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Carpal bone size and scaling in men versus in women
Carpal Bone Size and Scaling in Men Versus in Women Joseph J. Crisco, PhD, James C. Coburn, MS, Douglas C. Moore, MS, Mohammad A. Upal, MS, Providence, RI
Purpose: The purpose of this study was to quantify carpal bone size, to determine whether gender influences carpal size, and to determine whether small and large carpal bones differ in size only by simple isometric scaling. Methods: Cortical surfaces of all carpal bones in both wrists of 14 women and 14 men (ages 22–34 y) were reconstructed from computed tomography (CT) volume images. Carpal volume and boundingbox dimensions in 3 orthogonal directions were calculated and compared across genders. An average set of carpal bones were then scaled mathematically by a single factor in all directions (scaled isometrically) and compared across carpal bones of all sizes. Results: Although female carpal bones were significantly smaller than male carpal bones, individual carpal volume as a percentage of the volume of the entire carpus did not differ with gender. The 3 orthogonal bounding-box dimensions of the carpal bones scaled nearly isometrically from the smallest to the largest bones. Conclusions: Across the wide range of wrist sizes studied the individual carpal volumes were a consistent percentage of carpus volume and this percentage did not differ with gender. Despite their complex shape the bounding dimensions of the carpal bones increased isometrically with increasing volume. The extensive database of dimensions provided in this study should be useful in the design and insertion of fixation systems and implants. (J Hand Surg 2005;30A:35– 42. Copyright © 2005 by the American Society for Surgery of the Hand.) Key words: Carpals, volume, dimensions, scaling, 3-dimensional.
The carpus contains a uniquely passive set of bony articulations. Of the 19 muscles in the forearm that function to position the hand space, only the flexor carpi ulnaris generally inserts on the carpus (pisiform
From the Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, Providence, RI; and the Division of Engineering, Brown University, Providence, RI. Received for publication June 10, 2004; accepted in revised form August 24, 2004. Supported by a National Institutes of Health grant (AR44005). No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. Reprint requests: Joseph J. Crisco, PhD, Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, CORO West, Suite 404, 1 Hoppin St, Providence, RI 02903. Copyright © 2005 by the American Society for Surgery of the Hand 0363-5023/05/30A01-0005$30.00/0 doi:10.1016/j.jhsa.2004.08.012
and hook of the hamate); the remainder insert on the metacarpals or phalanges. Accordingly the motion of the hand relative to the arm is defined by the complex bone shapes, intricate bony articulations, and unique ligamentous attachments in the carpus. As the forearm muscles position the hand, carpal motion is determined by bony articulations and the range is limited by their ligament attachments. The contribution of the individual carpal bones to overall wrist motion appears to be similar in men and women. An early study of carpal motion during wrist flexion and extension revealed no gender-related differences in rotations at the midcarpal joint.1 Similarly more recent studies of carpal kinematics in vivo by using computed tomography (CT)-based markerless bone registration techniques have found no differences in the magnitude of carpal rotation in men The Journal of Hand Surgery
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The Journal of Hand Surgery / Vol. 30A No. 1 January 2005
and women during flexion and extension.2,3 In both men and women scaphoid rotation was measured to be 73% of capitate rotation in flexion and 99% of capitate rotation in extension, whereas lunate rotation was 46% as much as the capitate in flexion and 68% as much as the capitate in extension.2 Although carpal motion appears to be similar in men and women there are differences in the location of the rotation axes. In particular the rotation axes of the carpal bones in women are located more proximally than in men.3 This suggests that the differences in rotation axis location may be due to differences in bone size, as opposed to some functional differences. Anatomic studies of the carpal bones that verify or catalogue prominent anatomic features and sizes using 2-dimensional4 and 3-dimensional5 imaging tools have created general criteria for normal and abnormal bone shape and size, although scaling ratios and dimensions have not been addressed. This study was performed to determine whether the gender-related differences in carpal size are simply due to scaling. To determine this we tested the hypotheses that the volume of each carpal relative to the total volume of the carpus did not differ according to gender and that carpal dimensions scale isometrically, by an identical factor in all directions.
Materials and Methods Subjects and Image Acquisition With approval from our Institutional Review Board and after obtaining informed consent, 28 volunteers were recruited for study. Potential volunteers were eligible for inclusion if they were between the ages of 18 and 30 years and had no history of wrist injury or chronic disease that might affect the soft tissues in the wrist. Subjects specifically were excluded if they had a history of wrist or forearm fracture, prior wrist surgery, or severe osteoarthritis or connective tissue disease. At enrollment a detailed history was taken and a detailed wrist examination was performed by a fellowship-trained hand surgeon, and posteroanterior, lateral, and anteroposterior grip radiographs were performed. The enrolled study population included 14 men (mean age, 25.6 y; range, 22–34 y) and 14 women (mean age, 23.6 y; range, 22–30 y). Both wrists of each subject were imaged simultaneously with a computed tomography scanner (GE HiSpeed Advantage; GE Medical, Milwaukee, WI). During scanning the subjects were seated at the back of the scanner with their forearms and hands extended into the gantry, parallel to the long axis of the
Figure 1. The right wrist bones of 1 subject rendered from a volar (palmar) view with the centroid and inertial axes of each carpal. The centroid is the geometric center of the cortical bone shell and the inertial axes are colored by their inertial magnitude from smallest (red), to medium (green), to largest (blue) (see also Fig. 2). The proximal row contains the scaphoid (SCA), lunate (LUN), triquetrum (TRQ), and pisiform (PIS), and the distal row contains the trapezium (TPM), trapezoid (TPD), capitate (CAP), and hamate (HAM). The radius (RAD) and ulna (ULN) also are depicted.
scanner table. Contiguous 1.0-mm transverse slices were acquired of the entire carpus as the wrist was scanned from the distal radius to the proximal metacarpals. The images were acquired at either 120 kVp and 80 mA or 80 kVp and 120 mA. The voxel size of the reconstructed images ranged from 0.2 mm x 0.2 mm x 1.0 mm to 0.9 mm x 0.9 mm x 1.0 mm.
