Morphometric analysis of 70 bone biopsies was done in parallel by μCT and histomorphometry. μCT provided higher results for trabecular thickness and separation because of the 3D shape of these anatomical objects.

Introduction: Bone histomorphometry is used to explore the various metabolic bone diseases. The technique is done on microscopic 2D sections, and several methods have been proposed to extrapolate 2D measurements to the 3D dimension. X-ray μCT is a recently developed imaging tool to appreciate 3D architecture. Recently the use of 2D histomorphometric measurements have been shown to provide discordant results compared with 3D values obtained directly.

Material and Methods: Seventy human bone biopsies were removed from patients presenting with metabolic bone diseases. Complete bone biopsies were examined by μCT. Bone volume (BV/TV), Tb.Th, and Tb.Sp were measured on the 3D models. Tb.Th and Tb.Sp were measured by a method based on the sphere algorithm. In addition, six images were resliced and transferred to an image analyzer: bone volume and trabecular characteristics were measured after thresholding of the images. Bone cores were embedded undecalcified; histological sections were prepared and measured by routine histomorphometric methods providing another set of values for bone volume and trabecular characteristics. Comparison between the different methods was done by using regression analysis, Bland-Altman, Passing-Bablock, and Mountain plots.

Results: Correlations between all parameters were highly significant, but μCT overestimated bone volume. The osteoid volume had no influence in this series. Overestimation may have been caused by a double threshold used in μCT, giving trabecular boundaries less well defined than on histological sections. Correlations between Tb.Th and Tb.Sp values obtained by 3D or 2D measurements were lower, and 3D analysis always overestimated thickness by ∼50%. These increases could be attributed to the 3D shape of the object because the number of nodes and the size of the marrow cavities were correlated with 3D values.

Conclusion: In clinical practice, μCT seems to be an interesting method providing reliable morphometric results in less time than conventional histomorphometry. The correlation coefficient is not sufficient to study the agreement between techniques in histomorphometry. The architectural descriptors are influenced by the algorithms used in 3D.

THE MAIN FEATURES of trabecular bone at the macroscopical level are the high porosity and the intricate orientation and architecture of the trabeculae. Osteoporosis is now recognized as a decrease in bone mass associated with a deterioration of the trabecular bone architecture.^{(1)} Bone histomorphometry was developed in the 1950s to explore the various metabolic bone diseases by pioneers workers.^{(2–4)} The microscopic technique was done on 2D sections, and trabecular structures were measured by point and line counting using microscopic eyepieces or (more, recently) image analyzer systems. Several mathematical formulations have been proposed to extrapolate 2D measurements to the third spatial dimension (3D).^{(5)} However, these descriptors of the trabecular network are derived from measurements of trabecular area and trabecular perimeter and provide only a limited description of the architecture. New histomorphometric methods based on mathematical morphologic concepts have shown that architectural parameters fall in three groups: descriptors of the trabeculae, descriptors of the marrow cavities, and descriptors of the complexity of the network.^{(6,7)} Recently the use of 2D histomorphometric measurements have been shown to provide discordant results compared with 3D values obtained directly^{(8–10)} by X-ray μCT, a recently developed imaging tool to appreciate trabecular bone architecture. μCT is a miniaturized version of computerized axial tomography commonly used by radiologists, but the systems have a resolution of the order of a few micrometers. It is a completely nondestructive means of examining the interiors of opaque solid objects. It produces 2D slices where contrast is generated by differences in X-ray absorption that arise from a mixed combination of density and compositional information within the object. 3D models can be generated by reconstruction from 2D slices. The aims of this study were to compare the quantitative results obtained by “classical histomorphometry” processed without decalcification and μCT on a large series of human bone biopsies. The agreement between methods was compared by different statistical techniques.

MATERIALS AND METHODS

Bone biopsies

Seventy patients referred to our unit for a transiliac bone biopsy were included in this study. The clinical details appear in Table 1. Bone biopsy was removed under local anesthesia with a trephine having a 7.5 mm inner diameter to preserve bone architecture.^{(11)} The biopsy was performed 2 cm under the iliac crest and 2 cm behind the anterosuperior iliac spine. Biopsies were fixed in an alcohol-based fluid and transferred to the laboratory. Only complete (with two cortices) and unbroken biopsies were used in this study.

