-ray absorptiometry (DXA), and the combined cortical thickness (CCT) of the phalanges was measured from hand radiographs. After the measurements were completed, the radius was excised from the cadaver, embedded in polymethylmethacrylate and tested to failure on a servohydraulic testing machine. The configuration of the radius was chosen to simulate a fall onto the hand. Linear regression analysis showed a highly significant correlation between SOS (r = 0.76-0.94, p < 0.001), CCT (r = 0.86-0.90, p < 0.001) and BMD (r = 0.92-0.96, p < 0.0001) in the three proximal phalanges measured. SOS, BMD and CCT were significant predictors of fracture load (r = 0.60-0.69, p < 0.03) and stress (r = 0.65-0.77, p < 0.02). Cortical area and bone mineral content (BMC) of the radius were consistently higher predictors of fracture load (r = 0.76-0.82, p < 0.01 for area and r = 0.78-0.88, p < 0.01 for BMC) than BMD. The correlation of BMC and area was poorer with fracture stress. In a step-wise regression analysis using both phalangeal BMD and SOS, only SOS remained a significant predictor of fracture stress. In forward stepwise regression analysis, both cortical area and SOS were entered into the regression model to estimate fracture load. Only SOS remained significant in the model for estimating fracture stress. Phalangeal BMD was only entered in the combined model with the cortical area at the 4% site (r = 0.84, p = 0.002). Phalangeal SOS is a useful parameter in the assessment of bone status of the radius.

Early morphometric and anisotropic change in periarticular cancellous bone in a model of experimental knee osteoarthritis quantified using microcomputed tomography

OBJECTIVE

To quantify early stage microstructural changes of periarticular cancellous bone in a canine anterior cruciate ligament transection model for experimental osteoarthritis.

DESIGN

Unilateral transection of the anterior cruciate ligament was performed in 10 animals. Bone structure changes were quantified in five animals at 3-week post-transection and five animals at 12-week post-transection. An additional two non-operated animals were used as controls.

BACKGROUND

Changes in trabecular architecture of the periarticular cancellous bone in early stage post-traumatic osteoarthritis is not well understood. Previous studies have found alterations in bone mineral density in experimental osteoarthritis suggesting adaptation of the trabecular structure. Early change of the periarticular bone following a ligament injury may contribute to the long-term development of osteoarthritis.

METHODS

++. Bone cores from the medial condyles of the femoral and tibial pairs were scanned with a three-dimensional microtomographic system. Structural indices were quantified including bone volume ratio, bone surface ratio, trabecular thickness, trabecular separation, trabecular number, as well as structural anisotropy determined by the mean-intercept-length method.Results. Significant structural changes were observed at 3-week post-transection, and were more prominent at 12-week post-transection. These changes were accompanied by decreasing anisotropy.

CONCLUSIONS

Periarticular cancellous bone microstructure is significantly altered in experimental osteoarthritis. These changes occurred as early as 3-week post-transection, and were large at 12-week post-transection.

RELEVANCE

The pathogenesis of post-traumatic osteoarthritis is poorly understood, but it is clear that this disease involves the entire organ system of the joint, including the cartilages, synovium, ligaments, and bones. This study focuses on the changes that occur in the bones during the early stages following a joint injury, and contributes to a better overall understanding of the disease aetiology.

Effect of vitamin K2 on three-dimensional trabecular microarchitecture in ovariectomized rats