Image Processing and Bone Dimension Calculations Each of the 8 individual carpal bones from each wrist were segmented from the CT volume images and then bone centroid locations, principal inertial axes, and volumes were calculated (Fig. 1). In brief, for each CT slice a series of points, or surface contours, was generated for each bone. The contours then were grouped by bone and surface fit by using commercially available software programs (Analyze; Mayo Foundation, Rochester, MN; Geomagic; Raindrop, Durham, NC). The volumes, centroid locations, and principal inertial axes for each bone were calculated by using software routines written in a software program (Matlab; Mathworks, Natick, MA).6 For any object (bone) there are always 3 orthogonal principal inertial axes, each with an associated iner-
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Figure 2. The X, Y, and Z bounding-box dimensions for the average-sized set of carpal bones that also were used for carpal scaling. The dimensions of each carpal were defined by the rectangular bounding boxes whose sides are oriented parallel to the inertial axes and intersected the most distant points on the bone surface. The inertial axes are ordered by their inertial magnitude, from smallest (X), to medium (Y), to largest (Z).
tial magnitude. Inertial magnitudes are a measure of the mass distribution about the respective axis: the further the mass is distributed away from the axis the higher the inertial magnitude. In this article we assume all bones have the same density, therefore the inertial magnitude is a geometric measure of bone size when viewed along an inertial axis. Finally the volumes of each of the 8 carpal bones in a given wrist then were summed to yield a value for the total carpus volume. For the purposes of our analysis the dimensions of the carpal bones were defined to be the maximum lengths parallel to the principal axes of inertia. To calculate the lengths we generated rectangular bounding boxes with sides parallel to the inertial axes to enclose the bones. The sides of the bounding boxes were located at the most distant points on the bone surface in each inertial direction. The X, Y, and Z dimensions of the bounding box correspond to the dimensions parallel to the smallest, middle, and largest inertial magnitudes, respectively (Fig. 2).
Gender and Size Analysis Two comparisons were made to explore potential differences in carpal size in men and women. For the first we directly compared the mean volumes for each of the 8 carpals. For the second we compared the percentage of the entire carpus occupied by each carpal, defined as carpal bone volume divided by carpus volume. Statistical comparisons were made with Student t tests (only 1 randomly selected wrist was used from each volunteer); p values less then .05 were considered statistically significant.
Isometric Scaling Trends in carpal size (scaling) were examined by plotting bounding-box dimensions of each bone as a function of carpal volume, and then comparing these bounding-box dimensions with those generated by isometrically scaling the average-sized set of bones. The bones used for scaling were taken from a patient whose carpal volumes most closely matched the means for the carpals from all subjects (in this dataset
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we used a male subject with carpal volumes within 12% of the average for all subjects). Once an average-sized set of bones was identified (Fig. 2) a set of volume-scaling factors was calculated with respect to the scaphoid: the first scaled the scaphoid volume down to the smallest scaphoid volume in the database, the second scaled the scaphoid volume up to the largest scaphoid volume in the database, and then 5 additional scaling factors were calculated to yield volumes evenly spaced between the smallest and largest volumes. Cube roots were taken of each of these 7 volume-scaling factors, yielding a set of 7 linear scaling factors that then were multiplied by the x, y, and z surface coordinates of the average-sized set of bones, yielding 7 different scaled versions of each carpal. Each scaled version of the 8 carpal bones then was treated as a newly segmented bone for which bounding boxes were generated, and the linear dimensions and carpal volumes were calculated (as described earlier). An interpolating third-order polynomial then was fit in each dimension to the 7 scaled values as a function of bone volume. To evaluate whether the trend in increasing dimensions with volume could be attributed to isometric scaling the root-mean-square difference between all database values and the scaled interpolated values were calculated, along with R2 values.
Results Our first analysis revealed that the rank order of each carpal volume was the same in the men and women and that on average the carpal bones in the men were larger than those in the women (Fig. 3A, Table 1). For both genders the capitate was the largest bone, followed by the hamate, scaphoid, trapezium, lunate, triquetrum, trapezoid, and pisiform. On average the volumes of the carpal bones in the women were 38% smaller than the corresponding carpal volumes in the men; the difference was largest with the lunates (46%) and smallest with the triquetrums (34%). There were, however, no differences in the relative sizes of the carpal bones in men and women, and the carpal bones from both genders scaled on a continuum. When normalized carpus bone volumes (carpal bone volume/total carpus volume) were compared there were no significant gender-related differences for any of the bones (Fig. 3B). Across all bones the mean difference in normalized carpal volume was less than 1% with no discernable gender bias for any bone’s normalized volume. Graphs of the X, Y, and Z bounding-box dimensions of the carpal bones revealed that the carpal dimensions increased as a
Figure 3. Graphs of the (A) average and (B) average normalized carpal volumes for men and women. (A) All of the average carpal volumes in women were significantly smaller than the corresponding volumes in men (*, p ⬍ .05). (B) The percentage of the carpus volume occupied by each bone was the same, however, for both genders.