Table Table 1.. Clinical Characteristics of Patients Analyzed in This Series

μCT imaging

Bone cores were transferred to an Eppendorf tube containing the fixative, and polyethylene foam was used to insure immobilization of the biopsy. The tube was affixed on a brass stub with plasticine and examined with a Skyscan 1072 microcomputer tomograph (Skyscan, Aartselaar, Belgium) operating in the fan beam method. This system is composed of a sealed microfocus X-ray tube, air cooled with a spot size <8 μm and a CCD camera. Images were obtained at 80 V and 100 μA with a 1-mm aluminum filter, at a magnification of ×21 (pixel size = 14.64 μm in all three spatial directions). A rotation of 0.90° was used between each image acquisition. A stack of 2D sections was reconstructed for each biopsy (the number of sections depending of the core height) and stored in the bmp format with indexed grey levels ranging from 0 (black) to 255 (white). 3D modeling and analysis reconstruction of the bone were obtained with the ANT software (release 2.05; Skyscan). The program allows reconstruction of objects from the stack of 2D sections, after interactive thresholding. The reconstructed 3D models were obtained by a surface-rendering algorithm. An interesting possibility was to obtained 2D reslices of the objects across a plane, positioned in a specified direction (e.g., vertical, parallel to the core axis of the biopsy running through the cortices).

The 3D measurements were obtained with the CtAn software (release 2.5; Skyscan). The volume of interest (VOI) was designed by drawing interactively polygons on the 2D gray images before reconstruction. Polygons are drawn only on a few sections (e.g., starting, middle, and final sections), and a routine facility calculates all the intermediary masks by interpolation. The VOI was comprised of only cancellous bone, and the following parameters were determined: the bone volume fraction (BV/TV_{3D}) is the ratio of the volume of bone present (BV) to the total VOI (i.e., TV). Trabecular thickness is derived from the frequency distribution of trabecular thickness obtained with the sphere algorithm.^{(12)} Briefly, the diameter of nonoverlapping spheres filling the trabeculae is computed, and the mean trabecular thickness is calculated as:

where P(a) is the frequency of trabecular in the class a. Mean trabecular separation (Tb.Sp_{3D}) is measured in a similar way by fitting nonoverlapping spheres of maximal diameter to a 3D model of the marrow spaces.^{(13)} The structure model index (SMI) was determined according to previously published algorithms.^{(12)} Briefly, SMI quantifies the plate versus rod characteristics of trabecular bone; typical values range from 0 (purely plate-shape trabeculae) to 3 (purely rod like trabeculae). The calculation of SMI is based on a dilatation of the 3D model (artificial adding of one voxel thickness to trabecular surfaces). SMI is calculated as follows:

where BS stands for the trabecular surface area before dilatation and BS' is the new value in surface area caused by dilatation, BV being the initial undilated volume of the trabeculae.

The trabecular bone pattern factor (Tb.P_{f}) was computed in 3D with an adaptation of a previously proposed algorithm.^{(14)} Briefly, it is an index of connectivity based on the relative concavity/convexity of the total trabecular surface. Basically, concavity indicates the presence of enclosed marrow cavities and convexity corresponds to disconnected trabecular struts. Tb.P_{f} is calculated by comparing area and volume of trabeculae before and after an image dilatation as:

where the subscript numbers 1 and 2 indicate before and after image dilatation.

In addition, trabecular thickness and separation were also calculated from the raw values of TV, BV, and BS directly measured by μCT according to the formulae described for the “plate and rod” model by Parfitt.^{(15,16)} In this way, Tb.Th_{calc} Tb.N_{calc}, and Tb.Sp_{calc} were computed.

The 3D models of trabeculae were also used to prepare a set of six 2D-X-ray sections perpendicular to the transcortical axis. These parallel 2D sections were obtained in a random angle and were separated by 100 μm, both conditions that mimic section sampling in bone histomorphometry. The sections were downsized to 512 × 512 images (8 bits, tif format) and transferred to a Leica Q570 image analyzer (Leica, Rueil Malmaison, France). They were segmented using the same threshold as above and processed with the software used for bone histomorphometry. The parameters determined on the 2D-X-ray sections were trabecular bone volume (BV/TV_{2D}), trabecular characteristics derived from trabecular area (B.Ar), and trabecular perimeter (B.Pm) according to Parfitt.^{(15,16)} They will be referred to as Tb.Th_{2D}, Tb.N_{2D}, and Tb.Sp_{2D}.These parameters were determined on all the 70 bone biopsies.

Bone histomorphometry

Bone biopsies were processed undecalcified after embedding in methacrylate. Semi-serial sections (7 μm thick, separated by 100 μm) were stained by a Goldner's trichrome and measured with the Leica Q570 analyzer with software previously reported elsewhere.^{(7)} Measurements were performed on binarized images of histological sections, and the whole cancellous space (as usually recommended in histomorphometry) was used as the region of interest.^{(17)} It was determined by drawing manually two lines on the binary image from one cortex to the other to limit the upper and lower boundaries of the section. The trabecular network was disconnected from the endosteal surfaces by an interactive procedure. The following histomorphometric parameters were considered: BV/TV_{H}, Tb.Th_{H}, Tb.Sp_{H}, and Tb.N_{H}. All parameters were derived from T.Ar, B.Ar and B.Pm (surface area of the region of interest and surface and perimeter of trabeculae, respectively).

