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Keywords:

  • biomedical imaging;
  • bone architecture;
  • imaging;
  • magnetic resonance imaging;
  • MRI;
  • modeling;
  • osteoporosis;
  • three-dimensional microimaging;
  • computed tomography;
  • CT

Abstract

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

With the proportion of elderly people increasing in many countries, osteoporosis has become a growing public health problem, with rising medical, social, and economic consequences. It is well recognized that a combination of low bone mass and the deterioration of the trabecular architecture underlies osteoporotic fractures. A comprehensive understanding of the relationships between bone mass, the three-dimensional (3D) architecture of bone and bone function is fundamental to the study of new and existing therapies for osteoporosis. Detailed analysis of 3D trabecular architecture, using high-resolution digital imaging techniques such as magnetic resonance microimaging (MRμI), micro-computed tomography (μCT), and direct image analysis, has become feasible only recently. Rapid prototyping technology is used to replicate the complex trabecular architecture on a macroscopic scale for visual or biomechanical analysis. Further, a complete set of 3D image data provides a basis for finite element modeling (FEM) to predict mechanical properties. The goal of this paper is to describe how we can integrate three-dimensional microimaging and image analysis techniques for quantitation of trabecular bone architecture, FEM for virtual biomechanics, and rapid prototyping for enhanced visualization. The integration of these techniques provide us with an unique ability to investigate the role of bone architecture in osteoporotic fractures and to support the development of new therapies. Anat Rec (New Anat) 265:101–110, 2001. © 2001 Wiley-Liss, Inc.

Osteoporosis, the most prevalent bone disease affecting aging adults, is a major public health problem in many countries. The disease effects an estimated 75 million people in the United States, Europe, and Japan combined (Consensus Development Conference, 1991). In the United States alone, an estimated 1.3 million osteoporosis-related fractures occur each year, with attendant costs exceeding $10 billion per year. Vertebral fractures are most common, accounting for more than half of all osteoporotic fractures, and impair both the quality of life and functioning of osteoporotic subjects (Hall et al., 1999). Hip fractures, which generally require hospitalization and surgery, increase mortality within the year following the fracture, and cause many survivors to lose mobility and the ability to live independently. The mortality within 5 years after vertebral fracture is similar to that observed with hip fracture, that is, about 20% over that expected in an age-matched population (Cooper, 1997). The National Osteoporosis Foundation (1996) estimates that one in two women and one in eight men are at risk of suffering osteoporosis-related fractures during their lifetime.

A comprehensive understanding of the relationships between bone mass, the three-dimensional (3D) architecture of bone and bone function is fundamental to the study of new and existing therapies for osteoporosis.

Osteoporosis has been defined as “a skeletal disease characterized by low bone mass and microarchitectural deterioration of bone tissue, with a consequent increase in bone fragility and susceptibility to fracture” (Consensus Development Conference, 1991). The prevailing view that osteoporosis is caused by the excessive loss of bone mass is somewhat limited in scope, because bone mineral density alone cannot explain the difference in fracture frequency between osteoporotic and normal individuals (Krolner and Nielsen, 1982). While low bone mass is a major component of fracture risk, the bone architecture, which defines the distribution of bone mass in three-dimensional space, also contributes to the tissue's biomechanical integrity and, therefore, to fracture risk (Parfitt, 1992; Kleerkoper et al., 1985). Traditional, static two-dimensional histomorphometry (Parfitt, 1983) provides only a limited description of trabecular architecture. Detailed analysis of three-dimensional bone architecture, and its relation to bone strength, has become feasible only recently using high-resolution three-dimensional digital imaging techniques, such as magnetic resonance microimaging (MRμI) (Chung et al., 1995; Borah et al., 2000) and micro-computed tomography (μCT) (Feldkamp et al., 1989; Ruegsegger et al., 1996). Rapid prototyping technology can be used to reproduce the complex architecture of trabecular bone on a macroscopic scale for visual or biomechanical analysis. Further, a complete three-dimensional data set provides a basis for finite element modeling (FEM) to predict mechanical properties (Rietbergen et al., 1995).

In this paper, our objectives are: (1) to describe how three-dimensional microimaging (MRμI and μCT) and image analysis techniques can be used to quantify trabecular architecture and (2) to illustrate how 3D microimaging, FEM, and rapid prototyping combine to provide unique insight into the complex nature of trabecular architecture and its role in osteoporosis-related fracture.

BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

Osteoporosis is diagnosed clinically when the bone mineral density (BMD) of the spine, hip, or mid-radius is more than 2.5 standard deviations below the mean value for young adult women (Kanis et al., 1994). Although useful for clinical management, BMD measurement has limitations as a surrogate marker of bone strength and the risk of fragility fracture. There is considerable overlap of BMD measurements in populations with and without fractures, and the relation between bone mass and fracture risk is not linear (Wasnich et al., 1989). Most osteoporosis therapies increase BMD by a modest amount (3–8% in a year), yet reduce the risk of fractures by about 50% or more, a benefit that cannot be explained by the increase in bone mass alone. Further, individuals who have had a previous fracture are at increased risk for future fractures, independent of bone density (Ross et al., 1991). All of the evidence suggests that other factors besides low BMD contribute to bone fragility. A combination of factors such as decreased bone mass, mineralization defects, cortical porosity, and the loss of trabecular architecture may have major effects on bone fragility. The search for surrogate markers of bone strength and fracture risk is, therefore, becoming increasingly important.

OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The mechanical function of the trabecular bone is to transfer loads across joints (as in the hip), to resist compressive loads (as in the vertebrae), and to act as a shock absorber (as in the hip and knee). As might be expected, the relative proportion of trabecular bone varies at different skeletal sites, ranging from 1% at the mid-radius, to 25% at the distal radius and femoral neck of the hip, to a high of 66–90% in the vertebrae (Einhorn, 1992). In the early postmenopausal years, bone loss is predominantly trabecular (Wark, 1996). This may be due to the more rapid rate of bone turnover or remodeling in the trabecular bone compared with cortical bone. Trabecular perforations cause irreversible loss of structural elements, resulting in the deterioration of trabecular architecture. These effects are particularly evident in the vertebrae, where the loss of bone mass and trabecular architecture reduces the load-bearing capacity of the bone, resulting in atraumatic vertebral fracture (Fig. 1).

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Figure 1. A lateral radiograph of the spine of an osteoporotic patient showing a veretebral wedge fracture of the thoracic vertebral body (T12). Compared to a normal lumbar vertebra body (L4), the T12 has a characteristic wedge shape due to compression on the anterior side of the vertebral body.

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The photomicrographs (Eriksen et al., 1994) in Figure 2 provide an excellent visual and qualitative description of architectural changes that may occur in the vertebra during osteoporosis and aging. In the normal vertebra, more bone can be seen, and the trabecular bone consists of highly-oriented vertical plates and horizontal struts in a well-connected network. In the osteoporotic vertebra, the loss of bone mass is apparent, and the trabecular bone is more rod-like, less oriented, and thinner, with increased void spaces between trabecular elements. These visual changes can be assessed quantitatively using 3D microimaging and image analysis techniques, as described below.

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Figure 2. Photomicrographs of trabecular bone obtained from a normal (top) and osteoporotic subject (bottom). The loss of bone mass in the osteoporotic bone is apparent with associated changes in trabecular architecture. Reproduced from Eriksen et al. (1994) with permission of the publisher.

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ARCHITECTURE ANALYSIS

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

Quantification by 3D MRμI

Ex-vivo analysis of bone biopsy specimens can provide a wealth of information about trabecular architecture and its relationship to biomechanical strength. High-resolution magnetic resonance imaging permits non-destructive analysis of typically 1 cm3 sub-volumes of the whole bone with spatial resolution in the 50 to 100 μm range (Chung et al., 1995; Hipp et al., 1996; Borah et al., 2000) and has been applied in structural studies of both human and animal bone specimens.

Figure 3A shows a 3D MRμI image of a human cadaveric biopsy core from the proximal femur. The image resolution was 85 μm in all three directions. For imaging purposes, marrow was removed and the defatted core was suspended in an aqueous solution of Magnevist, an imaging contrast reagent. Details of the imaging protocol have been previously described (Borah et. al., 2000). As implemented in this study, MRμI detects the water surrounding the biopsy and, therefore, the bone is represented by the negative image. The image is segmented into bone and background (water) using histogram-based local thresholding scheme (Dufresne et al., 1998). The segmented image is then inverted and surface rendered for visualization.

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Figure 3. A: A surface rendered 3D MRμI image of a biopsy core from a human proximal femur (85 μm resolution) shown on a reverse gray scale. For imaging, the defatted core was refilled with water to generate the NMR signal, as bone has no detectable signal. The segmented image is then inverted and surface rendered to visualize the bone structure. Imaging was performed on a 4.7 Tesla, 30 cm horizontal NMR imaging spectrometer (Biospec, Bruker, Germany). A 3D spin-echo protocol (repetition time = 94.3 ms; echo time = 8.61 ms, matrix 256 × 128 × 128; field of view = 21.7 × 10.9 × 10.9 mm) was used for imaging. B: A surface rendered 3D μCT image of a biopsy core from the human iliac crest (25 μm resolution). Imaging was performed on a Scanco μCT-20 scanner (250 projections; 14 mm field of view; 512 × 512 matrix; 200 slices).

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Quantification by 3D μCT

Micro-computed tomography, an X-ray imaging method, has been more regularly used in recent years as an alternative technique for ex vivo imaging and quantifying trabecular architecture. Our laboratory uses a commercially available scanner (Scanco μCT-20, Scanco Medical AG, Zurich) that has 2D fan beam acquisition with a fixed microfocus X-ray source and detector configuration (Ruegsegger et al., 1996). The X-ray radiation is attenuated by the bone sample and the transmitted X-rays then pass through a collimator and a scintillator (to convert the X-rays into light) and into a one-dimensional array of CCD detectors. The sample is rotated incrementally, creating a series of projections that are combined to form a two-dimensional image of a single section. By incrementally translating the sample in the axial direction, a series of contiguous two-dimensional images can be acquired and stacked to form a three-dimensional image.

