COMPUTERS
AND
BlOMEDICAL
RESEARCH
25, l-16 (1992)
An Automated Method for the Analysis Trabecular Bone Structure JEAN E. AARON,* BEVERLEY A. OAKLEY,*
of
DAVID R. JOHNSON,* JOHN A. KANE,? PAUL O’HIGGINS,* AND STEPHEN K. PAXTON”
*Department of Anatomy, University of Leeds. England and tDepartment of Human Metabolism and Clinical Biochemistry, University of Sheffield, England Received October 16, 1990
Trabecular structure as well as bone mass is important in studies of bone disease and fracture. An automated method for the direct analysis of two-dimensional trabecular microanatomy and its application to human iliac crest bone biopsies is described. Compared with established methods which require expensive equipment and complex software, costs have been reduced and availability increased by using an image analyzer driven by a microcomputer. Routine histological sections are accepted and an editing function enables the removal of artifacts. An elastic window allows field expansion for large specimens. The program enables the rapid assessment of the bone volume and trabecular surface from the intact image, followed by image skeletonization and the deduction of the trabecular length, number, character, and spacing together with the number of trabecular junctions and discontinuities: the trabecular width is calculated indirectly. Images may be stored to disk or printed as permanent records for diagnostic or research purposes. o 19% Academic press. IX
Bone density is a major factor in determining skeletal strength. However, other factors are also important (1). Foremost among these is the topography of bony tissue, particularly at cancellous sites prone to osteoporotic fracture (2). Until recently, comparatively little attention has been paid to the microanatomy of the trabeculae remaining following a period of bone loss, or to the disposition of new bone apposed in response to treatment. Interest in the structural and therapeutic implications of trabecular configuration is now increasing (for example, 3, 4). The acquisition of data on trabecular topography can be time consuming. The histological analysis of bone sections has traditionally been performed manually using eyepiece graticules together with point counting and line intercept procedures (5). Not only is this process long and repetitive, but highly trained operators are required and there are limitations upon the characteristics of trabecular shape which can realistically be measured. OOlO-4809/92 $3.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
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AARON ETAL
Several systems of computer-aided microscopy have been developed in which the procedure is semi-automated by projecting the image of a section of bone on to a digitizing pad (see, for example, 3, 6-9). Computation time is reduced by these methods, but operator time and skill generally remains high. At the same time, other effective methods have been described but tend to pertain to limited and specific aspects of trabecular structure only (10-13). An almost fully automated and comprehensive method has been developed by Garrahan et al. (14, 15’) in which the binary image of the tissue is reduced to its minimum profile (i.e., “skeletonized”). An analysis of the two-dimensional structure in terms of “nodes” (i.e.. trabecular junctions). “struts” (i.e.. bony bars) and “free ends” (i.e.. trabecular discontinuities or termini) is rapidIS, derived. However, the hardware employed is large and expensive and the software not generally available (16). In addition. the histological stains which produce the necessary high contrast images (e.g.. the von Kossa stain) are often not the stains of choice for sections intended also for other histomorphometric purposes. Our present objective is to increase the accessibility of the automated analysis of trabecular structure to more laboratories by reducing hardware. expertise, and costs to a minimum. We have utilized methods described in the literature to produce a system of shape analysis whereby a defined area of a bone section prepared routinely for established histomorphometric analysis (for example. using toluidine blue stain, or the Goldner method) is captured in our system by a closed circuit television camera and processed by an image analyzer driven by a microcomputer. The results obtained automatically are compared with those measured manually. MATERIALS
AND METHODS
The iliac crest was chosen for analysis because it is the established site for biopsy in histological investigations of metabolic bone disease. Specimens were selected from a collection assembled over many years for regular histomorphometry. Twenty-six specimens were chosen to provide a range of bony tissue and trabecular configuration ranging from porotic to petrotic. Thirteen of these were of normal bone removed at autopsy by sawing transections approximately 1 cm thick and 2.5 cm long from a region 2 cm behind the anterosuperior spine of the ilium; the subjects had died suddenly as a result of accident or acute illness with no history of bone disease. The remaining 13 were biopsies removed following informed consent from patients with primary osteoporosis (51, secondary osteoporosis (3), and Paget’s disease (5). These transilial specimens had been obtained under local anaesthesia using a trephine with a 0.8-cm bore diameter in a region 2 cm behind the anterosuperior spine and 2 cm below the iliac crest. All samples were fixed in 10% buffered form01 saline, pH 7.2, and embedded in methylmethacrylate. Undecalcified sections 8 pm thick were cut from each using a Jung K heavy duty microtome (Reichert-Jung, Heidelberg,
AUTOMATED
ANALYSIS
OF BONE STRUCTURE
W. Germany). Sections were stained either in 0.1% toluidine 30 min or by a modification of the Goldner method (17).
3
blue, pH 3.5 for
Manual Analysis
Each section was composed of an area of cancellous bone encompassed by an inner and outer area of cortical bone. The microanatomical features measured were confined to the cancellous tissue and were analyzed by the methods described in detail by Aaron et al. (4). They comprised bone volume (percent relative to total tissue volume) assessed by means of an integrating eyepiece (No. 1, Zeiss, Oberkochen, W. Germany) and the application of regular point counting procedures using a magnification of 50 x (18); the bone surface (mm’/ mm3) by means of an integrating eyepiece, line intersecting procedures, and a magnification of 80 x ; the trabecular width (mcm; not corrected for section obliquity, 3), using a process of site selection similar to that of Wakamatsu and Sissons (19) and measuring directly from the image projected on a screen, using a magnification of 50 x ; the trabecular number using a field determined by the rectangular window in the viewing tube of the Zeiss photomicroscope II at a magnification of 20 x and defining individual trabeculae as isolated bars or domains of bone extending between junctions (a variable which correlates directly with the mean trabecular plate density of Pa&t et al. (3) and indirectly with the trabecular spacing or separation measurement of Wakamatsu and Sissons (19), see Aaron et al., (4)). Automatic Analysis
Following manual analysis each section was placed upon the microscope stage of a Wild M7A dissecting microscope with a zoom lens and viewed in transmitted light. An image of the whole section was obtained via a closed circuit black and white television camera attached to the viewing tube of the microscope. The overall magnification was 15 x . The frame was captured as a 256 x 256 pixel, 64 grey-level image by a VIP image analyzer (Sight Systems, Unit 1, Hambridge Lane, Newbury, Berks RG14 7TU, UK). We originally used a version designed for the Acorn (BBC) microcomputer in conjunction with a program written in Assembler. Our later system (Fig. 1) uses an IBM PC compatible machine (512k or better) and is written in Turbo Pascal v5, with some sections in Assembler for enhanced speed of computation. Thresholding the Image
The captured image was “thresholded” to separate the bone trabeculae from any background caused by the presence of marrow, uneven lighting, etc. as follows: The image was “thresholded” to produce a binary image made up of black and white pixels only. The original image consisted of pixels each of which had a value between 0 (black) and 63 (peak white). A threshold value is
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AARON
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FIG. 1. Systemfortheautomatedanalysisoftrabecularstructure. Theimageofthesectron(arrowed) under the microscope is captured by a closed circuit TV camera and processed by an image analyzer (right) driven by a microcomputer (left): (a) intact image on the screen (right) together with a magnified region; (b) the same image after “skeletonization.”