Menatetrenone, a vitamin K2 with four isoprene units, has been reported to improve osteoporotic bone loss. The purpose of this investigation was to clarify the effect of menatetrenone on the three-dimensional (3D) trabecular microarchitecture in ovariectomized (OVX) rats by using microcomputed tomography (MCT). Forty-two 13-week-old female rats were used and divided into four groups: the OVX (OVX + MK-4) group treated with menatetrenone, the (OVX untreated) group, the sham-operated (Sham + MK-4) group treated with menatetrenone, and the sham-operated group not treated with menatetrenone (Sham untreated) group. OVX rats were fed a calcium-deficient diet. Menatetrenone treatment was begun just after the ovariectomy, and the mean menatetrenone oral intake over the 8-week period was adjusted to 30 mg/kg BW per day. The proximal metaphyseal region of the right tibia was evaluated by dual X-ray absorptiometry (DXA) and MCT. A parametric analysis of the reconstructed trabecular volume was carried out using bone volume fractions, the fractal dimension calculated by the 3D box-counting method, and the connectivity density as determined by topological analysis. Menatetrenone significantly increased the trabecular bone volume, fractal dimension, and connectivity in the OVX + MK-4 group compared with the OVX-untreated group (p < 0.01). Our results suggest that an 8-week administration of menatetrenone protects against the loss of trabecular bone volume and its connectivity when treatment is begun just after the ovariectomy. Despite this apparent protection, it remains unknown whether it is possible to reestablish trabecular connectivity if therapeutic intervention occurs after the trabecular connectivity has been lost.

Evaluation of changes in trabecular bone architecture and mechanical properties of minipig vertebrae by three-dimensional magnetic resonance microimaging and finite element modeling

The study objective was to analyze the three-dimensional (3D) trabecular architecture and mechanical properties in vertebral specimens of young and mature Sinclair minipigs to assess the relative contribution of architecture to bone strength. We used 3D magnetic resonance microimaging (MRmicroI) and direct image analysis to evaluate a set of standard structural measurements and new architectural descriptors of trabecular bone in biopsy specimens from L2, L3, and L4 vertebrae (n = 16 in each group) from young (mean age, 1.2 years) and mature (mean age, 4.8 years) minipigs. The measurements included bone volume/tissue volume (BV/TV), marrow star volume (Ma.St.V), connectivity density (ConnD), and two new parameters, percent platelike trabeculae (% plate) and percent bone in the load direction (% boneLD). The % plate, calculated from surface curvature, allowed the delineation of plates from rods. The % boneLD quantified the percentage of bone oriented along the long axis of the vertebral body. We showed that 3D MRmicroI can detect the subtle changes in trabecular architecture between the two age groups. ConnD, star volume, % plate, % boneLD, and BV/TV were found to be more effective than the model-based, derived indices (trabecular thickness [Tb.Th], trabecular separation [Tb.Sp], and trabecular number [Tb.N]) in differentiating the structural changes. BV/TV, % plate, and % boneLD significantly increased (p < 0.05) in all three vertebral sites of the mature minipigs. The significant decrease in ConnD and star volume in the mature vertebra was consistent with the concurrent increase of platelike trabecular bone (p < 0.05). Overall, ConnD, star volume, % plate, and % boneLD provided a coherent picture of the architectural changes between the two age groups. Apparent modulus and maximum stress were determined experimentally on biopsy specimens from L2 vertebrae (n = 16). When apparent modulus was predicted using 3D MRmicroI data sets as input for finite element modeling (FEM), the results were similar to the experimentally determined apparent modulus (p = 0.12). Both methods were then used to compare the young and the mature animals; the experimental and predicted apparent modulus were significantly higher for the mature group (p = 0.003 and 0.012, respectively). The experimental maximum stress in the vertebra of the mature animals was twice as high as that for the young animals (p = 0.006). Bone quantity (BV/TV or bone mineral content [BMC]) alone could explain approximately 74-85% of the total variability in stress and modulus. The inclusion of either ConnD or % boneLD with BV/TV in a multiple regression analysis significantly improved the predictability of maximum stress, indicating that architecture makes additional contributions to compressive strength in normal minipig vertebra.

A new method of comprehensive static histomorphometry applied on human lumbar vertebral cancellous bone