Figure 3B shows a 3D μCT image at 20 μm isotropic resolution of a human iliac crest biopsy sample that was embedded in methyl methacrylate polymer. Typical resolution achieved in commercial scanners is in the 15 to 30 μm range, making a wide variety of samples, from small animal bones to clinical biopsy specimens, suitable for structure analysis. Specimens may be intact (i.e., the technique does not require removal of marrow), and may be dry or embedded in a polymer matrix.

Calculation of Architectural Parameters From a 3D Image (MRμI or μCT)

The age of osteoporosis-related architectural changes depicted in Figure 1 can be efficiently quantified by direct image analysis of a digital three-dimensional image. A number of parameters have been defined to measure different aspects of the bone architecture, including the following.

Bone Volume/Tissue Volume (BV/TV, %) quantifies the amount of bone and is calculated as the number of bone voxels in the volume of interest (VOI) divided by the total number of voxels in the VOI; BV/TV is expressed as a percentage.

Bone Surface/Tissue Volume (BS/TV, mm-1) is determined using stereological methods (Feldkamp et al., 1989) and provides the bone surface area per tissue volume.

Trabecular Thickness (Tb.Th, μm) is a quatitative estimate of trabecular thinning. Traditionally, Tb.Th is derived indirectly from bone volume and bone surface, assuming either a plate or a rod model. For a plate model, Tb.Th = 2* BV/BS (Feldkamp et. al., 1989). (The plate model may be appropriate for normal trabecular bone. However, as the shape of the trabecular bone changes with age or osteoporosis and becomes more rod-like, a rod model may be more appropriate.)

Direct Trabecular Thickness (Dir-Tb.Th, μm) is independent of any underlying model (plate or rod) and is measured directly at each surface voxel in the three-dimensional dataset. The length of continuous bone voxels along a surface normal calculated at each surface voxel is averaged over the total bone surface to derive Dir-Tb.Th (Borah et. al., 2000).

Connectivity Density (ConnD, mm-3) provides an estimate of the number of trabecular connections/mm3. It is defined as the number of trabecular elements that may be removed without separating the network. Well-connected trabecular elements may be thought of as constituting closed loops. Conceptually, ConnD may be considered as a measure of closed loops in a network of trabecular elements. Connectivity density is a topological parameter derived from the Euler Number (Odgaard and Gundersen, 1993) and is calculated as (1-Euler number)/VOI. Connectivity has been frequently referenced as a parameter mostly affected during the progression of osteoporosis (Parfitt, 1992). The removal of some trabecular bone completely will leave the trabecular network less well connected.

Marrow star volume (Ma.St.V, mm3) is a measure of the “voids” within the trabecular structure, which increase with progressive bone loss (Fig. 1). Marrow star volume is derived from line lengths in random directions measured from random points in the marrow to trabecular bone. The average cubed length (L3) is used to calculate the marrow star volume as 4π/3 * (L3) (Borah et al., 2000). It is a sensitive descriptor to quantify bone loss either through trabecular thinning or loss of entire trabeculae.

Percent Plate (% Plate) is a new parameter developed to delineate rods from plates. The measure of plates and rods is derived by comparing the direct and derived parameter of thickness. If the entire bone was rod-like, it should have a thickness measure equal to the thickness derived from the rod model. Likewise, if the bone was all plate-like, it would have a thickness value equal to the plate model. However, that the direct thickness measure usually falls between these two extremes is due to the fact that some of the bone is plate-like and some rod-like. The %Plate can be calculated as {2- (Direct Thickness/Plate Thickness)} × 100. It allows a quantitative estimate of the effect of bone resorption on the shape of the trabeculae.

Percent Bone in Load Direction (% BoneLD) is a sensitive measure of architectural changes related to the bone's alignment in the load direction (Borah et al., 2000). It assumes a priori knowledge of the major loading direction and the parameter represents the percentage of bone oriented in that direction. The measurement of % BoneLD can provide a quantitative estimate of amount of vertical and horizontal trabeculae and may be a useful indicator of preferential loss of horizontal struts in specimens of osteoporotic vertebrae. of iliac crest cores of a 60-year-old female and a 79-year-old male represent very different trabecular architecture. (The medical histories and demographic characteristics of these subjects were not available, so little is known about possible causes for any changes in bone architecture.) Several key parameters were quantified using direct image analysis algorithms (Table 1). The dramatic differences in the network structure (ConnD), the amount of void spaces (Ma.St.Vol), thinning of trabeculae (Tb.Th.), the transition from plate to rod (%Plate), and overall mass (BV/TV) can be fully appreciated by quantitative analysis of the images.

