This study shows that change to cancellous bone structure is bone volume-dependent in a nonlinear manner. At low bone volume (<15%), trabecular thickness and trabecular separation change at a much greater rate than at higher bone volume. This suggests that the structural integrity of the cancellous bone may become rapidly compromised when bone volume falls below a critical value.
Introduction: While bone mass is the major determinant of bone strength, this mass-based paradigm does not fully account for the contribution of the bone microstructure to mechanical efficiency. Geometric models of cancellous bone structure have been formulated based on stylized representations of the trabecular elements, where the relationships between bone volume and bone surface of cancellous bone are complex and reflect the modulating effect on the cancellous bone structure of bone remodeling at the trabecular surfaces. Using the plate model of cancellous bone structure, the interrelationships between parameters of cancellous bone structure have been studied.
Materials and Methods: Two hundred eighty histological sections of human cancellous bone from eight skeletal sites were analyzed. The structural parameters of cancellous bone (BV/TV, BS/TV, BS/BV, Tb.Th, Tb.Sp, Tb.N, and TBPf) were obtained.
Results and Conclusions: This study shows that change to cancellous bone structure is bone volume-dependent in a nonlinear manner. At low bone volume (<15%), structural parameters of cancellous bone, such as trabecular thickness and trabecular separation, change at a much greater rate than at higher bone volume. This suggests that the structural integrity of the cancellous bone may become rapidly compromised when bone volume falls below a critical value. These data describe the complex relationships between bone mass and structure in cancellous bone that are often overlooked in the mass-based paradigm of bone strength. Histomorphometric descriptors of cancellous bone structure highlight the potential for accelerated deterioration of the structure with low bone volume, which leads to increased risk of fracture. From a clinical viewpoint, estimation of an individual's fracture risk is constrained to noninvasive techniques, which only provide bone mineral density or bone mineral content. Therefore, there is a need to better correlate measurement of bone mass with measurements of structural parameters.
CANCELLOUS BONE LOSS with aging and/or menopause may result in the decreased ability of bones to withstand forces encountered in everyday life, resulting in fracture. The current World Health Organization (WHO) criteria for osteopenia and osteoporosis of −1.0 and −2.5 SD below the average for young healthy women, respectively, rely on DXA scans for measurement of bone density.(1) It has become obvious that these criteria identify individuals at risk of fracture but cannot identify individuals that will fracture. Whereas it has been shown that bone mass is the major determinant of bone strength,(2) this mass-based paradigm does not fully account for the contribution of the bone microstructure to mechanical efficiency.(3,4)
Structural parameters of cancellous bone from histological sections are obtained using well-established techniques that take advantage of the accurate visual resolution provided by these preparations. Geometric models of cancellous bone structure have been formulated based on stylized representations of the trabecular elements.(5–8) Remodeling activity is responsible for thickening, thinning, perforation, or disconnection of individual trabecular elements, which in turn, affects the mechanical integrity of the cancellous bone structure. Transformation of cancellous bone structure is not wholly independent of bone volume, and a given amount of bone mass may be distributed within the tissue space in a limited number of ways.(8) Analysis of secondary cancellous bone structure at the growth plate has shown that cancellous bone structure is not arbitrary but may be constrained by biological and mechanical criteria.(9–11) With aging, cancellous bone mass decreases in all individuals with women experiencing an accelerated bone loss at menopause. It has been shown in women with vertebral fractures, with the same bone volume as an age-matched nonfracture group, that cancellous bone from the iliac crest has a different distribution of trabecular elements, which is reflected in increased trabecular separation and decreased trabecular number.(12)
The activity of osteoclasts and osteoblasts affects the magnitude of the bone perimeter, where resorption lacunae have more perimeter per unit length than osteoid covered or quiescent bone. Also, perforation of trabeculae “creates” more perimeter. Therefore, the relative amount of bone turnover can influence the magnitude of bone surface. At the tissue and organ level, the dimensions of the trabeculae and the spatial arrangement of the trabeculae are affected by the need to provide an effective structure able to withstand normal physiological loads. Using the plate model of cancellous bone structure,(5) from measurement of bone perimeter, bone area, and tissue area, derived parameters such as trabecular separation (Tb.Sp), trabecular thickness (Tb.Th), and trabecular number (Tb.N) provide information on the spatial distribution of the bone, which enables the contribution of microstructure to bone strength to be assessed.
