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Coordinate systems for the carpal bones of the wrist
ARTICLE IN PRESS
Journal of Biomechanics 40 (2007) 203–209
Short communication
www.elsevier.com/locate/jbiomech www.JBiomech.com
Coordinate systems for the carpal bones of the wrist James C. Coburna, Mohammad A. Upalb, Joseph J. Criscoa,b, a
Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, 1 Hoppin Street, CORO West, Suite 404, Providence, Rhode Island 02903, USA b Division of Engineering, Brown University, Providence, RI, USA Accepted 18 November 2005
Abstract The eight small and complexly shaped carpal bones of the wrist articulate in six degrees of freedom with each other and to some extent with the radius and the metacarpals. With the increasing number and sophistication of studies of the carpus, a standardized definition for a coordinate system for each the carpal bones would aid in the reporting and comparison of findings. This paper presents a method for defining and constructing a coordinate system specific to each of the eight carpal bones based upon the inertial properties of the bone, derived from surface models constructed from three-dimensional (3-D) medical image volumes. Surface models from both wrists of 5 male and 5 female subjects were generated from CT image volumes in two neutral wrist positions (functional and clinical). An automated algorithm found the principal inertial axes and oriented them according to preset conditions in 85% of the bones, the remaining bones were corrected manually. Six of the eight carpal bones were significantly more extended in the functional neutral position than in the clinical neutral position. Gender had no significant effect on carpal bone posture in either wrist position. Correlations between the 3-D carpal posture and the commonly used 2-D clinical radiographic carpal angles are established. 3-D coordinate systems defined by the anatomy of the carpal bone, such as the ones presented here, are necessary to completely describe 3-D changes in the posture of the carpal bones. r 2005 Elsevier Ltd. All rights reserved. Keywords: Carpal bones; Coordinate system; Three-dimensional; Posture
1. Introduction The carpus of the wrist consists of eight complexly shaped carpal bones located between the radius and ulna and the five metacarpals. Diagnoses of ligament injuries or progressive deformities are supported by distance and angle measurements between the carpal bones made on plane radiographs (Watson et al., 1997). While they clearly have clinical value, 2-D measurements have limited research value because of the complex shape (Crisco et al., 2005) and 3-D motions Corresponding author. Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, 1 Hoppin Street, CORO West, Suite 404, Providence, Rhode Island 02903, USA. Tel.: 401 444 4231; fax: 401 444 4418. E-mail address: [email protected] (J.J. Crisco).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.11.015
of the carpal bones (Kobayashi et al., 1997). Methods employing the entire carpal geometry can improve clinical diagnosis (Belsole et al., 1991a). Recently, MRI and CT imaging has been used to visualize the 3-D function of the carpus and to measure its complex motions (Crisco and Neu, 2000; Crisco et al., 2003; Moojen et al., 2002b; Moojen et al., 2002a; Moritomo et al., 2000). Describing complete carpal motion is a difficult undertaking, however because each carpal bone can have up to six degrees of freedom. One hurdle is the lack of standardized coordinates systems in the carpus. The International Society of Biomechanics (ISB) has recently proposed joint coordinate system guidelines for the shoulder, elbow, wrist and hand (Wu et al., 2005). The task was vast and well executed, however they proposed carpal coordinate systems whose orientations were parallel to the radius in the neutral
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position. A limitation of this method is that crucial information on the variations in carpal posture is lost. The purpose of this communication is to present coordinate systems for each carpal bone and a method for constructing these coordinate systems. We also present data on the 3-D carpal postures for healthy wrists in two common reference positions, clinical and functional neutral, using these coordinate systems.
custom routines (Crisco and McGovern, 1998). The principal inertial axes, three orthogonal lines through the centroid of each bone, were arranged in order of ascending inertial magnitude, X-axis (red), Y-axis (green), and Z-axis (blue). The orientations of these axes, relative to the bone model, are unique and subject specific but their direction, or sense, is not (Fig. 1). The variation across subjects was the motivation for our analysis of postures.
2. Methods
2.4. Radius and ulna coordinate systems
2.1. Carpal bone models
The inertial axes of the radius and ulna cannot typically be calculated because they are not fully imaged. Radial and ulnar coordinate systems, however, can be crucial to studies of the carpus. Therefore, coordinate systems for the radius (XrYrZr) (Crisco et al., 2003) and ulna (XuYuZu) (Moore et al., 2002) were constructed from anatomical landmarks similar to Kobayashi et al. (1997). Radial coordinate systems have been used extensively to describe both carpal and wrist motion, while ulnar coordinate systems have typically been used only to describe the motion of the radius. Xr: A line fit through the centroids of the radial diaphysis (shaft). Simply, the axis coincides with the radial long axis. Pronation of the carpal bones and wrist corresponds to positive rotation. Yr: Directed through the radial styloid and defined perpendicular to the Xr. Flexion (+Yr) and extension (Yr) rotations were measured around this axis. Zr: Directed palmarly (volarly) and calculated from the cross product of Xr and Yr. Ulnar (+Zr) and radial (Zr) deviation were measured around this axis. Originr: Defined by the intersection of Xr and the distal radial articular surface. Xu: A line fit through the centroids of the ulnar diaphysis (shaft). Simply, the axis coincides with the ulnar long axis. Pronation corresponds to positive rotation. Yu: Directed radially, along a vector passing through the tip of the ulnar styloid, defined by the centroids of the styloid. Calculated from the cross product of Xu and Zu. Zu: Directed palmarly, perpendicular to a plane defined by Xu and the tip of the ulnar styloid. Originu: Defined by the intersection of Xu with the distal ulnar articular surface.
