Previous studies have shown that low-density,

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1 Mutual associations among microstructural, physical and mechanical properties of human cancellous bone Ming Ding, Anders Odgaard, Carl Christian Danielsen, Ivan Hvid From Aarhus University Hospital, Aarhus, Denmark Previous studies have shown that low-density, rod-like trabecular structures develop in regions of low stress, whereas high-density, plate-like trabecular structures are found in regions of high stress. This phenomenon suggests that there may be a close relationship between the type of trabecular structure and mechanical properties. In this study, 16 cancellous bone specimens were produced from 4 normal human tibiae aged from 16 to 85 years at post-mortem. The specimens underwent micro-ct and the microstructural properties were calculated using unbiased three-dimensional methods. The specimens were tested to determine the mechanical properties and the physical/compositional properties were evaluated. The type of structure together with anisotropy correlated well with Young s modulus of human tibial cancellous bone. The plate-like structure reflected high mechanical stress and the rod-like structure low mechanical stress. There was a strong correlation between the type of trabecular structure and the bone-volume fraction. The most effective microstructural properties for predicting the mechanical properties of cancellous bone seem to differ with age. J Bone Joint Surg [Br] 22;84-B:9-7. Received 13 December 2; Accepted after revision 29 October 21 The recently developed three-dimensional (3D) techniques allows unbiased and model-free quantification of the microstructural properties of cancellous bone. Bone-volume fraction, structure type, architectural anisotropy, connectivity M. Ding, MD, PhD, Senior Research Scientist A. Odgaard, MD, DMSci, Consultant Orthopaedic Surgeon I. Hvid, MD, DMSci, Professor Orthopaedic Research Laboratory, Aarhus University Hospital (ÅKH), Building 1A, Nørrebrogade 44, DK-8 Aarhus C, Denmark. C. C. Danielsen, MD, Associate Professor Department of Connective Tissue Biology, Institute of Anatomy, Aarhus University, DK-8 Aarhus C, Denmark. Correspondence should be sent to Dr M. Ding. 22 British Editorial Society of Bone and Joint Surgery 31-62X/2/ $2. and trabecular thickness are believed to be the characteristics of fundamental importance in describing the normal three-dimensional (3D) microstructure of cancellous bone. Apart from the bone density, these characteristics have attracted increasing interest in the relationship of mechanics and architecture. The type of trabecular structure changes continuously from one to another during ageing 1,2 and, in certain cases of remodelling of cancellous bone, 3 as trabecular plates are perforated and connecting rods are dissolved. The type of structure is also significantly different for various skeletal sites. 4 It has been shown that low-density rod-like structures develop in regions of low stress, whereas high-density plate-like structures are seen in regions of high stress. 5 This phenomenon suggests that the type of trabecular structure plays a significant role in the determination of the mechanical properties of cancellous bone. 6 Many studies have shown that density and architectural anisotropy together can largely explain the variances in mechanical strength and Young s modulus More recently, Ulrich et al 12 reported the ability of 3D microstructural properties to reflect the mechanical properties of cancellous bone calculated using finite-element analysis. They showed that microstructural properties, in addition to bone-volume fraction, could improve the explanation of Young s modulus of cancellous bone, and that the most effective microstructural properties varied with the different anatomical locations. A few attempts have been made to relate the connectivity of cancellous bone to mechanical properties. Studies based on stereological methods 13,14 or 3D methods, 15 have shown no 16 or only a weak relationship 17 between connectivity and Young s modulus. These suggest that connectivity density is not a primary determinant for the mechanical properties of cancellous bone. A volume-weighted measure of trabecular thickness 18 has been shown to differ for the skeletal sites 4 and to decrease with ageing. 1 It has also been shown that human tibial trabeculae may undergo thickening to compensate for the decrease in mechanical strength in ageing. 1 The effects of age and trabecular thickness in determining the mechanical properties remain unclear. We have tested the hypothesis that the type of trabecular structure significantly relates to the mechanical properties of cancellous bone and evaluated which of the micro- 9 THE JOURNAL OF BONE AND JOINT SURGERY