function of volume for each of the carpal bones (Fig. 4) and that the relationship was similar in both men and women (with substantial overlap of the bone dimensions and volume from some of the smaller men and larger women). Isometric scaling of the carpal bones provided a reasonable approximation of the experimentally acquired data. The plots of the isometrically scaled bones were slightly nonlinear (cubic) and closely matched the values plotted for the bones from all of the subjects (Fig. 4). The use of the scaphoidderived scaling factors, however, underpredicted the range of lunate, trapezium, and pisiform dimensions, and overpredicted the range of hamate dimensions (Fig. 4). The root-mean-square difference between the interpolated scaled and raw data was approximately 1 mm on average (Table 2). The R2 values for the interpolated scaled data
Crisco et al / Carpal Bone Size and the Genders
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Table 1. Average (ⴞ 1 SD) Carpal Bone Volume (mm3) and X, Y, and Z Bounding-Box Dimensions (mm) Were Significantly Smaller in Women Than in Men Men (n ⴝ 14) Scaphoid Vol X Y Z Lunate Vol X Y Z Triquetrum Vol X Y Z Pisiform Vol X Y Z Trapezium Vol X Y Z Trapezoid Vol X Y Z Capitate Vol X Y Z Hamate Vol X Y Z
Women (n ⴝ 14)
Men and Women
2,903.2 29.3 17.8 14.1
⫾ ⫾ ⫾ ⫾
461.0 2.7 1.2 0.9
1,877.0 24.8 15.3 12.2
⫾ ⫾ ⫾ ⫾
407.3 1.6 1.5 0.6
2,390.1 27.0 16.5 13.1
⫾ ⫾ ⫾ ⫾
673.6 3.1 1.8 1.2
2,252.0 20.9 20.1 14.4
⫾ ⫾ ⫾ ⫾
499.4 2.2 1.8 1.3
1,368.2 18.0 16.9 11.9
⫾ ⫾ ⫾ ⫾
165.0 1.1 0.8 0.8
1,810.1 19.4 18.5 13.2
⫾ ⫾ ⫾ ⫾
578.5 2.3 2.2 1.7
1,579.7 20.9 14.9 12.6
⫾ ⫾ ⫾ ⫾
261.3 1.8 0.7 0.9
1,103.9 18.5 13.3 10.8
⫾ ⫾ ⫾ ⫾
193.7 1.3 0.6 0.7
1,341.8 19.7 14.1 11.7
⫾ ⫾ ⫾ ⫾
331.0 2.0 1.0 1.2
854.3 15.7 12.3 10.0
⫾ ⫾ ⫾ ⫾
203.3 1.4 1.3 1.2
569.6 13.7 10.7 8.9
⫾ ⫾ ⫾ ⫾
121.8 1.4 1.0 0.7
712.0 14.7 11.5 9.5
⫾ ⫾ ⫾ ⫾
219.6 1.7 1.4 1.1
2,394.8 25.4 17.5 16.1
⫾ ⫾ ⫾ ⫾
443.6 1.8 1.8 1.8
1,547.1 21.8 15.8 13.1
⫾ ⫾ ⫾ ⫾
328.9 1.8 1.5 1.2
1,970.9 23.6 16.6 14.6
⫾ ⫾ ⫾ ⫾
576.7 2.5 1.8 2.2
1,497.1 20.6 15.5 12.3
⫾ ⫾ ⫾ ⫾
237.2 1.4 0.8 0.7
1,020.4 18.0 13.3 11.1
⫾ ⫾ ⫾ ⫾
191.5 0.9 1.2 0.8
1,258.7 19.3 14.4 11.7
⫾ ⫾ ⫾ ⫾
321.6 1.8 1.5 1.0
3,700.6 28.0 20.8 16.0
⫾ ⫾ ⫾ ⫾
563.9 1.8 1.7 1.6
2,547.1 24.6 18.2 13.9
⫾ ⫾ ⫾ ⫾
344.6 1.1 1.0 0.8
3,123.9 26.3 19.5 15.0
⫾ ⫾ ⫾ ⫾
743.7 2.3 1.9 1.6
2,940.7 27.5 23.0 16.9
⫾ ⫾ ⫾ ⫾
378.1 1.9 1.8 1.2
2,045.1 24.7 20.1 15.0
⫾ ⫾ ⫾ ⫾
264.2 1.4 0.8 0.9
2,492.9 26.1 21.6 16.0
⫾ ⫾ ⫾ ⫾
555.5 2.2 2.0 1.4
Values are for both wrists.
compared with the raw data ranged from .08 to .81 (Table 2).
Discussion This study was performed as a first step in determining whether the gender-related differences in carpal size are caused by scaling or whether they represent more complex changes in carpal shape. Our data suggest that the differences primarily are caused by simple scaling. Although we did find gender-related differences in carpal volume for each of the 8 carpal
bones, those differences vanished when we compared the normalized volumes of the bones (ie, the relative amount of the carpus that each bone occupies). In other words the size of each carpal remained fairly constant relative to the size of the rest of the carpus in both genders. Moreover when we plotted carpal dimensions we found that the dimensions of men’s and women’s bones fell on the same continuum; there was no distinct volume or dimension that separated the two genders. Finally we found that isometrically scaling an average-sized set of bones
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Figure 4. Each carpal dimension increased with increasing carpal volume and this relationship did not differ between men and women. When an average-sized set of carpal bones were scaled isometrically (by the factors for the smallest and largest scaphoid) the resulting relationship between dimension and volume shown by the scaled X, Y, and Z curves was similar to the values for all patients (see also Table 2). Some bones, such as the lunate, of some patients had a larger volume than predicted where the data points lie outside the volume range of the scaled X, Y, and Z curves.
Crisco et al / Carpal Bone Size and the Genders
Table 2. The Root–Mean–Square Differences (mm) in the Bounding-Box Dimensions Between the Isometrically Scaled and Carpal Bone Database for all Wrists X Scaphoid Lunate Triquetrum Pisiform Trapezium Trapezoid Capitate Hamate
1.39 1.10 1.27 0.81 1.31 1.21 1.10 1.14
(0.79) (0.76) (0.55) (0.77) (0.72) (0.50) (0.76) (0.72)
Y 0.91 1.04 0.98 0.81 1.34 1.39 1.30 0.97
(0.74) (0.75) (0.08) (0.66) (0.45) (0.11) (0.52) (0.76)
Z 0.71 1.17 0.53 0.55 1.31 0.80 1.38 0.74
(0.64) (0.48) (0.81) (0.75) (0.61) (0.32) (0.23) (0.71)
R2 values are listed in parentheses.