Digitally defined carpal bone meshes, such as those generated from CT volume images were used to generate the carpal coordinate systems. Approaches to generating these surfaces meshes have been described by Woolson et al. (Woolson et al., 1985) and others (Belsole et al., 1991a; Moritomo et al., 2000; Snel et al., 2000). The coordinate system definitions are independent of the method of surface generation, but we use the approach established by Crisco et al. (2001). Briefly, CT volume images of the carpus were acquired. The outer contours of each slice were digitized with a biomedical image processing program (Analyze, Rochester, MN). The contours were then grouped into bones using custom algorithms (MS Visual C++, Redmond WA) and fit with a surface mesh (Geomagic, Raindrop, Durham, NC). 2.2. Subjects and image acquisition With approval from our Institutional Review Board, and after obtaining informed consent, ten volunteers (five male, average age 31 years, range 22–47 years, and five female average age 21.8 years, range 21–22 years) were recruited into the study. Volunteers with no history of wrist injury or chronic disease that might affect the wrist were considered. Both wrists of each subject were imaged simultaneously with a GE HiSpeed Advantage CT scanner (GE Medical, Milwaukee, WI). Contiguous, 1.0 mm, transverse slices of the entire carpus were acquired at a resolution between 0.2 and 0.4 mm. The functional neutral wrist position was imaged while the subjects were comfortably grasping a rubber bicycle handle in neutral supination–pronation. The clinical neutral wrist position, defined as the position where the long axes of the radius, capitate and third metacarpal are parallel, was interpolated from multiple CT scans at both 30 and 601 of flexion and 30 and 601 of extension(Coburn and Crisco, 2005). 2.3. Calculating inertial properties and axes The mass centroids and principal inertial axes for each bone were calculated using previously described,
2.5. Carpal bones coordinate systems A unique positive direction, or sense, for each inertial axis must be defined for each carpal bone coordinate system (XcYcZc). To this end, the inertial axes in the functional neutral were described in the radial coordinate system (RCS) and then analyzed with a custom algorithm.
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Fig. 1. While inertia axes are unique for each bone surface model, the sense of the axes is not. The capitate bone is shown in the proposed, standardized inertial based coordinate system colored (X-red; Y-green; Z-blue) (a) and another possible version (b).
Fig. 2. (a) Definition of spherical coordinate angles in the radial coordinate system. (b) Measurement of the flexion angle, y, on the scaphoid. Carpal axes are scaled to their inertial magnitude.
The algorithm compared carpal axes Xc and Yc consecutively to each RCS axis and changed carpal axis sense by negating the inertial vector, based on testing criteria. A test was considered to be failed if the carpal axis was oriented within one determination interval (DI) of the orthogonal plane to that RCS axis and the next test was run. Once one test was passed, the remaining tests for that carpal axis were skipped. Xc was run with a DI of 7151, while Yc was tested using a DI of 751. Zc was calculated from the cross-product of Xc and Yc to ensure the coordinate system was right handed. 1st test: Carpal axis compared to Xr, making the sense distal if passed. 2nd test: Carpal axis compared to Zr, making the sense radial if passed. 3rd test: Carpal axis compared to Yr, making the sense palmar. This test used no DI. All inertial axes for all bones were then displayed concurrently for verification. The second or third
axes in some cylindrically shaped bones were not always uniquely defined so manual intervention was required. 2.6. Carpal bone posture in 3-D One inertial axis was chosen as a reference to describe carpal bone orientation with respect to the RCS, using spherical azimuth (y) and elevation (j) angles (Fig. 2a). Azimuth angle described flexion (positive) and extension (negative), whereas elevation angle described radial (negative) and ulnar (positive) deviation. Postures for all carpal bones except the lunate were calculated from Xc (Fig. 2b). The lunate’s posture was calculated from Zc. Flexion-extension and radioulnar carpal bone postures in the neutral positions were compared separately using Student’s t-tests. Effect of gender on neutral posture was also analyzed using Student’s t-tests. po0.05 was considered significant.
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2.7. Inertial defined coordinate systems and clinically defined angles
manually corrected to fit the standard definition of the coordinate system.