selected manually: all pixels below this value are set to white; all pixels above are set to black. The resulting binary “bitmap” was compressed and stored on disk. Editing the Image
Stored images may be recovered from disk when required for further processing. A mouse driven menu system allows the following editing functions to be carried out: (a) Single pixel removal. Since the analysis concerns a pattern of relatively large bony trabeculae, single pixels are likely to represent noise. A standard algorithm removes all single pixels surrounded by dissimilar ones.
AUTOMATED
ANALYSIS
OF BONE
STRUCTURE
5
(b) Erasure. Larger areas found to represent artifacts can be erased manually using the mouse. (c) Joining. Artifactual discontinuities in the image may be filled using the mouse. (d) Inversion. The binary image may be black/white reversed. (e) Magnification. Prior to editing, the binary image is presented in a window with a “rubber-banded” box. The contents of the box may be zoom magnified and displayed alongside the original image (Fig. la). Processing
the Image
Following editing, the image may be stored or processed. The “rubberbanded box” function is used to delineate a “working window” which may include all or part of the image as required or encompass a standard area. The dimensions of the “working window” were adjusted electronically until its width was equivalent to the shortest projected intercortical distance found among the specimens from the ilium to be analysed (c. 5.5 ems) and the corresponding height excluded the areas of trephine damage created along either edge of the section at biopsy. (a) Cropping. The image was “cropped” by a routine which removes all objects in the image which are outside the “working window” and do not cross its boundaries. This reduces the time subsequently taken to “skeletonize” the image. (b) Skeletonization. The selected part of the binary image was “skeletonized” or “thinned” to its medial axis (Fig. lb) by a modification of a standard Hilditch algorithm (20, Algorithm H) which reduces trabecular bars to strings of single pixels by repeated passes and deletions of the dark points, changing them to white points (Fig. 2). This process generates parameter 1, bone volume, from the “unthinned” bone area in mm2 or as a percentage of the total area, and parameter 2, bone surface, in mm2/mm3 or as the trabecular perimeter in millimeters. The ratio of parameters 1 and 2 provides parameter 3, trabecular width or thickness in microns (21, Table l), while parameter 4, trabecular length in millimeters is an expression of the total length of “thinned” trabeculae within the defined window. (c) Analysis. This routine works on the skeletonized image to produce counts of the following features: -the number of nodes (joint points of three or more strings of pixels, parameter 5). -the number of free ends or termini (end points of a pixel string, parameter 6). -the number of cut ends (where a pixel string hits the edge of the box, parameter 7). Individual trabeculae identified by the automatic method were measured in length and further classified (parameters 8-17) according to the scheme of Garrahan et aZ.(Z4) and include end-to-cut, node-to-cut, end-to-end, node-to-
AARON
ET AL
FIG. 2. (Top) Computer generated printout showing the image ofa bone biopsy with inner and outer cortices and the trabecular region for analysis within a rectangular window: (bottom) the thinned image ready for analysis.
end, and node-to-node. Other categories of trabeculae defined by Garrahan et al. (cortex-to-end, node-to-loop) were not used for simplicity, but may be added to the system if required. Also available within the program is the facility to measure isolated bone profiles (22), their number and length. All the data are stored to disk and may be analyzed further or printed as required. as may representations of the unedited, edited, or thinned images. (d) Threshold effect. The effect of the threshold levels selected to produce the most acceptable image on the TV screen was determined for some variables by repeating the analysis of a single specimen over a range of threshold settings. (e) Interobserver variation. Ten sections were analyzed independently by two observers and the coefficient of variation assessed. Indices derived automatically and their manually assessed counterparts are shown in Table 1 and are consistent with the nomenclature recommended for histomorphometry (22). On completion of the measurements the results obtained by the fully automated method were compared with those obtained manually and correlation coefficients were calculated for the principal variables, In addition, an approximate evaluation of the time required for the two methods was made.
AUTOMATED
ANALYSIS
OF BONE
TABLE INDICES
MEASURED
Intuct image Bone volume % (bone area : tissue area) Bone surface mm2/mm3 mcm
(Trabecular
Thinned
image -
Trabecular (direct)
AND AUTOMATICALLY
Automatic Window Window
width
1
MANUALLY
Manual
Trabecular (direct)
7
STRUCTURE
number/field
width/l
height length
Abbreviation
mm mm V or Ar
Bone volume % or area mm? (bone area : tissue area) Bone surface mmz/mm3 or perimeter mm Trabecular width mcm = 2.000 * bone area mm?/ trabecular perimeter (21) .2” = Trabecular thickness (22))
SorPm TbWi
Total trabecular length mm Nodes Ends Trabecular number, i.e., node-node (number. mean length) node-end (number, mean length) end-end (number, mean length) end-cut (number, mean length) node-cut (number, mean length)
0 The correction factor for section obliquity or 1.199 for iliac trabecular bone (3).
is 4/n (1.273)
for structures
or TbTh
TbLe NorNd EorTm TbN
without
spatial
orientation
RESULTS
The manual analysis of a single section by traditional methods takes approximately 20 min, while the automated method, which produces additional variables and a printed record took less than half this time. A comparison of the indices measured automatically and those determined manually is shown in Fig. 3. As might be expected close correlations were found for the bone volume (Fig. 3a) and for the bone surface (Fig. 3b), the two simplest variables to define. There was also a good relationship between trabecular width measured directly by the manual method and indirectly by the automatic procedure, despite the fact that the regions adjacent to trabecular junctions were excluded from the manual analyses but included in the automatic version (Fig. 3~). However, it is probably for this reason that the trabecular thickness tended to be higher when measured automatically. The most difficult of the four principal variables to define structurally is the trabecular number; nevertheless a significant correla-
8
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AARON
ET AL.
