The internal architecture of bone is made up of a mesh work of bony trabeculae, which confers strength to the bone while minimizing overall bone mass. The mechanical properties of trabecular bone depend, at least in part, on trabecular thickness (Tb.Th.) (Kleerekoper et al.,1985; Swartz et al.,1998; Ulrich et al.,1999), as will, to a certain extent, physiological processes such as mineral homeostasis (Swartz et.,1998). To this end, several studies have compared Tb.Th. across extinct and extant species (Swartz et al.,1998; Fajardo and Müller,2001; Ryan and Ketcham,2002a,2002b), between bones (Mullender et al.,1996; Swartz et al.,1998; Fajardo and Müller,2001; Macho et al.,2005), during early development (Glorieux et al.,2000; Salle et al.,2002; Mulder et al.,2005; Mulder and Koolstra,2006), and as part of the aging process (Rehman et al.,1994; Thomsen et al.,2002a,2002b; Cvijanovic et al.,2004; Macho et al.,2005). It would appear that a minimum thickness must be attained prenatally before mineralization commences (Mulder et al.,2005; Mulder and Koolstra,2006), while failure to achieve this minimum bone maturity before birth may result in long-term effects on bone structure and density (Backström et al.,2005). Conversely, loss of bone mass in adulthood may be compensated for by an increase in thickness of the remaining trabeculae (Frost,1999; Macho et al.,2005; Stauber and Müller,2006a).
Histological techniques are commonly regarded the method of choice to obtain accurate measures of trabecular architecture, despite their time-consuming and invasive nature. Alternatively, over the last few years, nondestructive visualization tools, especially μCT, have become increasingly popular for an assessment of trabecular bone morphology (Fajardo and Müller,2001; Ryan and Ketcham,2002a,2002b). In order to display the trabecular arrangement and to measure Tb.Th., such studies commonly employ uniform (often arbitrary) thresholds to distinguish the bone-air boundaries. However, differences in mineralization within and between bones will result in different average CT values and uniform thresholding will thus lead to differential display of trabeculae and hence over- or underestimation of structures (Ding et al.,1999; Hara et al.,2002). Scanning parameters and voxel size (i.e., resolution), and their effects on partial volume averaging, similarly result in inaccurate measurements (Kothari et al.,1998; Banse et al.,2002; Hara et al.,2002; Kim et al.,2004). In an attempt to distinguish accurately between rods and plates, more complex algorithms have recently been developed (Stauber and Müller,2006b), but these have not been adequately validated and the authors were content the results looked “reasonable” (p. 479) and were “intuitively correct” (p. 481). The need for an objective and repeatable method to determine trabecular measures from nondestructive techniques is thus as great as ever.
Zonneveld (1987) outlined the full-width, half-maximum-height (HMH) principle to determine the boundaries between structures. This was subsequently validated on biological specimens (Spoor et al.,1993) and the limitations, specifically with regard to the resolution of the images, were discussed. Recently, Prevrhal et al. (1999,2003) reevaluated the protocol (referred to as 50% method by them) on a phantom and similarly demonstrated that the main confounding factor for obtaining accurate measures is the resolution. Given the high resolution of modern μCT (i.e., below the average thickness of trabeculae), it should now be possible to overcome this major limitation and to apply the HMH principle to the measurement of thin structures such as trabeculae. Here we present a computer program that automatically calculates the HMHs and trabecular thicknesses within a CT slice. The results are validated against a phantom and histological sections. Subsequently, a biological structure is evaluated and the usefulness of the technique is discussed.
MATERIALS AND METHODS
An in-house automated computer program was written in C++. The program was used to collect measurements of Tb.Th. from CT slices sectioned in the plane of the original CT scan and utilized the full range of CT values (0–65,536). Pixel size/field of view was entered into the program and a transect was then sampled across the slice and subjected to a number of mathematical algorithms. First, in order to identify the peaks representing the external cortical surfaces, the difference in CT numbers between the presumptive air and the subsequent voxels along the transect were calculated. When this peak reached a level substantially higher (i.e., at least three times) than what could be considered artifact/noise, the external surfaces were identified. Second, the CT numbers between these external landmarks were searched for all maxima and minima, representing bone and nonbone, respectively (Fig. 1). Third, between adjacent peaks and troughs, the CT numbers were fitted to a cubic piecewise third-order polynomial spline. The bone-nonbone boundary was then identified using interpolation, whereby the halfway point between the maximum and minimum CT values was determined (Spoor et al.,1993). Trabecular thickness was measured as the distance along the transect between the two bone-nonbone boundaries of a single trabecula as adjusted to the spline, then outputted to an ASCII file. It was possible to calculate linear measurements within a single pixel width.
