Journal of Orthopaedic Research k833-842 Raven Press, Ltd., New York 0 1990 Orthopaedic Research Society
Evaluation of a Microcomputed Tomography System to Study Trabecular Bone Structure J. L. Kuhn, S. A. Goldstein, "L. A. Feldkamp, R. W. Goulet, and "G. Jesion Biomechanics, Trauma, and Sports Medicine Laboratory, Section of Orthopaedic Surgery, University of Michigan, Ann Arbor, and *Physics Department, Ford Motor Company, Dearborn, Michigan, U.S.A.
Summary: A new microcomputed tomography (micro-CT) system and thresholding procedure was evaluated as a tool for nondestructive analysis of trabecular bone. Images of 6-mm trabecular bone cubes acquired from the microCT system were compared with optical images of corresponding histologic sections to determine the accuracy of representation. The stereologic measures of bone volume fraction (P,) and trabecular plate density (PL) were used to quantify the comparisons. The results showed that the micro-CT measures of P, were not significantly different from those measured from histologic sections and therefore were very accurate. Measures of P, were different by approximately 14%, which translated into discrepancies in trabecular plate thicknesses of about 19 pn. This difference was significantly correlated to the microstructural characteristics of the specific specimen scanned. The precision of both measurements was excellent. Key Words: Trabecular boneMorphology-Architecture-Digital imaging.
The structure of trabecular bone has been the focus of investigation for many years. Using radiographs and dissections, early anatomists correlated the microstructure of trabecular bone to their presumed mechanical environments during normal function, and began to perceive trabecular bone as a material of optimized design (5,9). Singh (7) described different trabecular arrangements to be characteristically found in specific regions of human metaphyses and incorporated these distinguishing features into a classification scheme for trabecular architectures. Although such qualitative observations serve as useful clinical tools, more quantitative measures are necessary to derive empirical relationships between microstructure and
mechanical properties, to quantify the effects of bone disease and aging on bone morphology, or to test hypotheses of bone remodeling. Most present methods to quantify bone morphology and architecture at this level of microstructure rely on microscopic observations of thin sections of trabecular bone. Alternative methods include analyses of scanning electron micrographs or light microscopic observations of polished specimen surfaces. In all cases, the section selected for analysis must be assumed to represent the entire specimen, because a complete analysis of all serial sections would be prohibitively time consuming and tedious. A recent paper by Feldkamp et al. (2) introduced the usefulness and advantages of a three-dimensional (3D) microcomputed tomography (micro-CT) system for nondestructive examination of trabecular bone architecture in vitro. The purpose of this study was to further evaluate the ability of this unique system, combined with a new thresholding algorithm, to produce accurate digital images of a
Received March 21, 1988; accepted March 14, 1990. Address correspondence and reprint requests to J . L. Kuhn at the Biomechanics, Trauma, and Sports Medicine Laboratory, The University of Michigan, Section of Orthopaedic Surgery, G-0161, 400 N. Ingalls, Ann Arbor, MI 48109-0486.
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wide range of trabecular structures found in the human skeleton. MATERIALS AND METHODS For background, a brief description of the microcomputed tomography system and thresholding procedure are given. Microcomputed Tomography Scanner The microcomputed tomography scanner was developed by one of the authors (L.A.F.) at Ford Motor Company with the initial purpose of detecting small defects in ceramic materials. Figure 1 illustrates the main components: an x-ray source, a specimen stage, an image intensifier, a video camera, a digitizer and image processing system, and a host computer. The system operates similarly to commercial computed tomography scanners with some exceptions: (a) the specimen is rotated rather than the source and/or detectors; (b) a 2-D detector is used instead of a linear array of detectors, thereby providing direct 3-D image reconstructions; and (c) the specimen must be of limited dimensions. The most important difference is the resolution of the system. When set up appropriately for a scan of an 8-mm bone cube, the resolution is approximately 50 to 70 pm and individual trabeculae can be discerned easily. The resolution increases with geometric magnification, so small specimens positioned very close to the x-ray source can be imaged with even a higher resolution. Trabecular architectures of scanned specimens can be reconstructed and represented by a three-dimensional data set of grey scale values and stored on magnetic tape for later retrieval. Any number of algorithms can be utilized to study the microstructure without damag-
---H 1 I H microfocus x-ray source
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FIG. 1. A schematic diagram of the micro-CT system is shown.
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ing the original data. More complete and detailed descriptions of the system hardware, as well as the three-dimensional reconstruction algorithm, can be found elsewhere (24). Thresholding All images require some form of thresholding. Even in nonautomated analysis systems, the human eye and mind are forced to “threshold” images. The simplest threshold is one in which one number (grey scale value) is selected, above which all pixels are considered bone, and below which all pixels are considered nonbone. The effects of the choice of threshold on calculations of morphology and architecture are seldom discussed. X-ray images of bone present some special circumstances. Because of geometry and density variations within a bone cube specimen, a simple uniform threshold may be inappropriate for application to an entire image. Figure 2A aids in explaining this point. Density profiles across two trabeculae of equal density but different thickness appear as shown. The actual borders of each trabecula exist somewhere within the transition regions between the low density of marrow or air, and the high density corresponding to the center of the trabecula. If the trabecular thickness is much greater than the resolution of the system, the trabecular borders are defined at the points corresponding to exactly one half the difference between the extreme densities of the transition region. Conversely, for very thin trabeculae, the borders are more difficult to discern. Also, the density at the center of the thin trabecula is underestimated, even though the actual densities of the thick and thin trabecula are the same. It can be seen that within a certain range, selection of a uniform threshold would exclude the thin trabecula from the image. A second problem can arise from the normal variations in mineral densities of trabeculae contained within a single specimen. A uniform threshold, in this case, would entirely exclude some trabeculae, or cause artificial thickening or thinning of others (2). Use of fixed thresholds between specimens of very different average mineral densities present similar problems (2). For instance, if a fixed and uniform threshold were applied to two data sets-a healthy specimen and a diseased bone specimen of identical structure but overall lower density-an incorrect topology would result for the diseased specimen (Fig. 2B).