The aim of the present study was to assess age-related changes in the human spine by use of established static histomorphometry, and to determine how these static histomorphometric measures are interrelated in human cancellous bone tissue. The material comprised normal human lumbar vertebral bodies (L-2) from 12 women (19-96 years) and 12 men (23-91 years) selected from a larger autopsy material to give an even age and gender distribution. In addition, L-2 from three female subjects (80, 88, and 90 years) with a known vertebral fracture of L-2 were considered. Approximately 9-mm-thick frontal (mediolateral) slices were embedded in methylmetacrylate, stained with aniline blue, and scanned into a computer with a flatbed image scanner at a high resolution (2400 dpi). With a custom-made computer program the following static histomorphometric measures were determined: trabecular bone volume; marrow space star volume; bone space star volume; anisotropy of bone and marrow phase (star length distribution method); node-strut analysis (node:terminus ratio); trabecular thickness; trabecular number; trabecular separation; and trabecular bone pattern factor. In addition, connectivity density was determined (by the ConnEulor method). All 11 histomorphometric measures, except bone space star volume and the two measures of anisotropy, showed a significant correlation with age. Marrow space star volume (r = 0.82) and trabecular bone volume (r = -0.81) showed the highest correlation with age. Furthermore, it was found that all of the histomorphometric measures were correlated, to different degrees. Trabecular bone volume correlated significantly with all ten histomorphometric measures, whereas the two anisotropy measures were poorly correlated to the other measures. Finally, we found the histomorphometric values in this study to be in excellent accordance with various previously published results from studies of human trabecular vertebral bone, the sole exception being marrow space star volume, which was probably due to the small (artificial) region of interest (ROI) that was used in the earlier studies. In conclusion, the new method applied herein allows for easy assessment of age-related changes and also for assessment of relationships between histomorphometric measures in human vertebral cancellous bone.

The use of bone densitometry in clinical practice

Bone densitometry is an established method for the assessment of osteoporosis as, according to the definition of osteoporosis, an accurate determination of the level of bone mass is central to the diagnostic assessment of osteoporosis. The diversity of different bone densitometry techniques, however, needs to be acknowledged. The World Health Organization criteria of osteoporosis should not be used for peripheral measurements, and their application to subject groups other than white women is still controversial. A large variety of bone densitometry and quantitative ultrasound techniques can be used for fracture risk assessment. Their results should be interpreted in the context of other clinical examinations and can then be used in making treatment decisions. For monitoring purposes, the ratio of response rate and long-term precision error determines longitudinal sensitivity. For all of these applications, careful quality assurance procedures need to be implemented. If applied in a responsible fashion, bone densitometry represents a powerful approach that is indispensable for the assessment of osteoporosis.

Comparison of trabecular bone architecture in young and old bones

In this study, different parameters currently applied for the description of trabecular bone architecture in young and old subjects are compared. Moreover, new parameters are proposed and assessed. For the investigations, the two-dimensional images of vertebral body sections are acquired with the use of a low-magnification digital camera. The parameters were calculated both for the skeleton and for the bone/marrow interface distinguished in the images of the trabecular network. The following methods of the descriptions of the trabecular bone architecture were considered: histomorphometric analysis (BV/TV, asymmetry, mean trabeculae length), fractal geometry technique, Euler characteristic, star volume of the marrow cavity, the mean distance between two points of the trabecular network, and the probability of disconnection (is straightforwardly connected with the number of separated parts of the network). Moreover, bone mineral density (BMD) was determined for comparative purposes. The quantities directly extracted form the images are also combined to produce new indexes, which better differentiate young and old bones. It was found that the BMD, the BV/TV, the star volume, the Euler number, and the probability of disconnection might be used as indicators of the age-related changes of trabecular bone. The parameters could be measured with the precision comparable to that of the BMD. The only exception is the probability of disconnection. Highly significant correlations were demonstrated between bone density (BMD, BV/TV) and trabecular architecture (SV/GV, probability of disconnection).

3D micro-computed tomography of trabecular and cortical bone architecture with application to a rat model of immobilisation osteoporosis

Bone mass and microarchitecture are the main determinants of bone strength. Three-dimensional micro-computed tomography has the potential to examine complete bones of small laboratory animals with very high resolution in a non-invasive way. In the presented work, the proximal part of the tibiae of hindlimb unloaded and control rats were measured with 3D MicroCT, and the secondary spongiosa of the scanned region was evaluated using direct evaluation techniques that do not require model assumptions. For determination of the complete bone status, the cortex of the tibiae was evaluated and characterised by its thickness. It is shown that with the proposed anatomically conforming volume of interest (VOI), up to an eight-fold volume increase can be evaluated compared to cubic or spherical VOIs. A pronounced trabecular bone loss of -50% is seen after 23 days of tail suspension. With the new evaluation techniques, it is shown that most of this bone loss is caused by the thinning of trabeculae, and to a lesser extent by a decrease in their number. What changes most radically is the structure type: the remaining bone is more rod-like than the control group's bone. Cortical bone decreases less than trabecular bone, with only -18% after 23 days.

Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis

We analyzed the ability of the quantitative ultrasound (QUS) parameter, speed of sound (SOS), and bone mineral density (BMD), as measured by dual-energy X-ray absorptiometry (DXA), to predict Young's modulus, as assessed by microstructural finite element analysis (muFEA) from microcomputed tomography (muCT) reconstructions. With muFEA simulation, all bone elements in the model can be assigned the same isotropic Young's modulus; therefore, in contrast to mechanical tests, only the trabecular structure plays a role in the determination of the elastic properties of the specimen. SOS, BMD, and microCT measurements were performed in 15 cubes of pure trabecular bovine bone in three orthogonal directions: anteroposterior (AP); mediolateral (ML); and craniocaudal (CC). The anisotropy of the architecture was determined using mean intercept length (MIL) measurements. SOS, MIL, and Young's modulus (E) values were significantly different in all three directions (p < 0.001), with the highest values in the CC direction. There was a strong linear relationship between E and SOS in each of the three orthogonal directions, with r(2) being 0.88, 0.92, and 0.84 (all p < 0.0001) for the CC, ML, and AP directions, respectively. The relationship between E and BMD was less strong, with r(2) being between 0.66 and 0.85 (all p < 0.0001) in the different directions. There was also a significant, positive correlation between SOS and BMD in each of the three axes (r(2) being 0.81, 0.42, and 0.92 in the CC, ML, and AP directions, respectively; p < 0.0001). After correction for BMD, the correlations between SOS and E in each of the three directions remained highly significant (r(2) = 0.77, p < 0. 0001 for the AP direction; r(2) = 0.48, p < 0.001 for the CC direction; r(2) = 0.52, p < 0.005 for the ML direction). After correction for SOS, BMD remained significantly correlated with Young's modulus in the AP and CC directions (r(2) = 0.52, p < 0.005; r(2) = 0.30, p < 0.05, respectively), but the correlation in the ML direction was no longer statistically significant. In a stepwise regression model, E was best predicted by SOS in each of the orthogonal directions. These observations illustrate the ability of the SOS technique to assess the architectural mechanical quality of trabecular bone.

The three-dimensional cancellous bone architecture of the human mandibular condyle

In the present study, we tested the hypothesis that the cancellous bone of the mandibular condyle is inhomogeneous and anisotropic. For this purpose, 11 mandibular condyles from embalmed human cadavers were scanned in a micro-CT system. Within each condyle, 9 volumes of interest were selected from different mediolateral and supero-inferior regions. Several bone parameters were calculated to describe the morphology. It appeared that the cancellous bone of the condyle could be approximated by parallel plates. These plates were almost vertically oriented at an angle of 17 degrees relative to the sagittal plane, i.e., perpendicular to the condylar axis. In the superior regions of the condyle, the cancellous bone had the largest bone volume fraction (0.19), associated with the thickest trabeculae (0.11 mm), and the highest trabecular number (1.72 mm(-1)). The lowest bone volume fraction (0.15) was found more inferiorly. The degree of anisotropy increased from superior to inferior across the condyle. No mediolateral differences in bone morphology were found, but superiorly central regions contained more bone than peripheral regions. The plate-like trabeculae could indicate that the condyle is optimally adapted to sustain loads from all directions in a plane perpendicular to the condylar axis. The high bone mass and lower anisotropy in the superior regions could enable the condyle to sustain multiple load directions. Toward the collum, the trabeculae are more aligned. This could point to stresses acting predominantly in one direction.