The orientations of the inertial-defined coordinate systems were compared to six clinical angles, the radiocapitate (RC), radio-scaphoid (RS), radio-lunate (RL), scapho-lunate (SL), capito-lunate (CL), and capitoscaphoid (CS) angles defined by lines drawn on a lateral radiograph using clinical landmarks (Green et al., 1999):
3.2. Carpal posture
Radius: Capitate: Scaphoid: Lunate:
The long axis. The midline, long axis. The midline through each tubercle. The midline, perpendicular to the lunate horns.
Clinical and inertial posture were correlated by examining the difference between the clinical long axis of the capitate and its first inertial axis. Simulated X-rays of the distal radius, lunate, capitate, and proximal portions of the third metacarpal were made from a subset of the CT scans and the clinical angles were measured by multiple researchers. A computer algorithm found the approximate carpal angles using a projection of the appropriate inertial axes onto the anterior–posterior (XrZr) plane, a linear trend line was fit to the all data and an R2 value calculated.
Carpal bones of the functional neutral were significantly more extended (po0.05) than those in the clinical neutrals with the exception of the pisiform and lunate. (Fig. 4) Radioulnar deviation posture of the carpal bones was not different between the clinical and functional neutral wrist positions. Gender also had no significant effect on carpal bone posture in either neutral wrist position (Fig. 5). 3.3. Comparing coordinate systems with clinically defined angles In clinical neutral, the capitate inertial axis was in an average 13.3174.91 extension. 3-D reconstruction in a computed wrist posture of 13.31 extension confirmed this. (Fig. 6) A linear regression between the clinically measured carpal angles and inertial-computed carpal angles showed high correlation values (R24.85) for the RC, RS and RL angles and low correlation values (R2 p.6) for the CS,CL, and SL angles. (Fig. 7)
4. Discussion 3. Results 3.1. Coordinate system standardization The standardized neutral inertial axes (Fig. 3) were automatically computed, without manual intervention, from 85% of the carpal bones. The remaining 15% had senses either 901 or 1801 to the majority and were
In this communication, we presented a standardized coordinate system for each carpal bone, radius, and ulna and compared carpal bone posture between the clinical and functional neutral wrist positions. The method presented here can be used to represent the posture and motion of each carpal bone or the whole wrist, using the capitate coordinate system to represent the wrist. Defining the coordinate system by the inertial axes
Fig. 3. Standardized coordinate systems for all bones in a palmar view of functional neutral (a). RAD ¼ radius, ULN ¼ ulna, CAP ¼ capitate, SCA ¼ scaphoid, LUN ¼ lunate, TPM ¼ trapezium, TPD ¼ trapezoid, HAM ¼ hamate, PIS ¼ pisiform, TRQ ¼ triquetrum, MCx ¼ metacarpal x. An exploded view, not to scale, is also provided (b). Further visualization of these coordinate systems can be found in Moore et al. (2002) and Crisco et al. (2005).
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150
Functional Neutral Clinical Neutral
207
*
120 * 90 *
Angle (deg)
* 60 * 30 *
0 -30
ϕ m
m
θ
Ha
pϕ
Ha
Ca
ϕ
pθ
Ca
θ
Tp m
ϕ
Tp m
θ
Tp d
sϕ
Tp d
ϕ
θ
ϕ
θ
sθ
Pi
Pi
Tr q
Tr q
Lu n
aϕ
Lu n
Sc
Sc
aθ
-60
Bone Angle Fig. 4. Average (71 SD) posture for all carpals in functional neutral and clinical neutral. * denotes significance (po0.05).
120
Male Neutral Female Neutral
105 90 75
Angle (deg)
60 45 30 15 0 -15 -30 -45 -60 a θ ca ϕ un θ un ϕ rq θ rq ϕ is θ is ϕ pd θ pd ϕ m θ m ϕ ap θ ap ϕ m θ m ϕ a P a P T T S C T L L T C Tp Tp H H Bone Angle
Sc
Fig. 5. Average (71 SD) posture for male and female carpals in functional neutral position. No statistical significances appear (po0.05). Comparison of clinical neutral produces the same result.
permits individual description of carpal bone posture, not possible using the previously proposed coordinate systems (Wu et al., 2005). An underlying necessity of our approach is that it requires the entire surface model of each carpal bone. Our approach is not applicable to the study of pathologies that cause changes in bone shape; however, it is ideally suited for studies of other pathologies, such as ligamentous injuries, that alter carpal bone posture or kinematics. The ISB proposed coordinate system for the carpal bones does not account for inter-subject variability in
the orientation of the carpal bones in the neutral position. Further, the radial coordinate system (RCS) origin is located midway between the distal radius the proximal radius, away from the center of wrist motion. Many CT based studies of the wrist only scan distal portions of the radius (Belsole et al., 1991b; Feipel et al., 1994; Snel et al., 2000; Wolfe et al., 2000), the origin of the ISB’s RCS cannot be determined from these datasets. It is clinically important to study carpal bone posture because misalignment of the carpal bones can lead to
ARTICLE IN PRESS J.C. Coburn et al. / Journal of Biomechanics 40 (2007) 203–209
208
Inertially-defined Angles (deg)
Fig. 6. The clinical neutral wrist position illustrated with 3-D surface models where the long axis of the third metacarpal, capitate, and radius as measured by anatomical landmarks are aligned. The inertial-defined coordinate system of the capitate is also shown. In this typical subject, the capitate coordinate system is slightly extended (8.51) from the neutral line.