Table 1. Architectural parameters in human bone samples as determined by 3D MRμI and 3D μCT*
Parameters3D MRμI (iliac crest samples)3D μCT (vertebral samples)
60-year-old female79-year-old male52-year-old female without osteoporosis84-year-old female with osteoporosis
  • *

    BV/TV = bone volume; BS/TV = bone surface area; Dir-Tb.Th = direct trabecular thickness; ConnD = connectivity density; Ma.St.Vol = marrow star volume; %BoneLD = % bone in load direction, NA = not available.

BV/TV (%)23.586.0610.455.68
BS/TV (mm−1)3.531.212.501.51
Dir-Tb.Th (μm)241192132126
ConnD (mm−3)16.426.436.333.35
%Plate19.618.3142.1132.30
Ma.St.Vol (mm3)3.2339.2833.72113.09
%BoneLDNANA43.3747.09

There are several other parameters that are used to describe architecture. Trabecular Number (a measure of plate density) and Trabecular Separation (a measure of distance between trabeculae) are either derived on the basis of a plate model (Feldkamp et al., 1989) or obtained as direct 3D measurements (Hildebrand et al., 1999). Anisotropy is a parameter that defines the direction of preferred orientation of trabeculae and is important for directionally dependent mechanical properties (Goulet et al., 1994). Structure Model Index, SMI, is a parameter recently proposed to provide an estimate of plate-rod characteristics of the structure (Hildebrand et al., 1999).

ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The 3D MRμI images (Fig. 4) of iliac crest cores of a 60-year-old female and a 79-year-old male represent very different trabecular architecture. (The medical histories and demographic characteristics of these subjects were not available, so little is known about possible causes for any changes in bone architecture.) Several key parameters were quantified using direct image analysis algorithms (Table 1). The dramatic differences in the network structure (ConnD), the amount of void spaces (Ma.St.Vol), thinning of trabeculae (Tb.Th.), the transition from plate to rod (%Plate), and overall mass (BV/TV) can be fully appreciated by quantitative analysis of the images.

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Figure 4. Comparison of trabecular architecture by 3D MRμI in images at 85 μm isotropic resolution of cadaveric iliac crest biopsies. A: A 60-year-old female. B: A 79-year-old male. The architectural differences are quantified in Table 1.

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Similarly, Figure 5 shows the 3D μCT images (30 μm resolution) of lumbar spine biopsies obtained at autopsy of a 52-year-old female with no osteoporosis and an 84-year-old female with clinically manifested fracture. The visual differences in architecture between the two vertebral samples are expressed quantitatively in Table 1. In the osteoporotic sample, both bone volume and ConnD are at least 50% reduced in comparison to the sample from the healthy subject. The voids in space in the image of osteoporotic bone are clearly reflected in the higher value of marrow star volume. The relatively higher value of %BoneLD in the osteoporotic vertebrae is consistent with the observation that horizontal trabeculae (in the plane orthogonal to the load direction, Fig. 4) appears to be fewer in comparison to the healthy subject.

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Figure 5. Comparison of trabecular architecture by 3D μCT in images of cadaveric vertebral biopsies from a 52-year-old woman with no osteoporosis (A) and an 84-year-old woman with clinically manifested osteoporosis (B). The arrow shows the load direction along the long axis of the vertebral body. The architectural differences are quantified in Table 1.

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EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

Investigation of osteoporosis therapies in controlled small animal models of osteopenia has grown steadily during the last few years. Kapadia et al. (1998) have demonstrated that estrogen therapy effectively inhibits bone loss and the deterioration of trabecular architecture in a rat osteopenia model. The effect of intermittent treatment with human parathyroid hormone, hPTH(1-34), a bone anabolic, was evaluated in a rat model of osteopenia using synchrotron-based μCT (Lane et al., 1995). The anabolic therapy increased trabecular bone volume in the proximal tibias of the ovariectomized (OVX) rats by thickening the existing trabeculae. Therapy did not increase trabecular connectivity density.

We compared the treatment effects of hPTH (1-34) and fluprostenol, a bone anabolic prostaglandin FP receptor agonist, in a severely osteopenic rat model (Lundy et al., 1999; Borah et al., 1999). Both agents significantly increased trabecular bone volume in the lumbar vertebra compared to the pre-treatment OVX group. However, the therapy-induced changes in trabecular architecture differed greatly for the two therapies, as can be seen in the 3D μCT images of rat vertebra (Fig. 6). While PTH caused extensive trabecular thickening, the formation of new trabecular bone is visually evident with fluprostenol. All quantitative analyses were made in comparison to the pre-treatment OVX group. The 3D analysis showed that PTH treatment increased the trabecular bone volume (89%, P < 0.003) primarily by increasing trabecular thickness (69%, P < 0.0001) as the 3D connectivity density decreased (−17%, not significant, P = 0.26). These results are in agreement with those of Lane et al. (1995). With fluprostenol, however, bone volume increased (54%, P < 0.0001) both through an increase in trabecular thickness (19%, P < 0.0001) and by formation of new trabeculae, which was confirmed by an increase in 3D connectivity density (87%, P < 0.0001) in comparison to the pre-treatment OVX group (Borah et al., 1999). Although both PTH and fluprostenol provided the desired anabolic effect as evidenced by increasing bone volume (or mass), the results clearly differentiated the unique effects of the two anabolic therapies on trabecular architecture.

