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Keywords:

  • local morphometry;
  • Young's modulus;
  • finite element method;
  • bone quality;
  • trabecular bone;
  • trabecular plates;
  • trabecular rods;
  • vertebrae

Abstract

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

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

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

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

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

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


INTRODUCTION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Osteoporosis is now recognized as one of the major public health problems facing postmenopausal women and aging individuals irrespective of sex.(1) It is defined as a skeletal disorder characterized by compromised bone strength predisposing to an increased risk of fracture. Bone strength reflects the integration of two main features: BMD, expressed as grams of mineral per area or volume, and bone quality, referring to bone architecture, turnover, damage accumulation, collagen cross-linking, and mineralization.(2)

To assess bone mechanical properties, different experimental testing methods have been proposed.(3) For trabecular bone, compression(4–9) and tensile testing(5,7) were used to assess apparent Young's modulus and ultimate strength. Additional to these experimental methods, the stiffness of trabecular bone samples was also computed by finite element model simulations,(10–12) which showed to yield qualitatively similar results as experimental approaches.

The assessment of bone stiffness and strength has traditionally been related to surrogate measures potentially predicting and explaining the variation in stiffness and strength. Among those, the most established one certainly is bone volume density (BV/TV), which has been shown to explain a great amount of the variance in both stiffness and strength when fitting a power law.(13–15) However, it has also been recognized that, although older persons may lose bone as expressed by a decrease in BMD, they do not develop fractures. This is not necessarily unexpected because BMD, geometry of bone, microarchitecture of bone, and quality of the bone material are all components that determine bone strength.(16,17) For this reason, efforts in the quantification of structural properties gained in importance and many different methods have been proposed.(18) Among the basic parameters were the measurement of bone volume (BV) and bone surface (BS), which can be derived from volumetric and surface meshes, respectively.(19,20) Bone volume density (BV/TV) or specific bone surface (BS/BV) can be derived from these primary measures. Additionally, the mean trabecular thickness (Tb.Th), the mean trabecular separation (Tb.Sp), and the trabecular number (Tb.N) are often determined parameters that can be computed directly from the 3D image without any model assumption.(21) Furthermore, the connectivity density (Conn.D) was introduced to characterize the 3D trabecular network.(22) To estimate the plate-rod characteristic of a trabecular bone structure, a parameter called structure model index (SMI) was invented,(23) which was shown to be closely related to the mean curvature (<H>) of the bone surface.(24) Also related is the trabecular bone pattern factor (TBPf),(25) which equals 2<H>. Mean intercept length (MIL) and other measures of architectural anisotropy (DA) such as volume orientation, star volume distribution, and star length distribution(18) were used to improve the prediction of multiaxial elastic properties of trabecular bone from bone volume density alone.(26)

A common feature to all these studies is that they were applied to the trabecular structures as a whole and hence were not able to capture structural changes on an elemental level (i.e., a single rod or plate). Only a few attempts have been made to study local parameters of the trabecular network. Pothuaud et al.(27) presented a method called line skeleton graph analysis (LSGA) to compute topological parameters as well as the length and volume of single trabecular elements. They showed that LSGA can be applied in vivo(28) and had the potential to improve the prediction of mechanical properties when combined with bone volume fraction.(29) Their method, however, was based on a line-skeleton where shape information was lost, and identification of plates and rods was not possible. An attempt to also assess shape information was done by Saha et al,(30) who first introduced a method for the digital topological characterization of the trabecular bone architecture. Their method is based on an thinning algorithm(31) followed by a classification algorithm(32) and allowed them to subdivide the trabecular structure into its rods and plates. This method was later used for orientation analyses of the trabecular bone networks,(33) and it could be shown that the locally determined orientations better described anisotropy than the MIL. Only recently, we presented a new approach, conceptually combining the 3D identification of trabecular elements(27) with the classification of shape-preserved skeletons.(32) With this method, the structural elements (i.e., rods and plates) could be analyzed in their full 3D and volumetric extent, which is referred to as local bone morphometry.(34)