120
RC angle RL angle RS angle CL angle SL angle CS angle
100 80 60 40 20
-80
-60
-40
-20
0 0 -20
20
40
60
80
100
-40 -60 -80 -100
Clinically Measured Angles (deg) Fig. 7. Correlations between inertially-defined coordinate system angles and clinically measured angles. R ¼ radius; C ¼ capitate; S ¼ scaphoid; L ¼ lunate. Least-square regression lines displayed only for R240.85. Angles measured between the radius and the carpal bone had a higher correlation than inter-carpal angles. This is likely due to the errors associated with measuring 3-D posture with 2-D clinical angles.
carpal instability typically diagnosed by abnormal two-plane radiographic angles. The advantage of using a 3-D coordinates system based upon inertia is that it allows the individualized study of both posture and kinematics without limiting the degrees of freedom. Despite the importance of normal carpal bone posture, most studies of the carpus report carpal motion using only vectorized components of helical axes of motion (Feipel and Rooze, 1999; Kobayashi et al., 1997; Moojen et al., 2002a; Wolfe et al., 2000). While very useful, these descriptions cannot be correlated to the clinical angle measurements of carpal bone posture. Previously, Belsole used an inertial coordinate system to define the orientation of the several carpal bones (Belsole et al., 1991b), using the same posture reference axis for the scaphoid, capitate and triquetrum, as the one proposed here.
We found that the 2-D radio-carpal clinical angle measurements were closely related to the inertial axis angles, while the inter-carpal angle measurements were not. 2-D clinical measurements do not contain out-ofplane data and may not be able to represent out-ofplane orientation of carpal bones. 3-D inertial measurements may increase detection of abnormalities in posture or kinematics. The complexity and variability of the carpal bones 3-D shapes require a unique coordinate system for each carpal bone. Methods for constructing inertial coordinate systems based upon 3-D surface models of the bones have been presented and are put forth in hopes of providing a standardized approach to describing the complexities of the carpus.
Acknowledgments This study was supported by a National Institutes of Health Grant, AR44005. We gratefully acknowledge the assistance and insights provided by Edward Akelman, M.D., Arnold-Peter C. Weiss, M.D., and Scott W. Wolfe, M.D.
References Belsole, R.J., Hilbelink, D.R., Llewellyn, J.A., Dale, M., Greene, T.L., Rayhack, J.M., 1991a. Computed analyses of the pathomechanics of scaphoid waist nonunions. Journal of Hand Surgery American Volume 16, 899–906. Belsole, R.J., Hilbelink, D.R., Llewellyn, J.A., Dale, M., Ogden, J.A., 1991b. Carpal orientation from computed reference axes. Journal of Hand Surgery American Volume 16, 82–90. Coburn, J., Crisco, J.J., 2005. Interpolating three-dimensional kinematic data using quaternion splines and hermite curves. Journal of Biomechanical Engineering 127, 311–317. Crisco, J.J., McGovern, R.D., 1998. Efficient calculation of mass moments of inertia for segmented homogenous three-dimensional objects. Journal of Biomechanics 31, 97–101.
ARTICLE IN PRESS J.C. Coburn et al. / Journal of Biomechanics 40 (2007) 203–209 Crisco, J.J., Neu, C.P., 2000. In vivo carpal bone rotations are linear and depend on the direction of wrist rotation. Transactions 46th Annual Meeting Orthopaedic Research Society. Crisco, J.J., Wolfe, S.W., Neu, C.P., Pike, S., 2001. Advances in the in vivo measurement of normal and abnormal carpal kinematics. Orthopaedic Clinics of North America 32, 219–231 vii. Crisco, J.J., Pike, S., Hulsizer-Galvin, D.L., Akelman, E., Weiss, A.P., Wolfe, S.W., 2003. Carpal bone postures and motions are abnormal in both wrists of patients with unilateral scapholunate interosseous ligament tears. Journal of Hand Surgery American Volume 28, 926–937. Crisco, J.J., Coburn, J.C., Moore, D.C., Upal, M.A., 2005. Carpal bone size and scaling in men versus in women. Journal of Hand Surgery American Volume 30, 35–42. Feipel, V., Rooze, M., 1999. Three-dimensional motion patterns of the carpal bones: an in vivo study using three-dimensional computed tomography and clinical applications. Surgical Radiologic Anatomy 21, 125–131. Feipel, V., Rooze, M., Louryan, S., Lemort, M., 1994. Functional anatomy of the carpus in radio–ulnar deviation and in flexion and extension: an bi- and three-dimensional CT study. In: Schuind, F., An, K.N., Cooney, III, W.P., Garcia-Elias, M. (Eds.), Advances in the Biomechanics of the Hand and Wrist. Plenum Press, New York. Green, D.P., Hotchkiss, R.N., Pederson, W.C., 1999. Green’s Operative Hand Surgery. vol. 2, fourth ed. pp. 1406–1417. Kobayashi, M., Berger, R.A., Nagy, L., Linscheid, R.L., Uchiyama, S., Ritt, M., An, K.N., 1997. Normal kinematics of carpal bones: a three-dimensional analysis of carpal bone motion relative to the radius. Journal of Biomechanics 30, 787–793. Moojen, T.M., Snel, J.G., Ritt, M.J., Kauer, J.M., Venema, H.W., Bos, K.E., 2002a. Three-dimensional carpal kinematics in vivo. Clinical Biomechanics (Bristol, Avon) 17, 506–514.