A nonlinear relationship has been described between bone volume/total volume (BV/TV) and bone surface/total volume (BS/TV),(8) which at the tissue level, shows that for low bone volume there is more rapid change in bone surface than for high bone volume. Nonlinear relationships between bone volume and bone surface over physiological ranges of BV/TV, for both “real” samples and theoretical structures, have been previously reported.(5,7) Computer simulations of bone loss algorithms have shown nonlinearity between BV/TV and mechanical stiffness, particularly when BV/TV decreases below 15%.(13) Furthermore, nonlinear relationships have been reported between BV/TV and other measures of cancellous bone structure, such as star volume and trabecular separation.(14–16)
The aim of this study, using the plate model of cancellous bone structure,(5) was to investigate the interrelationships between parameters of cancellous bone structure. In particular, the rate of change in the structural parameters, BS/TV, BS/BV, Tb.Th, Tb.Sp, Tb.N, and TBPf as a function of BV/TV, were examined in normal human cancellous bone samples from multiple skeletal sites.
MATERIALS AND METHODS
Two hundred eighty histological sections of human cadaveric cancellous bone from eight skeletal sites were analyzed. Cancellous bone samples were collected from 113 cadavers (75 males with a mean age of 60 ± 22 years and 38 females with a mean age of 55 ± 22 years). However, not all of the eight skeletal sites were sampled from each individual. The cancellous bone samples were taken from (1) sagittal slice of T12 vertebral body; (2) sagittal slice of L1 vertebral body; (3) the femoral head, superior to the fovea; (4) the femoral head, infero-medial to the fovea; (5) Medial condyle from the femoral aspect of the knee; (6) medial condyle from the tibial aspect of the knee; (7) the patella; and (8) the iliac crest, 2.5 cm behind the anterior spine. All samples were from individuals with no clinically identified skeletal disease. Exclusion criteria were the presence of renal impairment, metastatic cancer, bed-ridden for greater than 3 days, drugs that affect calcium metabolism, or sero-positive for HIV or hepatitis B. Ethics approval for collection of samples was granted by the Human Ethics Committee of the Royal Adelaide Hospital.
The cancellous bone specimens were processed undecalcified and embedded in epoxy resin. Seven-micron sections were impregnated with silver and counterstained by van Gieson's method, which provides high optical contrast between the bone mineral and the marrow space.(17)
The Quantimet Image Analyser (Leica, Cambridge, UK) was used to determine the three-dimensional (3D) structural parameters of cancellous bone (BV/TV, BS/TV, BS/BV, Tb.Th, Tb.Sp, and Tb.N) from 2D measurements of bone perimeter, bone area, and tissue area,(17) according to Parfitt's “plate” model for cancellous bone structure. (7,18)
Interrelationships of derived parameters
Formulation of the “plate” model of cancellous bone structure shows that there are mathematical relationships between the structural parameters. Specifically,
Trabecular bone pattern factor (TBPf), the ratio of convex to concave trabecular surfaces, was calculated from measurements of bone perimeter and bone area before and after binary dilation, according to the method of Hahn et al.,(19) where binary dilation is the addition of a row of pixels to all boundaries in the binary image of the cancellous bone section.
where P1 and P2 are perimeter measurements before and after binary dilation of the 2D image of the bone, and A1 and A2 are area measurements before and after binary dilation of the 2D image of the bone.
Based on the work by Hahn et al.(19) low values of TBPf (less than 0) indicate more concave trabecular surfaces, hence, greater connectivity. In addition, high values of TBPf (greater than 0) indicate more convex trabecular surfaces, hence, less connectivity.