2 ASSOCIATIONS AMONG MICROSTRUCTURAL, PHYSICAL AND MECHANICAL PROPERTIES OF CANCELLOUS BONE 91 structural, physical/compositional properties correlate well with Young s modulus of cancellous bone. Moreover, we have determined the mutual associations among various properties of human peripheral cancellous bone, and examined whether there are the same associations overall and in young-, middle- and old-age groups. Materials and Methods We used 4 human proximal tibiae, each from a Caucasian donor, which were removed at post-mortem and stored at 2. The donors were aged from 16 to 85 years and were free from macroscopical pathological changes or a history of musculoskeletal diseases. There were ten women and 3 men and all had died suddenly either from trauma or acute disease. None had been immobilised for more than two weeks before death. 16 Two cylindrical cancellous bone specimens were produced from standardised locations on both the medial and lateral condyles of each tibia, yielding a total of 16 specimens. 19 These specimens were drilled out of frozen bone using a trephine with an inner diameter of 7.5 mm. The axis of the cylindrical specimens corresponded to the longitudinal axis of the tibia. The specimens were further cut 1mm below the subchondral bone plate and at the distal end to obtain specimens with a diameter and length of 7.5 mm. They were stored in sealed plastic tubes at 2, and care was taken to keep them moist during scanning and testing. 19 Microcomputed tomography (micro-ct) scanning. The specimens were scanned with a high resolution micro-ct system ( -CT 2; Scanco Medical AG, Zürich, Switzerland). Each 3D image data set consisted of approximately 35 micro-ct slide images ( pixels) with 16-bit-graylevels, and the voxel size was m 3. After scanning, the micro-ct images were segmented using individual optimal thresholds to obtain the accurate 3D datasets. 2 Calculation of 3D microstructural parameters. From the segmented accurate 3D datasets, the bone-volume fraction (bone voxel per total specimen voxel) was calculated. 2 The type of structure was assessed by calculating the structure model index (SMI). 21 This technique quantifies the type of structure, such as plates, rods and spherical objects and mixtures of plates and rods. The SMI was calculated from the 3D image analysis using a differential analysis of the triangulated bone surface. The SMI value is in an ideal flat plate structure and 3 in an ideal cylindrical rod structure, independent of the physical dimensions of the structure. If a structure consists of both plates and rods of equal thickness, the SMI will lie between and 3 depending on the volume ratio of rods and plates. 21 The quantification of architectural anisotropy was based on a 3D star volume distribution (SVD). 22 The degree of anisotropy was defined as the eigenvalue of the primary direction divided by the eigenvalue of the tertiary direction. 23 Unbiased quantification of connectivity, the number of trabeculae per volume in mm -3, was based on a topological approach. 15 3D volume-weighted trabecular thickness in mm, 3D trabecular spacing in mm, bone surface density in mm -1 (bone surface area per total volume of specimen), and bone surface-to-volume ratio in mm -1 (bone surface area per bone volume) were calculated 18 as were the mean trabecular volume in m 3 and the mean marrow space volume in m Mechanical testing. The specimens were tested in compression on an 858 Bionix MTS hydraulic materials testing machine (MTS Systems Corporation, Minneapolis, Minnesota). A load cell of 1kN was used and a static strain-gauge extensometer (Model F-2; MTS Systems Corporation) was attached to the testing column close to the specimen. The testing machine was computer-controlled (TestStar II; MTS Systems Corporation), and the forcedeformation data were collected by a PC and then converted to stress and strain data. 19 The specimens were tested non-destructively in compression to.6 strain with a strain rate of.2/s. Young s modulus was determined as the tangent to the loading curve at.6 strain. 19 Measurement of density, collagen and volume fraction. An accurate protocol was used for measuring the Archimedes-based bone-volume fraction, 25 with a slight modification. 2 Bone-tissue density, apparent density, collagen density, collagen concentration, apparent ash density and mineral concentration were determined by techniques which have been described in detail elsewhere. 