MICRO-CT TO STUDY TRABECULAR BONE
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image representations of trabeculae in both specimens when a uniform threshold is used
We use an approach (2) in which multiple local thresholds within a single image data set are allowed. Each local threshold reflects the density variations in a local neighborhood of pixels about the point of interest. The concept can best be explained by considering a histogram plot of pixel grey levels along one Cartesian axis through a point. Figure 3 represents fluctuations in density from a trabecular bone specimen, where high grey levels correspond to bone, and low grey levels correspond to either marrow, a plastic embedding medium, air, or even soft tissues such as the endosteum of trabeculae. Three parameters of variable setting guide the evaluation of this line plot for local minima and maxima: a centerline, a spread, and a confidence number. The following three criteria are set: (a) a potential local maximum must have a pixel value greater than the sum of the centerline value and one half the spread; (b) a potential minimum must have a pixel value less than the difference of the centerline value and one half the spread; and (c) points that satisfy either of the first two criteria are
only considered valid extrema if pixels that follow descend in value (for a maximum) or ascend in value (for a minimum). The number of pixels that must follow in this mode is determined by the confidence number. A local neighborhood of pixels is then defined by the region between a local minimum and a local maximum. These conditions avoid the acceptance of small rapid fluctuations due to noise or insignificant structures as extrema. A fourth parameter is required to calculate the local threshold for each local neighborhood. This parameter is a percent of the difference between the two extrema (for trabeculae much thicker than the resolution, a percentage of 50% should exactly define the trabecular borders). The local threshold is then calculated by adding this percent of the difference to the grey level value of the local minimum. In the actual algorithm, this evaluation procedure is performed in all three Cartesian directions, and the final threshold for a point is resolved by taking the average of local thresholds determined in each of the three directions through the point. To produce binary data
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FIG. 3. The thresholding procedure used in this study is illustrated. Multiple local threshold values are calculated based on pixel density fluctuations within small neighborhoods about a point. A: Unthresholded data. Threshold parameters: centerline = 80; spread = 20; confidence = 2; percent = 60. Bold numbers are the calculated local thresholds. B: Thresholded data.
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sets, the remaining pixels with nonzero grey level values are set equal to one. Evaluation of Thresholded Microcomputed Tomography Images Because analysis of histologic sections represents the standardly accepted method to quantify trabecular bone morphology and architecture, the accuracy of the thresholded micro-CT images was tested by comparing extracted planar images from the micro-CT 3-D data set (slices) with optical images of corresponding histologic sections taken from the actual bone cube (sections). Images were compared by (a) visual observations of topology, and (b) the stereologic measures of P,, the number of bone pixels divided by the total number of pixels in an area of analysis, and P, the number of intersections be-
J Orthop Res, Vol. 8, N o . 6, 1990
tween bone d onbone ixels er unit test li length (8). An average P, (calculated in two perpendicular directions) was used in the comparisons. Specimens of human trabecular bone were obtained from fresh frozen cadavers: 31- and 69year-old men and a 55-year-old woman. Two 6-mm cube specimens were prepared from each of the following anatomic locations: proximal tibia, proximal humerus, L1 vertebra, L2 vertebra, distal femur, and distal radius. A proximal femur and iliac crest provided one specimen each for a total of 14 specimens. These bone cube specimens were cut using a numerically controlled milling machine and stainless steel blade operated at low speed and under constant water irrigation. In order to histologically section and visualize the interior planes of bone cube specimens, the cubes were embedded in polymethylmethacrylate
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(PMMA). The plastic blocks were then trimmed to 8-mm cubes, leaving a border of approximately 1 mm around the cube sides and 2 mm above. A small hole was drilled into the center of the top face to a depth of about 1 to 1.5 mm. This hole was easily delineated from the surrounding higher density plastic in displayed micro-CT images and thus served as a landmark to assist in matching the histologic sections to the micro-CT slices of each specimen. All 14 specimens were scanned on the microCT scanner (in the standard setup for 8-mm bone cubes) and reconstructed on a 50-pm mesh. The reconstructions were stored on magnetic tape. After scanning, each specimen was re-embedded to produce a larger plastic block, preserving the orientation of the cube and presence of the drill hole. This allowed the specimen to be securely fixed in the grips of a Jung sledge microtome for histologic analysis. Optical images of a specimen’s interior planes were obtained by serial sectioning until a desired plane was reached. At this point, optical images were taken directly from the exposed cut surface of the bone cube, which remained clamped in the microtome until the analysis was complete for the entire cube. Such a method was necessary to avoid the damage and distortion artifacts often associated with thin sectioning of embedded tissues. The main components of the histologic imaging system were a digital camera (MTI Dage, series 86, Model NC-86D), image processing system (Recognition Technology Inc., RTI), a microcomputer (IBM PC), a color display monitor, and a low-noise illuminator (Cole Parmer, Model 9741-50). The camera was attached to a frame over the microtome for variable translational and rotational positioning. With a Nikon Micro-Nikkor 55-mm 0 . 8 lens and an extension tube attached to the camera, images of an entire bone cube’s cross-section at a magnification of approximately .025 mm/pixel by 0.02 mdpixel were obtained. These images were purposely centered to avoid possible geometric distortions near the edges of the imaging field. The magnification in the horizontal and vertical directions was always recalibrated for each bone cube. After careful alignment and positioning of the specimens in the microtome, sectioning gradually proceeded from the cube top until the drill hole disappeared. This plane marked the reference level. Any set of sections at a distance from the reference equal to some multiple of 50 pm (the physical thickness represented by each micro-CT slice) consti-
tuted a potential region to be imaged. In general, each region consisted of 5 sequential 10-pm sections for a total of 50 pm. Measurements from five consecutive histologic sections were averaged (the “average section measure”) and compared with one micro-CT slice. The biological stain, Sudan Black B, was used as a surface stain to distinguish between trabecular bone and its plastic background. A solution of this dye in 95% ethyl alcohol preferentially stained the plastic background black, leaving the trabeculae uncolored. The contrast was intensified when the underlying plastic base was illuminated, giving bone regions a bright golden hue. The efficacy of this reverse staining technique was supported by comparison with surface staining with hematoxylin and eosin. The images from the optical histologic analysis and the microcomputed tomography scanner were transferred to an Apollo Domain computer system (DN 3000), where they were displayed and analyzed. Micro-CT images were thresholded using different input parameter sets to the thresholding algorithm as described earlier. Limits were carefully chosen to outline the areas of analysis for the stereology algorithm. Although the fundamental comparison between matched slices and sections was in the measures of P, and P,, common bone morphologic variables were also calculated from these two basic measures using the following equations (2,6) and compared: trabecular bone volume fraction (FRAC) = P, (1) surface to volume ratio (SV)
=
2 x PL/Pp (2)
mean trabecular plate thickness (MTPT) = 2/SV (3) mean trabecular plate density (MTPD) = 0.5X FRAC X SV = P,
(4)
mean trabecular plate separation (MTPS) = (1 - FRAC)/MTPD (5) The percent differences and actual differences in quantitative measures from matched micro-CT slices and histologic sections were calculated and used as indicators of accuracy. The actual difference was defined as d = slice measure - average section measure, whereas the percent difference was defined as % difference = (actual difference/ average of the 2 measures) X 100.