For validation purposes, a hairbrush with synthetic bristles and an adult pig calcaneus were scanned at the University of Liverpool using an ACTIS 420/600 system (BIR, IL) equipped with a tungsten X-ray target, a 250 μm thick columnar caesium iodide scintillator, and a Toshiba AI5877 JP dual-field image intensifier. Voltage was set at 60 kV and current at 200 mA, giving an effective monochromatic X-ray energy of 30 kV. Focal spot size was 50 μm and contrast resolution was ∼ 0.5%. Slice thickness and slice increment were 100 μm with a 44.91 mm field of view and a matrix size of 512 × 512, resulting in a voxel size of 80 μm × 80 μm × 100 μm. This voxel size is below the average adult trabecular thickness and below the resolution considered critical for the accurate representation of trabeculae (Kothari et al.,1998; Ding,1999); it is also below the size of the bristles. The bristles of the brush and the presumed long axes of trabecular bones were oriented perpendicularly to the beam, thus ensuring maximum resolution in the section analyzed (Kothari et al.,1998). Stacks made up of two-dimensional μCT slices were used to produce a three-dimensional reconstruction of the bristles and the calcaneus using VGStudio MAX v1.1 (employing a maximum-intensity projection reconstruction algorithm).
In order to test the usefulness of the automated measures further, the program was subsequently applied to a cross-sectional series of modern human fetal ilia. Thirty-eight specimens of known sex, aged 16–36 weeks at 4-week intervals, originated from a Liverpool workhouse at the turn of the 19th–20th century and are held in the Department of Human Anatomy and Cell Biology, Liverpool. The specimens were stillbirths and the age was originally ascertained to the nearest months according to the mother's testimony. Specimens had been defleshed using bicuspid beetles and stored wrapped in newspaper without further treatment. All specimens were kept under the same conditions and, although postmortem alterations cannot be ruled out, these biases would be internally consistent across specimens. All bones were available for study, but the ilia were chosen because of their unusual principal alignment of trabeculae, i.e., fan-shaped, and because of the great interest in the ilium in clinical research, i.e., biopsies. The principal orientation of trabeculae was established through radiographs, although in more mature specimens it can always be predicted from the main direction of load transfer, bearing in mind that trabeculae align along the main axis of stress (Biewener et al.,1996; Gefen and Seliktar,2004). Scan parameters for the ilia were effectively the same as those stated above for the pig calcaneus except for voltage (40–60 kV), current (140–200 mA), effective monochromatic X-ray energy (20–30 kV), and voxel size of 40 μm × 40 μm × 100 μm for smaller (younger) specimens and 60 μm × 60 μm × 100 μm for larger (older) specimens. The resolution chosen was considered sufficient given that fetal trabeculae were reported to range from 45 to 118.2 μm in thickness (Salle et al.,2002; Nuzzo et al.,2003). Measures of Tb.Th. were collected from two transects, one superior and one inferior (Fig. 2) in a plane defined by the posterior superior iliac spine, the point where the iliac crest meets the posterior iliac buttress and the acetabular notch; these landmarks are commonly used in the anthropological literature (Scheuer and Black,2000). These transects were chosen to ascertain the average Tb.Th. (i.e., close to the primary ossification center and toward the epiphysis at the iliac crest) rather than to answer a specific biological question.
Ten slices of 50 μm thickness were cut from the previously scanned calcaneus in the coronal plane using a diamond saw. A mark made at the level of the first scan was used as a guide for obtaining the first histological section; this should ensure minimal difference in plane of section between scans and histology. Sections were then removed with minimal bone loss. Sections were decalcified and stained with eosin red (1% solution) for 15 min. Subsequently, sections were washed in distilled water to remove any loose particles and were dehydrated in 70% ethanol. The stained specimens were immediately photographed before further shrinkage could occur with a slide scale using a Nikon Coolpix 990 camera (Nikon, Tokyo, Japan) mounted on an Olympus SZH-ILLO microscope (Olympus Optical, Tokyo, Japan). Linear measurements of Tb.Th. were taken from photos of the histological region of interest (pixel size = 5 μm) following the line-intercept method (Underwood,1970). Ten transects were taken through each of the 10 histological slices analyzed. Statistical analyses were carried out using SPSS version 12.