Although BMD was shown to be a relatively good predictor for bone stiffness,(15) this measure cannot account for changes in bone quality, which may be altered in aging or people affected by a bone disease. The goal of this study was thus to investigate the relative importance of bone architecture, as one of the major components of bone quality, in the prediction of bone stiffness. An emphasis was placed on the contribution of local morphometric indices allowing separate analysis for rods and plates on an elemental level. In this endeavor, both global and local morphometric indices were related to the apparent Young's modulus, which was assessed by combined uniaxial compression testing and computational finite element analysis. We hypothesize that local morphometric indices, which are a new method for quantifying bone architectural features, do significantly contribute to bone stiffness. Furthermore, these indices do not only predict bone stiffness but may also improve our understanding of the relative importance of local measures of bone architecture in the assessment of bone mechanical properties.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Direct mechanical testing

Forty-two human trabecular bone samples were extracted from intact spinal columns of nine donors who took part in an anatomical donation program. A specially developed drill was used to core the cylindrical specimens (10 mm height and 8 mm in diameter) from lumbar and thoracic vertebrae under constant water irrigation. Preceding drilling, contact radiographs were taken from each vertebra to orient them into a position such that the main trabecular orientation was aligned with the longitudinal axis of the cored specimen. No data were available on age and disease state of the donors. The specimens were cleaned from soft tissue, embedded in polymethylmethacrylate (PMMA) to minimize end artifacts, and after five preconditioning cycles, tested in compression with a speed of 0.05%/s. An external extensometer was used to measure strain over a length of 9.3 mm. The apparent Young's modulus (Emeas) was calculated form the stress-strain curve.

Assessment of bone microarchitecture

Before mechanical testing, all specimens were scanned using a μCT system (μCT40, Scanco Medical AG, Bassersdorf, Switzerland) with a nominal resolution of 20 μm to assess the trabecular bone architecture. The reconstructed images were filtered using a constrained 3D Gaussian filter to partially suppress noise in the volumes (σ = 1.2 voxel, support = 1 voxel), and binarized using a global threshold (22.4%). A cylindrical region with a diameter of 7 mm was digitally cut to exclude bone fragments that might have resulted from the cutting process. Component labeling was performed to remove unconnected parts of the structure.

Finite element analysis

From the component labeled images, finite element (FE) models consisting of identical hexahedral elements were created using a standard voxel conversion technique. To decrease computational time, but still ensuring accurate outcomes, the voxel size was reduced to 40 μm, which is about one-fourth of the mean trabecular thickness, as recommended for numerical convergence.(35) To represent the experimental set-up, the nodes on the bottom plane were fully fixed, whereas the nodes on the top surface underwent an axial displacement to obtain 1% apparent strain. The FE models were used to calculate the force needed to achieve this displacement. From this data, the apparent Young's modulus (EFE) was computed and scaled (Etissue = 10.7 GPa) such that the slope of Emeas versus EFE equaled 1. To solve the models, an element-by-element method(36) was used running on a HP Superdome System with 64 RISC (550 MHz) processors.

Global morphometry

We used standard 3D morphometry to compute bone volume density (BV/TV), bone surface density (BS/TV), and specific bone surface (BS/BV). These indices were derived from a triangulated mesh allowing for computation of surface and volume.(19,20) Furthermore, the mean curvature (<H>),(24) which is proportional to the trabecular bone pattern factor (TBPf = 2<H>), was computed based on a parallel surface method.(23,37) It is negative for mainly concave shaped objects, zero for a perfect plate, and positive for mainly convex shaped objects such as rods. Additionally, the SMI,(23) as well as the mean trabecular thickness (Tb.Th), the mean trabecular separation (Tb.Sp),(21) and the degree of anisotropy (DA), were computed. All theses indices were computed directly from the component labeled images without any inherent model assumption.

Local morphometry

The component labeled images were skeletonized to a homotopic and shape-preserving one-voxel-thick skeleton, followed by a topological optimization procedure,(34) which means that the bone structure was reduced to a one-voxel-thick skeleton structure, where each rod was represented by a one-voxel-thick arc and each plate was represented by a one-voxel-thick surface. The optimized skeleton was characterized by a slightly modified point classification algorithm originally devised by Saha et al.(32) This classification computed for each point in the skeleton whether it was an arc, a surface, or an intersection point. Based on this classification, the skeleton was spatially decomposed into rods and plates according to the intersection points, where rods were identified to be the elements having exactly two nodes. The elements were expanded to their original size by applying a so-called multicolor dilation algorithm,(34) which assigned each voxel within the original bone structure a color value related to the closest skeleton element. This operation resulted in a spatially decomposed bone structure where all rods and plates were labeled with an individual color (Fig. 1). A more detailed description of this volumetric spatial decomposition method can be found elsewhere.(34)

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Figure Figure 1. Spatial decomposition of trabecular bone. A and B show a rod and plate structure, respectively, where each trabecula is coded by its color. C and D show the same structures but display rods in blue and plates in red.