The osteoid volume was measured, and the mineralized volume (MdV/BV; which represents the calcified fraction of trabecular bone volume) was derived according to standard formulae. 2D architectural descriptors of the trabecular network were determined using previously described algorithms^{(6,7)}: Euler-Poincaré's number,^{(18)} interconnectivity index of marrow cavities (ICI),^{(19)} strut analysis with determination of the nodecount (NC), free-end count (FE), and the various types of trabeculae: node-to-node struts (NNC); node-to-free end struts (NFC); free-end-to-free-end struts (FFN),^{(20)} star volume of marrow spaces (V*_{m.space}) and star volume of trabeculae (V*_{Tb}), and Kolmogorov fractal dimension of the trabecular network (D).

Statistical analysis

Statistical analysis was done using Excel XP (Microsoft) and Systat statistical software, release 10 (SPSS, Chicago, IL, USA). Correlations were searched for between parameters. (1) Linear correlation analysis used Pearson's r based on the model y = a + bx, where y is the dependent variable and x the independent variable. (2) Regression analysis was performed according to the method of Passing-Bablock, which makes no assumptions regarding the distribution of the samples and the measurement error and does not depend on the assignment of a method to x and y.^{(21)} The slope b of the regression line and the intercept a were calculated with their 95% CIs. This allows testing of the following hypotheses:

• b = 1; the hypothesis is accepted if the CI for b contains the value 1. If the hypothesis is rejected, b significantly differs from 1, and there is at least a proportional difference between the two methods.

• a = 0; the hypothesis is accepted if the CI for a contains the value of 0. If the hypothesis is rejected, both methods differ at least by a constant bias.

(3) To assess better the agreement between two methods, the difference plot method reported by Bland-Altman was also used.^{(22)} In this graphical method, the differences (expressed as percentage of the averages) between two techniques are plotted against the mean of the two methods. The Bland-Altman plots are useful to reveal a relationship between the differences and averages (indicating a proportional error), to identify a systematic bias and outliers. If there is no bias, the mean of differences is centered on 0; otherwise, the mean difference ±2 SD can easily be plotted on the graph. (4) When more than two series were compared, the Mountain plot method was used.^{(23)} This graphic method, also called “folded empirical cumulative distribution plot” is done by computing a percentile for each ranked difference between a new method and a reference method. To get a folded plot, one performs the subtraction 100 − percentile for all percentiles >50. This value is plotted against the differences between the two methods. This method is a useful complementary plot to the Bland-Altman technique; it allows comparison between multiple series and provides information about the distribution of the differences between methods. If two assays are unbiased, the mountain is centered over zero. The method also allows visualizing a systematic bias between techniques; when long tails are observed on a curve, this reflects large differences between the methods.

RESULTS

This series of patients obtained from January 2000 to September 2002 comprised a wide range of bone volume values ranging from osteoporotic to markedly condensed bone in cases of Paget's disease, polycytemia vera, and condensing myeloma. Typical examples of 3D reconstructed models from such patients are shown in Fig. 1. The reslicing of the 3D models provided 2D images that had a quasi-histological definition, although trabecular boundaries were not as sharply defined as on Goldner's-stained histological sections (Fig. 2).

A summary of statistical results of regression analysis, linear correlation (according to Passing-Bablock), and bias estimation (expressed in percent according to Bland-Altman) is presented in Table 2. Significant linear correlations were observed (p < 0.0001) in every couple of analyzed variables.

Table Table 2.. Relationships Between Data Compared With Linear Regression (r), Passing-Bablock, and Bland-Altman Methods

Trabecular bone volume

μCT provided very similar results at the 3D level than those obtained by classical histomorphometry performed on regularly sampled histological sections (Fig. 3A). μCT tended to slightly overestimate BV/TV, but the bias remained relatively low (+2.8%; Fig. 3B). The amount of osteoid volume had little influence on BV/TV_{3D} in this series, and using MdV/TV instead of BV/TV_{H} did not significantly improved the coefficient correlation (r = 0.937). However, the average of osteoid volume remained in the normal range in this series (3.1 ± 4.1%), and only eight patients had abnormal values (i.e., relative osteoid volume exceeding 6%). The correlation appeared somewhat better between BV/TV_{2D} and BV/TV_{H}, but there was a higher systematic bias of 11.2%. On the Mountain plot (Fig. 3C), the light overestimation was easily evidenced, and the narrow peak reflected the better agreement between the two methods.