Quantitative analysis of three-dimensional complexity and connectivity changes in trabecular microarchitecture in relation to aging, menopause, and inflammation

There are several types of bone loss besides that associated with normal aging, eg, that associated with the menopause, and that associated with chronic inflammation, and these are considered to be caused by different mechanisms. The microarchitecture that results from these different bone-loss mechanisms would not be the same. The purpose of this study was to investigate differences in the three-dimensional trabecular microarchitecture in various types of osteopenia, using microcomputed tomography (Micro-CT). Thirty-five Fisher 344 rats were divided into five groups (control, young, senile, ovariectomized [OVX], and inflammation-mediated osteopenia [IMO]) and distal femoral metaphysis was scanned by Micro-CT to nondestructively acquire a 3-D CT stack consisting of 50 consecutive slices at a spatial resolution of 26 microm. The volume of interest, consisting of the secondary spongiosa, was prepared to analyze the 3-D trabecular microarchitecture. A parametric analysis was carried out using bone volume fractions, fractal dimensions, and the first Betti number in order to quantitatively express the mass, complexity, and connectivity of the trabecular microarchitecture. Complexity tended to decrease with age, and decreased significantly in estrogen deficiency-induced and inflammation-mediated osteopenia. Connectivity did not appear to change with aging, but was significantly decreased in estrogen deficiency-induced and inflammation-mediated osteopenia. There was no significant difference between the OVX and the IMO groups.

Age changes in bone

Changes in bone structure as a function of age have been studied by simple inspection, x-ray imaging, stereo-photography, deep field optical microscopy, circularly polarised light microscopy, and scanning electron microscopy (SEM), including both topographic and compositional backscattered electron (BSE) imaging modes. The study of bone as a three-dimensional object, rather than in thin sections, enables us to envisage modelling and remodelling processes in context. The study of ultra-flat block surfaces permits the acquisition of data from an effectively very thin layer in the block face, and to examine bone as a spectrum of tissue types varying in the degree of mineralisation. Particular attention has been paid in our earlier studies to the iliac crest, lumbar vertebral bodies, femoral mid-shaft, neck and head and parietal and frontal skull bones. Recently, we have compared findings from these sites with observations on the mandible. We conclude, from our new imaging data, that common generalisations about the changes in bone in ageing and osteoporosis are too simplified, and that the mandible differs sufficiently from post-cranial skeletal sites that it would be unwise to extrapolate from findings in the jaw to the circumstances elsewhere.

A fabric-dependent fracture criterion for bone

A fracture criterion for bone tissue is proposed. Bone material is considered to be anisotropic and its properties are described by invoking the concept of directional variation of porosity. The fracture criterion is expressed as a scalar-valued function of the stress tensor and it incorporates an orientation-dependent distribution of compressive/tensile strength. The proposed mathematical framework is applied to a numerical analysis of fracture in the proximal femur due to a fall from standing height. The risk of fracture is assessed in the context of two different porosity distributions, simulating a healthy and an osteoporotic bone.

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

The hypothesis that trabecular morphology can predict the elastic properties of cancellous bone has only partly been verified and no predictive analytical model is currently available. Such models are becoming increasingly relevant as the resolution levels of three-dimensional scanning techniques approach the size of trabeculae. This study took advantage of micro-finite-element methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. Numerical analysis was based on high-resolution three-dimensional computer reconstructions of cancellous bone specimens from which the complete elastic characteristics and trabecular morphology, represented by three different fabric measures (the mean intercept length and two volume-based ones), were calculated. Each fabric measure was analyzed individually using the tensorial relationships derived by Cowin (Mech Mater 4:137-147; 1985). Models for both stiffness and compliance entries were developed. The models based on stiffness entries could explain 93.4%-95.6% of the variance, whereas those based on compliance entries could explain 89.2%-89.4%. When using the former model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star volume distribution), with 23% less remaining variance. The high correlations found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtain considerably better estimates of bone quality in vivo compared with the rough two-dimensional density measurements used today.

Three-dimensional microstructural analysis of human trabecular bone in relation to its mechanical properties

The purpose of this preliminary study is to explore the relationship between elastic modulus, bone mineral density (BMD), and trabecular microstructure in three dimensions. Twenty cubes of trabecular bone were processed from two lumbar vertebrae obtained from one individual. The BMD of each cube was measured by dual-energy X-ray absorptiometry and peripheral quantitative computed tomography. Each cube was serially scanned by microcomputed tomography to produce three-dimensional data sets. By analyzing these data sets, three-dimensional trabecular microstructural indices of connectivity density and fractal dimension were calculated as well as histomorphometric parameters. The cubes were tested mechanically in a nondestructive manner for measurement of their elastic modulus. This preliminary study showed that: (1) bone mass index is correlated with mechanical properties, with coefficients of correlation ranging from 0.552 to 0.601; and (2) when controlling for BMD, no association could be detected between measures of structural complexity (connectivity density and fractal dimension) and elastic modulus in the craniocaudal direction of human vertebral bodies.