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From this decomposed structure, we computed local morphometric indices, which means that we applied standard 3D morphometry to all rods and plates individually on a true elemental level. To follow the naming conventions proposed by Parfitt et al.,(38) we previously suggested to use the prefix Pl for plates, and Ro for rods. The volume, surface, and thickness of one single element were denoted with V, S, and Th, and the sum of the volume and surface over all elements with BV, and BS, respectively. Furthermore, we use brackets (<>) to denote mean values that are averaged over all elements of the same type.

In this study, we concentrated on the mean volume (<Ro.V>, <Pl.V>), the mean surface (<Ro.S>, <Pl.S>), and the mean thickness (<Ro.Th>, <Pl.Th>) averaged for each structure over all rods and plates separately. Additionally, the mean curvature (<Ro.<H>>, <Pl.<H>>) was computed for each element, using the same algorithms as for the global morphometry. For the rods, we also computed the mean slenderness (<Ro.Sl>) as the ratio of its length over its thickness, where the length was derived from the skeleton as the node distance and the thickness was computed as the mean thickness of each element. Furthermore, the mean orientation (<Ro.Θ>) was computed as the angle between the orientation of the element and the image axis. Additionally, the percent plate (Pl.BV/BV) and rod volume fraction (Ro.BV/BV = 100% − Pl.BV/BV) were determined.

Statistical analysis

Descriptive statistics were computed for all global and local morphometric indices (Table 1). The experimentally measured Young's modulus (Emeas) was linearly related to the FE derived Young's modulus (EFE) and the Pearson correlation coefficient was computed to test for the relative deviation of the two methods (Fig. 2). Furthermore, BV/TV was related to both moduli by fitting a power law (Fig. 3). Young's modulus as predicted by BV/TV [Epred(BV/TV)] was also plotted versus Emeas and compared with the log-transformed data of Emeas and BV/TV (Fig. 4). All global and local morphometric indices were related to EFE using linear and power laws as appropriate (Tables 2 and 3). Because the morphometric indices and EFE were derived from the same digital images, we could also prevent introducing unwanted variance caused by measurement errors as they are implicitly included in Emeas and caused by errors in image processing like thresholding of the images. Stepwise multiple linear regression analysis was performed with global and local morphometric indices to find a model that accurately predicted EFE. In cases where the data showed no linear but rather a potential law with EFE, the data were log-transformed for the regression analysis. For all statistical analyses, the GNU statistical computation and graphics package R (Version 2.0.1) was used.(39)

Table Table 1.. Descriptive Statistics of Global and Local Morphometric Parameters
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Table Table 2.. Regression Models of Global and Local Morphometric Parameters vs. the Finite Element Young's Modulus (EFE)
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Table Table 3.. Correlation Matrix for All Global and Local Indices Showing the R Values of the Linear Relations
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Figure Figure 2. The Young's modulus from the finite element analysis (EFE) was in good agreement (r2 = 0.85) with the Young's modulus from the measurement (Emeas).

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Figure Figure 3. BV/TV was in good agreement with measured and FE-determined apparent modulus. (A) Emeas (r2 = 0.87). (B) EFE (r2 = 0.89). Dashed lines show the CI, and dotted lines show the prediction interval.

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Figure Figure 4. (A) In the log-transformed data, the relation Emeas ∼ BV/TV becomes linear, and the variance is constant over the range. (B) If the relation found from the log-transformed data are applied [Epred(BV/TV)], the variation is not constant over the range anymore and no simple linear relation can be fitted.

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RESULTS

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

Young's modulus, as assessed by experimental two platen compression testing (Emeas), was in good agreement (r2 = 0.85) with the Young's modulus as assessed by standard finite element simulation (EFE). However, the fit was not perfect (Fig. 2) because of the relatively large voxel size (40 μm) compared with the trabecular thickness and measurement errors in the experimental approach.

Bone volume density (BV/TV) predicted Emeas (∼BV/TV1.81; r2 = 0.87) and EFE (∼BV/TV1.65; r2 = 0.89) equally well by fitting a power law. The prediction intervals in Fig. 3 nicely show that the variance of Young's modulus increases with increasing BV/TV. The log-transformed data had a constant variance over the whole range (Fig. 4A), wherefore a linear relation could be plotted and the corresponding Pearson correlation coefficient could be computed. To show the effect of increasing variance, the power law was used to compute the predicted modulus [Epred(BV/TV)], which was plotted versus Emeas (Fig. 4B). In this linear model, only 70% percent of the variance in Emeas could be explained by the BV/TV-based stiffness prediction.