The accuracy of measurements taken by the computer program was first assessed against the phantom with known dimensions. Forty bristles of the brush were measured with digital callipers, resulting in an average thickness of 0.468 ± 0.013 mm. The average thickness obtained by the automated method was 0.464 ± 0.036 and deviated from the actual measurements by less than 1%; these differences are not statistically significant. While this good correspondence between results is encouraging, it needs to be considered that biological specimens differ in material properties and geometry and may display less well-defined boundaries. To validate the automated program, comparisons were first carried out between automated HMH measurements taken from transects through a pig calcaneus and histomorphometric measures taken from comparable histological slices of the same specimen.
Variation in Tb.Th. was higher when histomorphometric techniques were employed (t = 3.286; P = 0.001). The statistically significant difference between the samples is reflected in the histomorphometrically derived data being 13% lower than those taken automatically from CT images (Fig. 3).
In order to test for the applicability of the automated method for biological purposes, the program was applied to a cross-sectional series of modern human fetal ilia. No statistically significant differences in mean Tb.Th. were found between sexes or between transects for each subset. However, there is a trend for trabecular thickness to increase from an average of 99 μm in the youngest specimens to 240 μm in the oldest (Fig. 4). These results are statistically significant (F = 11.850; P = 0.000), mainly due to the youngest and, to a lesser extent, the oldest group according to the Tukey HSD postdoc test. When compared with similar-aged data presented for histological sections of femora (Salle et al.,2002), the trends are comparable, but the absolute values differ considerably.
Although nondestructive techniques are becoming increasingly popular in addressing biological questions with regard to bone structure and integrity, an accurate appraisal of Tb.Th. is problematic due to limitations associated with uniform thresholding, partial volume averaging, and voxel size (Kothari et al.,1998; Ding et al.,1999; Hara et al.,2002, Kim et al.,2004). For many biological investigations, and especially for clinical applications, researchers tend to be satisfied with high correlations between histological measures and those taken from CT images (Thomsen et al.,2004; Chappard et al.,2005), rather than accurate measures. However, even though the errors may be regarded systematic if the correlation coefficients are relied on, further biological investigations, such as structural and biomechanical assessments, may be hampered (Tabor,2006). The present study aimed to overcome these fundamental problems and explored the usefulness of the HMH method (Zonneveld,1987; Spoor et al.,1993; Prevrhal et al.,1999) for the determination of Tb.Th. Owing to the high resolution of present-day μCT, this should no longer be a problem.
When the data collected are compared with the results of a phantom, whose width has been measured manually, good agreement was found and the error was less than 1%. This would argue for the accuracy and applicability of the software presented here. The somewhat higher standard deviation for the CT measurements could be the result of slight obliquity of the bristles with regard to the transect in some instances; in contrast, the physical measurements are always perpendicular to the long axis of the bristle shaft. However, when examining biological structures, the findings are more complex.
The automated technique consistently gave higher (and less variable) values for Tb.Th. compared to the histomorphometric measurements. For example, the lowest histomorphometric measurement of Tb.Th. was 16 μm, whereas that of the automated computer program was only 27 μm (Fig. 3). Previous studies have highlighted the effects of partial volume averaging on an overestimation of structures (Müller et al.,1996; Kothari et al.,1998). Although the high resolution of the images employed in this study would generally argue against this having been a major problem here, it is recognized that this may have affected the measurements of very thin structures. Perhaps more important, though, the thickness measurements made in this study are one-dimensional and, despite attempts to align the bones so that the predominant orientation of trabecular is perpendicular to the scan, this is not possible for the ilium. This bone exhibits a fanned distribution of trabeculae (Fig. 2), and the obliquity in measurements may have led to an overestimation of dimensions. Trabeculae of the pig calcaneus are aligned more parallel and the automated measurement was therefore probably less affected by this one-dimensional error. Nonetheless, deviation in measurements obtained remain between the techniques. On initial inspection, this casts doubts on the usefulness of the automated method presented here, especially as regards the measures taken for the ilia (Fig. 4).