19,26,27 Statistical analysis. All the statistical analyses were performed using SPSS 1. (SPSS Inc, Chicago, Illinois). The mean value for each tibia was used in analysis of multiple associations among various microstructural, physical/compositional, and mechanical properties. Each individual was represented by one set of values, thus all observations were independent. Bivariate correlation analysis was done to obtain Pearson s correlation coefficient (R) among various properties. Linear regression analyses were used to assess the associations between one of the primary microstructural properties (bonevolume fraction, structure model index, anisotropy, connectivity and trabecular thickness) or Young s modulus and all other properties. Assuming that the structure model index or bonevolume fraction was a good predictor for Young s modulus, the degree of anisotropy was added in a multiple regression model to test the hypothesis that it could significantly improve the explanation for the variance of Young s modulus. Because of the skewness of data in linear regression analysis, connectivity density and marrow space volume were logarithmically transformed to obtain normal distribution. These data were further divided into three age groups: young (16 to 39 years), middle (4 to 59 years) and old age (6 to 85 years) to assess the multiple associations among properties in different age groups. The correlation coefficient (R) or determination coefficient (R 2 ) was used to express the proportional variation due to linear or multiple regression and a p value <.5 was considered to be significant. VOL. 84-B, NO. 6, AUGUST 22

3 92 MING DING, ANDERS ODGAARD, CARL CHRISTIAN DANIELSEN, IVAN HVID Results Associations between Young s modulus and other properties. The linear analyses between Young s modulus and five primary microstructural properties are shown in Figure 1. 3D reconstructions of two samples from micro-ct images with extreme values of degree of anisotropy are presented in Figure 2. Linear regression analysis showed that the structure model index was the best predictor for Young s modulus (R 2 =.45, Fig. 1, Table I). Anisotropy increased this explanation to 53% in a multiple regression model. Bone 12 b=2477 (146 to 3547), r 2 = b=-388 (-529 to -247), r 2 = Bone volume fraction (-) Structure model index (-) Fig. 1a Fig. 1b 12 b=-24.6 (-36.3 to -13.), r 2 = b=13.2 (-27. to 53.4), r 2 =.1 p= Degree of anisotropy (-) Fig. 1c Connectivity density (mm -3 ) Fig. 1d b=5173 (2649 to 7697), r 2 = Relationships between Young s modulus and a) bone-volume fraction, b) structure model index, c) degree of anisotropy, d) connectivity density and e) trabecular thickness. The data are presented as slope (b) (95% confidence interval), determination coefficient (R 2 ) and p value derived from linear regression analysis ( = young age, = middle age, = old age) Trabecular thickness (mm) Fig. 1e THE JOURNAL OF BONE AND JOINT SURGERY

4 ASSOCIATIONS AMONG MICROSTRUCTURAL, PHYSICAL AND MECHANICAL PROPERTIES OF CANCELLOUS BONE 93 Fig. 2 3D reconstruction of two samples with extreme values of degree of anisotropy from micro-ct images of human tibial cancellous bone. Sample A (upper) from a 32-year-old donor showed the degree of anisotropy to be 1.41 with a nearly isotropic structure. Sample B (lower) from an 8-year-old donor showed a degree of anisotropy of 62.1 and an extremely anisotropic structure. This architectural change is of considerable significance since the remaining trabeculae align strongly to the primary direction (i.e. the longitudinal loading axis of the tibia) to compensate for bone loss as the consequence of ageing. apparent ash density or volume fraction together with the degree of anisotropy could explain the variance of Young s modulus by 46% or 45%, respectively. Bone apparent ash density or volume fraction alone could explain 4% or 39% of the variance of Young s modulus (Table II). The data were further divided into young-, middle- and old-age groups. Thus, in the young-age group connectivity density alone could explain 57% variance of Young s modulus, and marrow space volume increased this explanation to 79%. In the middle-age group, trabecular thickness could explain 52% of the variance of Young s modulus. In the old-age group, bone apparent density and the degree of anisotropy together could explain 58% of the variance of Young s modulus, while apparent density alone could explain 47% of the variance of Young s modulus (Tables I and II). Associations between primary microstructural properties and other properties. Tables I and II give Pearson s correlation coefficient between primary microstructural properties and other properties. Apparent density, collagen density, and apparent ash density were equally good as the best predictors for the bone-volume fraction (R 2 >.96, Fig. 3) and these relations were consistent overall and in young-, middle- or old-age groups (Table II). The variance of the structure model index was strongly explained by the apparent ash density (R 2 = 78%) or bonevolume fraction (R 2 = 77%, Fig. 3). Apparent ash density could explain 48% of variance of the structure model index VOL. 84-B, NO. 6, AUGUST 22