FIG. 5. Sites of discrepancy between manual and automatic analysis. (Top) Small intratrabecular resorption cavities (horizontal arrows) create an over complex skeletonised image. (Bottom) Small trabecular protruberances (vertical arrows) appear more significant in size in the skeletonised image.
bone volume in idiopathic osteoporosis was characterized by trabeculae of normal thickness but small in number. This contrasts with the low bone volume in steroid osteoporosis in which the trabeculae were reduced in thickness but not in number. This morphological distinction has both structural and therapeutic implications (23). The topography of pagetic bone, with both abnormally thick and numerous trabeculae. on the other hand, may provide insight into trabecular regeneration (24). In addition to the measurements described above, the printouts include the computed number of trabecularjunctions (nodes) and trabecular termini (ends). While in our mixed sample there was a general correlation between the number of nodes and bone volume, no such relationship existed between ends and bone volume (Fig. 7a). However, a relationship is maintained if the ratio nodes : ends (an index of spatial connectivity in a section (1.5)) was used (Fig. 7b). The utility of these additional aspects of trabecular structure with respect to bone strength and pathogenesis remains to be assessed. Table 3 shows the effect of changing the thresholding function upon bone area and some of the other variables measured. If the threshold was too low some areas of bone failed to appear in the image and were lost in the background. As the level selected approached the optimum the trabecular structure of the section became more accurately represented by the projected image. If the
AUTOMATEDANALYSISOFBONESTRUCTURE Al
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STEROID
11
NORMAL
OP
FIG. 6. Computerized analyses of four structurally contrasting iliac biopsies: (a) normal trabecular number and continuity in a healthy subject; (b) loss of trabecular number and continuity in idiopathic osteoporosis; (c) trabecular thinning in steroid-induced osteoporosis; (d) trabecular thickening and increased trabecular number in the sclerotic bone of Paget’s disease.
optimum setting for the bone area was exceeded, an increasing quantity of irrelevant detail, for example, marrow tissue or folds in the plastic embedding medium, was detected and included in the subsequent analysis. While an incorrect threshold can profoundly influence results, a departure from the correct range for the bone area is immediately obvious on the monitor screen. If the stain was too pale, because of elution or because the section was particularly thin (i.e., less than 4 pm thick), areas of bone failed to appear in the image without raising the threshold function beyond its optimum value. This risked the capture of irrelevant background detail. However, the routinely prepared sections described above generally required little, or no, editing, and the most common artifacts were dehydration cracks and peripheral bone fragments resulting from displaced trephine damage (Table 2). The reliability of the technique is borne out by the similarity in the results when 1Q sections were analyzed independently by two observers (Table 4). DISCUSSION
The osteoporoses are heterogeneous in both their aetiology and in the topography of their remaining trabecular bone (23). An awareness of the structural character of the trabeculae may provide a better discriminant between fracture
12
AARON
ET AL.
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and nonfracture prone subjects than does bone volume alone (25). It now seems axiomatic that trabecular microanatomy will become as central to an understanding of osteoporosis and fracture risk as bone mass. The inexpensive and fully automated system described above facilitates this approach and makes the generation of such information accessible to all laboratories with an interest in abnormal bone. Moreover, the results are consistent with those obtained using manual methods and reproducibility is high. The size of the “working window” was set in this study to accommodate a typical average-sized transilial bone biopsy while allowing latitude to avoid peripheral trephine damage. For a larger specimen, such as a sectioned femoral
AUTOMATED
ANALYSIS TABLE
THE EFFECT
OF INCREASING
Threshold 10 12 14 16 18 20 22 24 26 28” 30” 32 34 36
THRESHOLD
VALUES
13
OF BONE STRUCTURE 3 ON THE VARIABLES
IN A SINGLE
FIELD
OF VIEW
BAr
NTm
NNd
TbN
BPm
16.3 18.2 19.2 19.8 20.8 21.1 22.5 23.5 24.4 25.6 26.8 28.6 32.0 42.1
150 139 141 141 122 115 115 120 110 112 126 118 165 195
63 63 63 18 66 52 54 53 53 59 53 68 108 250
184 187 186 207 178 168 159 164 157 161 171 186 286 248
61.3 66.3 67.9 10.3 68.3 67.5 69.4 69.5 71.3 71.8 71.5 74.4 85.0 115.7
Nore. When the setting is too low the proportion of bone is underestimated; when the setting is too high bone volume is overestimated. a Optimum threshold values for BAr; BAr = % bone area: NTm = number of ends or termini; NNd = number of nodes; TbN = trabecular number; BPm = bone perimeter mm.
TABLE INTEROBSERVER
Biopsy no. 1 2 3 4 5 6 7 8 9 10
VARIATION:
NTm
BAr I
II
13 9.1 4.6 7.1 9.0 10.8 11.4 4.2 14.6 24.6
12.1 8.6 4.3 7.7 8.9 11.5 11.2 3.8 12.5 23.3
NS P cv 1.51 (SD/Mean difference)
4
THE ANALYSIS OF TEN SECTIONS BY Two STUDENT’S t TEST FOR PAIRED DATA
NNd
OBSERVERS
TbN
II
I
II
I
II
76 57 45 13 73 116 84 64 87 90
88 58 47 72 73 117 80 80 83 79
11 4 4 9 14 11 13 0 18 44
15 5 5 9 10 12 6 0 18 33
63 45 34 62 73 86 72 3-l 82 127
79 46 35 59 63 87 57 43 83 100
NS 3.00
THE
BPm
I
NS 6.48
USING
NS 4.10
I
II
42.2 27.8 15.6 25.9 31.2 39.3 33.6 15.6 39.4 62.2
42.1 21.2 15.3 25.5 30.2 42.2 33.5 14.4 34.6 62.2 NS 3.33
Note. BAr = % bone area; NTm = number of ends or termini; NNd = number of nodes; TbN = trabecular number: BPm = bone perimeter mm; CV = coefficient of variation.