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To further assess the accuracy and precision of the imaging and analysis procedure-scanning, reconstruction, thresholding, selection of analysis region, and stereologic analysis-a set of five 8-mm trabecular bone specimens were scanned. These specimens (one from a canine distal femur, one from a human lumbar spine and proximal femur, and two from an iliac crest) represented diverse architectures and a wide range in bone volume fraction (approximately 1545%). To test repeatability, these specimens were each scanned a total of four times, each time on a different day. The data from the repeatability tests were analyzed for measurement variability. In addition, independent measures of bone volume fraction were obtained from calculations of the tissue volume to bulk volume ratio. This ratio was obtained by subtracting the submerged weight of specimens from their wet weight using Archimedes Principle and the assumption that the specific gravity of water is equal to unity (1). Bulk volume was calculated from micrometer measurements of the cube dimensions. These data were analyzed by a linear regression of micro-CT computed P, on the tissue volume to bulk volume ratio. The standard error of this regression was used to further indicate the precision of the P, measure. RESULTS Visual comparisons of the 2-D topology of trabecular bone as represented by micro-CT slices and
optical images of histologic sections provided the first evidence that the micro-CT system was functioning effectively as a tool for the analysis of bone morphology and architecture. Although the general trabecular patterns matched quite well, the boldness and continuity of the trabeculae varied depending on the input parameters to the thresholding procedure. This variation is demonstrated in Fig. 4. The micro-CT image designated “threshold set D” seemed to best match the optical image of the histologic section. Support for this choice of thresholding input parameters was also provided by comparisons of stereologic measures. The accuracy as inferred from the mean percent differences in stereologic measures was l .35% for P, (95% confidence interval of *6%), and - 14.3% for P, (95% confidence interval of 24%). A pairwise t test of these data showed the difference in P, to be insignificant (p > .6), whereas the difference in P, was significantly different from zero (p < .01). Table 1 shows the raw data for 14 specimens. The mean actual differences in P, and P, were .0027 and - .2483. Using equations 1 to 5 for the calculation of the morphology variables, the percent differences in P, and P, translated into percent differences of 1.35% for FRAC, -15.7% for SV, 15.7% for TPT, -14.3% for TPD, and 13.7% for TPS. It is more useful to interpret the accuracy of TPT in terms of the mean actual difference rather than the percent difference. This value was 19.2 pm (95% confidence
FIG. 4. The same micro-CT image is shown here, thresholded with four different thresholding parameter sets, along with an optical image from one of the corresponding physical planes of bone. (The optical image has been redigitized to the same magnification scale as the micro-CT image for display purposes.)
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MICRO-CT TO STUDY TRABECULAR BONE TABLE 1. P, and P, measures from matching histologic sections and micro-CT slices of I4 different trabecular bone cubes Micro-CT slice
Histology sectionn Cube identification
Proximal tibia Proximal tibia Proximal tibia Proximal tibia Proximal tibia Proximal humerus Proximal humerus Proximal humerus Proximal humerus Proximal humerus Distal femur Distal femur Distal femur Distal femur Distal femur Proximal tibia Proximal humerus Proximal humerus Iliac crest Lumbar 1 Lumbar 1 Lumbar 2 Lumbar 2 Distal femur Distal radius Distal radius
4b 4b 4b 4b 4e 5b 5b 5b
5b 5b 19 15b 15b 1 9 15b 6 7 8 9 11 12 13 14 16 17 18
Mean actual difference Pp Mean actual difference P,
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0.3311 0.3648 0.3346 0.2484 0.2062 0.156 0.1604 0.1712 0.1543 0.164 0.3 0.2999 0.2933 0.302 0.294 0.1266 0.2188 0.1218 0.2781 0.1442 0.157 0.1212 0.1463 0.3999 0.28 0.2253
1.775 1.7822 1.734 1.6573 1.429 1.4542 1S282 1S956 1.4409 1.5414 2.033 2.0081 1.9152 1.9617 1.7559 1.4142 1.5373 1.1501 1.7572 1.1816 1.3626 0.9098 1.1936 2.0962 1.4735 1.6287
PP 0.3424 0.3294 0.3258 0.2703 0.2233 0.137 0.1457 0.1653 0.1508 0.1544 0.2787 0.3213 0.3415 0.3463 0.2999 0.1798 0.2159 0.1195 0.1796 0.1359 0.1807 0.0972 0.1651 0.3426 0.2486 0.2327
P, (mm-') 2.0354 1.8393 1.6881 1.7941 1.6187 1.7148 1.8196 1.9447 1.8244 1.8459 2.4246 2.4495 2.4853 2.3899 2.1634 1.8821 1.4416 1.4199 1.8137 1.4374 1.8828 1.0252 1.3669 2.0691 1.5395 1.8567
0.0027
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Average of five consecutive 10 pm sections. In some cases only four 10-pm sections were obtained. These cubes were tested at five different levels within the cube depth to determine whether the accuracy was dependent on position. No significant linear or power relationship was found (p > .05). This supported the imaging of only one region from each of the remaining 11 cubes.
interval of 13.2 to 25 pm), which is less than one half a pixel of a micro-CT image. The mean actual difference in TPD (which is numerically equal to the mean actual difference in PL) was significantly correlated to the TPD (Y = - .57, p < .Ol) and TPT (Y = .46, p < .05) measured from histologic sections. Figure 5A and B shows scatter plots of the discrepancy in TPD measures versus the histologic TPD and TPT. The results from the repeatability tests are shown in Table 2. The standard deviations in the micro-CT computed bone volume fraction ranged from .002 to .009, and the standard deviation in P, ranged from .017 to .088. Figure 6 shows a graph of micro-CT computed bone volume fraction versus the calculated ratio of tissue volume to bulk volume. It can be seen that the four separate scans for each cube are closely clustered. Two linear regression equations are also shown, one that allowed a non-zero y intercept, and a second that forced the regression
through zero. In either case, the standard error of the regression was very small: 0.018 in the first case and 0.027 in the second case. The slopes of these two equations were 0.87 and 1.03, respectively. DISCUSSION Visual comparisons between micro-CT slices and matching histology sections provided great confidence in the ability of the micro-CT system to produce representative images of trabecular bone. Similarities in trabecular patterns could be easily identified in corresponding sets of micro-CT slices and histological sections. Although the general structural pattern seemed rather insensitive to changes in the parameters of the thresholding procedure, the thicknesses and continuity of trabeculae did seem affected. This served to emphasize the importance of using an appropriate thresholding technique. The thresholding technique used in this study
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provided digital images with a mean discrepancy in P, of - 14.3% when compared with standard optical images of matching histologic sections. This implied that, on the average, the counted number of bone-nonbone intersections per unit test line length was greater in the higher magnified optical image of a histology section than in its micro-CT image representation. This tendency can be understood when the limited resolution of the micro-CT system is considered. Whereas P, is only dependent on the presence or absence of bone pixels, P, is dependent on the arrangement of bone pixels. If, due to the finite resolution of the system, there is some chance that pixels that should be bone are represented as not bone, there is probably an equal chance that the reverse occurs. Thus, on average the discrepancy in P, is not significantly different from zero, and a good accuracy in calculating bone volume fraction is expected. However, P, is more greatly affected by resolution and threshold. Small holes or thin trabeculae of a size less than the resolution of the miTABLE 2. Data from a test of repeatability on the microcomputed tomography system Cube
average P, (SD)
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0.147 (.009) 0.215 (.004) 0.274 (.008) 0.272 (.002) 0.454 (.007)
1.231 (.088) 1.217 (.017) 1.452 (.025) 1.802 (.037) 2.291 (.06)
Five bone cube specimens were scanned four times, and P, and P, were measured from the acquired three-dimensional images.