For the remainder of the analyses, only relationships with EFE are presented, because our aim was to assess the effects of microstructure on bone stiffness. Nevertheless, it has to be noted that correlations with Emeas were equally well but always slightly lower.

The single linear regression models of global and local morphometric indices versus EFE are shown in Table 2. Apart from Tb.Th and DA, all global indices showed a good correlation with EFE and explained >60% of the variance. Best single predictors were BV/TV by fitting a power law and BS/TV by using a linear fit. These two parameters were also in excellent agreement (r2 = 0.94) with each other and hence not independent. Other important interdependencies were found for the following pairs; SMI versus <H> (r2 = 0.93), BS/TV versus Tb.Sp (r2 = 0.85), BV/TV versus Tb.Sp (r2 = 0.77), and BV/TV versus <H> (r2 = 0.77; see also Table 3).

From local morphometry, it was found that the mean curvature of the rods was the best single predictor with an excellent correlation to EFE (r2 = 0.80). The predictive power of the other local morphometric indices was generally lower, where indices derived from rods explained in average 40–50%, but indices derived from plates up to only 20%, of the variance in EFE. Furthermore, we found that most SDs were highly related to the mean of a given parameter. For this reason, the variation in local morphometric indices did not add any additional explanatory information to EFE. Moreover, multiple linear regression analysis revealed that a model based on trabecular spacing, slenderness of the rods, and the percent rod volume fraction was able to explain 90% of the variance in EFE in a very linear fashion (Fig. 5). The formula was found to be Epred = (1745 ± 78) − (394 ± 73)Tb.Sp − (637 ± 62)Ro.BV/BV – (121 ± 21)<Ro.Sl>, where the values in brackets denote estimate ± SE of the estimate. All parameters were highly significant (p < 0.001). A detailed analysis of the contributions of the three indices is summarized in Table 4. This correlation could not be improved by adding BV/TV as an additional independent variable.

Table Table 4.. Coefficients of Determination for Single and Multiple Linear Regression Analyses for the Prediction of the Finite Element Young's Modulus (EFE)
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Figure Figure 5. Epred = 1745 − 394 × Tb.Sp − 637 × Ro.BV/BV − 121 × <Ro.SI>. The model was in very good agreement (r2 = 0.90) with Young's modulus as derived from the finite element analysis (EFE).

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DISCUSSION

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

In this study, we related the elastic properties of human trabecular bone samples to local and global morphometric indices. Only recently, a new method has been proposed for the volumetric spatial decomposition of trabecular bone structures enabling local morphometry as applied on individual rods and plates.(34) In this study, we relate these new indices to bone stiffness to investigate the relative importance of structural differences between trabecular elements. These differences could be analyzed separately for rods and plates.

Bone stiffness was assessed by standard compression testing as well as by finite element model simulation. The Young's modulus of these two independent methods was in good agreement (r2 = 0.85). However, the fit was not perfect, and Fig. 2 implies that the relation could also have been modeled as a power law. This can be explained by the two limitations of the models. First, the mechanical compressions testing technique is not perfect and the concept of effective elastic modulus depends on many factors such as specimen size and geometry,(4,6) boundary conditions,(9) and strain rate.(40) Thus, in mechanical compression experiments there is always an intrinsic error that cannot be neglected and may result in a relatively high variation (mostly damage of the sample during preparation, bending of the sample during compression, precise location, and gauge length of the strain measure). Second, our finite element model simulation only accounted for structure and did not include variations in local material properties of the bone matrix. Additionally, the geometry of the FE model is highly sensitive to image segmentation, and thin structures may behave too stiff in bending. For these two reasons, it is clear that both moduli deviate from the true apparent Young's modulus, and that Emeas and EFE do not necessarily build a linear relationship. Because the global and local morphometric parameters investigated in our study are derived from digital images, we chose to compare them to EFE; hence, our findings are not biased by material properties but only take into account structural effects.