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Figure 6. Surface-rendered 3D μCT images of the L5 rat vertebra following 7 months of treatment in the ovariectomized rat. Female Sprague-Dawley rats were ovariectomized at 6 months, aged without treatment for 4 months (pre-treatment OVX), and then treated with saline, hPTH (1-34) 20 μg/kg and fluprostenol 300 μg/mg for 7 months. The 3D images show 20 contiguous sections. A: Age-matched intact animal. B: The pre-treatment OVX. C: PTH treated animal showing increased bone volume and thickening of trabecular bone. D: Fluprostenol treated animal showing increased bone volume with higher number of trabeculae leading to increased connectivity.

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IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

In vivo quantitative assessment of trabecular architecture in the vertebrae and the femur, which are load-bearing bones and primary sites of osteoporotic fracture, is beyond current technology. However, measurements at several peripheral skeletal sites, such as the wrist, the calcaneus, and the phalanges, are possible using MRI (Majumdar,1998) and peripheral 3D quantitative computed tomography (Laib et al., 1998). The spatial resolution obtained in human MRI ranged from 78–195 μm in plane and up to 1,000 μm in the slice orientation, depending on the anatomical site being imaged (Majumdar, 1998). MRI-derived structural indices (BV/TV, Tb.Th, Tb.N and Tb.Sp) were found to be good descriptors of architecture changes in postmenopausal women with and without hip fractures. The potential for the assessment of bone biomechanical properties in vivo from finite element analysis based on MRI and pQCT images has been recently reported (Rietbergen et al., 1998).

FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The quantification of the mechanical function of bone can be complicated because the anatomy of bone is intricate. It is, therefore, often necessary to use computational tools, such as Finite Element Modeling and Analysis, in order to understand how bone will function under various conditions. Finite Element Modeling (FEM) is the division of a structure or object into discrete shaped elements that have precise mathematical equations to describe their mechanical behavior. Structural Finite Element Analysis (FEA) is the calculation of the mechanical behavior (stress and strain) at any point within the structure under specific loading conditions. The foundation of every finite element model is the three-dimensional data of the object or structure. Digital FEM, which directly transforms 3D geometry into a structural model by converting each 3D voxel into a 3D FEA element (Fig. 7), is an efficient way to minimize errors in prediction of properties. This technique can easily result in huge structural models with more than a million FE elements. By using an iterative FEA solver program, FE models of this magnitude can be efficiently and rapidly analyzed.

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Figure 7. A comparison of the 3D surface rendering of 3D μCT for a cadaveric human vertebral biopsy (A) and the finite element model of the same sample (B). The FEM is shown with Von Mises Stress results contoured in color (C). Colors range from red (high stress) to dark blue (low stress).

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FEA has been used to study bone behavior on a microscopic and macroscopic level. Models can be analyzed over and over again under different conditions to simulate various types of loading conditions. Furthermore, bone FEA models provide greater insight into the relationship of structure to strength by allowing us to look inside the bone to see where stresses are localizing and may cause fracture.

In FEA studies, the computational technique must first be validated for the specific species. In such a validation study, both experimental and computational analyses must be completed to compare the predicted and actual mechanical properties. In a recent MRμI study, we showed that the computational and experimental values of apparent modulus—the bone's resistance to deformation—in the lumbar vertebra of young and mature minipigs were statistically similar (Borah et al., 2000). Good agreement was also found between the results of compression tests and those of FE analysis of 3D μCT images of human trabecular bone samples (Ulrich et al., 1997). The ex vivo validation studies provide evidence supporting the promise of 3D imaging as a basis for accurate modeling of bone at an architectural level and may provide a basis for in vivo determination of the structural integrity of a patient's skeleton.

Disease Simulation by FEA: The Role of Horizontal Trabeculae

In addition to modeling the actual architecture of a bone biopsy, FEA is extremely useful for simple analyses to better understand the function of bone. We have used FEA analysis to simulate disease to understand how trabecular connectivity relates to bone properties. Specifically, we were interested in quantifying the role of horizontal trabeculae to overall bone properties. A planar three-dimensional model of trabecular bone was created and evaluated for baseline mechanical properties (Fig. 8). The structure was subjected to sequential bone loss through either loss of horizontal struts or uniform thinning of the trabecular elements. After each iteration, the model was evaluated to determine the functional consequence. We found that bone removal via horizontal trabeculae perforation was over twice as devastating to the overall structural integrity compared to bone loss through uniform thinning of trabeculae (Fig.8). The FEA analysis suggests that the type of connectivity found in trabecular bone or the removal of horizontal struts may be very important in defining bone fragility.