The empirical relationships between BV/TV and structural parameters of cancellous bone were determined. Based on the model-dependent interrelationships between BV/TV and derived cancellous bone structural parameters, power curve regression fits (y = k × 1/xn or y = k × xn, where x = BV/TV, y = structural parameter, k = structure constant, and n = exponent) were calculated for BV/TV versus BS/TV, BS/BV, Tb.Th, Tb.Sp, and Tb.N. A constant of five was added to make all values of TBPf greater than zero, which enabled a logarithmic curve fit for BV/TV versus TBPf.(14)
Structural parameters measured from computational output of a bone remodeling algorithm,(13) which simulates age-related bone loss, were compared with the data from the 280 histological sections. Bone loss was simulated from six cancellous bone samples where initial BV/TV ranged from 10% to 30%. Comparison of the power curves from the 280 histological sections was made with power curves from pooled data of the six bone loss simulations.
All statistical analyses were performed using SAS (SAS Institute, Cary, NC, USA) software. Statistical significance was set at p < 0.05, and data are expressed as mean ± SD.
The multiple sites from which histological sections were prepared represent the continuum of cancellous bone structure extant within the skeleton. This is indicated by the minimum and maximum values at each skeletal site and by the overlap of minimum and maximum values between skeletal sites for the structural parameters of cancellous bone (Table 1).
Table Table 1. Minimum and Maximum Values for BV/TV, Tb.Th, and Tb.Sp at Each Skeletal Site, Which Show the Degree of Overlap in These Parameters Within the Skeleton
Table 2 shows the power curve equations for BV/TV versus the structural parameters of cancellous bone, where, in particular, Tb.Th decreases as BV/TV decreases and Tb.Sp increases as BV/TV decreases (Figs. 1 and 2, respectively). It should be noted that there are identical exponents (n) and correlation coefficients (r) in the power curve equations where the parameters are mathematically related (BS/BV and Tb.Th; BS/TV and Tb.N). BV/TV versus TBPf shows a statistically significant logarithmic relationship (Table 2).
Table Table 2. Power Curve Statistics of Cancellous Bone Structure as a Function of BV/TV
Table 3 shows changes in Tb.Th and Tb.Sp for increments of 5% BV/TV, which indicates that as BV/TV decreases, the rate of change to Tb.Th and Tb.Sp increases markedly.
Table Table 3. Change in Tb.Th and Tb.Sp Over Defined Ranges of BV/TV, Which Shows That as BV/TV Decreases in Increments of 5%, the Rate of Change in Tb.Th and Tb.Sp Increases Markedly
For males and females separately, the power curves for BV/TV versus Tb.Th and Tb.Sp showed similar statistically significant relationships. For BV/TV versus Tb.Th, Pearson's regression coefficients were identical for males and females (r = 0.78, p < 0.0001). In addition, for BV/TV versus Tb.Sp, Pearson's regression coefficients were identical for males and females (r = −0.87, p < 0.0001).
For the “bone remodeling” algorithm, the power curve equations for BV/TV versus Tb.Th (Tb.Th = 69 × BV/TV0.29) and BV/TV versus Tb.Sp (Tb.Sp = 7636 × BV/TV−0.81) of the six simulations pooled show that for the same range of BV/TV as the 280 histological sections the exponents (n) are similar (0.38 versus 0.29 and −0.79 versus −0.81). Figure 3 shows a scatter plot of BV/TV versus Tb.Sp for the “bone remodeling” algorithm, where the six simulations are plotted individually, and the regression line for the histological sections data are overlaid.
This study shows that change to cancellous bone structure is bone volume-dependent in a nonlinear manner. Specifically, at low bone volume (<15%), structural parameters of cancellous bone such as trabecular thickness and trabecular separation change at a much greater rate than at higher bone volume. This suggests that the structural integrity of the cancellous bone may become rapidly compromised when bone volume falls below a critical value.
The diverse skeletal sampling reported in this study has provided a wide range of cancellous bone structure for analysis (Table 1). If the cancellous bone from each skeletal site is examined separately, the power relationships between BV/TV and the structural parameters generally are not evident because of the relatively narrow range of BV/TV often found within each skeletal site.(20)
The power curve relationship between BV/TV and BS/TV is consistent with that described in the literature,(8) for both theoretical and “real” data, where change to the power curve exponent indicates transformation of the cancellous bone structure.(7) However, Tb.Th and Tb.Sp as descriptors of the structural components that comprise the trabecular network enable the assessment of the effect of structural change on the determination of cancellous bone stiffness.(21) This allows the contribution of the trabecular microstructure to bone strength to be assessed.