14
AARON
ET AL
head or vertebral body, the window can be enlarged to accommodate a wider field of view. Obversely for small biopsies within a group, or to separately assess a discrete area of abnormality such as a metastasis within a specimen. the window can be reduced to a half or a quarter (or less), followed by the appropriate scaling of the results to correspond to the original standard window size of choice. The trabecular structure lends itself well to automated analysis since. unlike much histomorphometry. there is no subjective element. Also. because the method is concerned with simple, gross structures requiring only minimal magnification, small artifacts are not resolved. The system is sufficiently fast to enable serial sections in quantity to be assessed. For example, we are currently comparing microanatomical and ultrasonic attenuation measurements in a project which requires the evaluation of many sections of large specimens from a range of skeletal sites; this would be too demanding in time and patience to contemplate using manual methods alone. In the automated assessment of trabecular width, the failure of the system to recognize and separate the wide junctional regions may be a disadvantage. These sites, which are thought of as important determinants of bone strength may be less responsive to remodelling imbalance and may be subject to changes that are entirely different (such as compensatory hypertrophy (2.5)) from those taking place in the internodal regions. However, in a broader sense the significant relationship between the manual and automatic measurements of trabecular thickness shown above suggests that for most practical purposes this is not a major problem. The system can be programmed to exclude small intratrabecular resorption cavities to avoid the unnecessary complexity that they create in the image and the consequent extra editing. This option was not taken. however, since the presence of the small intratrabecular cavities or canals is an inconvenience only in certain pathologies (such as Paget’s disease or fluoride-treated osteoporosis) and it was envisaged that questions concerning trabecular development may arise to which consideration of this feature may be of future significance. The interpretation of trabecular “free ends” or termini in a two-dimensional section is problematical, since their real status is unknown without their threedimensional reconstruction. However, their failure to decline in number with diminishing bone volume, together with the relationship between the “node : end” ratio and the bone volume, suggests that they may provide an index of trabecular connectivity: this is being further examined using serial sections. An approach such as this is, of course, far more time-consuming than the high resolution three-dimensional computed tomography adopted by Feldkamp ef al. (26), but the latter is unavailable to most laboratories or beyond their financial means. The variables described above are those most basic to a structural analysis. From these a number of other variables may be derived by simple equations reported in the literature cited. For example. the trabecular separation (mcm) = trabecular thickness mcm ((100/c% bone volume) - 1) and the trabecu-
AUTOMATED
ANALYSIS
OF BONE STRUCTURE
15
lar plate density (per mm) = % bone volume x lO/trabecular thickness mcm (3). These variables, together with counts of isolated trabecular profiles (27), an assessment of deviation of shapes from circularity, and trabecular anisotrophy (22, 27) are included in the software package. Finally, there is available for use at any stage within the program a general function for the measurement of point to point distance. The trabecular spacing, for example, can be determined by indicating with a mouse cursor a trabecula within the skeletonized image, then its neighbor; the program proceeds to seek midpoints along the length of each bar and to calculate the distance separating them. “Radial” scans of path lengths through cavities and trabeculae (13) can also be performed and there is a facility, presently being evaluated, for measuring the star volume (28). The completed program is now available’ and has the flexibility to accommodate any other personal requirements for shape analysis. ACKNOWLEDGMENTS The authors wish to acknowledge the skilled assistance of T. J. McAndrew for the statistical analysis and T. Lee for the artwork. This research was supported by the Medical Research Council Programme Grant 8600806.
REFERENCES 1. OXNARD, C. E., AND YANG, H. L. Beyond biometrics: Studies of complex biological patterns. Symp. Zoo/. Sot. London 46, 127 (1981). 2. PARFITT, A. M. Trabecular bone architecture in the pathogenesis and prevention of fracture. Am. J. Med. 82, (Suppl. lB), 68 (1987). 3. PARFITT, A. M., MATHEWS, C. H. E., VILLANUEVA, A. R. KLEEREKOPER, M., FRAME, B., AND RAO, D. S. Relationships between surface, volume and thickness of iliac trabecular bone in aging and osteoporosis. J. C/in. Inues1.72, 1396 (1983). 4. AARON, J. E., MAKINS, N. B., AND SAGREIYA. K. The microanatomy of trabecular bone loss in normal aging men and women. Clin. Orthop. 215, 260 (1987). 5. UITWAAL, P. J. M.. LIPS, P.. NETELENBOS, J. C. An analysis of bone structure in patients with hip fracture. Bone Miner. 3, 63 (1987). 6. BIRKENHAGER-FRENKEL, D. H.. COURPRON. P.. CLERMONTS. E., HUPSCHER E., COUTINHO, M. R.. AND MEUNIER, P. J. Trabecular thickness. intertrabecular distance and age-related bone loss. Proceedings of the Fourth International Workshop on Bone Histomorphometry. Bone 6, 401 (1985). 7. BIRKENHAGER-FRENKEL, D. H., COURPRON,P., HUPSCHER,E. A., CLERMOTS, E., COUTINHO, M. F., SCHMITZ, P. I. M., AND MEUNIER, P. J. Age-related changes in cancellous bone stmcture. Bone Miner. 4, 197 (1988). 8. DALLANT, P., MEUNIER, A., CHRISTEL. P. S., AND SEDEL, L. Semi-automatic image analysis applied to the quantification of bone microstructure. J. Biomed. Eng. 8, 320 (1986). 9. PARISIEN. M. V., MCMAHON, D., PUSHPARAJ,N.. AND DEMPSTER, D. W. Trabeculararchitecture in iliac crest bone biopsies: Intra-individual variability in structural parameters and changes with age. Bone 9,289 (1988). 10. GARRAHAN, N. J., MELLISH, R. W. E., VEDI, S., AND COMPSTON, J. E. Measurement of mean trabecular plate thickness by a new computerized method. Bune 8, 227 (1987). ’ This equipment including the associated software is available through: Marketing Department, University of Leeds Industrial Services, 175 Woodhouse Lane, Leeds LS2 3AR, UK. Telephone: 0532 333444; Fax: 0532 445270.
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ET AL.