Trabecular thickness

Although highly significantly correlated, the linear correlation coefficients were lower (Fig. 4A). 3D values overestimated considerably Tb.Th compared with 2D measurements obtained on histological sections, μCT reslices, and calculated results (Fig. 4B). On the other hand, the bias was lower between Tb.Th_{2D} and Tb.Th_{H} (23%), and the coefficient correlation was improved (Fig. 4C). On the Passing-Bablock curves, the hypothesis that b = 1 could not be accepted was evidenced, emphasizing the influence of a proportional factor between measurements.

Similar conclusions could be drawn when comparing Tb.Th_{H} and Tb.Th_{calc}, and a proportional factor was evidenced from Passing-Bablock, Bland-Altman, and Mountain plot analyses (Fig. 4D). When Tb.Th_{3D} was correlated with architectural parameters describing trabecular connectivity, significant values were obtained (r = −0.49 for Tb.P_{f}, 0.44 for NC and NNS, 0.49 for V*_{Tb}, and −0.50 for Euler-Poincaré's number; all significant with p < 0.001).

Trabecular separation

All results provided by the different methods were highly correlated, but hereagain, proportional differences were noted (Figs. 5A and 5B). Tb.Sp_{3D} was markedly increased compared with Tb.Sp_{H} values (bias ≃ 25%; Fig. 5B) and Tb.Sp_{2D} (bias reduced to 19.5%). On the contrary, Tb.Sp_{2D} and Tb.Sp_{H} were accepted with a limited bias (5%; Fig. 5C). Tb.Sp_{3D} appeared well correlated with several 2D architectural parameters: a significant linear correlation was found with log(V*_{m.space}) (r = 0.86, p < 0.0001 and log(NC) (r = 0.86, p < 0.0001).

Trabecular number

All results provided by the different techniques were highly correlated (p < 0.0001), but no special attempt was done to characterize further the relationships between the techniques because Tb.N is always a derived parameter. Tb.N_{3D} highly correlated with D (r = 0.71, p < 0.00001).

Architectural parameters

The algorithm used to calculate SMI provided abnormal negative values in four patients with BV/TV > 40%. When these values were excluded, significant correlations were obtained with 2D descriptors of the trabecular network connectivity (NC: r = −0.47; NNS: r = −0.57; FFS: r = 0.58; V*_{m.space}: r = 0.51; D: r = 0.50; all with p < 0.0001). Tb.P_{f} was linearly correlated with Euler-Poincaré's number (r = 0.93, p < 0.001) and exponentially correlated with ICI (r^{exp} = 0.84, p < 0.0001).

DISCUSSION

Although differences appeared in the morphometric results when comparing μCT 2D and 3D data with classical histomorphometric analysis, highly significant linear correlations were obtained between the various techniques. However, to evaluate the agreement between two, or more, techniques, the estimation of the Pearson's correlation coefficient is clearly inadequate. Determination of the correlation coefficient r and linear regression (calculating to equation y = a + bx) are not suited to measure agreement between methods because both are strongly influenced by outliers and observations with large values. High values from broad data ranges are know to improve r and the slope of the line.^{(24,25)} Clinical chemistry is one of the medical areas where the comparison of a new method with a reference method plays a major role in the statistical evaluation of experiments. A large body of the chemical literature is concerned with statistical analyses for method-comparison experiments: the use of regression analysis tends to be discouraged and replaced with other graphical presentations in the form of a difference/average plot according to Bland-Altman.^{(26)} However, this graph makes the assumption that one method is the “gold standard” (histomorphometry in this study) for calculating the bias. In addition, the method is best used when the range of absolute values is narrow, and the absolute differences are small.^{(25)} Clearly, this was not the case in this series where BV/TV_{H} ranged from 5.5% to 82.4%. The method is cumbersome when multiple method comparisons are required, and some difficulties of interpretation have been stressed.^{(27)} The Mountain plot used here allows graphical comparison of multiple methods and provides additional results (normal distribution of the dot plots, skewness, and long tails). Other graphical methods have been recently presented, such as percentage similarity^{(25)} or graphical analysis of concordance,^{(24)} but seem to be less intuitively appreciable.