Trabecular thickness in the ilia appears to be substantially higher in the cross-sectional fetal sample than it is for similar-aged femora (Salle et al.,2002). To explain these discrepancies, a number of issues should be considered. First, it needs to be borne in mind that trabeculae differ in thickness between bones, even within the same individual (Macho et al.,2005). Such differences are probably functionally related, and it is conceivable that muscular-related biomechanical constraints experienced intrauterine could similarly account for differences in Tb.Th. between femora and ilia. Second, and probably of greater significance, the method employed for collecting Tb.Th. differed between the present study and that of Salle et al. (2002). While the former took direct measurements of individual trabeculae, the latter employed the parallel-plate model (Parfitt et al.,1983) to obtain trabecular dimensions. It has, however, been long known that the parallel-plate model consistently, and considerably, underestimates trabecular thickness (Birkenhager-Frenkel et al.,1988; Ding and Hvid,2000). Third, problems associated with histological sections may have further exacerbated the trends toward overall thinner trabeculae reported for the histological sections, both for the pig calcaneus measured here for validation and the Tb.Th. of the fetal sample presented in Figure 4.
Preparation of histological sections involves a number of processes, e.g., cutting, embedding, decalcification, staining, and dehydration, which will lead to alterations of the tissue. As a case in point, Uchiyama et al. (1997) reported 25% shrinkage perpendicular to and about 6% parallel to the cutting knife, while the figures given in the older literature are even higher (Lane and Ralis,1983). Fixation, dehydration, and embedding will have an additional effect (Ferguson et al.,1999). Perhaps even more problematic for the present investigation (or any study that involves immature bone) are reports that cartilaginous tissue may shrink to up to 50% (Ferguson et al.,1999). In light of these considerations, the 13% differences between CT-derived Tb.Th. and those derived histologically for the pig calcaneus seem negligible and may be the result of histological preparation rather than the potential inaccuracies of our automated technique. This discrepancy could probably have been reduced, or even eliminated, if the tissue had not been decalcified (Buesche et al.,2006). Hence, while the discrepancies can be explained and do not invalidate the program presented here, more fundamental issues are raised by the present findings, especially when histological sections are used as the gold standard.
For ontogenetic studies, the lower mineralization of bone (Mulder et al.,2005; Mulder and Koolstra,2006) would be expected to lead to greater shrinkage (and artifacts) in histological sections compared with measures taken from μCT. This may lead to an inaccurate assessment of the maturity of the specimens. Where clinical studies are concerned, the incompatibility of measures taken from biopsies vis-à-vis those obtained through imaging techniques (Fox et al.,2005) may render invalid any appraisal of the functional properties of the tissue investigated. The same argument may apply to functional analyses of bone from extant and extinct species (Ryan and Ketcham,2005). In other words, without due regard of the limitations inherent in histological techniques (either preparation or measuring), the results obtained may not be comparable between studies while rendering some of the functional interpretations questionable. Histological sections provide invaluable information, which cannot be gleaned by other methods, but caution must be exercised when using histological data for purposes for which they were not intended (e.g., biomechanical assessment). Conversely, the method presented here has the advantage that structural measures of trabeculae can be obtained accurately (and noninvasively), irrespective of differences in the properties of the tissue. Provided the resolution of the images is high and below that of the average structure to be measured, the HMH method appears suitable for the determination of trabecular thickness. However, this is only the first step toward analyses of bone structure.
Although Tb.Th. is of paramount importance for an assessment of trabecular architecture and bony integrity, it constitutes only one aspects. Interconnectivity, overall density, and structural characteristics, such as plates and rods, are of similar or even greater significance. While the program presented here was specifically designed to obtain Tb.Th. measures, it can also be used to create a more realistic representation of the trabecular architecture. By determining the HMH values across every row of pixels, the appropriate bone-specific threshold can be determined easily and efficiently, while areas of very disparate average HMH values can be easily found and excluded from the area of interest. This allows the entire bone structure to be visualized and analyzed further. Figure 5 shows the trabecular architecture in a small block of the fetal ilium; transverse trabeculae can be seen clearly, although plates have not yet developed. This further highlights the usefulness of the technique presented here and, with further modification, may provide an effective tool for three-dimensional analysis of irregular trabeculae.
This study was supported by a Joint Research Equipment Initiative (JREI) grant (JR99LIREQ; to G.A.M.), a Leverhulme Trust grant (F00569C; to G.A.M. and I.R.S.), and a Natural Environment Research Council studentship (NER/S/A/2001/06485; to R.L.A.). The help of Professor J.A. Gallagher and Mrs. Brenda Wlodarski with the histological sections is greatly appreciated. The comments of two anonymous reviewers improved an earlier version of the manuscript.