Measurement of intraspecimen variations in vertebral cancellous bone architecture

A three-dimensional technique was developed for the quantification of the number and cross-sectional geometry of individual trabeculae oriented along a given direction. As an example application, the number of vertical and horizontal trabeculae and their respective cross-sectional geometry were determined for a set of six vertebral cancellous bone specimens (L3-L4 female vertebral bodies; age range 39-63 years). Three-dimensional optical images at a spatial resolution of 20 microm were obtained using an automated serial milling technique. The thickness distributions were generally right skewed. The mean true thickness for both the vertically and horizontally oriented trabeculae showed a strong relationship with volume fraction (vertical: r2 = 0.86; p < 0.05; horizontal: r2 = 0.80; p < 0.05), and mean trabecular thickness (Tb.Th.) (vertical: r2 = 0.81; p < 0.05; horizontal: r2 = 0.72; p < 0.05). The horizontal trabeculae were greater in number and were thinner than the vertical trabeculae. The coefficient of variation of the intraspecimen vertical trabecular thicknesses ranged from 25% to 42%, and showed a weak, albeit insignificant, positive correlation with volume fraction (r2 = 0.46). The findings demonstrated substantial intraspecimen variations exist in trabecular thickness that are not related to volume fraction. Further studies are recommended to determine the potential role of such intraspecimen variations in architecture on biomechanical properties.

Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus

The appearance of cancellous bone architecture is different for various skeletal sites and various disease states. During aging and disease, plates are perforated and connecting rods are dissolved. There is a continuous shift from one structural type to the other. So traditional histomorphometric procedures, which are based on a fixed model type, will lead to questionable results. The introduction of three-dimensional (3D) measuring techniques in bone research makes it possible to capture the actual architecture of cancellous bone without assumptions of the structure type. This requires, however, new methods that make direct use of the 3D information. Within the framework of a BIOMED I project of the European Union, we analyzed a total of 260 human bone biopsies taken from five different skeletal sites (femoral head, vertebral bodies L2 and L4, iliac crest, and calcaneus) from 52 donors. The samples were measured three-dimensionally with a microcomputed tomography scanner and subsequently evaluated with both traditional indirect histomorphometric methods and newly developed direct ones. The results show significant differences between the methods and in their relation to the bone volume fraction. Based on the direct 3D analysis of human bone biopsies, it appears that samples with a lower bone mass are primarily characterized by a smaller plate-to-rod ratio, and to a lesser extent by thinner trabecular elements.

Comparison of eight histomorphometric methods for measuring trabecular bone architecture by image analysis on histological sections

Osteoporosis is defined as a disease characterized by low bone mass and microarchitectural deterioration of trabecular bone leading to enhanced bone fragility. Various histomorphometric methods have been described to measure bone architecture on histological sections. However, not all of the methods are strictly equivalent and some of them appear able to detect differences earlier in the course of the disease. We have compared 8 histomorphometric methods known to characterize the architecture of trabecular bone in 154 male osteoporotic patients. Measurements were done on transiliac bone biopsies: Trabecular number, thickness, and separation (Tb.N, Tb.Th, Tb.Sp); Trabecular Bone Pattern Factor (TBPf); Euler-Poincare's number (E); Interconnectivity Index (ICI); strut analysis of the trabecular network with the ratio of nodes/free-end (N/F); star volume of the bone marrow (V*m.space) and trabeculae (V*Tb) and the Kolmogorov fractal dimension of the trabecular boundaries (D). Relationships between the various architectural parameters were studied by hierarchical cluster analysis. Linear, hyperbolic, and exponential correlations were found between trabecular bone volume (BV/TV) and architectural parameters. Cluster analysis demonstrates the link between these architectural parameters. ICI, E, and TBPf, which reflect the amount of open/closed marrow cavities clustered together and appeared related to Tb.Sp, V*m.space which are indicators of the mean size of marrow cavities. Tb.Th, V*Tb and N/F flocked together as they reflect the trabecular size. Tb.N and D segregated together and seemed to best describe the trabecular network complexity. These histomorphometric techniques are correlated but correlations may be linear or nonlinear. Several histomorphometric techniques need to be used in parallel to appreciate the pathophysiological mechanisms of osteoporotic states.