5 94 MING DING, ANDERS ODGAARD, CARL CHRISTIAN DANIELSEN, IVAN HVID Table I. Pearson s correlation coefficient (R) between Young s modulus or five primary microstructural properties and all measured microstructural parameters for overall (bold) and three age groups Pearson s correlation Young s Volume Structure Degree of Connectivity Trabecular coefficient (R) modulus fraction model index anisotropy density thickness Bone-volume fraction.62 Young.29 Middle.32 Old.74 Structural model index Young Middle * Old Degree of anisotropy Young Middle Old *.37 Connectivity density (mm -3 ) Young -.75* Middle Old * Trabecular thickness (mm) Young Middle.72* Old * -.8 Trabecular spacing (mm).33* Young Middle Old -.49* Bone surface density (mm -1 ) Young Middle Old *.49* Surface-to-volume ratio (mm -1 ) Young Middle * Old * Trabecular volume (µm 3 ) Young Middle Old.45* Marrow space volume (µm 3 ) -.38* Young Middle Old * p <.5; p <.1; p <.1 in the young-age group. Bone-volume fraction was the strong predictor of the structure model index in the middleage group (R 2 =.75). Apparent ash density highly explained the variance of the structure model in the old-age group (R 2 =.81, Table II). The variance of the degree of anisotropy was well explained by the marrow space volume by 42%. Bonevolume fraction alone could explain 37% of the variance of the degree of anisotropy (Fig. 3). No relationship was found between the degree of anisotropy and other properties in either the young- or the middle-age groups. The relationships between the degree of anisotropy and other properties in the old-age group were similar as in the overall group (Table I). The variance of connectivity was highly explained by the marrow space volume (R 2 =.92, Fig. 3), and the latter was consistently a strong predictor for connectivity density in the young-, middle- or old-age groups (Table II). The variance of trabecular thickness was highly explained by the bone surface-to-volume ratio (R 2 =.81, Fig. 3). Trabecular volume was the only predictor of trabecular thickness in the young-age group (R 2 =.72), and the bone surface-to-volume ratio was the only predictor of trabecular thickness in the middle-age group (R 2 =.91). Collagen density highly explained the variance of trabecular thickness in the old-age group (R 2 =.81, Table II). Discussion We have investigated the mutual associations among the microstructural, physical/compositional and mechanical properties of normal human tibial cancellous bone. We showed THE JOURNAL OF BONE AND JOINT SURGERY

6 ASSOCIATIONS AMONG MICROSTRUCTURAL, PHYSICAL AND MECHANICAL PROPERTIES OF CANCELLOUS BONE 95 Table II. Pearson s correlation coefficient (R) between Young s modulus or five primary microstructural properties and all measured physical/compositional parameters for overall (bold) and three age groups Pearson s correlation Young s Volume Structure Degree of Connectivity Trabecular coefficient (R) modulus fraction model index anisotropy density thickness Apparent density (g/cm 3 ) *.87 Young Middle * Old Apparent ash density (g/cm 3 ) *.86 Young * Middle * Old Tissue density (g/cm 3 ).38* * Young Middle Old Collagen density (g/cm 3 ) *.88 Young * Middle * Old *.26.9 Collagen concentration Young Middle Old *.9 Mineral concentration Young Middle Old * p <.5; p <.1; p <.1 that Young s modulus was mainly determined by the structure model index or the bone-volume fraction together with the degree of anisotropy. The structure model index and the bone-volume fraction are strongly correlated and are both primary determinants for the mechanical properties of cancellous bone. A plate-like structure reflects high mechanical stress, whereas a rod-like structure indicates low mechanical stress for normal cancellous bone. The effects of the microstructural properties in predicting the mechanical properties of cancellous bone seem to be age-dependent. Connectivity was a good predictor for Young s modulus in young individuals whereas trabecular thickness did so for Young s modulus in middle-age individuals and bone apparent density and degree of anisotropy for old individuals. Recent investigations have shown that bone-volume fraction and anisotropy together accounted for 68% to 9%, 23 or more than 8% 1 of the variances of Young s modulus and ultimate stress for human cancellous bone. The relationship between Young s modulus and density has been reported to be in a range of R 2 =.4 to Our result of the correlation between Young s modulus and density was at the lower end but still within the normal expected range. The degree of anisotropy increased significantly the explanation of the variance of Young s modulus. Interestingly, the ability of anisotropy for predicting Young s modulus was valid only in the old individuals. These results have significant application for ageing cancellous bone suggesting a bone remodelling mechanism which may change the orientation of trabecular volume (Fig. 2). 