predicted reasonably well the dimensions of the bones from most subjects. We used 3-dimensional imaging techniques that built on data that traditionally has been generated via the analysis of plane radiographs. Because they are widely used clinically, plane radiographs are used most often to classify the shape or determine the size of the carpal bones.7–9 The accuracy of the data generated with plane radiographs, however, is dependent on the orientation of the wrist as the x-ray is taken. For example, lunate morphology, which may influence wrist stability, can be assigned incorrectly with relatively minor changes in x-ray technique.9 Three-dimensional techniques are an improvement because they capture shape and volume information that is unavailable on plane films and they reflect the true cortical size and volume of the carpals. We calculated our carpal dimensions with the use of bounding boxes whose sides were parallel to the principal axes of inertia. We chose to base our bounding boxes on the inertial axes because their calculation from CT volume images is accurate and robust (ie, only minimally affected by small changes in carpal shape). The error associated with locating and orienting the inertia axes is less than 1.0 mm and 2.0°, respectively.10 The objectivity of bounding-box placement and the simplicity of dimensioning ensures the accuracy and repeatability of these measurements. This method, however, also has inherent limitations. Although the method is useful to explain overall dimensions and size relationships, it oversimplifies the more intricate and complex features of the bones’ irregular shapes. A more rigorous definition of shape should lead to a more exact description of each bone and a more detailed understanding of how different factors change with size. Another potential
41
disadvantage is that the dimensions we report, which reflect lengths parallel to the principal inertial axes, do not necessarily correlate with the dimensions typically measured on standard clinical radiographs. Ultimately this can be solved with relatively straightforward kinematic transformations, however, this is beyond the scope of the current article. Our findings regarding the dimensions of the carpals generally are consistent with previous studies of carpal bone geometry performed with both 2-dimensional and 3-dimensional methodologies. Typically they have found that the carpals in women are smaller than those in men.4,5,11 Extensive 2-dimensional measurements were made by Schuind et al4 on posteroanterior radiographs of men and women in 2 age groups (25– 40 y, 41– 60 y). All of their average linear measurements were smaller in women than in men, but their measurements of intercarpal angles were the same in both genders. This lack of difference in angles by gender is consistent with our finding that normalized carpal size was the same in men and women because angles do not change with isometric scaling. Our study population was limited to a single age group, but Schuind et al4 found no differences in carpal size with age other than some agerelated narrowing in joint space. They also found that maximum grip force correlated with increasing length of the third metacarpal. Patterson et al5 measured carpal volume and antipodal axis length (the distance between the 2 most distant points on the bone surface) from reconstructed CT scans. They found that on average both were larger in men than in women. It is impossible to make direct comparisons between our bone dimension measurements and theirs, however, because the antipodal axis is not necessarily the same as the inertial axis. Subsequently Gupta and Al-Moosawi11 characterized lunate morphology, again using reconstructed CT scans. They did not stratify their results by gender, however, and their dimensions reflect lengths in the axial, coronal, and sagittal planes. Our dimensions for the lunate are larger than theirs but this most likely reflects differences in the method of measurement rather than true differences in bone size. We found that the gender-related differences in carpal size completely disappeared when the individual bone volumes were normalized by total carpus volume. Although the mean sizes of the carpal bones in the women were smaller than those of the men, they each occupied the same percentage of the total carpus volume. This suggests that there are not any large, systematic, gender-specific variations in bone
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size. It does not rule out the presence of smaller local changes (or combinations of changes that offset one another), however, which simple volume analysis would miss. In a 3-dimensional study of carpal size with bone maturation, Canovas et al12 reported that the volume of each carpal was highly correlated with the volume of all other carpals across the ages of 4 to 15 years. Although we cannot compare these values directly with ours, it is fascinating to note that the mineralized volume of one carpal relative to others remains relatively consistent during skeletal maturation, as we found in mature skeletons of different sizes. By using a single set of factors generated by scaling an average-sized scaphoid bone to the largest and smallest volumes recorded in the study we were able to match the trends between bone dimension and bone volume determined experimentally for each of the other 7 carpals. Simple isometric scaling worked remarkably well despite the different complex shapes of the individual carpals. This suggests that the trend between bone dimension and bone volume is independent of the specific carpal. The major drawback of our simple scaphoid-based scaling technique is that it underestimated the full range of bone volumes for 3 of the carpals (lunate, pisiform, trapezium) and it overestimated the range of volumes for 1 of the carpals (the hamate). This fact can best be appreciated by comparing the ends of the scaled curves in Figure 4 with the volume data of some subjects. It is possible that a more sophisticated extrapolation scheme may result in tighter coverage of the volume range for all of the carpals. The accuracy of this very simple strategy, however, is compelling and it has tremendous potential for scaling throughout the midrange of carpal sizes. As good as our simple scaling algorithm is, it only correlates the linear dimensions of the carpals with carpal volume; the change in carpal shape is ignored. Clearly carpal shape is complex, and simply describing it mathematically, let alone scaling it, is extremely difficult. Although we found no gender-related differences in normalized carpal volume or carpal dimensions, there is evidence that there are gender-related shape differences in at least one of the carpals that may predispose to an increased risk for osteoarthritis. In particular the portion of the trape-
zium that articulates with the first metacarpal in women is smaller, relatively more convex, and less congruent than that in men.13 Ultimately models that incorporate shape may provide added benefit, as would those that include information about the location and thickness of articular cartilage. The authors gratefully acknowledge the assistance and insights provided by Edward Akelman, MD, Arnold-Peter C. Weiss, MD, and Scott W. Wolfe, MD.
References 1. Brumfield RH Jr, Nickel VL, Nickel E. Joint motion in wrist flexion and extension. South Med J 1966;59:909 –910. 2. Wolfe SW, Neu C, Crisco JJ. In vivo scaphoid, lunate, and capitate kinematics in flexion and in extension. J Hand Surg 2000;25A:860 – 869. 3. Neu CP, Crisco JJ, Wolfe SW. In vivo kinematic behavior of the radio-capitate joint during wrist flexion– extension and radio-ulnar deviation. J Biomech 2001;34:1429 –1438. 4. Schuind FA, Linscheid RL, An K-N, Chao EYS. A normal data base of posteroanterior roentgenographic measurements of the wrist. J Bone Joint Surg 1992;74A:1418 –1429. 5. Patterson RM, Elder KW, Viegas SF, Buford WL. Carpal bone anatomy measured by computer analysis of threedimensional reconstructions of computed tomography images. J Hand Surg 1995;20A:923–929. 6. Crisco JJ, McGovern RD. Efficient calculation of mass moments of inertia for segmented homogenous three-dimensional objects. J Biomech 1998;31:97–101. 7. Kaawach W, Ecklund K, Di Canzio J, Zurakowski D, Waters PM. Normal ranges of scapholunate distance in children 6 to 14 years old. J Pediatr Orthop 2001;21:464 – 467. 8. Middleton A, MacGregor D, Compson JP. An anatomical database of carpal bone measurements for intercarpal arthrodesis. J Hand Surg 2003;28B:315–318. 9. Watson HK, Yasuda M, Guidera PM. Lateral lunate morphology: an x-ray study. J Hand Surg 1996;21A:759 – 763. 10. Neu CP, McGovern RD, Crisco JJ. Kinematic accuracy of three surface registration methods in a three-dimensional wrist bone study. Trans ASME, J Biomech Eng 2000;122: 528–533. 11. Gupta A, Al-Moosawi NM. Lunate morphology. J Biomech 2002;35:1451–1457. 12. Canovas F, Banegas F, Cyteval C, Jaeger M, DiMéglio A, Bonnel F, et al. Carpal bone maturation assessment by image analysis from computed tomography scans. Horm Res 2000; 54:6 –13. 13. Ateshian GA, Rosenwasser MP, Mow VC. Curvature characteristics and congruence of the thumb carpometacarpal joint: differences between female and male joints. J Biomech 1992;25:591– 607.