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cro-CT system may be lost in the micro-CT image. For the matching optical image with a higher magnification and greater resolution, these small holes and thin trabeculae will not be lost, and a higher intersection count for the same length of test line will result. This discrepancy will increase as the number of trabeculae increase, which was demonstrated in Fig. 5A. Likewise, as the trabeculae of the section become thicker, resolution limitations decrease and the discrepancy in P, should also decrease. This was demonstrated in Figure 5B. Because the accuracy was significantly correlated to the variables of trabecular plate density and trabecular plate thickness, correction factors could be proposed based on this data. It is also valuable to discuss the accuracy in terms of the mean actual difference rather than the mean percent difference. The mean actual difference between micro-CT computed TPT and TPT calculated from histology sections was 19.2 pm. As stated earlier, this corresponds to less than one half a pixel of the micro-CT image. To expect better than this is to expect more than the physics of the system can deliver. However, it is important to recognize that the resolution of the system is not a fixed value. This accuracy in TPT of 19.2 um was determined under the specific conditions of this experiment, which include a geometric magnification of approximately .045 mm/pixel, this being the typical setting for a scan of an 8-mm trabecular bone cube. Options are available to improve the resolution of an 8-mm trabecular bone cube image, but present comtime are the limputer memory and iting factors. If only a subvolume of an 8-mm cube
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MICRO-CT TO STUDY TRABECULAR BONE
- y = .049 + 0 . 8 7 2 ~ R”2 = 0.97 SE = 0.018
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BVF from Archimedes is of interest, the specimen can be scanned with higher geometric magnification and a potential accuracy of less than 10 km without computational problems. Standard histology of 2-D sections may still be the best method to use if better accuracy than this is desired. On the other hand, if the level of accuracy found from this study is sufficient, and the advantage of the nondestructive examination important, then the micro-CT system has a great deal to offer. The precision of the P, measurement from microCT images was demonstrated by the results of the repeatability tests, which showed a range of standard deviations from .017 to .088 intersection counts per mm. This translates into a standard deviation of less than one intersection count for a test line length of 10 mm. For a typical trabecular bone cube of P, = 1.6, this represents a 1.06 to 5.5% coefficient of variation. Therefore, even with a limited accuracy in the P, measurement of approximately 14% (k4%), this level of precision should still allow valid comparisons between specimens. The accuracy of the micro-CT P, measurement was demonstrated by the comparison with matching histology sections, which resulted in a 1.35% mean difference, and by the independent measure of bone volume fraction using Archimedes Principle. The slopes of the regressions shown in Fig. 6 are close to one. Statistically, the constant coefficient (y intercept) of the first linear model was significantly
different from zero, and the slope was significantly different from unity. Because the model should pass through the origin, the second linear model without a constant is presented. The slope for this model was not significantly different from unity. Though the independent measurement of bone volume fraction was especially desirable because thresholding is not involved, the procedure had variations of its own because of the continuous evaporation of water during the wet weight measurement. This may in part be responsible for the deviations of the slope and intercept of the first linear model from unity and zero. The precision of the P, measurement was demonstrated by the small standard deviations in the repeatability experiment as well as the low standard errors (2-3%) of the linear regressions. These data support the fact that the micro-CT system and thresholding procedure produce very accurate and precise representations of bone volume fraction. The measurements of accuracy in this experiment had some limitations that should be considered. First, some errors naturally arose in creating the “control” optical images of histologic sections. Although the differentiation between bone and nonbone pixels was much less ambiguous than in x-ray images, subjective thresholding of the optical images was required. The surface staining did provide high contrast, but lighting conditions and selection of gain and range levels within the imaging software
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can affect the bone surface profile. Any study using images of histologic sections is confronted with this dilemma. Second, the optical images that served as controls were of limited resolution themselves. A better control image might be obtained in future experiments with a camera of higher resolution. Third, the matching of micro-CT planes to histologic sections met with practical limitations?both in the ability to discern the exact position of the landmark for the reference level and in preserving rotational alignments between the optical and corresponding micro-CT images. Fourth, the specimens in this study were composed entirely of trabecular bone. The presence of low porosity cortical bone might require more specialized thresholding techniques. This study has provided estimates of the present accuracy and precision of a system. This system includes the whole process of acquiring the 3-D image of a trabecular bone specimen; from placement of the specimen on the scanner stage, to thresholding of the reconstructed image, to the selection of analysis regions, and finally to the stereologic measurements of P, and P,, the basic measures from which all bone morphology and anisotropy measures can be calculated. Certainly, further work can be conducted to improve the thresholding procedure and resolution, or to elucidate the nature of the errors; that is, to determine what proportion of the errors can be attributed to digitization, resolution, noise, and thresholding. However, the required level of accuracy and precision will always depend on the specific goals of an investigation, as well as
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the relative accuracy of other measurements that might be included in a study. At the present time, we feel that the accuracy and precision of the system is sufficient to make the micro-CT scanner a valuable and useful tool to nondestructively study isolated specimens of trabecular bone in vitro. Acknowledgment: This work was supported by grants from the National Institutes of Health (AR 31793, AR 34399, AR 20557). We thank Dawn Lundin of Henry Ford Hospital for the histologic embedding of the bone cube specimens.
REFERENCES 1 . Carter DR, Hayes WC: The compressive behavior of bone as a two-phase porous structure. JBone Joint Surg 59A:954 62, 1977 2. Feldkamp LA, Goldstein SA, Parfitt AM, Jesion G,
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8. 9.