16 Our results have shown that the type of structure played an important role in determining the mechanical properties of cancellous bone. In our study, the specimens were tested non-destructively to.6% bone strain, and therefore only Young s modulus was calculated. We have recently shown that the structure model index, out of 15 measured microstructural and physical/compositional properties, was the best predictor for ultimate stress, Young s modulus and failure energy in both normal and early-stage osteoarthritic human tibial cancellous bone (unpublished data). The relationship between connectivity and bone-volume fraction has been of considerable interest. 3,1,14,15,17,29-31 A high correlation between connectivity and the bone-volume fraction of normal cancellous bone (R 2 = ) was found. 3,23 On the other hand, other investigations have shown that connectivity density of trabecular bone was not simply proportionally related to bone-volume fraction, neither in 3D reconstruction, 15,17 in the bone histomorphometry method 14 nor on 3D MRI. 31 Our data support these latter findings. Connectivity is a 3D architectural scalar, a measure of topology with no anisotropy information. Connectivity and bone-volume fractions are two conceptually different parameters, which do not necessarily correlate proportionally. Connectivity has been reported to have a low negative correlation with the micromechanical finite-element calculated Young s modulus for human cancellous bone (R 2 =.12, p <.5). 17 Our data showed that there was no relationship between connectivity and Young s modulus as VOL. 84-B, NO. 6, AUGUST 22

7 96 MING DING, ANDERS ODGAARD, CARL CHRISTIAN DANIELSEN, IVAN HVID.4 b=2.2 (1.92 to 2.13), r 2 =.97 2 b=-6.2 (-7.3 to -5.1), r 2 =.78 Bone volume fraction (-).3.2 Structure model index (-) Bone collagen density (g/cm 3 ) Bone volume fraction (-) Fig. 3a Fig. 3b Degree of anisotropy (-) b=-58.8 (-82.3 to -32.8), r 2 =.37 Log (connectivity density) b=-.95 (-1.4 to -.86), r 2 = Bone volume fraction (-) Log (mean marrow space vol.) Fig. 3c Fig. 3d 3 b=-5.3 (-6.2 to -4.5), r 2 =.81 Trabecular thickness (µm) 2 1 The significant predictors for the primary microstructural properties of normal human tibial cancellous bone are shown. The data are presented as slope (b) (95% confidence interval), determination coefficient (R 2 ) and p value derived from linear regression analysis ( = young age, = middle age, = old age) Bone surface/volume ratio (mm -1 ) Fig. 3e 3 determined by mechanical testing, when the entire data set was included in regression analysis. Connectivity was, however, negatively correlated with Young s modulus in young individuals. This result proposed a possible agedependent nature of connectivity for predicting Young s modulus. Nevertheless, the results must be interpreted carefully since the sample size in the young-age group was relatively small. Further study is needed to clarify this issue. Connectivity density showed a strong negative correlation with marrow space volume (R 2 =.92, Fig. 3). This THE JOURNAL OF BONE AND JOINT SURGERY

8 ASSOCIATIONS AMONG MICROSTRUCTURAL, PHYSICAL AND MECHANICAL PROPERTIES OF CANCELLOUS BONE 97 finding supports a previous hypothesis that marrow space star volume may give an indirect estimation of the connectivity of trabecular structure. 32 Thus, the changes in marrow space volume highly reflect the changes in trabecular connectivity. We have previously shown that human tibial trabeculae may undergo thickening in the relatively old-age group to compensate for the decrease in mechanical strength. 1 Studies based on histological methods have also shown that iliac trabecular thickness remains relatively constant in ageing, 33 whereas no compensatory thickening in vertebral trabeculae occurs in ageing. 34 It has been assumed that trabecular structures undergo preferential removal of the thinnest trabeculae, but tend to preserve thicker trabeculae during ageing. 29 The ability of cancellous bone to compensate for the mechanical strength is, however, dependent largely on the quality of cancellous bone. For example, the mechanical properties are significantly reduced both at the level of cancellous bone and at the tissue level 35 in earlystage osteoarthritis, despite a significant increase in trabecular thickness. Therefore, trabecular thickening alone cannot entirely compensate for the decrease in mechanical properties of early-stage osteoarthritic cancellous bone. The research was financially supported by the Danish Health Research Council (Grant no _lpa) and Aarhus University Fond (E Sun-1-152). The authors thank Eva Mikkelsen for skilful technical assistance, and Associate Professor Morten Frydenberg, Department of Biostatistics, Aarhus University for statistical advice. No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. References 