With this panel of graphical techniques, it seems that 3D measurements tend to provide higher values than histomorphometry for the different parameters considered. For bone volume, the bias is very limited and may rely on the differences in the selection of the thresholds. μCT uses two thresholds: one when images are reconstructed from acquisition files and another one when images are binarized before morphometry. Although μCT images have a quasi-histological appearance, the trabecular boundaries are less well defined than on histological sections stained by the Goldner's trichrome. The Bland-Altman plot indicated a larger bias comparing BV/TV_{2D} and BV/TV_{H}, showing the limit of the method when broad variations are considered. On the Mountain plot, the peak was narrower than for BV/TV_{3D} and was symmetric without tail. Also, on the Passing-Bablock plot, the CI for slope b had a reduced range. A possible explanation would be that both 2D and histomorphometric techniques have the same criterion for selecting the region of interest. Other authors have found similarly higher values for BV/TV when using other types of μCT apparatus.^{(28,29)}

The mean Tb.Th and mean Tb.Sp provided by μCT were much higher in 3D than with any other method. Clearly the sphere algorithm is responsible for this increase. Measurements obtained either on a phantom or on objects with a regular and known thickness (e.g., pins) and scanned with the μCT were unbiased (data not shown). The Passing-Bablock and Bland-Altman plots revealed an error proportional to the thickness of trabeculae (the size of marrow cavities). Correlation studies of these 3D parameters with architectural descriptors of connectivity evidenced that the shape of the object measured influenced the results. Tb.Th_{3D} was significantly correlated with the number of nodes, the node-to-node struts, and the star volume of trabeculae, among others. Clearly, in the third dimension, nodes represent volumes that can be filled by much larger spheres than rods can contain. Because the mean Tb.Th is derived from the frequency distribution of the sphere diameter, the more connected the trabeculae, the more skewed the distribution will be on the right. Figure 6A shows the influence of nodes on the sphere diameter. Trabecular separation in 3D also appeared to be influenced by connectivity parameters. Relationships were found to be highly significant with several 2D descriptors measured with algorithms that do not rely on B.Ar and T.Ar. However, the relationships were logarithmic (a finding that was previously reported for 2D histomorphometry by our group^{(6,7,30,31)} and confirmed by others^{(32,33)}). This reflects the (partially) fractal nature of the trabecular network^{(6,34–36)} and emphasizes the major role of a small number of perforations on the mechanical resistance according to the percolation theory.^{(37,38)} In condensed bones, the shape of the marrow cavities tends to flatten and become an ellipsoid (Fig. 1B). The shape of marrow cavities is not taken into account in histomorphometry or in 3D, but it is likely that the sphere algorithm minors the mean size of Tb.Sp (Fig. 6B).

The 3D descriptors of connectivity provided by μCT were correlated with 2D descriptors of the trabecular architecture: SMI reflect the decrease of connectivity but provided erroneous values in sclerotic bones. Tb.P_{f} (being based on a dilatation algorithm) was correlated with descriptors of the marrow cavities, a finding in agreement with the proposed algorithm.^{(14)} Because SMI and Tb.P_{f} are both based on the dilatation algorithm, these parameters are correlated (r = 0.85, p < 0.0001) and behave similarly. When bones are sclerotic, the enclosed marrow cavities are small and numerous, and the dilatation algorithm reduces surface area considerably with the possibility of negative values for BS'. As a consequence, SMI seems to be a parameter influenced by the bone volume, and this can artificially accentuate differences between experimental groups in the measured SMI value.

μCT is faster than histology (about 6 h from acquisition to analysis) and permits the nondestructive examination of bone specimens before pathological analysis. The method lightly overestimates bone volume and was little influenced by the amount of osteoid in this series. The descriptors of trabeculae and marrow space are much higher than those provided by histomorphometry. The influence of thresholds used during image reconstruction and binarization may play a role but the sphere algorithm used for measurement is influenced by the number of nodes (for Tb.Th_{3D}) or shape and opening of the narrow cavities (for Tb.Sp_{3D}). Should groups of patients be compared, the frequency distribution of these parameters should be compared instead of their mean value. Because different μCTs exist on the market with different algorithms for the measurement of 3D parameters, careful precautions must be taken when comparing parameters between different authors. Although the ratios between quantities (e.g., BV/TV; expressed in percent) are comparable, this may be false when trying to compare parameters expressed in a given unit (e.g., Tb.Th or Tb.Sp, in μm). This is because of the fact that bone surface has a fractal dimension under some limits, and measurements can be modified by various factors such as the magnification and the structuring elements used by the software.^{(6,36,39)} The use of internal controls in each series is a prerequisite to appreciate differences within groups.

Acknowledgements

The authors thank Laurence Bourdais for secretarial assistance. Other experts of the NEMO (Network in Europe on Male Osteoporosis) working group are also acknowledged for their interest.