The scatter plots of BV/TV versus Tb.Th and BV/TV versus Tb.Sp indicate that low BV/TV is associated with lower Tb.Th and higher Tb.Sp. Thus, at low bone volume, for a defined range of BV/TV, the cancellous bone structure may show large differences, whereas at high bone volume, the structural parameters for a defined range of BV/TV limit the potential structural differences (Table 3). These observations are consistent with the putative spontaneous fracture threshold of 15% BV/TV proposed for vertebral body cancellous bone.(4,14,22) Therefore, the observation that all individuals with osteoporotic range bone mineral density (BMD) do not fracture, a deficiency in the mass-based paradigm of bone strength in identifying individuals at risk of fracture, may be partly explained by the nature of the interrelationships between BV/TV and cancellous bone architecture.
The formulation of the “plate” model reveals interrelationships between the independent measures (BV, BS, and TV) and the derived measures (Tb.Th, Tb.Sp, and Tb.N), which are reflected in the power curve equations of BV/TV versus the structural parameters (Table 2). The identical magnitude of the exponents in the power curve equations for BS/BV and Tb.Th and for BS/TV and Tb.N describe the same morphological characteristics. The independent morphological measurement is the surface measurement while Tb.Th and Tb.N are derived. As shown in equation form (Interrelationships of derived parameters) in the methods, this model-based analysis of cancellous bone structural parameters clearly shows that Tb.N can be derived from Tb.Sp. Thus, the interpretation of the cancellous structural data in this study focused on Tb.Th and Tb.Sp.
Increased separation between trabeculae requires perforation and removal of whole trabecular elements. Therefore, Tb.Sp increases in quanta of much greater magnitude than is the case for decrease in Tb.Th. These processes do not occur in isolation, and there is likely to be different proportions of either mechanism in any population. However, the end result of whichever mechanism is involved further shows that low bone volume is associated with accelerated transformation of the cancellous bone structure.
Ding and Hvid(23) have shown that, in human tibial cancellous bone, BV/TV decreases two decades earlier than detectable changes in trabecular thickness. Furthermore, Ding et al.(21) have shown that the principle morphological determinants of cancellous bone stiffness change with age (i.e., connectivity density in the young, trabecular thickness in middle age, and bone apparent density in old age). These observations are consistent with the data presented in this study, where an apparent low BV/TV threshold (<15%) is reached, below which the cancellous microstructure changes rapidly.
The “bone remodeling” algorithm enables the effect of combining the dynamics of bone remodeling and the deterministic processes associated with bone adaptation to be investigated,(13) in particular, the relationships between bone density, architectural arrangement, and mechanical stiffness.(24) In this study, the high correlation for BV/TV versus Tb.Th and Tb.Sp between the “bone remodeling” algorithm and the 280 histological sections supports the use of this approach to describe the transformation of cancellous bone structure. This provides a potential tool to predict the effects on the cancellous bone structure of age-related or pathological change from a defined point in time. The potential also exists to use the bone remodeling algorithm to enable assessment of the risk of osteoporotic fracture, as a function of time, in individuals. These simulations are ideally suited for use in finite element modeling, which enable the effects of mechanical loading to be quantified.
The data presented in this study describe the complex relationships between BV/TV and structure in cancellous bone often overlooked in the mass-based paradigm of bone strength. Histomorphometric descriptors of cancellous bone structure highlight the potential for accelerated deterioration of the structure with low BV/TV, which leads to increased risk of fracture. From a clinical viewpoint, estimation of an individual's fracture risk is constrained by available noninvasive techniques, which only provide BMD or bone mineral content (BMC). Therefore, there is a need to better correlate measurement of bone mass with measurements of structural parameters.
Funding for this study was provided by the National Health and Medical Research Council, the Royal Adelaide Hospital, Michelle Caitlin, Jessica de Ryk, and Dr Karen Reynolds, School of Informatics and Engineering, Flinders University.