C.. LAVAL-JEANTET. A-M.. PRETEUX. F.. AND Mtunr~~. A. Measurement ofanisotropic vertebral trabecular bone loss during aging by quantitative image analysis. Ctr/c,$ ?‘i,\,s/rta fnf. 43. 143 I 1988). 12. VESTEREZY, A., GUNDERSEN. H. J. G., MELSEN. F.. AND MOSEKILDE. L. Normal postmenopausal women show iliac crest trabecular thickening on vertical sections. Barze 10, 333 (1989). 13. SPIERS. F. W., AND BEDDOE. A. H. “Radial” scanning of trabecular bone: Consideration of the probability distributions of path lengths through cavities and trabeculae. Plrv,. Met/. Bir~l. 22, 670 (1977). 14. GARRAHAN. N. J.. MELLISH, R. W.. AND COMPSTOK, J. E. A new method for the two dimensional analysis ofbone structure in human iliac crest biopsies. J. Microsc~. 142,341 I 1986). 15. COMPSTON. J. E.. MELLISH. R. W. E.. AND GARRAHAN. N. J. Age-related changes in iliac crest trabecular microanatomic bone structure in man. Bone 8. 289 t 19871. 16. MELLISH. R. W. E., FERGUSON-PELL, M. W.. COCHRAN, G. V. B.. PARISIEK. M. V.. .+.No DEMPSTER. D. W. A new manual method for assessing two-dimensional cancellous bone structure: Comparison between iliac crest and lumbar vertebra. J. Rcmc Miner. Rr.r. 4s. S19:! (1989). 17. SCHENK. R. K.. MERZ. W. A.. AND MULER. J. A. A quantitative htstologtcal study on bone resorption in human cancellous bone. Acra Anat. 74, 44 f 1969). IR. AARON. J. E. Laboratory methods. In “Calcium. Phosphate and Magnesium Metabolism” (B. E. C. Nordin. Ed.). pp. 566-568. Churchill Livingstone. Edinburgh, 1976. IY. WAKAMATSU. E., AND SISSONS. H. A. The cancellous bone of the iliac crest. (‘ct/ciJ. 7i,\.)~(, Res. 4, 147 (1969). 20. NACCACHE. N. J.. AND SHINGHAL. R. An investigation into the skeletoniLatmn approach of Hilditch. Partem Recognit. 17, 279 (1984). 2/. WHITEHOUSE. W. J. The quantitative morphology of amsotropic trabecular bone. J. Mic~r~~c. 101. 153 (1974).
II.
BERGOT.
22.
PARFITT, A. M., DREZNER, M. K.. GLORIEUX. P. J.. OTT. S. M.. AND RECKER, R. R. Bone
23. 23. 25.
F. H..
KANIS.
J. A.. MALLUCHE.
H..
ME~NIER.
histomorphometry: Standardization of nomenclature, symbols and units. J. Bone Miner. Res. 2, 595 (1987). AARON. J. E., FRANCIS, R. M., PEACOCK. M.. AND MAKINS. N. B. Contrasting mtcroanatomy of idiopathic and corticosteroid-induced osteoporosis. C/in. Orthop. 243, 294 f 1989). AARON. J. E., DE VERNEJOLJL. M-C., KANIS. J. A. Bone hypertrophy and trabeculargeneration in Paget’s disease and in fluoride-treated osteporosis. &I/V Mit7cr. In press.
KLEEREKOPER.
of three-dimensional fractures. Crr/c$
M..
VILLANUEVA.
A. R..
STANCIU.
J.. RAO.
D. S.. .~ND P.4rwn.r.
M. The
role
trabecular microstructure in the pathogenesis of vertebral compression Tissrre Inf. 37, 594 (1985). 26. FELDKAMP, L. A.. GOLDSTEIN. S. A., PARFITT. M., JESIOIV. G.. AND KLEEKEKOPER. M. The direct examination of three-dimensional bone architecture in vitro by computed tomography. J. Bone Miner. Res. 4, 3 f 1989). 27. HODGKINSON, R.. AND CURRY. J. D. Effects of structural variation on Young’s modulus ot non-human canceilous bone. Proc. Inst. Mech. Enp. 204. 43 (1990). 2X. VESTERBY. A. Star volume of marrow space and trabeculae in iliac crest. BUUC> 11, 149 I 19901.
AND
BlOMEDICAL
RESEARCH
25, l-16 (1992)
An Automated Method for the Analysis Trabecular Bone Structure JEAN E. AARON,* BEVERLEY A. OAKLEY,*
of
DAVID R. JOHNSON,* JOHN A. KANE,? PAUL O’HIGGINS,* AND STEPHEN K. PAXTON”
*Department of Anatomy, University of Leeds. England and tDepartment of Human Metabolism and Clinical Biochemistry, University of Sheffield, England Received October 16, 1990
Trabecular structure as well as bone mass is important in studies of bone disease and fracture. An automated method for the direct analysis of two-dimensional trabecular microanatomy and its application to human iliac crest bone biopsies is described. Compared with established methods which require expensive equipment and complex software, costs have been reduced and availability increased by using an image analyzer driven by a microcomputer. Routine histological sections are accepted and an editing function enables the removal of artifacts. An elastic window allows field expansion for large specimens. The program enables the rapid assessment of the bone volume and trabecular surface from the intact image, followed by image skeletonization and the deduction of the trabecular length, number, character, and spacing together with the number of trabecular junctions and discontinuities: the trabecular width is calculated indirectly. Images may be stored to disk or printed as permanent records for diagnostic or research purposes. o 19% Academic press. IX
Bone density is a major factor in determining skeletal strength. However, other factors are also important (1). Foremost among these is the topography of bony tissue, particularly at cancellous sites prone to osteoporotic fracture (2). Until recently, comparatively little attention has been paid to the microanatomy of the trabeculae remaining following a period of bone loss, or to the disposition of new bone apposed in response to treatment. Interest in the structural and therapeutic implications of trabecular configuration is now increasing (for example, 3, 4). The acquisition of data on trabecular topography can be time consuming. The histological analysis of bone sections has traditionally been performed manually using eyepiece graticules together with point counting and line intercept procedures (5). Not only is this process long and repetitive, but highly trained operators are required and there are limitations upon the characteristics of trabecular shape which can realistically be measured. OOlO-4809/92 $3.00 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
7
AARON ETAL
Several systems of computer-aided microscopy have been developed in which the procedure is semi-automated by projecting the image of a section of bone on to a digitizing pad (see, for example, 3, 6-9). Computation time is reduced by these methods, but operator time and skill generally remains high. At the same time, other effective methods have been described but tend to pertain to limited and specific aspects of trabecular structure only (10-13). An almost fully automated and comprehensive method has been developed by Garrahan et al. (14, 15’) in which the binary image of the tissue is reduced to its minimum profile (i.e., “skeletonized”). An analysis of the two-dimensional structure in terms of “nodes” (i.e.. trabecular junctions). “struts” (i.e.. bony bars) and “free ends” (i.e.. trabecular discontinuities or termini) is rapidIS, derived. However, the hardware employed is large and expensive and the software not generally available (16). In addition. the histological stains which produce the necessary high contrast images (e.g.. the von Kossa stain) are often not the stains of choice for sections intended also for other histomorphometric purposes. Our present objective is to increase the accessibility of the automated analysis of trabecular structure to more laboratories by reducing hardware. expertise, and costs to a minimum. We have utilized methods described in the literature to produce a system of shape analysis whereby a defined area of a bone section prepared routinely for established histomorphometric analysis (for example. using toluidine blue stain, or the Goldner method) is captured in our system by a closed circuit television camera and processed by an image analyzer driven by a microcomputer. The results obtained automatically are compared with those measured manually. MATERIALS
AND METHODS
The iliac crest was chosen for analysis because it is the established site for biopsy in histological investigations of metabolic bone disease. Specimens were selected from a collection assembled over many years for regular histomorphometry. Twenty-six specimens were chosen to provide a range of bony tissue and trabecular configuration ranging from porotic to petrotic. Thirteen of these were of normal bone removed at autopsy by sawing transections approximately 1 cm thick and 2.5 cm long from a region 2 cm behind the anterosuperior spine of the ilium; the subjects had died suddenly as a result of accident or acute illness with no history of bone disease. The remaining 13 were biopsies removed following informed consent from patients with primary osteoporosis (51, secondary osteoporosis (3), and Paget’s disease (5). These transilial specimens had been obtained under local anaesthesia using a trephine with a 0.8-cm bore diameter in a region 2 cm behind the anterosuperior spine and 2 cm below the iliac crest. All samples were fixed in 10% buffered form01 saline, pH 7.2, and embedded in methylmethacrylate. Undecalcified sections 8 pm thick were cut from each using a Jung K heavy duty microtome (Reichert-Jung, Heidelberg,