It is important to mention that, in this study, we only compared structural properties to stiffness as assessed by Young's modulus, although other mechanical properties such as ultimate strength or toughness might be equally important. Motivation to only use stiffness in our approach was based on findings in other studies,(15,41) showing that bone stiffness was relatively well correlated to both bone strength and bone toughness. To test whether this would also be the case for our study, we assessed both ultimate strength and toughness in a subset of 24 specimens that we compressed to failure. Correlation between stiffness and strength showed excellent agreement (r2 = 0.96). The correlation with toughness was less high (r2 = 0.79) but still very strong, indicating that the relations with local morphometry presented in this study should be very similar for stiffness, strength, and toughness. It is also important to note that we concentrated on mechanical results from linear-elastic finite element analysis, which in our current implementation is limited to the analysis of stiffness only. Nevertheless, issues related to parameters such as strength and toughness will need more thorough attention as local or global morphometry may play an important role in postyield properties.

Young's modulus of human vertebral trabecular bone samples could accurately be predicted by combining mean trabecular spacing (Tb.Sp), mean slenderness of the rods (<Ro.Sl>), and the relative rod volume fraction (Ro.BV/BV) in a multiple linear regression model. The presented model was able to explain 90% of the variance in EFE, where all three parameters were negatively correlated with the FE-based stiffness (Table 3). This means that increased trabecular spacing yields in a decrease in bone stiffness; an intuitive result, which was corroborated by the statistical analysis, showing that Tb.Sp accounted for 62% of the variance in EFE (Table 4). An increase in Tb.Sp means that the trabecular elements are generally further separated from each other, which can be achieved by a general increase in the intertrabecular distance or by the occurrence of larger areas with no trabeculae at all (“wholes”). Both cases clearly reduce bone strength because of a reduction in bone material. Thus, assuming a constant trabecular element, Tb.Sp could be seen as a surrogate measure for BV/TV, and the corresponding correlation was actually found to be pretty good (r2 = 0.77). However, the variation in trabecular elements is large and cannot be captured by measures such as Tb.Sp. Furthermore, it has been proposed that, in aging, the reduction in bone volume is mainly caused by a reduction in plate density, where the process of plate removal is initiated by an excessive depth of osteoclastic resorption cavities, leading to focal perforation of plates, followed by progressive enlargement of the perforation with conversion of plates to rods.(42,43) Such a transformation could occur at a constant Tb.Sp. It is therefore important to also include information of the structure type; we also included Ro.BV/BV as an indicator for the relative amount of rods within the structure into the model. Adding Ro.BV/BV to Tb.Sp increased the prediction of EFE up to 83% (Table 4), also indicating that these two parameters are measures of independent structural features. This also means that, at a given Tb.Sp, structures with a higher amount of plate volume behave stiffer. Also this result is not unexpected because it is generally accepted that a plate behaves stiffer than a set of rods. Finally, we found that the addition of the mean slenderness of rods (<Ro.Sl>) increased the predictability of EFE an additional 7% to 90% (Fig. 5; Table 4). An increase in the slenderness of the rods results in a higher likelihood for the elements to undergo bending and buckling. Thus, as this likelihood is increased, bones become less stiff and are more likely to fail. It is also noteworthy that the proposed model only included structural information not directly related to BMD or bone mass. The addition of BV/TV or BV did not add predictive power to this model.

Nevertheless, because BMD plays an important role in the prediction of the mechanical behavior of trabecular bone and can be assessed relatively easily at different anatomical sites of interest, it is still the subject of many studies. The precise relation between Young's modulus and BV/TV remains still controversial(44) and has been modeled by power laws with exponents ranging from 1–3.(13–15,45,46) In our study, we used a power law to predict both Emeas and EFE, resulting in equally good correlations (Fig. 3). The exponents were found to be 1.81 for Emeas and 1.65 for EFE. However, the correlation plots showed heteroscedasticity (increasing variance with increasing BV/TV), which is nicely shown in Fig. 3. This is also obvious in Fig. 4B, where the determined power law was applied to the data to predict Young's modulus [Epred(BV/TV)]. After transformation, the linear model only explained 70% of the variance in Emeas compared with 87% when fitting the log-transformed data (Fig. 4A). For this reason, BV/TV will typically lack predictive power when used to assess bone stiffness in real applications of strength prediction.

From global morphometry, we found that besides BV/TV, bone surface density (BS/TV), specific bone surface (BS/BV), SMI, mean curvature (<H>), trabecular separation (Tb.Sp), and trabecular number (Tb.N) also all had a high predictive power and were able to explain >60% of the variance in EFE (Table 2). However, none of these parameters were as good as BV/TV alone, and we could not find a multiple linear regression model that could improve the predictive power over that of BV/TV alone. A reason for this may lie in the fact that many of the global morphometric indices were in excellent agreement with each other (r2 > 0.77), indicating a lack of parameter independence on the global level.