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Moojen, T.M., Snel, J.G., Ritt, M.J., Venema, H.W., Kauer, J.M., Bos, K.E., 2002b. Scaphoid kinematics in vivo. Journal of Hand Surgery American Volume 27, 1003–1010. Moore, D.C., Hogan, K.A., Crisco 3rd., J.J., Akelman, E., Dasilva, M.F., Weiss, A.P., 2002. Three-dimensional in vivo kinematics of the distal radioulnar joint in malunited distal radius fractures. Journal of Hand Surgery American Volume 27, 233–242. Moritomo, H., Viegas, S.F., Elder, K.W., Nakamura, K., Dasilva, M.F., Boyd, N.L., Patterson, R.M., 2000. Scaphoid nonunions: a 3-dimensional analysis of patterns of deformity. Journal of Hand Surgery American Volume 25, 520–528. Snel, J.G., Venema, H.W., Moojen, T.M., Ritt, J.P., Grimbergen, C.A., den Heeten, G.J., 2000. Quantitative in vivo analysis of the kinematics of carpal bones from three-dimensional CT images using a deformable surface model and a three-dimensional matching technique. Medical Physics 27, 2037–2047. Watson, H.K., Weinzweig, J., Zeppieri, J., 1997. The natural progression of scaphoid instability. Hand Clinics 13, 39–49. Wolfe, S.W., Neu, C., Crisco, J.J., 2000. In vivo scaphoid, lunate, and capitate kinematics in flexion and in extension. Journal of Hand Surgery American Volume 25, 860–869. Woolson, S., Fellingham, L., Dev, P., Vassiliadis, A., 1985. Three dimensional imaging of bone from analysis of computed tomography data. Orthopedics 8, 1269–1273. Wu, G., van der Helm, F.C., Veeger, H.E., Makhsous, M., Van Roy, P., Anglin, C., Nagels, J., Karduna, A.R., McQuade, K., Wang, X., Werner, F.W., Buchholz, B., 2005. ISB recommendation on definitions of joint coordinate systems of various joints for the reporting of human joint motion—Part II: shoulder, elbow, wrist and hand. Journal of Biomechanics 38, 981–992.
Journal of Biomechanics 40 (2007) 203–209
Short communication
www.elsevier.com/locate/jbiomech www.JBiomech.com
Coordinate systems for the carpal bones of the wrist James C. Coburna, Mohammad A. Upalb, Joseph J. Criscoa,b, a
Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, 1 Hoppin Street, CORO West, Suite 404, Providence, Rhode Island 02903, USA b Division of Engineering, Brown University, Providence, RI, USA Accepted 18 November 2005
Abstract The eight small and complexly shaped carpal bones of the wrist articulate in six degrees of freedom with each other and to some extent with the radius and the metacarpals. With the increasing number and sophistication of studies of the carpus, a standardized definition for a coordinate system for each the carpal bones would aid in the reporting and comparison of findings. This paper presents a method for defining and constructing a coordinate system specific to each of the eight carpal bones based upon the inertial properties of the bone, derived from surface models constructed from three-dimensional (3-D) medical image volumes. Surface models from both wrists of 5 male and 5 female subjects were generated from CT image volumes in two neutral wrist positions (functional and clinical). An automated algorithm found the principal inertial axes and oriented them according to preset conditions in 85% of the bones, the remaining bones were corrected manually. Six of the eight carpal bones were significantly more extended in the functional neutral position than in the clinical neutral position. Gender had no significant effect on carpal bone posture in either wrist position. Correlations between the 3-D carpal posture and the commonly used 2-D clinical radiographic carpal angles are established. 3-D coordinate systems defined by the anatomy of the carpal bone, such as the ones presented here, are necessary to completely describe 3-D changes in the posture of the carpal bones. r 2005 Elsevier Ltd. All rights reserved. Keywords: Carpal bones; Coordinate system; Three-dimensional; Posture
1. Introduction The carpus of the wrist consists of eight complexly shaped carpal bones located between the radius and ulna and the five metacarpals. Diagnoses of ligament injuries or progressive deformities are supported by distance and angle measurements between the carpal bones made on plane radiographs (Watson et al., 1997). While they clearly have clinical value, 2-D measurements have limited research value because of the complex shape (Crisco et al., 2005) and 3-D motions Corresponding author. Bioengineering Laboratory, Department of Orthopaedics, Brown Medical School and Rhode Island Hospital, 1 Hoppin Street, CORO West, Suite 404, Providence, Rhode Island 02903, USA. Tel.: 401 444 4231; fax: 401 444 4418. E-mail address: [email protected] (J.J. Crisco).