Comparison of structure extraction methods for in vivo trabecular bone measurements

In vivo trabecular bone structure measurements have become available recently using high resolution quantitative computed tomography (3D-QCT) or magnetic resonance imaging. In this work different structure extraction and morphometric evaluation techniques are compared, which are of potential use for in vivo assessment of human cancellous bone structure. Given the spatial resolution of actual in vivo examination procedures, best results are obtained by extracting first the skeleton of the structure and applying model independent 3D techniques to calculate trabecular number, then deriving mean trabecular thickness and separation from densitometric bone volume fraction and Tb.N*. Traditional histomorphometric methods based on bone surface and volume ratios and assuming a plate model performed less well.

Accuracy of cancellous bone volume fraction measured by micro-CT scanning

Volume fraction, the single most important parameter in describing trabecular microstructure, can easily be calculated from three-dimensional reconstructions of micro-CT images. This study sought to quantify the accuracy of this measurement. One hundred and sixty human cancellous bone specimens which covered a large range of volume fraction (9.8-39.8%) were produced. The specimens were micro-CT scanned, and the volume fraction based on Archimedes' principle was determined as a reference. After scanning, all micro-CT data were segmented using individual thresholds determined by the scanner supplied algorithm (method I). A significant deviation of volume fraction from method I was found: both the y-intercept and the slope of the regression line were significantly different from those of the Archimedes-based volume fraction (p < 0.001). New individual thresholds were determined based on a calibration of volume fraction to the Archimedes-based volume fractions (method II). The mean thresholds of the two methods were applied to segment 20 randomly selected specimens. The results showed that volume fraction using the mean threshold of method I was underestimated by 4% (p = 0.001), whereas the mean threshold of method II yielded accurate values. The precision of the measurement was excellent. Our data show that care must be taken when applying thresholds in generating 3-D data, and that a fixed threshold may be used to obtain reliable volume fraction data. This fixed threshold may be determined from the Archimedes-based volume fraction of a subgroup of specimens. The threshold may vary between different materials, and so it should be determined whenever a study series is performed.

Connectivity and the elastic properties of cancellous bone

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14-91 years and a wide range of trabecular architecture was found. Each specimen was three-dimensionally reconstructed with a voxel size of either 20 or 25 microm. Using the detailed three-dimensional reconstructions as input for microstructural finite-element models, the complete elastic properties of the trabecular architecture were obtained and maximum and mean stiffness could be calculated. Volume fraction and true three-dimensional architectural measurements of connectivity density and surface density were determined. Connectivity density was determined in an unbiased manner by the Euler number, which is a topological property. Using multiple regression analysis it was found that volume fraction explained by far the greatest part (84%-94%) of the variation in both mean and maximum stiffness. When connectivity density and surface density were included, the correlations increased marginally to 89%-95%. Noticeably negative regression coefficients were found for connectivity density. The results suggest that, in normal cancellous bone, the connectivity density has very limited value for assessment of elastic properties by morphological variables, but if a relation exists then stiffness decreases with increasing connectivity.

Subchondral bone remodeling increases in early experimental osteoarthrosis in young beagle dogs