Kleerekoper M: The direct examination of three dimensional bone architectures in vitro by computed tomography. J Bone Mineral Res 4:3-11, 1989 Feldkamp LA, Jesion G : 3D x-ray computed tomography. In: Thompson DO, Chimenti DE, eds. Review ofprogress in nondestructive evaluation. New York: Plenum, 1986 Feldkamp LA, Davis LC, Kress JW: Practical cone-beam algorithm. J Opt Soc A1:612, 1984 Koch JC: The laws of bone architecture. A m J A n a t 21:177298, 1917 Parfitt AM: The physiological and clinical significance of bone histomorphometric data. In: Recker RR, ed. Bone histomorphometry: techniques and interpretation. Boca Raton, FL: CRC Press, 1983 Singh I: The architecture of cancellous bone. J Anat 127: 305-10, 1978 Underwood EE: Quantitative stereology. Reading, MA: Addison-Wesley, 1970 Wolff J: Die innere architekture der knochen. Arch Anat Phys 50:389453, 1870
Evaluation of a Microcomputed Tomography System to Study Trabecular Bone Structure J. L. Kuhn, S. A. Goldstein, "L. A. Feldkamp, R. W. Goulet, and "G. Jesion Biomechanics, Trauma, and Sports Medicine Laboratory, Section of Orthopaedic Surgery, University of Michigan, Ann Arbor, and *Physics Department, Ford Motor Company, Dearborn, Michigan, U.S.A.
Summary: A new microcomputed tomography (micro-CT) system and thresholding procedure was evaluated as a tool for nondestructive analysis of trabecular bone. Images of 6-mm trabecular bone cubes acquired from the microCT system were compared with optical images of corresponding histologic sections to determine the accuracy of representation. The stereologic measures of bone volume fraction (P,) and trabecular plate density (PL) were used to quantify the comparisons. The results showed that the micro-CT measures of P, were not significantly different from those measured from histologic sections and therefore were very accurate. Measures of P, were different by approximately 14%, which translated into discrepancies in trabecular plate thicknesses of about 19 pn. This difference was significantly correlated to the microstructural characteristics of the specific specimen scanned. The precision of both measurements was excellent. Key Words: Trabecular boneMorphology-Architecture-Digital imaging.
The structure of trabecular bone has been the focus of investigation for many years. Using radiographs and dissections, early anatomists correlated the microstructure of trabecular bone to their presumed mechanical environments during normal function, and began to perceive trabecular bone as a material of optimized design (5,9). Singh (7) described different trabecular arrangements to be characteristically found in specific regions of human metaphyses and incorporated these distinguishing features into a classification scheme for trabecular architectures. Although such qualitative observations serve as useful clinical tools, more quantitative measures are necessary to derive empirical relationships between microstructure and
mechanical properties, to quantify the effects of bone disease and aging on bone morphology, or to test hypotheses of bone remodeling. Most present methods to quantify bone morphology and architecture at this level of microstructure rely on microscopic observations of thin sections of trabecular bone. Alternative methods include analyses of scanning electron micrographs or light microscopic observations of polished specimen surfaces. In all cases, the section selected for analysis must be assumed to represent the entire specimen, because a complete analysis of all serial sections would be prohibitively time consuming and tedious. A recent paper by Feldkamp et al. (2) introduced the usefulness and advantages of a three-dimensional (3D) microcomputed tomography (micro-CT) system for nondestructive examination of trabecular bone architecture in vitro. The purpose of this study was to further evaluate the ability of this unique system, combined with a new thresholding algorithm, to produce accurate digital images of a
Received March 21, 1988; accepted March 14, 1990. Address correspondence and reprint requests to J . L. Kuhn at the Biomechanics, Trauma, and Sports Medicine Laboratory, The University of Michigan, Section of Orthopaedic Surgery, G-0161, 400 N. Ingalls, Ann Arbor, MI 48109-0486.
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wide range of trabecular structures found in the human skeleton. MATERIALS AND METHODS For background, a brief description of the microcomputed tomography system and thresholding procedure are given. Microcomputed Tomography Scanner The microcomputed tomography scanner was developed by one of the authors (L.A.F.) at Ford Motor Company with the initial purpose of detecting small defects in ceramic materials. Figure 1 illustrates the main components: an x-ray source, a specimen stage, an image intensifier, a video camera, a digitizer and image processing system, and a host computer. The system operates similarly to commercial computed tomography scanners with some exceptions: (a) the specimen is rotated rather than the source and/or detectors; (b) a 2-D detector is used instead of a linear array of detectors, thereby providing direct 3-D image reconstructions; and (c) the specimen must be of limited dimensions. The most important difference is the resolution of the system. When set up appropriately for a scan of an 8-mm bone cube, the resolution is approximately 50 to 70 pm and individual trabeculae can be discerned easily. The resolution increases with geometric magnification, so small specimens positioned very close to the x-ray source can be imaged with even a higher resolution. Trabecular architectures of scanned specimens can be reconstructed and represented by a three-dimensional data set of grey scale values and stored on magnetic tape for later retrieval. Any number of algorithms can be utilized to study the microstructure without damag-
---H 1 I H microfocus x-ray source
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ing the original data. More complete and detailed descriptions of the system hardware, as well as the three-dimensional reconstruction algorithm, can be found elsewhere (24). Thresholding All images require some form of thresholding. Even in nonautomated analysis systems, the human eye and mind are forced to “threshold” images. The simplest threshold is one in which one number (grey scale value) is selected, above which all pixels are considered bone, and below which all pixels are considered nonbone. The effects of the choice of threshold on calculations of morphology and architecture are seldom discussed. X-ray images of bone present some special circumstances. Because of geometry and density variations within a bone cube specimen, a simple uniform threshold may be inappropriate for application to an entire image. Figure 2A aids in explaining this point. Density profiles across two trabeculae of equal density but different thickness appear as shown. The actual borders of each trabecula exist somewhere within the transition regions between the low density of marrow or air, and the high density corresponding to the center of the trabecula. If the trabecular thickness is much greater than the resolution of the system, the trabecular borders are defined at the points corresponding to exactly one half the difference between the extreme densities of the transition region. Conversely, for very thin trabeculae, the borders are more difficult to discern. Also, the density at the center of the thin trabecula is underestimated, even though the actual densities of the thick and thin trabecula are the same. It can be seen that within a certain range, selection of a uniform threshold would exclude the thin trabecula from the image. A second problem can arise from the normal variations in mineral densities of trabeculae contained within a single specimen. A uniform threshold, in this case, would entirely exclude some trabeculae, or cause artificial thickening or thinning of others (2). Use of fixed thresholds between specimens of very different average mineral densities present similar problems (2). For instance, if a fixed and uniform threshold were applied to two data sets-a healthy specimen and a diseased bone specimen of identical structure but overall lower density-an incorrect topology would result for the diseased specimen (Fig. 2B).