0021-9290/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2005.11.015
of the carpal bones (Kobayashi et al., 1997). Methods employing the entire carpal geometry can improve clinical diagnosis (Belsole et al., 1991a). Recently, MRI and CT imaging has been used to visualize the 3-D function of the carpus and to measure its complex motions (Crisco and Neu, 2000; Crisco et al., 2003; Moojen et al., 2002b; Moojen et al., 2002a; Moritomo et al., 2000). Describing complete carpal motion is a difficult undertaking, however because each carpal bone can have up to six degrees of freedom. One hurdle is the lack of standardized coordinates systems in the carpus. The International Society of Biomechanics (ISB) has recently proposed joint coordinate system guidelines for the shoulder, elbow, wrist and hand (Wu et al., 2005). The task was vast and well executed, however they proposed carpal coordinate systems whose orientations were parallel to the radius in the neutral
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position. A limitation of this method is that crucial information on the variations in carpal posture is lost. The purpose of this communication is to present coordinate systems for each carpal bone and a method for constructing these coordinate systems. We also present data on the 3-D carpal postures for healthy wrists in two common reference positions, clinical and functional neutral, using these coordinate systems.
custom routines (Crisco and McGovern, 1998). The principal inertial axes, three orthogonal lines through the centroid of each bone, were arranged in order of ascending inertial magnitude, X-axis (red), Y-axis (green), and Z-axis (blue). The orientations of these axes, relative to the bone model, are unique and subject specific but their direction, or sense, is not (Fig. 1). The variation across subjects was the motivation for our analysis of postures.
2. Methods
2.4. Radius and ulna coordinate systems
2.1. Carpal bone models
The inertial axes of the radius and ulna cannot typically be calculated because they are not fully imaged. Radial and ulnar coordinate systems, however, can be crucial to studies of the carpus. Therefore, coordinate systems for the radius (XrYrZr) (Crisco et al., 2003) and ulna (XuYuZu) (Moore et al., 2002) were constructed from anatomical landmarks similar to Kobayashi et al. (1997). Radial coordinate systems have been used extensively to describe both carpal and wrist motion, while ulnar coordinate systems have typically been used only to describe the motion of the radius. Xr: A line fit through the centroids of the radial diaphysis (shaft). Simply, the axis coincides with the radial long axis. Pronation of the carpal bones and wrist corresponds to positive rotation. Yr: Directed through the radial styloid and defined perpendicular to the Xr. Flexion (+Yr) and extension (Yr) rotations were measured around this axis. Zr: Directed palmarly (volarly) and calculated from the cross product of Xr and Yr. Ulnar (+Zr) and radial (Zr) deviation were measured around this axis. Originr: Defined by the intersection of Xr and the distal radial articular surface. Xu: A line fit through the centroids of the ulnar diaphysis (shaft). Simply, the axis coincides with the ulnar long axis. Pronation corresponds to positive rotation. Yu: Directed radially, along a vector passing through the tip of the ulnar styloid, defined by the centroids of the styloid. Calculated from the cross product of Xu and Zu. Zu: Directed palmarly, perpendicular to a plane defined by Xu and the tip of the ulnar styloid. Originu: Defined by the intersection of Xu with the distal ulnar articular surface.
Digitally defined carpal bone meshes, such as those generated from CT volume images were used to generate the carpal coordinate systems. Approaches to generating these surfaces meshes have been described by Woolson et al. (Woolson et al., 1985) and others (Belsole et al., 1991a; Moritomo et al., 2000; Snel et al., 2000). The coordinate system definitions are independent of the method of surface generation, but we use the approach established by Crisco et al. (2001). Briefly, CT volume images of the carpus were acquired. The outer contours of each slice were digitized with a biomedical image processing program (Analyze, Rochester, MN). The contours were then grouped into bones using custom algorithms (MS Visual C++, Redmond WA) and fit with a surface mesh (Geomagic, Raindrop, Durham, NC). 2.2. Subjects and image acquisition With approval from our Institutional Review Board, and after obtaining informed consent, ten volunteers (five male, average age 31 years, range 22–47 years, and five female average age 21.8 years, range 21–22 years) were recruited into the study. Volunteers with no history of wrist injury or chronic disease that might affect the wrist were considered. Both wrists of each subject were imaged simultaneously with a GE HiSpeed Advantage CT scanner (GE Medical, Milwaukee, WI). Contiguous, 1.0 mm, transverse slices of the entire carpus were acquired at a resolution between 0.2 and 0.4 mm. The functional neutral wrist position was imaged while the subjects were comfortably grasping a rubber bicycle handle in neutral supination–pronation. The clinical neutral wrist position, defined as the position where the long axes of the radius, capitate and third metacarpal are parallel, was interpolated from multiple CT scans at both 30 and 601 of flexion and 30 and 601 of extension(Coburn and Crisco, 2005). 2.3. Calculating inertial properties and axes The mass centroids and principal inertial axes for each bone were calculated using previously described,
2.5. Carpal bones coordinate systems A unique positive direction, or sense, for each inertial axis must be defined for each carpal bone coordinate system (XcYcZc). To this end, the inertial axes in the functional neutral were described in the radial coordinate system (RCS) and then analyzed with a custom algorithm.