AUTOMATED
ANALYSIS
OF BONE STRUCTURE
W. Germany). Sections were stained either in 0.1% toluidine 30 min or by a modification of the Goldner method (17).
3
blue, pH 3.5 for
Manual Analysis
Each section was composed of an area of cancellous bone encompassed by an inner and outer area of cortical bone. The microanatomical features measured were confined to the cancellous tissue and were analyzed by the methods described in detail by Aaron et al. (4). They comprised bone volume (percent relative to total tissue volume) assessed by means of an integrating eyepiece (No. 1, Zeiss, Oberkochen, W. Germany) and the application of regular point counting procedures using a magnification of 50 x (18); the bone surface (mm’/ mm3) by means of an integrating eyepiece, line intersecting procedures, and a magnification of 80 x ; the trabecular width (mcm; not corrected for section obliquity, 3), using a process of site selection similar to that of Wakamatsu and Sissons (19) and measuring directly from the image projected on a screen, using a magnification of 50 x ; the trabecular number using a field determined by the rectangular window in the viewing tube of the Zeiss photomicroscope II at a magnification of 20 x and defining individual trabeculae as isolated bars or domains of bone extending between junctions (a variable which correlates directly with the mean trabecular plate density of Pa&t et al. (3) and indirectly with the trabecular spacing or separation measurement of Wakamatsu and Sissons (19), see Aaron et al., (4)). Automatic Analysis
Following manual analysis each section was placed upon the microscope stage of a Wild M7A dissecting microscope with a zoom lens and viewed in transmitted light. An image of the whole section was obtained via a closed circuit black and white television camera attached to the viewing tube of the microscope. The overall magnification was 15 x . The frame was captured as a 256 x 256 pixel, 64 grey-level image by a VIP image analyzer (Sight Systems, Unit 1, Hambridge Lane, Newbury, Berks RG14 7TU, UK). We originally used a version designed for the Acorn (BBC) microcomputer in conjunction with a program written in Assembler. Our later system (Fig. 1) uses an IBM PC compatible machine (512k or better) and is written in Turbo Pascal v5, with some sections in Assembler for enhanced speed of computation. Thresholding the Image
The captured image was “thresholded” to separate the bone trabeculae from any background caused by the presence of marrow, uneven lighting, etc. as follows: The image was “thresholded” to produce a binary image made up of black and white pixels only. The original image consisted of pixels each of which had a value between 0 (black) and 63 (peak white). A threshold value is
4
AARON
ET AL
FIG. 1. Systemfortheautomatedanalysisoftrabecularstructure. Theimageofthesectron(arrowed) under the microscope is captured by a closed circuit TV camera and processed by an image analyzer (right) driven by a microcomputer (left): (a) intact image on the screen (right) together with a magnified region; (b) the same image after “skeletonization.”
selected manually: all pixels below this value are set to white; all pixels above are set to black. The resulting binary “bitmap” was compressed and stored on disk. Editing the Image
Stored images may be recovered from disk when required for further processing. A mouse driven menu system allows the following editing functions to be carried out: (a) Single pixel removal. Since the analysis concerns a pattern of relatively large bony trabeculae, single pixels are likely to represent noise. A standard algorithm removes all single pixels surrounded by dissimilar ones.
AUTOMATED
ANALYSIS
OF BONE
STRUCTURE
5
(b) Erasure. Larger areas found to represent artifacts can be erased manually using the mouse. (c) Joining. Artifactual discontinuities in the image may be filled using the mouse. (d) Inversion. The binary image may be black/white reversed. (e) Magnification. Prior to editing, the binary image is presented in a window with a “rubber-banded” box. The contents of the box may be zoom magnified and displayed alongside the original image (Fig. la). Processing
the Image
Following editing, the image may be stored or processed. The “rubberbanded box” function is used to delineate a “working window” which may include all or part of the image as required or encompass a standard area. The dimensions of the “working window” were adjusted electronically until its width was equivalent to the shortest projected intercortical distance found among the specimens from the ilium to be analysed (c. 5.5 ems) and the corresponding height excluded the areas of trephine damage created along either edge of the section at biopsy. (a) Cropping. The image was “cropped” by a routine which removes all objects in the image which are outside the “working window” and do not cross its boundaries. This reduces the time subsequently taken to “skeletonize” the image. (b) Skeletonization. The selected part of the binary image was “skeletonized” or “thinned” to its medial axis (Fig. lb) by a modification of a standard Hilditch algorithm (20, Algorithm H) which reduces trabecular bars to strings of single pixels by repeated passes and deletions of the dark points, changing them to white points (Fig. 2). This process generates parameter 1, bone volume, from the “unthinned” bone area in mm2 or as a percentage of the total area, and parameter 2, bone surface, in mm2/mm3 or as the trabecular perimeter in millimeters. The ratio of parameters 1 and 2 provides parameter 3, trabecular width or thickness in microns (21, Table l), while parameter 4, trabecular length in millimeters is an expression of the total length of “thinned” trabeculae within the defined window. (c) Analysis. This routine works on the skeletonized image to produce counts of the following features: -the number of nodes (joint points of three or more strings of pixels, parameter 5). -the number of free ends or termini (end points of a pixel string, parameter 6). -the number of cut ends (where a pixel string hits the edge of the box, parameter 7). Individual trabeculae identified by the automatic method were measured in length and further classified (parameters 8-17) according to the scheme of Garrahan et aZ.(Z4) and include end-to-cut, node-to-cut, end-to-end, node-to-
AARON
ET AL
FIG. 2. (Top) Computer generated printout showing the image ofa bone biopsy with inner and outer cortices and the trabecular region for analysis within a rectangular window: (bottom) the thinned image ready for analysis.