1. Ding M, Hvid I. Quantification of age-related changes in the structure model type and trabecular thickness of human tibial cancellous bone. Bone 2;26: Vogel M, Hahn M, Delling G. Relation between 2- and 3-dimensional architecture of trabecular bone in the human spine. Bone 1993;14: Kinney JH, Lane NE, Haupt DL. In vivo, three-dimensional microscopy of trabecular bone. J Bone Miner Res 1995;1: Hilderbrand T, Laib A, Muller R, Dequeker J, Ruegsegger P. Direct three-dimensional morphometric analysis of human cancellous bone: microstructural data from spine, femur, iliac crest, and calcaneus. J Bone Miner Res 1999;14: Whitehouse WJ, Dyson ED. Scanning electron microscope studies of trabecular bone in the proximal end of the human femur. J Anat 1974;118: Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech 1985;18: Turner CH, Cowin SC, Rho JY, Ashman RB, Rice JC. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech 199;23: Kabel J, van Rietbergen B, Odgaard A, Huiskes R. Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture. Bone 1999;25: Hodgskinson R, Currey JD. The effect of variation in structure on the Young s modulus of cancellous bone: a comparison of human and non-human material. Proc Inst Mech Eng H 199;24: Goldstein SA, Goulet R, McCubbrey D. Measurement and significance of three-dimensional architecture to the mechanical integrity of trabecular bone. Calcif Tissue Int 1993;53 Suppl 1:S van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstruction. J Orthop Res 1998;16: Ulrich D, van Rietbergen B, Laib A, Ruegsegger P. The ability of three-dimensional structural indices to reflect mechanical aspects of trabecular bone. Bone 1999;25: Katz JL, Meunier A. Scanning acoustic microscope studies of the elastic properties of osteons and osteon lamellae. J Biomech Eng 1993;115: Thomsen JS, Ebbesen EN, Mosekilde L. Relationships between static histomorphometry and bone strength measurements in human iliac crest bone biopsies. Bone 1998;22: Odgaard A, Gundersen HJ. Quantificatioon of connectivity in cancellous bone, with special emphasis on 3-D reconstruction. Bone 1993;14: Ding M, Odgaard A, Linde F, Hvid I. Age-related variations in the microstructure of human tibial cancellous bone. J Orthop Res 22;2: Kabel J, Odgaard A, van Rietbergen B, Huiskes R. Connectivity and the elastic properties of cancellous bone. Bone 1999;24: Hildebrand T, Rüegsegger P. A new method for the model-independent assessment of thickness in three-dimensional images. J Micro 1997;185: Ding M, Dlastra M, Danielsen CC, et al. Age variations in the properties of human tibial trabecular bone. J Bone Joint Surg [Br] 1997;79-B: Ding M, Odgaard A, Hvid I. Accuracy of cancellous bone volume fraction measured by micro-ct scanning. J Biomech 1999;32: Hildebrand T, Rüegsegger P. Quantification of bone microarchitecture with the structure model index. Comput Methods Biomech Biomed Engin 1997;1: Odgaard A, Jensen EB, Gundersen HJ. Estimation of structural anisotropy based on volume orientation: a new concept. J Microsc 199;157: Goulet RW, Goldstein SA, Ciarelli MJ, et al. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech 1994;27: Odgaard A. Three-dimensional methods for quantification of cancellous bone architecture. Bone 1997;2: Sharp DJ, Tanner KE, Bonfield W. Measurement of the density of trabecular bone. J Biomech 199;23: Woessner JF Jr. Determination of hydroxyproline in connective tissues. In: Hall DA, ed. The methodology of connective tissue research. Vol. 1. Oxford, Joynson-Bruvvers Ltd, 1976: Neuman RE, Logan MA. The determination of collagen and elastin in tissues. J Biol Chem 195;186: Ciareli MJ, Goldstein SA, Kuhn JL, Cody DD, Brown MB. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. J Orthop Res 1991;9: Frost HM. On the trabecular thickness -number problem. J Bone Miner Res 1999;14: Kinney JH, Ryaby JT, Haupt DL, Lane NE. Three-dimensional in vivo morphometry of trabecular bone in the OVX rat model of osteoporosis. Technol Health Care 1998;6: Wessels M, Mason RP, Antich PP, Zerwekh JE, Pak CY. Connectivity in human cancellous bone by three-dimensional magnetic resonance imaging. Med Phys 1997;24: Vesterby A. Marrow space star volume can reveal change of trabecular connectivity. Bone 1993;14: Han ZH, Palnitkar S, Rao DS, Nelson D, Parfitt AM. Effect of ethnicity and age or menopause on the structure and geometry of iliac bone. J Bone Miner Res 1996;11: Bergot C, Laval-Jeantet AM, Preteux F, Meunier A. Measurement of anisotropic vertebral trabecular bone loss during ageing by quantitative image analysis. Calcif Tissue Int 1988;43: Day JS, Ding M, van der Linden JC, Hvid I, Sumner DR. Weinans H. A decreased subchondral trabecular bone tissue elastic modulus is associated with pre-arthritic cartilage damage. J Orthop Res 21;19: VOL. 84-B, NO. 6, AUGUST 22