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Fig. 1. While inertia axes are unique for each bone surface model, the sense of the axes is not. The capitate bone is shown in the proposed, standardized inertial based coordinate system colored (X-red; Y-green; Z-blue) (a) and another possible version (b).
Fig. 2. (a) Definition of spherical coordinate angles in the radial coordinate system. (b) Measurement of the flexion angle, y, on the scaphoid. Carpal axes are scaled to their inertial magnitude.
The algorithm compared carpal axes Xc and Yc consecutively to each RCS axis and changed carpal axis sense by negating the inertial vector, based on testing criteria. A test was considered to be failed if the carpal axis was oriented within one determination interval (DI) of the orthogonal plane to that RCS axis and the next test was run. Once one test was passed, the remaining tests for that carpal axis were skipped. Xc was run with a DI of 7151, while Yc was tested using a DI of 751. Zc was calculated from the cross-product of Xc and Yc to ensure the coordinate system was right handed. 1st test: Carpal axis compared to Xr, making the sense distal if passed. 2nd test: Carpal axis compared to Zr, making the sense radial if passed. 3rd test: Carpal axis compared to Yr, making the sense palmar. This test used no DI. All inertial axes for all bones were then displayed concurrently for verification. The second or third
axes in some cylindrically shaped bones were not always uniquely defined so manual intervention was required. 2.6. Carpal bone posture in 3-D One inertial axis was chosen as a reference to describe carpal bone orientation with respect to the RCS, using spherical azimuth (y) and elevation (j) angles (Fig. 2a). Azimuth angle described flexion (positive) and extension (negative), whereas elevation angle described radial (negative) and ulnar (positive) deviation. Postures for all carpal bones except the lunate were calculated from Xc (Fig. 2b). The lunate’s posture was calculated from Zc. Flexion-extension and radioulnar carpal bone postures in the neutral positions were compared separately using Student’s t-tests. Effect of gender on neutral posture was also analyzed using Student’s t-tests. po0.05 was considered significant.
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2.7. Inertial defined coordinate systems and clinically defined angles
manually corrected to fit the standard definition of the coordinate system.
The orientations of the inertial-defined coordinate systems were compared to six clinical angles, the radiocapitate (RC), radio-scaphoid (RS), radio-lunate (RL), scapho-lunate (SL), capito-lunate (CL), and capitoscaphoid (CS) angles defined by lines drawn on a lateral radiograph using clinical landmarks (Green et al., 1999):
3.2. Carpal posture
Radius: Capitate: Scaphoid: Lunate:
The long axis. The midline, long axis. The midline through each tubercle. The midline, perpendicular to the lunate horns.
Clinical and inertial posture were correlated by examining the difference between the clinical long axis of the capitate and its first inertial axis. Simulated X-rays of the distal radius, lunate, capitate, and proximal portions of the third metacarpal were made from a subset of the CT scans and the clinical angles were measured by multiple researchers. A computer algorithm found the approximate carpal angles using a projection of the appropriate inertial axes onto the anterior–posterior (XrZr) plane, a linear trend line was fit to the all data and an R2 value calculated.
Carpal bones of the functional neutral were significantly more extended (po0.05) than those in the clinical neutrals with the exception of the pisiform and lunate. (Fig. 4) Radioulnar deviation posture of the carpal bones was not different between the clinical and functional neutral wrist positions. Gender also had no significant effect on carpal bone posture in either neutral wrist position (Fig. 5). 3.3. Comparing coordinate systems with clinically defined angles In clinical neutral, the capitate inertial axis was in an average 13.3174.91 extension. 3-D reconstruction in a computed wrist posture of 13.31 extension confirmed this. (Fig. 6) A linear regression between the clinically measured carpal angles and inertial-computed carpal angles showed high correlation values (R24.85) for the RC, RS and RL angles and low correlation values (R2 p.6) for the CS,CL, and SL angles. (Fig. 7)
4. Discussion 3. Results 3.1. Coordinate system standardization The standardized neutral inertial axes (Fig. 3) were automatically computed, without manual intervention, from 85% of the carpal bones. The remaining 15% had senses either 901 or 1801 to the majority and were
In this communication, we presented a standardized coordinate system for each carpal bone, radius, and ulna and compared carpal bone posture between the clinical and functional neutral wrist positions. The method presented here can be used to represent the posture and motion of each carpal bone or the whole wrist, using the capitate coordinate system to represent the wrist. Defining the coordinate system by the inertial axes
Fig. 3. Standardized coordinate systems for all bones in a palmar view of functional neutral (a). RAD ¼ radius, ULN ¼ ulna, CAP ¼ capitate, SCA ¼ scaphoid, LUN ¼ lunate, TPM ¼ trapezium, TPD ¼ trapezoid, HAM ¼ hamate, PIS ¼ pisiform, TRQ ¼ triquetrum, MCx ¼ metacarpal x. An exploded view, not to scale, is also provided (b). Further visualization of these coordinate systems can be found in Moore et al. (2002) and Crisco et al. (2005).