Purpose: The purpose of this study was to quantify carpal bone size, to determine whether gender influences carpal size, and to determine whether small and large carpal bones differ in size only by simple isometric scaling. Methods: Cortical surfaces of all carpal bones in both wrists of 14 women and 14 men (ages 22–34 y) were reconstructed from computed tomography (CT) volume images. Carpal volume and boundingbox dimensions in 3 orthogonal directions were calculated and compared across genders. An average set of carpal bones were then scaled mathematically by a single factor in all directions (scaled isometrically) and compared across carpal bones of all sizes. Results: Although female carpal bones were significantly smaller than male carpal bones, individual carpal volume as a percentage of the volume of the entire carpus did not differ with gender. The 3 orthogonal bounding-box dimensions of the carpal bones scaled nearly isometrically from the smallest to the largest bones. Conclusions: Across the wide range of wrist sizes studied the individual carpal volumes were a consistent percentage of carpus volume and this percentage did not differ with gender. Despite their complex shape the bounding dimensions of the carpal bones increased isometrically with increasing volume. The extensive database of dimensions provided in this study should be useful in the design and insertion of fixation systems and implants. (J Hand Surg 2005;30A:35– 42. Copyright © 2005 by the American Society for Surgery of the Hand.) Key words: Carpals, volume, dimensions, scaling, 3-dimensional.
The carpus contains a uniquely passive set of bony articulations. Of the 19 muscles in the forearm that function to position the hand space, only the flexor carpi ulnaris generally inserts on the carpus (pisiform
From the Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, Providence, RI; and the Division of Engineering, Brown University, Providence, RI. Received for publication June 10, 2004; accepted in revised form August 24, 2004. Supported by a National Institutes of Health grant (AR44005). No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article. Reprint requests: Joseph J. Crisco, PhD, Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, CORO West, Suite 404, 1 Hoppin St, Providence, RI 02903. Copyright © 2005 by the American Society for Surgery of the Hand 0363-5023/05/30A01-0005$30.00/0 doi:10.1016/j.jhsa.2004.08.012
and hook of the hamate); the remainder insert on the metacarpals or phalanges. Accordingly the motion of the hand relative to the arm is defined by the complex bone shapes, intricate bony articulations, and unique ligamentous attachments in the carpus. As the forearm muscles position the hand, carpal motion is determined by bony articulations and the range is limited by their ligament attachments. The contribution of the individual carpal bones to overall wrist motion appears to be similar in men and women. An early study of carpal motion during wrist flexion and extension revealed no gender-related differences in rotations at the midcarpal joint.1 Similarly more recent studies of carpal kinematics in vivo by using computed tomography (CT)-based markerless bone registration techniques have found no differences in the magnitude of carpal rotation in men The Journal of Hand Surgery
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The Journal of Hand Surgery / Vol. 30A No. 1 January 2005
and women during flexion and extension.2,3 In both men and women scaphoid rotation was measured to be 73% of capitate rotation in flexion and 99% of capitate rotation in extension, whereas lunate rotation was 46% as much as the capitate in flexion and 68% as much as the capitate in extension.2 Although carpal motion appears to be similar in men and women there are differences in the location of the rotation axes. In particular the rotation axes of the carpal bones in women are located more proximally than in men.3 This suggests that the differences in rotation axis location may be due to differences in bone size, as opposed to some functional differences. Anatomic studies of the carpal bones that verify or catalogue prominent anatomic features and sizes using 2-dimensional4 and 3-dimensional5 imaging tools have created general criteria for normal and abnormal bone shape and size, although scaling ratios and dimensions have not been addressed. This study was performed to determine whether the gender-related differences in carpal size are simply due to scaling. To determine this we tested the hypotheses that the volume of each carpal relative to the total volume of the carpus did not differ according to gender and that carpal dimensions scale isometrically, by an identical factor in all directions.
Materials and Methods Subjects and Image Acquisition With approval from our Institutional Review Board and after obtaining informed consent, 28 volunteers were recruited for study. Potential volunteers were eligible for inclusion if they were between the ages of 18 and 30 years and had no history of wrist injury or chronic disease that might affect the soft tissues in the wrist. Subjects specifically were excluded if they had a history of wrist or forearm fracture, prior wrist surgery, or severe osteoarthritis or connective tissue disease. At enrollment a detailed history was taken and a detailed wrist examination was performed by a fellowship-trained hand surgeon, and posteroanterior, lateral, and anteroposterior grip radiographs were performed. The enrolled study population included 14 men (mean age, 25.6 y; range, 22–34 y) and 14 women (mean age, 23.6 y; range, 22–30 y). Both wrists of each subject were imaged simultaneously with a computed tomography scanner (GE HiSpeed Advantage; GE Medical, Milwaukee, WI). During scanning the subjects were seated at the back of the scanner with their forearms and hands extended into the gantry, parallel to the long axis of the
Figure 1. The right wrist bones of 1 subject rendered from a volar (palmar) view with the centroid and inertial axes of each carpal. The centroid is the geometric center of the cortical bone shell and the inertial axes are colored by their inertial magnitude from smallest (red), to medium (green), to largest (blue) (see also Fig. 2). The proximal row contains the scaphoid (SCA), lunate (LUN), triquetrum (TRQ), and pisiform (PIS), and the distal row contains the trapezium (TPM), trapezoid (TPD), capitate (CAP), and hamate (HAM). The radius (RAD) and ulna (ULN) also are depicted.
scanner table. Contiguous 1.0-mm transverse slices were acquired of the entire carpus as the wrist was scanned from the distal radius to the proximal metacarpals. The images were acquired at either 120 kVp and 80 mA or 80 kVp and 120 mA. The voxel size of the reconstructed images ranged from 0.2 mm x 0.2 mm x 1.0 mm to 0.9 mm x 0.9 mm x 1.0 mm.