The type of connectivity found in trabecular bone or the removal of horizontal struts may be very important in defining bone fragility.

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Figure 8. A: A planar 3D trabecular structure model used to determine structural consequences of reduction of bone volume on apparent modulus (the bone's resistance to deformation) via loss of horizontal struts or uniform thinning. B: Graphs indicate that loss of horizontal struts through perforations decreased modulus 2× as large as uniform trabecular thinning.

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RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

Three-dimensional images have provided a significant enhancement in our ability to understand trabecular architecture and its potential role in osteoporosis. Building of physical replicas using rapid prototyping (RP) technologies, such as Stereolithography (SLA) and Selective Laser Sintering (SLS), has added another new dimension to our visualization techniques. Rapid prototyping involves a layer-by-layer construction of a three-dimensional object from a computer file containing the three-dimensional image. The physical synthesis of three-dimensional trabecular architecture can be obtained from MRμI, μCT, or QCT images of bone samples. In stereolithography, objects are directly constructed from a photoreactive liquid polymer through the sequential curing of thin layers representing a cross-section of the object. Two SLA models of 3D μCT images of normal and osteoporotic vertebral samples are shown in Figure 9. The physical replicas provide excellent reproduction of the intricate bone architecture as seen in the images.

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Figure 9. The stereolithography (SLA) models of trabecular bone of a 24-year-old female (top) and that of an 84-year-old female with osteoporosis (bottom), shown side-by-side with the 3D μCT images used to create the replicas. The SLA models were synthesized from a photoreactive liquid polymer through the sequential curing with lasers of thin layers representing a cross-section of the object. The μCT image of the 84-year-old female is reproduced from Muller and Ruegsegger (1997) with permission of the publisher.

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The advantages of RP technology are several:

  1. (1) The enlarged physical replicas of actual bone biopsies can illustrate first-hand the three-dimensional morphology of bone to a clinician, researcher, or a patient, providing new insight into the effects of aging and osteoporosis on bone structure.

  2. (2) It is possible to reconstruct a bone model using material with homogeneous and well-characterized mechanical properties. This process may allow us to evaluate an independent effect of architecture on mechanical properties through the elimination of tissue variations within samples.

  3. (3) The digital image can also be altered to reflect a change in architecture, such as removal of horizontal struts or loss of trabecular connectivity. The physical replica can then be reconstructed to evaluate how these changes affect mechanical properties.

ARCHITECTURE AND STRENGTH

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The compressive strength of the trabecular structure is proportional to its radius squared and to the square of the distance between the supporting struts (Moskilde, 1993). The biomechanical consequence of loss of trabecular bone through thinning and perforations is, therefore, a much weakened loadbearing vertebral network. Scanning electron microscopy showed preferential perforation and ultimate loss of horizontal trabeculae in the vertebral specimens of elderly women (Moskilde, 1993). These changes may be observed by three-dimensional μCT in an osteoporotic vertebral body (Fig. 5). The results of architecture modeling and biomechanical simulation suggested that the perforation of horizontal struts leading to loss of connectivity decreased modulus twice as much as did uniform thinning of trabeculae (Fig. 8). Euler buckling theory suggests that the strength of a vertically compressed trabeculae is proportional to the square of the unsupported length or the distance between horizontal trabeculae (Bell et al., 1967). Once the structure is compromised, the vertebral body is prone to fracture through buckling even under normal loading conditions such as bending or lifting of light weight.

It has been reported that the relative risk of vertebral fractures in women having prevalent fractures is much higher compared with women having no fractures (Ross et al., 1991; Lindsay et al., 2000). Further, while the bone loss that leads to osteoporosis may be gradual, once patients start to experience vertebral fracture, the progression of subsequent fractures is relatively rapid. The most recent clinical data suggest that in a population of osteoporotic patients with prevalent vertebral fractures, one in five, or 20%, will fracture again within one year of an observed fracture (Lindsay et al., 2000). Because lost trabeculae cannot be replaced, there remains a significant possibility that once the trabecular network is disrupted, pharmacologic intervention will have little effect on the strength of the bone that remains (Parfitt, 1992). The prevention of the first fracture, therefore, is the desired goal of osteoporosis therapies. The antiresorptive therapies (e.g., bisphosphonates, estrogen, calcitonin) prevent further bone loss and reduce the occurrence of vertebral fractures by about 50% or more. Although this is a major benefit, the desired goal is the complete reduction of fractures. There is, therefore, a clinical need for an anabolic therapy that will reverse osteoporosis by building bone of good quality, which may be defined by its mass, architecture, and material properties. The technologies described in this paper have the potential to demonstrate the effectiveness of such novel therapies.