MICRO-CT TO STUDY TRABECULAR BONE
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We use an approach (2) in which multiple local thresholds within a single image data set are allowed. Each local threshold reflects the density variations in a local neighborhood of pixels about the point of interest. The concept can best be explained by considering a histogram plot of pixel grey levels along one Cartesian axis through a point. Figure 3 represents fluctuations in density from a trabecular bone specimen, where high grey levels correspond to bone, and low grey levels correspond to either marrow, a plastic embedding medium, air, or even soft tissues such as the endosteum of trabeculae. Three parameters of variable setting guide the evaluation of this line plot for local minima and maxima: a centerline, a spread, and a confidence number. The following three criteria are set: (a) a potential local maximum must have a pixel value greater than the sum of the centerline value and one half the spread; (b) a potential minimum must have a pixel value less than the difference of the centerline value and one half the spread; and (c) points that satisfy either of the first two criteria are
only considered valid extrema if pixels that follow descend in value (for a maximum) or ascend in value (for a minimum). The number of pixels that must follow in this mode is determined by the confidence number. A local neighborhood of pixels is then defined by the region between a local minimum and a local maximum. These conditions avoid the acceptance of small rapid fluctuations due to noise or insignificant structures as extrema. A fourth parameter is required to calculate the local threshold for each local neighborhood. This parameter is a percent of the difference between the two extrema (for trabeculae much thicker than the resolution, a percentage of 50% should exactly define the trabecular borders). The local threshold is then calculated by adding this percent of the difference to the grey level value of the local minimum. In the actual algorithm, this evaluation procedure is performed in all three Cartesian directions, and the final threshold for a point is resolved by taking the average of local thresholds determined in each of the three directions through the point. To produce binary data
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sets, the remaining pixels with nonzero grey level values are set equal to one. Evaluation of Thresholded Microcomputed Tomography Images Because analysis of histologic sections represents the standardly accepted method to quantify trabecular bone morphology and architecture, the accuracy of the thresholded micro-CT images was tested by comparing extracted planar images from the micro-CT 3-D data set (slices) with optical images of corresponding histologic sections taken from the actual bone cube (sections). Images were compared by (a) visual observations of topology, and (b) the stereologic measures of P,, the number of bone pixels divided by the total number of pixels in an area of analysis, and P, the number of intersections be-
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tween bone d onbone ixels er unit test li length (8). An average P, (calculated in two perpendicular directions) was used in the comparisons. Specimens of human trabecular bone were obtained from fresh frozen cadavers: 31- and 69year-old men and a 55-year-old woman. Two 6-mm cube specimens were prepared from each of the following anatomic locations: proximal tibia, proximal humerus, L1 vertebra, L2 vertebra, distal femur, and distal radius. A proximal femur and iliac crest provided one specimen each for a total of 14 specimens. These bone cube specimens were cut using a numerically controlled milling machine and stainless steel blade operated at low speed and under constant water irrigation. In order to histologically section and visualize the interior planes of bone cube specimens, the cubes were embedded in polymethylmethacrylate
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(PMMA). The plastic blocks were then trimmed to 8-mm cubes, leaving a border of approximately 1 mm around the cube sides and 2 mm above. A small hole was drilled into the center of the top face to a depth of about 1 to 1.5 mm. This hole was easily delineated from the surrounding higher density plastic in displayed micro-CT images and thus served as a landmark to assist in matching the histologic sections to the micro-CT slices of each specimen. All 14 specimens were scanned on the microCT scanner (in the standard setup for 8-mm bone cubes) and reconstructed on a 50-pm mesh. The reconstructions were stored on magnetic tape. After scanning, each specimen was re-embedded to produce a larger plastic block, preserving the orientation of the cube and presence of the drill hole. This allowed the specimen to be securely fixed in the grips of a Jung sledge microtome for histologic analysis. Optical images of a specimen’s interior planes were obtained by serial sectioning until a desired plane was reached. At this point, optical images were taken directly from the exposed cut surface of the bone cube, which remained clamped in the microtome until the analysis was complete for the entire cube. Such a method was necessary to avoid the damage and distortion artifacts often associated with thin sectioning of embedded tissues. The main components of the histologic imaging system were a digital camera (MTI Dage, series 86, Model NC-86D), image processing system (Recognition Technology Inc., RTI), a microcomputer (IBM PC), a color display monitor, and a low-noise illuminator (Cole Parmer, Model 9741-50). The camera was attached to a frame over the microtome for variable translational and rotational positioning. With a Nikon Micro-Nikkor 55-mm 0 . 8 lens and an extension tube attached to the camera, images of an entire bone cube’s cross-section at a magnification of approximately .025 mm/pixel by 0.02 mdpixel were obtained. These images were purposely centered to avoid possible geometric distortions near the edges of the imaging field. The magnification in the horizontal and vertical directions was always recalibrated for each bone cube. After careful alignment and positioning of the specimens in the microtome, sectioning gradually proceeded from the cube top until the drill hole disappeared. This plane marked the reference level. Any set of sections at a distance from the reference equal to some multiple of 50 pm (the physical thickness represented by each micro-CT slice) consti-
tuted a potential region to be imaged. In general, each region consisted of 5 sequential 10-pm sections for a total of 50 pm. Measurements from five consecutive histologic sections were averaged (the “average section measure”) and compared with one micro-CT slice. The biological stain, Sudan Black B, was used as a surface stain to distinguish between trabecular bone and its plastic background. A solution of this dye in 95% ethyl alcohol preferentially stained the plastic background black, leaving the trabeculae uncolored. The contrast was intensified when the underlying plastic base was illuminated, giving bone regions a bright golden hue. The efficacy of this reverse staining technique was supported by comparison with surface staining with hematoxylin and eosin. The images from the optical histologic analysis and the microcomputed tomography scanner were transferred to an Apollo Domain computer system (DN 3000), where they were displayed and analyzed. Micro-CT images were thresholded using different input parameter sets to the thresholding algorithm as described earlier. Limits were carefully chosen to outline the areas of analysis for the stereology algorithm. Although the fundamental comparison between matched slices and sections was in the measures of P, and P,, common bone morphologic variables were also calculated from these two basic measures using the following equations (2,6) and compared: trabecular bone volume fraction (FRAC) = P, (1) surface to volume ratio (SV)
=
2 x PL/Pp (2)
mean trabecular plate thickness (MTPT) = 2/SV (3) mean trabecular plate density (MTPD) = 0.5X FRAC X SV = P,
(4)
mean trabecular plate separation (MTPS) = (1 - FRAC)/MTPD (5) The percent differences and actual differences in quantitative measures from matched micro-CT slices and histologic sections were calculated and used as indicators of accuracy. The actual difference was defined as d = slice measure - average section measure, whereas the percent difference was defined as % difference = (actual difference/ average of the 2 measures) X 100.