Image Processing and Bone Dimension Calculations Each of the 8 individual carpal bones from each wrist were segmented from the CT volume images and then bone centroid locations, principal inertial axes, and volumes were calculated (Fig. 1). In brief, for each CT slice a series of points, or surface contours, was generated for each bone. The contours then were grouped by bone and surface fit by using commercially available software programs (Analyze; Mayo Foundation, Rochester, MN; Geomagic; Raindrop, Durham, NC). The volumes, centroid locations, and principal inertial axes for each bone were calculated by using software routines written in a software program (Matlab; Mathworks, Natick, MA).6 For any object (bone) there are always 3 orthogonal principal inertial axes, each with an associated iner-
Crisco et al / Carpal Bone Size and the Genders
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Figure 2. The X, Y, and Z bounding-box dimensions for the average-sized set of carpal bones that also were used for carpal scaling. The dimensions of each carpal were defined by the rectangular bounding boxes whose sides are oriented parallel to the inertial axes and intersected the most distant points on the bone surface. The inertial axes are ordered by their inertial magnitude, from smallest (X), to medium (Y), to largest (Z).
tial magnitude. Inertial magnitudes are a measure of the mass distribution about the respective axis: the further the mass is distributed away from the axis the higher the inertial magnitude. In this article we assume all bones have the same density, therefore the inertial magnitude is a geometric measure of bone size when viewed along an inertial axis. Finally the volumes of each of the 8 carpal bones in a given wrist then were summed to yield a value for the total carpus volume. For the purposes of our analysis the dimensions of the carpal bones were defined to be the maximum lengths parallel to the principal axes of inertia. To calculate the lengths we generated rectangular bounding boxes with sides parallel to the inertial axes to enclose the bones. The sides of the bounding boxes were located at the most distant points on the bone surface in each inertial direction. The X, Y, and Z dimensions of the bounding box correspond to the dimensions parallel to the smallest, middle, and largest inertial magnitudes, respectively (Fig. 2).
Gender and Size Analysis Two comparisons were made to explore potential differences in carpal size in men and women. For the first we directly compared the mean volumes for each of the 8 carpals. For the second we compared the percentage of the entire carpus occupied by each carpal, defined as carpal bone volume divided by carpus volume. Statistical comparisons were made with Student t tests (only 1 randomly selected wrist was used from each volunteer); p values less then .05 were considered statistically significant.
Isometric Scaling Trends in carpal size (scaling) were examined by plotting bounding-box dimensions of each bone as a function of carpal volume, and then comparing these bounding-box dimensions with those generated by isometrically scaling the average-sized set of bones. The bones used for scaling were taken from a patient whose carpal volumes most closely matched the means for the carpals from all subjects (in this dataset
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we used a male subject with carpal volumes within 12% of the average for all subjects). Once an average-sized set of bones was identified (Fig. 2) a set of volume-scaling factors was calculated with respect to the scaphoid: the first scaled the scaphoid volume down to the smallest scaphoid volume in the database, the second scaled the scaphoid volume up to the largest scaphoid volume in the database, and then 5 additional scaling factors were calculated to yield volumes evenly spaced between the smallest and largest volumes. Cube roots were taken of each of these 7 volume-scaling factors, yielding a set of 7 linear scaling factors that then were multiplied by the x, y, and z surface coordinates of the average-sized set of bones, yielding 7 different scaled versions of each carpal. Each scaled version of the 8 carpal bones then was treated as a newly segmented bone for which bounding boxes were generated, and the linear dimensions and carpal volumes were calculated (as described earlier). An interpolating third-order polynomial then was fit in each dimension to the 7 scaled values as a function of bone volume. To evaluate whether the trend in increasing dimensions with volume could be attributed to isometric scaling the root-mean-square difference between all database values and the scaled interpolated values were calculated, along with R2 values.
Results Our first analysis revealed that the rank order of each carpal volume was the same in the men and women and that on average the carpal bones in the men were larger than those in the women (Fig. 3A, Table 1). For both genders the capitate was the largest bone, followed by the hamate, scaphoid, trapezium, lunate, triquetrum, trapezoid, and pisiform. On average the volumes of the carpal bones in the women were 38% smaller than the corresponding carpal volumes in the men; the difference was largest with the lunates (46%) and smallest with the triquetrums (34%). There were, however, no differences in the relative sizes of the carpal bones in men and women, and the carpal bones from both genders scaled on a continuum. When normalized carpus bone volumes (carpal bone volume/total carpus volume) were compared there were no significant gender-related differences for any of the bones (Fig. 3B). Across all bones the mean difference in normalized carpal volume was less than 1% with no discernable gender bias for any bone’s normalized volume. Graphs of the X, Y, and Z bounding-box dimensions of the carpal bones revealed that the carpal dimensions increased as a
Figure 3. Graphs of the (A) average and (B) average normalized carpal volumes for men and women. (A) All of the average carpal volumes in women were significantly smaller than the corresponding volumes in men (*, p ⬍ .05). (B) The percentage of the carpus volume occupied by each bone was the same, however, for both genders.