We evaluated subchondral bone remodeling and structure in the condyles of the femur and the patellar surface of the femur in early experimental osteoarthrosis of young female beagle dogs. 14 littermate (twin) dogs were divided into operation (n 7) and control groups (n 7). The dogs in the operation group underwent surgically a 30 degrees valgus angulation of the right tibia to induce osteoarthrotic articular cartilage lesions in the knee (stifle) joint. 7 months postoperatively, bone samples were harvested from both condyles and the patellar surface of the femur and evaluated by histomorphometry of subchondral bone. Cartilage samples from the same areas were taken for histology. In the operated dogs, subchondral bone remodeling increased strikingly in the patellar surface of the femur; osteoid thickness and osteoblast surface/bone surface increased up to 42% and 94% (p < 0.05), as compared to controls. Total and active erosion depths increased by 14% and 30% in the same area (p < 0.05). However, in bone structural parameters no significant difference could be observed between the groups. In the medial condyle of the femur, the trabecular number decreased in operated dogs, as compared to controls (p < 0.05). The lateral condyle of the femur in operated animals did not differ from controls in the parameters tested. In the operated dogs, histology from cartilage samples showed initial osteoarthrotic changes in the patellar surface and the medial condyle of the femur. Histologic changes were greatest in the patellar surface of the femur, as assessed by the Mankin scores. At the very onset of osteoarthrosis, subchondral bone remodeling increases, but the bone structural changes are indistinct. It seems that in this osteoarthrosis model, cartilage lesions precede major subchondral changes in the structure of the bone.

Comparison of two methods for measuring orientation

At the Department of Dental Radiology of ACTA, the line fraction deviation (LFD) method was developed to measure orientation on radiographic trabecular patterns. This article explains the measurement of the LFD index of orientation in a downscaled model. When investigations began to produce noteworthy results, the need for deeper understanding of the method and the resulting diagrams increased. Because it had previously been applied on rather complex patterns originating from bone it seemed worthwhile to study simpler images as well, which might yield a more intuitive understanding of the diagrams. Moreover, it seemed useful to compare the new LFD method with the well-accepted mean intercept length (MIL) method. Fifty images originating from cancellous bone structures and 25 drawings were analyzed. The results show that the MIL method tends to produce ellipses (not only on images originating from bone), and also that the LFD method is more sensitive to anisotropy.

The relationship between three-dimensional connectivity and the elastic properties of trabecular bone

A finite-element model was used to explore the relationship between connectivity density and the elastic modulus of trabecular bone. Six cubic specimens of trabecular bone, three prepared from human distal radii and three from L1 vertebrae, were imaged with synchrotron microtomography. The three-dimensional images were reconstructed into binary volumes of mineralized bone and soft tissue, and incorporated into the finite-element model. The relationship between three-dimensional connectivity and elastic modulus was explored by uniform thinning (atrophy) and thickening (recovery) of the trabecular bone. Though no functional relationship was found between connectivity and elastic modulus, there was a linear relationship, after a full cycle of atrophy and recovery, between the loss of elastic modulus and the overall loss of connectivity. The results indicate that recovery of mechanical function depends on preserving or restoring trabecular connectivity.

Impact of spatial resolution on the prediction of trabecular architecture parameters

Although the efficacy of various measures for the assessment of trabecular bone architecture has been widely studied, the impact of spatial resolution on the estimation of these measures has remained relatively unexplored. In this study, ten cubes each of human trabecular bone from the femur and vertebral bodies were obtained from nine cadavers (four males and five females), aged 23-67 years (mean 42.3 years). These specimens were serially milled and imaged at a resolution of 40 microm to produce three-dimensional digitizations from which traditional morphometric and structural anisotropy measures could be computed based on a three-dimensional approach. The cubes were then artificially degraded to an in-plane resolution of 100 microm and an out-of-plane (slice) resolution of 100-1000 microm. These resolutions mimicked in vivo resolutions as seen using magnetic resonance (MR) imaging. All images, original and degraded, were individually segmented using a thresholding algorithm, and both the traditional morphometric and structural anisotropy measures were recomputed. The choice of slice direction was varied along the superior-inferior (axial), anterior-posterior (coronal), and medial-lateral (sagittal) directions to minimize the impact of the lower slice resolution on the architectural measures. It was found that traditional morphometric measures such as trabecular spacing and trabecular number showed weak resolution dependency; measures such as trabecular thickness, however, showed strong resolution dependency and required very high resolutions for precise measurement. In the case of the femur specimens, both structural anisotropy as well as the preferred orientation showed a strong resolution dependency. The resolution dependency of these parameters could be minimized for the femur and the vertebral body specimens if the slice direction was taken along the superior-inferior direction.