From local morphometry, we found the best single predictor for EFE to be the mean curvature of the rods (<Ro.<H>>). This relation (r2 = 0.80) was negative, which means that as rods are transformed from a relatively flat element (plate-like element) to a perfect cylindrical element with circular cross-section (rod-like element), the trabecular bone structure becomes less stiff. This result is not unexpected, because one would expect a single plate to be relatively stiff compared with a set of rods as mentioned already earlier. A transformation from plates to rods has previously been described as a mechanism, where plates first are perforated and finally turned into rods.(42,43) Such a transformation would result in a higher mean curvature of the elements and thus to a decrease in stiffness. The other local morphometric indices were relatively moderate single predictors for EFE, where in general, indices derived from rods showed better correlations to EFE than indices derived from plates (Table 2). It is noteworthy that the mean trabecular thickness as measured by global morphometry was only poorly correlated to EFE, whereas the mean trabecular thickness of the rods was able to explain 42% of the variance in EFE. Furthermore, the mean trabecular thickness of the plates showed no significant correlation at all. Because the computation of global Tb.Th does not discriminate between rods and plates, this measure is averaged over the whole structure and all element types. This is a strong indication that it is important to also include local morphometry in the characterization of trabecular bone samples to look at individual contributions of rods and plates to the stiffness of bone.

This study discusses autopsy data that can be imaged by means of μCT at a very high resolution, which is currently not accessible in vivo. Thus, it has not been proven yet whether the proposed local morphometry framework can be used in the clinical fracture risk assessment. However, it was shown that structural parameters such as Tb.Sp, Tb.Th, or Tb.N could accurately be assessed by in vivo pQCT systems at a nominal resolution of 165 μm,(47) and two recent publications(48,49) used in vivo imaging systems with a nominal resolution of <90 μm to show that the assessment of bone microarchitecture may enhance fracture risk prediction. Thus, it can be assumed that with these new imaging systems, it should be possible to assess the structural features needed for our multiple linear regression model and, that thus, this new technique could have advantages over classical densitometric measures in clinical fracture risk assessment.

This paper discusses trabecular bone architecture and proposes a method on how to measure new structural features on an elemental rod/plate level. With these new measures, we hope to improve the understanding of the relative importance of “bone quality” in the assessment of bone competence. However, the term “bone quality” does not only refer to bone architecture but also to features such as damage accumulation (microcracks, microfractures), collagen cross-linking, and mineralization, which can not be assessed by the proposed method. Nevertheless, these features may also be important in the fracture risk assessment and cannot be neglected in the definition of “bone quality.” The problem with these additional features is that they are difficult to assess in vivo.

In conclusion, BMD was shown to be the most important single predictor of bone stiffness. Nevertheless, in this study we showed for the first time that bone density or mass is not required to predict bone stiffness when structural properties are incorporated in the analysis. A multiple linear regression model based on locally and globally determined structural information was able to predict the axial Young's modulus of human vertebral trabecular bone samples independent of BMD or bone mass. Although indices based on density or mass and indices based on local structural measures performed almost the same in the prediction of stiffness, these newly proposed local parameters have clear advantages over traditional density-based measures. They not only allow overall stiffness prediction but also include information on which structural features actually determine the mechanical properties of bone. Additionally, it is now possible to assess why and how a structure is changing, for example, in the course of a certain pathology or with treatment. One can imagine scenarios where BMD is changing only mildly after treatment, whereas changes of bone competence can be very pronounced. Local morphometry might be a tool to explain those disproportional changes in bone change as a new measure of bone quality and the competence of bone. In that sense, separate analysis of individual rods and plates may help to better predict age and disease-related fractures as well as to shed new light on the effect of pharmaceutical intervention in the prevention of such fractures beyond BMD.

Acknowledgements

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES

This study was partly supported by the SNF Professorship in Bioengineering of the Swiss National Science Foundation (FP 620-58097.99 and PP-104317/1).

REFERENCES

  1. Top of page
  2. Abstract
  3. INTRODUCTION
  4. MATERIALS AND METHODS
  5. RESULTS
  6. DISCUSSION
  7. Acknowledgements
  8. REFERENCES