function of volume for each of the carpal bones (Fig. 4) and that the relationship was similar in both men and women (with substantial overlap of the bone dimensions and volume from some of the smaller men and larger women). Isometric scaling of the carpal bones provided a reasonable approximation of the experimentally acquired data. The plots of the isometrically scaled bones were slightly nonlinear (cubic) and closely matched the values plotted for the bones from all of the subjects (Fig. 4). The use of the scaphoidderived scaling factors, however, underpredicted the range of lunate, trapezium, and pisiform dimensions, and overpredicted the range of hamate dimensions (Fig. 4). The root-mean-square difference between the interpolated scaled and raw data was approximately 1 mm on average (Table 2). The R2 values for the interpolated scaled data
Crisco et al / Carpal Bone Size and the Genders
39
Table 1. Average (ⴞ 1 SD) Carpal Bone Volume (mm3) and X, Y, and Z Bounding-Box Dimensions (mm) Were Significantly Smaller in Women Than in Men Men (n ⴝ 14) Scaphoid Vol X Y Z Lunate Vol X Y Z Triquetrum Vol X Y Z Pisiform Vol X Y Z Trapezium Vol X Y Z Trapezoid Vol X Y Z Capitate Vol X Y Z Hamate Vol X Y Z
Women (n ⴝ 14)
Men and Women
2,903.2 29.3 17.8 14.1
⫾ ⫾ ⫾ ⫾
461.0 2.7 1.2 0.9
1,877.0 24.8 15.3 12.2
⫾ ⫾ ⫾ ⫾
407.3 1.6 1.5 0.6
2,390.1 27.0 16.5 13.1
⫾ ⫾ ⫾ ⫾
673.6 3.1 1.8 1.2
2,252.0 20.9 20.1 14.4
⫾ ⫾ ⫾ ⫾
499.4 2.2 1.8 1.3
1,368.2 18.0 16.9 11.9
⫾ ⫾ ⫾ ⫾
165.0 1.1 0.8 0.8
1,810.1 19.4 18.5 13.2
⫾ ⫾ ⫾ ⫾
578.5 2.3 2.2 1.7
1,579.7 20.9 14.9 12.6
⫾ ⫾ ⫾ ⫾
261.3 1.8 0.7 0.9
1,103.9 18.5 13.3 10.8
⫾ ⫾ ⫾ ⫾
193.7 1.3 0.6 0.7
1,341.8 19.7 14.1 11.7
⫾ ⫾ ⫾ ⫾
331.0 2.0 1.0 1.2
854.3 15.7 12.3 10.0
⫾ ⫾ ⫾ ⫾
203.3 1.4 1.3 1.2
569.6 13.7 10.7 8.9
⫾ ⫾ ⫾ ⫾
121.8 1.4 1.0 0.7
712.0 14.7 11.5 9.5
⫾ ⫾ ⫾ ⫾
219.6 1.7 1.4 1.1
2,394.8 25.4 17.5 16.1
⫾ ⫾ ⫾ ⫾
443.6 1.8 1.8 1.8
1,547.1 21.8 15.8 13.1
⫾ ⫾ ⫾ ⫾
328.9 1.8 1.5 1.2
1,970.9 23.6 16.6 14.6
⫾ ⫾ ⫾ ⫾
576.7 2.5 1.8 2.2
1,497.1 20.6 15.5 12.3
⫾ ⫾ ⫾ ⫾
237.2 1.4 0.8 0.7
1,020.4 18.0 13.3 11.1
⫾ ⫾ ⫾ ⫾
191.5 0.9 1.2 0.8
1,258.7 19.3 14.4 11.7
⫾ ⫾ ⫾ ⫾
321.6 1.8 1.5 1.0
3,700.6 28.0 20.8 16.0
⫾ ⫾ ⫾ ⫾
563.9 1.8 1.7 1.6
2,547.1 24.6 18.2 13.9
⫾ ⫾ ⫾ ⫾
344.6 1.1 1.0 0.8
3,123.9 26.3 19.5 15.0
⫾ ⫾ ⫾ ⫾
743.7 2.3 1.9 1.6
2,940.7 27.5 23.0 16.9
⫾ ⫾ ⫾ ⫾
378.1 1.9 1.8 1.2
2,045.1 24.7 20.1 15.0
⫾ ⫾ ⫾ ⫾
264.2 1.4 0.8 0.9
2,492.9 26.1 21.6 16.0
⫾ ⫾ ⫾ ⫾
555.5 2.2 2.0 1.4
Values are for both wrists.
compared with the raw data ranged from .08 to .81 (Table 2).
Discussion This study was performed as a first step in determining whether the gender-related differences in carpal size are caused by scaling or whether they represent more complex changes in carpal shape. Our data suggest that the differences primarily are caused by simple scaling. Although we did find gender-related differences in carpal volume for each of the 8 carpal
bones, those differences vanished when we compared the normalized volumes of the bones (ie, the relative amount of the carpus that each bone occupies). In other words the size of each carpal remained fairly constant relative to the size of the rest of the carpus in both genders. Moreover when we plotted carpal dimensions we found that the dimensions of men’s and women’s bones fell on the same continuum; there was no distinct volume or dimension that separated the two genders. Finally we found that isometrically scaling an average-sized set of bones
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The Journal of Hand Surgery / Vol. 30A No. 1 January 2005
Figure 4. Each carpal dimension increased with increasing carpal volume and this relationship did not differ between men and women. When an average-sized set of carpal bones were scaled isometrically (by the factors for the smallest and largest scaphoid) the resulting relationship between dimension and volume shown by the scaled X, Y, and Z curves was similar to the values for all patients (see also Table 2). Some bones, such as the lunate, of some patients had a larger volume than predicted where the data points lie outside the volume range of the scaled X, Y, and Z curves.
Crisco et al / Carpal Bone Size and the Genders
Table 2. The Root–Mean–Square Differences (mm) in the Bounding-Box Dimensions Between the Isometrically Scaled and Carpal Bone Database for all Wrists X Scaphoid Lunate Triquetrum Pisiform Trapezium Trapezoid Capitate Hamate
1.39 1.10 1.27 0.81 1.31 1.21 1.10 1.14
(0.79) (0.76) (0.55) (0.77) (0.72) (0.50) (0.76) (0.72)
Y 0.91 1.04 0.98 0.81 1.34 1.39 1.30 0.97
(0.74) (0.75) (0.08) (0.66) (0.45) (0.11) (0.52) (0.76)
Z 0.71 1.17 0.53 0.55 1.31 0.80 1.38 0.74
(0.64) (0.48) (0.81) (0.75) (0.61) (0.32) (0.23) (0.71)
R2 values are listed in parentheses.