SUMMARY

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The importance of trabecular architecture in maintaining the biomechanical integrity of bone tissue is well recognized. In bone architecture studies, precise non-destructive imaging of trabecular bone, accurate characterization of architecture, and quantification of functional measurements are paramount to a better understanding of bone health. The experimental approach described in the paper integrates several novel technologies that take us from an animal or human bone sample to a high-resolution 3D image for architecture analysis, to finite element analysis for virtual biomechanical testing, and to an enlarged physical recreation for visualization. The benefits of this approach are many. As new therapies are developed for osteoporosis, the need to better understand the effects of drugs on bone tissue cannot be overemphasized. The increased use of densitometry throughout the last decades resulted in a focus on bone density as the most important predictor of osteoporotic fractures; the techniques we describe enable us to look beyond simple bone density measurements. Our ability to integrate three-dimensional microimaging techniques, direct image analysis for architecture measurement, FEM for virtual biomechanics, and rapid prototyping for enhanced visualization provides us with a unique opportunity to probe the role of bone architecture in osteoporosis-related fractures and to assist in the development of new osteoporosis therapies.

Acknowledgements

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

The authors thank Prof. Peter Ruegsegger (Institute of Biomedical Engineering, University of Zurich) and Dr. Bruno Koller (Scanco Medical AG, Zurich) for providing us with two μCT images (in Fig. 9). We are thankful to Dr. David Lester (US Food and Drug Administration) for his encouragement in the preparation of the manuscript. We thank Dr. Lisa Bosch for editing the manuscript.

LITERATURE CITED

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information
  • Bell GH, Dunbar O, Beck JS, Gibb A. 1967. Variations in strength in vertebrae with age and their relation to osteoporosis. Calcif Tissue Res 1: 7586.
  • Borah B, Dufresne TE, Chmielewski PA, Pierce SA, Hartke JR, Lundy MW. 1999. Fluprostenol, a prostaglandin FP agonist, improves 3-dimensional trabecular architecture in rat vertebrae as measured by micro-computed tomography. [abstract] J Bone Miner Res 14: S401.
  • Borah B, Dufresne TE, Cockman MD, Gross GJ, Sod EW, Myers WR, Combs KS, Higgins RE, Pierce SA, Stevens ML. 2000. Evaluation of changes in trabecular bone architecture and mechanical properties of minipig vertebrae by 3-dimensional magnetic resonance microimaging and finite element modeling. J Bone Miner Res 15: 17861797.
  • Chung HW, Wehrli FW, William JL, Kugelmass SD, Wehrli SL 1995. Quantitative analysis of trabecular microstructure by 400 MHz nuclear magnetic resonance imaging. J. Bone Miner Res 10: 803811.
  • Consensus Development Conference, 1991. Prophylaxis and treatment of osteoporosis. Am J Med 90(1): 107110.
  • Cooper C. 1997. The crippling consequences of fractures and their impact on quality of life. Am J Med. 103(2A): 12S19S.
  • Dufresne TE. 1998. Segmentation techniques for analysis of bone by three-dimensional computed-tomographic imaging. Technol Health Care 6: 351359.
  • Einhorn TA. 1992. Bone strength: The bottom line. Calcif Tissue Int. 51: 333339.
  • Eriksen EF, Axelrod DW, Melsen F. 1994. Bone Histomorphometry. New York: Raven Press.
  • Feldkamp LA, Goldstein SA, Parfitt AM, Jesion G, Kleerekoper M. 1989. The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Miner Res 4: 311.
  • Goulet RW, Goldstein SA, Ciarelli MJ, Kuhn JL, Brown MB, Feldkamp LA. 1994. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech 27: 375389.
  • Hall SE, Criddle RA, Comito TL, Prince RL. 1999. A case-control study of quality of life and functional impairment with long-standing vertebral osteoporotic fracture. Osteoporosis Int 9: 508515.
  • Hildebrand T, Laib A, Muller R, Dequeker J, Ruegsegger P. 1999. Direct three-dimensinal morphometric analysis of human cancellous bone : Microstructural data from spine, femur, iliac crest and calcaneus. J Bone Miner Res 14: 11671174.
  • Hipp JA, Jansujwicz A, Simmons CA, Snyder BD. 1996. Trabecular bone morphology from micro-magnetic resonance imaging. J Bone Miner Res 11(2): 286292.
  • Kanis JA, Melton LJ III, Christiansen C, Johnston CC, Khaltaev N. 1994. The diagnosis of osteoporosis. J Bone Miner. Res 9: 11371141.
  • Kapadia RD, Stroup GB, Badger AM, Koller B, Levin JM, Coatney RW, Dodds RA, Liang X, Lark MW, Gowen M. 1998. Applications of micro-CT and MR microscopy to study pre-clinical models of osteoporosis and osteoarthritis. Technol Health Care 6: 361372.
  • Kleerekoper M, Villanueva AR, Stanciu J, Rao DS, and Parfitt AM. 1985. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tissue Int 37: 594597.
  • Krolner B and Nielsen SP. 1982. Bone mineral content of the lumbar spine in normal and osteoporotic women: Cross sectional and longitudinal studies. Clin Sci 62: 329336.
  • Laib A, Hauselmann HJ, Ruegsegger P. 1998. In vivo high resolution 3D-QCT of human forearm. Technol Health Care 6: 329337.
  • Lane NE, Thomson JM, Strewler GJ, Kinney JH. 1995. Intermittent treatment with human parathyroid hormone (hPTH[1-34]) increased trabecular bone volume but not connectivity in osteopenic rats. J Bone Miner Res 10: 14701477.
  • Lindsay R, Watts N, Roux C, Barton I, Flowers K, Cooper C. 2000. One in five osteoporotic women will fracture again within 1 year of an incident vertebral fracture. Calcif Tissue Int 66(Suppl 1): S58.
  • Lundy MW, Delong MA, Combs KH, Gross GJ, Soehner ME, Pierce SA, Hartke JR. 1999. Restoration of cancellous architecture and increased bone strength in aged osteopenic rats treated with fluprostenol. [abstract] J Bone Miner Res 14(Suppl 1): S401.
  • Majumdar S. 1998. A review of magnetic resonance (MR) imaging of trabecular bone micro-architecture: contribution to the prediction of biomechanical properties and fracture prevalence. Technol Health Care 6: 321327.
  • Moskilde L. 1993. Vertebral structure and strength in vivo and in vitro. Calcif Tissue Int 53(Suppl): S121S126.
  • Muller R, Ruegsegger P. 1997. Microtomographic imaging for the nondestructive evaluation of trabecular bone architecture. In: LoweG, et al., editors. Bone research in biomechanics. Amsterdam: IOS Press, p 66.
  • National Osteoporosis Foundation, Washington D.C. 1996. Osteoporosis: the silent disease. slide presentation #6.
  • Odgaard A, Gundersen HJ. 1993. Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone 14: 173182.
  • Parfitt AM. 1983. The stereologic basis of bone histomorphometry. Theory of quantitative microscopy and reconstruction of the third dimension. In: ReckerR, editor. Bone histo-morphometry. Techniques and interpretations. Boca Raton, FL: CRC Press. p 5387.
  • Parfitt AM. 1992. Implications of architecture for the pathogenesis and prevention of vertebral fracture. Bone 13: S41S47.
  • Rietbergen van B, Weinans H, Huiskes R, Odgaard A. 1995. A new method to determine trabecular bone elastic properties and loading using micromechanical finite element models. J Biomech 28: 6981.
  • Rietbergen van B, Majumdar S, Pistoia W, Newitt DC, Kothari M, Laib A, Ruegsegger P. 1998. Assessment of cancellous bone mechanical properties from micro-FE models based on micro-CT, pQCT and MR images. Technol Health Care 6: 413420.
  • Ross PD, Davis JW, Epstein R, Wasnich RD. 1991. Pre-existing fractures and bone mass predict vertebral fractures in women. Ann Intern Med 114: 913–923.
  • Ruegsegger P, Koller B, Muller R. 1996. A microtomographic system for the nondestructive evaluation of bone architecture. Calcif Tissue Int 58: 2429.
  • Ulrich D, Hildebrand T, Van Rietbergen B, Muller R, Ruegsegger P. 1997. The quality of trabecular bone evaluated with micro-CT, FEA and mechanical testing. In: LoweG, et al., editors. Bone research in biomechanics. Amsterdam: IOS Press, 97112.
  • Wark JD. 1996. Osteoporotic fractures: background and prevention strategies. Maturitas 23: 193207.
  • Wasnich RD, Ross PD, Davis JW, Vogel JM. 1989. A comparison of single and multi-site BMC measurements for assessment of spine fracture probability. J Nucleic Med 30: 11661171.