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To further assess the accuracy and precision of the imaging and analysis procedure-scanning, reconstruction, thresholding, selection of analysis region, and stereologic analysis-a set of five 8-mm trabecular bone specimens were scanned. These specimens (one from a canine distal femur, one from a human lumbar spine and proximal femur, and two from an iliac crest) represented diverse architectures and a wide range in bone volume fraction (approximately 1545%). To test repeatability, these specimens were each scanned a total of four times, each time on a different day. The data from the repeatability tests were analyzed for measurement variability. In addition, independent measures of bone volume fraction were obtained from calculations of the tissue volume to bulk volume ratio. This ratio was obtained by subtracting the submerged weight of specimens from their wet weight using Archimedes Principle and the assumption that the specific gravity of water is equal to unity (1). Bulk volume was calculated from micrometer measurements of the cube dimensions. These data were analyzed by a linear regression of micro-CT computed P, on the tissue volume to bulk volume ratio. The standard error of this regression was used to further indicate the precision of the P, measure. RESULTS Visual comparisons of the 2-D topology of trabecular bone as represented by micro-CT slices and
optical images of histologic sections provided the first evidence that the micro-CT system was functioning effectively as a tool for the analysis of bone morphology and architecture. Although the general trabecular patterns matched quite well, the boldness and continuity of the trabeculae varied depending on the input parameters to the thresholding procedure. This variation is demonstrated in Fig. 4. The micro-CT image designated “threshold set D” seemed to best match the optical image of the histologic section. Support for this choice of thresholding input parameters was also provided by comparisons of stereologic measures. The accuracy as inferred from the mean percent differences in stereologic measures was l .35% for P, (95% confidence interval of *6%), and - 14.3% for P, (95% confidence interval of 24%). A pairwise t test of these data showed the difference in P, to be insignificant (p > .6), whereas the difference in P, was significantly different from zero (p < .01). Table 1 shows the raw data for 14 specimens. The mean actual differences in P, and P, were .0027 and - .2483. Using equations 1 to 5 for the calculation of the morphology variables, the percent differences in P, and P, translated into percent differences of 1.35% for FRAC, -15.7% for SV, 15.7% for TPT, -14.3% for TPD, and 13.7% for TPS. It is more useful to interpret the accuracy of TPT in terms of the mean actual difference rather than the percent difference. This value was 19.2 pm (95% confidence
FIG. 4. The same micro-CT image is shown here, thresholded with four different thresholding parameter sets, along with an optical image from one of the corresponding physical planes of bone. (The optical image has been redigitized to the same magnification scale as the micro-CT image for display purposes.)
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MICRO-CT TO STUDY TRABECULAR BONE TABLE 1. P, and P, measures from matching histologic sections and micro-CT slices of I4 different trabecular bone cubes Micro-CT slice
Histology sectionn Cube identification
Proximal tibia Proximal tibia Proximal tibia Proximal tibia Proximal tibia Proximal humerus Proximal humerus Proximal humerus Proximal humerus Proximal humerus Distal femur Distal femur Distal femur Distal femur Distal femur Proximal tibia Proximal humerus Proximal humerus Iliac crest Lumbar 1 Lumbar 1 Lumbar 2 Lumbar 2 Distal femur Distal radius Distal radius
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5b 5b 19 15b 15b 1 9 15b 6 7 8 9 11 12 13 14 16 17 18
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0.3311 0.3648 0.3346 0.2484 0.2062 0.156 0.1604 0.1712 0.1543 0.164 0.3 0.2999 0.2933 0.302 0.294 0.1266 0.2188 0.1218 0.2781 0.1442 0.157 0.1212 0.1463 0.3999 0.28 0.2253
1.775 1.7822 1.734 1.6573 1.429 1.4542 1S282 1S956 1.4409 1.5414 2.033 2.0081 1.9152 1.9617 1.7559 1.4142 1.5373 1.1501 1.7572 1.1816 1.3626 0.9098 1.1936 2.0962 1.4735 1.6287
PP 0.3424 0.3294 0.3258 0.2703 0.2233 0.137 0.1457 0.1653 0.1508 0.1544 0.2787 0.3213 0.3415 0.3463 0.2999 0.1798 0.2159 0.1195 0.1796 0.1359 0.1807 0.0972 0.1651 0.3426 0.2486 0.2327
P, (mm-') 2.0354 1.8393 1.6881 1.7941 1.6187 1.7148 1.8196 1.9447 1.8244 1.8459 2.4246 2.4495 2.4853 2.3899 2.1634 1.8821 1.4416 1.4199 1.8137 1.4374 1.8828 1.0252 1.3669 2.0691 1.5395 1.8567
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Average of five consecutive 10 pm sections. In some cases only four 10-pm sections were obtained. These cubes were tested at five different levels within the cube depth to determine whether the accuracy was dependent on position. No significant linear or power relationship was found (p > .05). This supported the imaging of only one region from each of the remaining 11 cubes.