end, and node-to-node. Other categories of trabeculae defined by Garrahan et al. (cortex-to-end, node-to-loop) were not used for simplicity, but may be added to the system if required. Also available within the program is the facility to measure isolated bone profiles (22), their number and length. All the data are stored to disk and may be analyzed further or printed as required. as may representations of the unedited, edited, or thinned images. (d) Threshold effect. The effect of the threshold levels selected to produce the most acceptable image on the TV screen was determined for some variables by repeating the analysis of a single specimen over a range of threshold settings. (e) Interobserver variation. Ten sections were analyzed independently by two observers and the coefficient of variation assessed. Indices derived automatically and their manually assessed counterparts are shown in Table 1 and are consistent with the nomenclature recommended for histomorphometry (22). On completion of the measurements the results obtained by the fully automated method were compared with those obtained manually and correlation coefficients were calculated for the principal variables, In addition, an approximate evaluation of the time required for the two methods was made.
AUTOMATED
ANALYSIS
OF BONE
TABLE INDICES
MEASURED
Intuct image Bone volume % (bone area : tissue area) Bone surface mm2/mm3 mcm
(Trabecular
Thinned
image -
Trabecular (direct)
AND AUTOMATICALLY
Automatic Window Window
width
1
MANUALLY
Manual
Trabecular (direct)
7
STRUCTURE
number/field
width/l
height length
Abbreviation
mm mm V or Ar
Bone volume % or area mm? (bone area : tissue area) Bone surface mmz/mm3 or perimeter mm Trabecular width mcm = 2.000 * bone area mm?/ trabecular perimeter (21) .2” = Trabecular thickness (22))
SorPm TbWi
Total trabecular length mm Nodes Ends Trabecular number, i.e., node-node (number. mean length) node-end (number, mean length) end-end (number, mean length) end-cut (number, mean length) node-cut (number, mean length)
0 The correction factor for section obliquity or 1.199 for iliac trabecular bone (3).
is 4/n (1.273)
for structures
or TbTh
TbLe NorNd EorTm TbN
without
spatial
orientation
RESULTS
The manual analysis of a single section by traditional methods takes approximately 20 min, while the automated method, which produces additional variables and a printed record took less than half this time. A comparison of the indices measured automatically and those determined manually is shown in Fig. 3. As might be expected close correlations were found for the bone volume (Fig. 3a) and for the bone surface (Fig. 3b), the two simplest variables to define. There was also a good relationship between trabecular width measured directly by the manual method and indirectly by the automatic procedure, despite the fact that the regions adjacent to trabecular junctions were excluded from the manual analyses but included in the automatic version (Fig. 3~). However, it is probably for this reason that the trabecular thickness tended to be higher when measured automatically. The most difficult of the four principal variables to define structurally is the trabecular number; nevertheless a significant correla-
8
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AARON
ET AL.
FIG. 5. Sites of discrepancy between manual and automatic analysis. (Top) Small intratrabecular resorption cavities (horizontal arrows) create an over complex skeletonised image. (Bottom) Small trabecular protruberances (vertical arrows) appear more significant in size in the skeletonised image.
bone volume in idiopathic osteoporosis was characterized by trabeculae of normal thickness but small in number. This contrasts with the low bone volume in steroid osteoporosis in which the trabeculae were reduced in thickness but not in number. This morphological distinction has both structural and therapeutic implications (23). The topography of pagetic bone, with both abnormally thick and numerous trabeculae. on the other hand, may provide insight into trabecular regeneration (24). In addition to the measurements described above, the printouts include the computed number of trabecularjunctions (nodes) and trabecular termini (ends). While in our mixed sample there was a general correlation between the number of nodes and bone volume, no such relationship existed between ends and bone volume (Fig. 7a). However, a relationship is maintained if the ratio nodes : ends (an index of spatial connectivity in a section (1.5)) was used (Fig. 7b). The utility of these additional aspects of trabecular structure with respect to bone strength and pathogenesis remains to be assessed. Table 3 shows the effect of changing the thresholding function upon bone area and some of the other variables measured. If the threshold was too low some areas of bone failed to appear in the image and were lost in the background. As the level selected approached the optimum the trabecular structure of the section became more accurately represented by the projected image. If the
AUTOMATEDANALYSISOFBONESTRUCTURE Al
Cl
STEROID
11
NORMAL
OP
FIG. 6. Computerized analyses of four structurally contrasting iliac biopsies: (a) normal trabecular number and continuity in a healthy subject; (b) loss of trabecular number and continuity in idiopathic osteoporosis; (c) trabecular thinning in steroid-induced osteoporosis; (d) trabecular thickening and increased trabecular number in the sclerotic bone of Paget’s disease.
optimum setting for the bone area was exceeded, an increasing quantity of irrelevant detail, for example, marrow tissue or folds in the plastic embedding medium, was detected and included in the subsequent analysis. While an incorrect threshold can profoundly influence results, a departure from the correct range for the bone area is immediately obvious on the monitor screen. If the stain was too pale, because of elution or because the section was particularly thin (i.e., less than 4 pm thick), areas of bone failed to appear in the image without raising the threshold function beyond its optimum value. This risked the capture of irrelevant background detail. However, the routinely prepared sections described above generally required little, or no, editing, and the most common artifacts were dehydration cracks and peripheral bone fragments resulting from displaced trephine damage (Table 2). The reliability of the technique is borne out by the similarity in the results when 1Q sections were analyzed independently by two observers (Table 4). DISCUSSION
The osteoporoses are heterogeneous in both their aetiology and in the topography of their remaining trabecular bone (23). An awareness of the structural character of the trabeculae may provide a better discriminant between fracture
12
AARON
ET AL.