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Functional Neutral Clinical Neutral
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*
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Bone Angle Fig. 4. Average (71 SD) posture for all carpals in functional neutral and clinical neutral. * denotes significance (po0.05).
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60 45 30 15 0 -15 -30 -45 -60 a θ ca ϕ un θ un ϕ rq θ rq ϕ is θ is ϕ pd θ pd ϕ m θ m ϕ ap θ ap ϕ m θ m ϕ a P a P T T S C T L L T C Tp Tp H H Bone Angle
Sc
Fig. 5. Average (71 SD) posture for male and female carpals in functional neutral position. No statistical significances appear (po0.05). Comparison of clinical neutral produces the same result.
permits individual description of carpal bone posture, not possible using the previously proposed coordinate systems (Wu et al., 2005). An underlying necessity of our approach is that it requires the entire surface model of each carpal bone. Our approach is not applicable to the study of pathologies that cause changes in bone shape; however, it is ideally suited for studies of other pathologies, such as ligamentous injuries, that alter carpal bone posture or kinematics. The ISB proposed coordinate system for the carpal bones does not account for inter-subject variability in
the orientation of the carpal bones in the neutral position. Further, the radial coordinate system (RCS) origin is located midway between the distal radius the proximal radius, away from the center of wrist motion. Many CT based studies of the wrist only scan distal portions of the radius (Belsole et al., 1991b; Feipel et al., 1994; Snel et al., 2000; Wolfe et al., 2000), the origin of the ISB’s RCS cannot be determined from these datasets. It is clinically important to study carpal bone posture because misalignment of the carpal bones can lead to
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Inertially-defined Angles (deg)
Fig. 6. The clinical neutral wrist position illustrated with 3-D surface models where the long axis of the third metacarpal, capitate, and radius as measured by anatomical landmarks are aligned. The inertial-defined coordinate system of the capitate is also shown. In this typical subject, the capitate coordinate system is slightly extended (8.51) from the neutral line.
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100 80 60 40 20
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Clinically Measured Angles (deg) Fig. 7. Correlations between inertially-defined coordinate system angles and clinically measured angles. R ¼ radius; C ¼ capitate; S ¼ scaphoid; L ¼ lunate. Least-square regression lines displayed only for R240.85. Angles measured between the radius and the carpal bone had a higher correlation than inter-carpal angles. This is likely due to the errors associated with measuring 3-D posture with 2-D clinical angles.
carpal instability typically diagnosed by abnormal two-plane radiographic angles. The advantage of using a 3-D coordinates system based upon inertia is that it allows the individualized study of both posture and kinematics without limiting the degrees of freedom. Despite the importance of normal carpal bone posture, most studies of the carpus report carpal motion using only vectorized components of helical axes of motion (Feipel and Rooze, 1999; Kobayashi et al., 1997; Moojen et al., 2002a; Wolfe et al., 2000). While very useful, these descriptions cannot be correlated to the clinical angle measurements of carpal bone posture. Previously, Belsole used an inertial coordinate system to define the orientation of the several carpal bones (Belsole et al., 1991b), using the same posture reference axis for the scaphoid, capitate and triquetrum, as the one proposed here.
We found that the 2-D radio-carpal clinical angle measurements were closely related to the inertial axis angles, while the inter-carpal angle measurements were not. 2-D clinical measurements do not contain out-ofplane data and may not be able to represent out-ofplane orientation of carpal bones. 3-D inertial measurements may increase detection of abnormalities in posture or kinematics. The complexity and variability of the carpal bones 3-D shapes require a unique coordinate system for each carpal bone. Methods for constructing inertial coordinate systems based upon 3-D surface models of the bones have been presented and are put forth in hopes of providing a standardized approach to describing the complexities of the carpus.
Acknowledgments This study was supported by a National Institutes of Health Grant, AR44005. We gratefully acknowledge the assistance and insights provided by Edward Akelman, M.D., Arnold-Peter C. Weiss, M.D., and Scott W. Wolfe, M.D.
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