predicted reasonably well the dimensions of the bones from most subjects. We used 3-dimensional imaging techniques that built on data that traditionally has been generated via the analysis of plane radiographs. Because they are widely used clinically, plane radiographs are used most often to classify the shape or determine the size of the carpal bones.7–9 The accuracy of the data generated with plane radiographs, however, is dependent on the orientation of the wrist as the x-ray is taken. For example, lunate morphology, which may influence wrist stability, can be assigned incorrectly with relatively minor changes in x-ray technique.9 Three-dimensional techniques are an improvement because they capture shape and volume information that is unavailable on plane films and they reflect the true cortical size and volume of the carpals. We calculated our carpal dimensions with the use of bounding boxes whose sides were parallel to the principal axes of inertia. We chose to base our bounding boxes on the inertial axes because their calculation from CT volume images is accurate and robust (ie, only minimally affected by small changes in carpal shape). The error associated with locating and orienting the inertia axes is less than 1.0 mm and 2.0°, respectively.10 The objectivity of bounding-box placement and the simplicity of dimensioning ensures the accuracy and repeatability of these measurements. This method, however, also has inherent limitations. Although the method is useful to explain overall dimensions and size relationships, it oversimplifies the more intricate and complex features of the bones’ irregular shapes. A more rigorous definition of shape should lead to a more exact description of each bone and a more detailed understanding of how different factors change with size. Another potential
41
disadvantage is that the dimensions we report, which reflect lengths parallel to the principal inertial axes, do not necessarily correlate with the dimensions typically measured on standard clinical radiographs. Ultimately this can be solved with relatively straightforward kinematic transformations, however, this is beyond the scope of the current article. Our findings regarding the dimensions of the carpals generally are consistent with previous studies of carpal bone geometry performed with both 2-dimensional and 3-dimensional methodologies. Typically they have found that the carpals in women are smaller than those in men.4,5,11 Extensive 2-dimensional measurements were made by Schuind et al4 on posteroanterior radiographs of men and women in 2 age groups (25– 40 y, 41– 60 y). All of their average linear measurements were smaller in women than in men, but their measurements of intercarpal angles were the same in both genders. This lack of difference in angles by gender is consistent with our finding that normalized carpal size was the same in men and women because angles do not change with isometric scaling. Our study population was limited to a single age group, but Schuind et al4 found no differences in carpal size with age other than some agerelated narrowing in joint space. They also found that maximum grip force correlated with increasing length of the third metacarpal. Patterson et al5 measured carpal volume and antipodal axis length (the distance between the 2 most distant points on the bone surface) from reconstructed CT scans. They found that on average both were larger in men than in women. It is impossible to make direct comparisons between our bone dimension measurements and theirs, however, because the antipodal axis is not necessarily the same as the inertial axis. Subsequently Gupta and Al-Moosawi11 characterized lunate morphology, again using reconstructed CT scans. They did not stratify their results by gender, however, and their dimensions reflect lengths in the axial, coronal, and sagittal planes. Our dimensions for the lunate are larger than theirs but this most likely reflects differences in the method of measurement rather than true differences in bone size. We found that the gender-related differences in carpal size completely disappeared when the individual bone volumes were normalized by total carpus volume. Although the mean sizes of the carpal bones in the women were smaller than those of the men, they each occupied the same percentage of the total carpus volume. This suggests that there are not any large, systematic, gender-specific variations in bone
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size. It does not rule out the presence of smaller local changes (or combinations of changes that offset one another), however, which simple volume analysis would miss. In a 3-dimensional study of carpal size with bone maturation, Canovas et al12 reported that the volume of each carpal was highly correlated with the volume of all other carpals across the ages of 4 to 15 years. Although we cannot compare these values directly with ours, it is fascinating to note that the mineralized volume of one carpal relative to others remains relatively consistent during skeletal maturation, as we found in mature skeletons of different sizes. By using a single set of factors generated by scaling an average-sized scaphoid bone to the largest and smallest volumes recorded in the study we were able to match the trends between bone dimension and bone volume determined experimentally for each of the other 7 carpals. Simple isometric scaling worked remarkably well despite the different complex shapes of the individual carpals. This suggests that the trend between bone dimension and bone volume is independent of the specific carpal. The major drawback of our simple scaphoid-based scaling technique is that it underestimated the full range of bone volumes for 3 of the carpals (lunate, pisiform, trapezium) and it overestimated the range of volumes for 1 of the carpals (the hamate). This fact can best be appreciated by comparing the ends of the scaled curves in Figure 4 with the volume data of some subjects. It is possible that a more sophisticated extrapolation scheme may result in tighter coverage of the volume range for all of the carpals. The accuracy of this very simple strategy, however, is compelling and it has tremendous potential for scaling throughout the midrange of carpal sizes. As good as our simple scaling algorithm is, it only correlates the linear dimensions of the carpals with carpal volume; the change in carpal shape is ignored. Clearly carpal shape is complex, and simply describing it mathematically, let alone scaling it, is extremely difficult. Although we found no gender-related differences in normalized carpal volume or carpal dimensions, there is evidence that there are gender-related shape differences in at least one of the carpals that may predispose to an increased risk for osteoarthritis. In particular the portion of the trape-
zium that articulates with the first metacarpal in women is smaller, relatively more convex, and less congruent than that in men.13 Ultimately models that incorporate shape may provide added benefit, as would those that include information about the location and thickness of articular cartilage. The authors gratefully acknowledge the assistance and insights provided by Edward Akelman, MD, Arnold-Peter C. Weiss, MD, and Scott W. Wolfe, MD.
References 1. Brumfield RH Jr, Nickel VL, Nickel E. Joint motion in wrist flexion and extension. South Med J 1966;59:909 –910. 2. Wolfe SW, Neu C, Crisco JJ. In vivo scaphoid, lunate, and capitate kinematics in flexion and in extension. J Hand Surg 2000;25A:860 – 869. 3. Neu CP, Crisco JJ, Wolfe SW. In vivo kinematic behavior of the radio-capitate joint during wrist flexion– extension and radio-ulnar deviation. J Biomech 2001;34:1429 –1438. 4. Schuind FA, Linscheid RL, An K-N, Chao EYS. A normal data base of posteroanterior roentgenographic measurements of the wrist. J Bone Joint Surg 1992;74A:1418 –1429. 5. Patterson RM, Elder KW, Viegas SF, Buford WL. Carpal bone anatomy measured by computer analysis of threedimensional reconstructions of computed tomography images. J Hand Surg 1995;20A:923–929. 6. Crisco JJ, McGovern RD. Efficient calculation of mass moments of inertia for segmented homogenous three-dimensional objects. J Biomech 1998;31:97–101. 7. Kaawach W, Ecklund K, Di Canzio J, Zurakowski D, Waters PM. Normal ranges of scapholunate distance in children 6 to 14 years old. J Pediatr Orthop 2001;21:464 – 467. 8. Middleton A, MacGregor D, Compson JP. An anatomical database of carpal bone measurements for intercarpal arthrodesis. J Hand Surg 2003;28B:315–318. 9. Watson HK, Yasuda M, Guidera PM. Lateral lunate morphology: an x-ray study. J Hand Surg 1996;21A:759 – 763. 10. Neu CP, McGovern RD, Crisco JJ. Kinematic accuracy of three surface registration methods in a three-dimensional wrist bone study. Trans ASME, J Biomech Eng 2000;122: 528–533. 11. Gupta A, Al-Moosawi NM. Lunate morphology. J Biomech 2002;35:1451–1457. 12. Canovas F, Banegas F, Cyteval C, Jaeger M, DiMéglio A, Bonnel F, et al. Carpal bone maturation assessment by image analysis from computed tomography scans. Horm Res 2000; 54:6 –13. 13. Ateshian GA, Rosenwasser MP, Mow VC. Curvature characteristics and congruence of the thumb carpometacarpal joint: differences between female and male joints. J Biomech 1992;25:591– 607.