interval of 13.2 to 25 pm), which is less than one half a pixel of a micro-CT image. The mean actual difference in TPD (which is numerically equal to the mean actual difference in PL) was significantly correlated to the TPD (Y = - .57, p < .Ol) and TPT (Y = .46, p < .05) measured from histologic sections. Figure 5A and B shows scatter plots of the discrepancy in TPD measures versus the histologic TPD and TPT. The results from the repeatability tests are shown in Table 2. The standard deviations in the micro-CT computed bone volume fraction ranged from .002 to .009, and the standard deviation in P, ranged from .017 to .088. Figure 6 shows a graph of micro-CT computed bone volume fraction versus the calculated ratio of tissue volume to bulk volume. It can be seen that the four separate scans for each cube are closely clustered. Two linear regression equations are also shown, one that allowed a non-zero y intercept, and a second that forced the regression
through zero. In either case, the standard error of the regression was very small: 0.018 in the first case and 0.027 in the second case. The slopes of these two equations were 0.87 and 1.03, respectively. DISCUSSION Visual comparisons between micro-CT slices and matching histology sections provided great confidence in the ability of the micro-CT system to produce representative images of trabecular bone. Similarities in trabecular patterns could be easily identified in corresponding sets of micro-CT slices and histological sections. Although the general structural pattern seemed rather insensitive to changes in the parameters of the thresholding procedure, the thicknesses and continuity of trabeculae did seem affected. This served to emphasize the importance of using an appropriate thresholding technique. The thresholding technique used in this study
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provided digital images with a mean discrepancy in P, of - 14.3% when compared with standard optical images of matching histologic sections. This implied that, on the average, the counted number of bone-nonbone intersections per unit test line length was greater in the higher magnified optical image of a histology section than in its micro-CT image representation. This tendency can be understood when the limited resolution of the micro-CT system is considered. Whereas P, is only dependent on the presence or absence of bone pixels, P, is dependent on the arrangement of bone pixels. If, due to the finite resolution of the system, there is some chance that pixels that should be bone are represented as not bone, there is probably an equal chance that the reverse occurs. Thus, on average the discrepancy in P, is not significantly different from zero, and a good accuracy in calculating bone volume fraction is expected. However, P, is more greatly affected by resolution and threshold. Small holes or thin trabeculae of a size less than the resolution of the miTABLE 2. Data from a test of repeatability on the microcomputed tomography system Cube
average P, (SD)
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0.147 (.009) 0.215 (.004) 0.274 (.008) 0.272 (.002) 0.454 (.007)
1.231 (.088) 1.217 (.017) 1.452 (.025) 1.802 (.037) 2.291 (.06)
Five bone cube specimens were scanned four times, and P, and P, were measured from the acquired three-dimensional images.
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cro-CT system may be lost in the micro-CT image. For the matching optical image with a higher magnification and greater resolution, these small holes and thin trabeculae will not be lost, and a higher intersection count for the same length of test line will result. This discrepancy will increase as the number of trabeculae increase, which was demonstrated in Fig. 5A. Likewise, as the trabeculae of the section become thicker, resolution limitations decrease and the discrepancy in P, should also decrease. This was demonstrated in Figure 5B. Because the accuracy was significantly correlated to the variables of trabecular plate density and trabecular plate thickness, correction factors could be proposed based on this data. It is also valuable to discuss the accuracy in terms of the mean actual difference rather than the mean percent difference. The mean actual difference between micro-CT computed TPT and TPT calculated from histology sections was 19.2 pm. As stated earlier, this corresponds to less than one half a pixel of the micro-CT image. To expect better than this is to expect more than the physics of the system can deliver. However, it is important to recognize that the resolution of the system is not a fixed value. This accuracy in TPT of 19.2 um was determined under the specific conditions of this experiment, which include a geometric magnification of approximately .045 mm/pixel, this being the typical setting for a scan of an 8-mm trabecular bone cube. Options are available to improve the resolution of an 8-mm trabecular bone cube image, but present comtime are the limputer memory and iting factors. If only a subvolume of an 8-mm cube
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- y = .049 + 0 . 8 7 2 ~ R”2 = 0.97 SE = 0.018
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BVF from Archimedes is of interest, the specimen can be scanned with higher geometric magnification and a potential accuracy of less than 10 km without computational problems. Standard histology of 2-D sections may still be the best method to use if better accuracy than this is desired. On the other hand, if the level of accuracy found from this study is sufficient, and the advantage of the nondestructive examination important, then the micro-CT system has a great deal to offer. The precision of the P, measurement from microCT images was demonstrated by the results of the repeatability tests, which showed a range of standard deviations from .017 to .088 intersection counts per mm. This translates into a standard deviation of less than one intersection count for a test line length of 10 mm. For a typical trabecular bone cube of P, = 1.6, this represents a 1.06 to 5.5% coefficient of variation. Therefore, even with a limited accuracy in the P, measurement of approximately 14% (k4%), this level of precision should still allow valid comparisons between specimens. The accuracy of the micro-CT P, measurement was demonstrated by the comparison with matching histology sections, which resulted in a 1.35% mean difference, and by the independent measure of bone volume fraction using Archimedes Principle. The slopes of the regressions shown in Fig. 6 are close to one. Statistically, the constant coefficient (y intercept) of the first linear model was significantly
different from zero, and the slope was significantly different from unity. Because the model should pass through the origin, the second linear model without a constant is presented. The slope for this model was not significantly different from unity. Though the independent measurement of bone volume fraction was especially desirable because thresholding is not involved, the procedure had variations of its own because of the continuous evaporation of water during the wet weight measurement. This may in part be responsible for the deviations of the slope and intercept of the first linear model from unity and zero. The precision of the P, measurement was demonstrated by the small standard deviations in the repeatability experiment as well as the low standard errors (2-3%) of the linear regressions. These data support the fact that the micro-CT system and thresholding procedure produce very accurate and precise representations of bone volume fraction. The measurements of accuracy in this experiment had some limitations that should be considered. First, some errors naturally arose in creating the “control” optical images of histologic sections. Although the differentiation between bone and nonbone pixels was much less ambiguous than in x-ray images, subjective thresholding of the optical images was required. The surface staining did provide high contrast, but lighting conditions and selection of gain and range levels within the imaging software
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can affect the bone surface profile. Any study using images of histologic sections is confronted with this dilemma. Second, the optical images that served as controls were of limited resolution themselves. A better control image might be obtained in future experiments with a camera of higher resolution. Third, the matching of micro-CT planes to histologic sections met with practical limitations?both in the ability to discern the exact position of the landmark for the reference level and in preserving rotational alignments between the optical and corresponding micro-CT images. Fourth, the specimens in this study were composed entirely of trabecular bone. The presence of low porosity cortical bone might require more specialized thresholding techniques. This study has provided estimates of the present accuracy and precision of a system. This system includes the whole process of acquiring the 3-D image of a trabecular bone specimen; from placement of the specimen on the scanner stage, to thresholding of the reconstructed image, to the selection of analysis regions, and finally to the stereologic measurements of P, and P,, the basic measures from which all bone morphology and anisotropy measures can be calculated. Certainly, further work can be conducted to improve the thresholding procedure and resolution, or to elucidate the nature of the errors; that is, to determine what proportion of the errors can be attributed to digitization, resolution, noise, and thresholding. However, the required level of accuracy and precision will always depend on the specific goals of an investigation, as well as
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the relative accuracy of other measurements that might be included in a study. At the present time, we feel that the accuracy and precision of the system is sufficient to make the micro-CT scanner a valuable and useful tool to nondestructively study isolated specimens of trabecular bone in vitro. Acknowledgment: This work was supported by grants from the National Institutes of Health (AR 31793, AR 34399, AR 20557). We thank Dawn Lundin of Henry Ford Hospital for the histologic embedding of the bone cube specimens.
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