Biographical Information

  1. Top of page
  2. Abstract
  3. BONE MINERAL DENSITY AS A SURROGATE MEASURE OF BONE STRENGTH
  4. OSTEOPOROTIC CHANGES IN TRABECULAR ARCHITECTURE
  5. ARCHITECTURE ANALYSIS
  6. ARCHITECTURAL DIFFERENCES DETECTED BY MRμI AND μCT
  7. EX VIVO μ CT FOR OSTEOPOROSIS DRUG DEVELOPMENT
  8. IN VIVO ASSESSMENT OF TRABECULAR ARCHITECTURE
  9. FINITE ELEMENT MODELING TO PREDICT BONE FUNCTION
  10. RAPID PROTOTYPING: REPLICAS FOR ENHANCED VISUALIZATION
  11. ARCHITECTURE AND STRENGTH
  12. SUMMARY
  13. Acknowledgements
  14. LITERATURE CITED
  15. Biographical Information

Dr. Borah, Mr. Gross, Dr. Dufresne, Mr. Smith, Dr. Cockman, Ms. Chmielewski, Dr. Lundy, Dr. Hartke, and Dr. Sod comprise an interdisciplinary group of scientists and engineers at Procter & Gamble Pharmaceuticals. They are involved in the research and development of novel methods of bone imaging and modeling and the application of these methods to the study of new therapies for osteoporosis.