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w of
and nonfracture prone subjects than does bone volume alone (25). It now seems axiomatic that trabecular microanatomy will become as central to an understanding of osteoporosis and fracture risk as bone mass. The inexpensive and fully automated system described above facilitates this approach and makes the generation of such information accessible to all laboratories with an interest in abnormal bone. Moreover, the results are consistent with those obtained using manual methods and reproducibility is high. The size of the “working window” was set in this study to accommodate a typical average-sized transilial bone biopsy while allowing latitude to avoid peripheral trephine damage. For a larger specimen, such as a sectioned femoral
AUTOMATED
ANALYSIS TABLE
THE EFFECT
OF INCREASING
Threshold 10 12 14 16 18 20 22 24 26 28” 30” 32 34 36
THRESHOLD
VALUES
13
OF BONE STRUCTURE 3 ON THE VARIABLES
IN A SINGLE
FIELD
OF VIEW
BAr
NTm
NNd
TbN
BPm
16.3 18.2 19.2 19.8 20.8 21.1 22.5 23.5 24.4 25.6 26.8 28.6 32.0 42.1
150 139 141 141 122 115 115 120 110 112 126 118 165 195
63 63 63 18 66 52 54 53 53 59 53 68 108 250
184 187 186 207 178 168 159 164 157 161 171 186 286 248
61.3 66.3 67.9 10.3 68.3 67.5 69.4 69.5 71.3 71.8 71.5 74.4 85.0 115.7
Nore. When the setting is too low the proportion of bone is underestimated; when the setting is too high bone volume is overestimated. a Optimum threshold values for BAr; BAr = % bone area: NTm = number of ends or termini; NNd = number of nodes; TbN = trabecular number; BPm = bone perimeter mm.
TABLE INTEROBSERVER
Biopsy no. 1 2 3 4 5 6 7 8 9 10
VARIATION:
NTm
BAr I
II
13 9.1 4.6 7.1 9.0 10.8 11.4 4.2 14.6 24.6
12.1 8.6 4.3 7.7 8.9 11.5 11.2 3.8 12.5 23.3
NS P cv 1.51 (SD/Mean difference)
4
THE ANALYSIS OF TEN SECTIONS BY Two STUDENT’S t TEST FOR PAIRED DATA
NNd
OBSERVERS
TbN
II
I
II
I
II
76 57 45 13 73 116 84 64 87 90
88 58 47 72 73 117 80 80 83 79
11 4 4 9 14 11 13 0 18 44
15 5 5 9 10 12 6 0 18 33
63 45 34 62 73 86 72 3-l 82 127
79 46 35 59 63 87 57 43 83 100
NS 3.00
THE
BPm
I
NS 6.48
USING
NS 4.10
I
II
42.2 27.8 15.6 25.9 31.2 39.3 33.6 15.6 39.4 62.2
42.1 21.2 15.3 25.5 30.2 42.2 33.5 14.4 34.6 62.2 NS 3.33
Note. BAr = % bone area; NTm = number of ends or termini; NNd = number of nodes; TbN = trabecular number: BPm = bone perimeter mm; CV = coefficient of variation.
14
AARON
ET AL
head or vertebral body, the window can be enlarged to accommodate a wider field of view. Obversely for small biopsies within a group, or to separately assess a discrete area of abnormality such as a metastasis within a specimen. the window can be reduced to a half or a quarter (or less), followed by the appropriate scaling of the results to correspond to the original standard window size of choice. The trabecular structure lends itself well to automated analysis since. unlike much histomorphometry. there is no subjective element. Also. because the method is concerned with simple, gross structures requiring only minimal magnification, small artifacts are not resolved. The system is sufficiently fast to enable serial sections in quantity to be assessed. For example, we are currently comparing microanatomical and ultrasonic attenuation measurements in a project which requires the evaluation of many sections of large specimens from a range of skeletal sites; this would be too demanding in time and patience to contemplate using manual methods alone. In the automated assessment of trabecular width, the failure of the system to recognize and separate the wide junctional regions may be a disadvantage. These sites, which are thought of as important determinants of bone strength may be less responsive to remodelling imbalance and may be subject to changes that are entirely different (such as compensatory hypertrophy (2.5)) from those taking place in the internodal regions. However, in a broader sense the significant relationship between the manual and automatic measurements of trabecular thickness shown above suggests that for most practical purposes this is not a major problem. The system can be programmed to exclude small intratrabecular resorption cavities to avoid the unnecessary complexity that they create in the image and the consequent extra editing. This option was not taken. however, since the presence of the small intratrabecular cavities or canals is an inconvenience only in certain pathologies (such as Paget’s disease or fluoride-treated osteoporosis) and it was envisaged that questions concerning trabecular development may arise to which consideration of this feature may be of future significance. The interpretation of trabecular “free ends” or termini in a two-dimensional section is problematical, since their real status is unknown without their threedimensional reconstruction. However, their failure to decline in number with diminishing bone volume, together with the relationship between the “node : end” ratio and the bone volume, suggests that they may provide an index of trabecular connectivity: this is being further examined using serial sections. An approach such as this is, of course, far more time-consuming than the high resolution three-dimensional computed tomography adopted by Feldkamp ef al. (26), but the latter is unavailable to most laboratories or beyond their financial means. The variables described above are those most basic to a structural analysis. From these a number of other variables may be derived by simple equations reported in the literature cited. For example. the trabecular separation (mcm) = trabecular thickness mcm ((100/c% bone volume) - 1) and the trabecu-
AUTOMATED
ANALYSIS
OF BONE STRUCTURE
15
lar plate density (per mm) = % bone volume x lO/trabecular thickness mcm (3). These variables, together with counts of isolated trabecular profiles (27), an assessment of deviation of shapes from circularity, and trabecular anisotrophy (22, 27) are included in the software package. Finally, there is available for use at any stage within the program a general function for the measurement of point to point distance. The trabecular spacing, for example, can be determined by indicating with a mouse cursor a trabecula within the skeletonized image, then its neighbor; the program proceeds to seek midpoints along the length of each bar and to calculate the distance separating them. “Radial” scans of path lengths through cavities and trabeculae (13) can also be performed and there is a facility, presently being evaluated, for measuring the star volume (28). The completed program is now available’ and has the flexibility to accommodate any other personal requirements for shape analysis. ACKNOWLEDGMENTS The authors wish to acknowledge the skilled assistance of T. J. McAndrew for the statistical analysis and T. Lee for the artwork. This research was supported by the Medical Research Council Programme Grant 8600806.
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