- Email: [email protected]
A protocol for clinical evaluation of the carrying angle of the elbow by anatomic landmarks
A protocol for clinical evaluation of the carrying angle of the elbow by anatomic landmarks Maria Luisa Zampagni, MSc, PhD, Daniela Casino, MSc, Sandra Martelli, MSc, Andrea Visani, MD, and Maurilio Marcacci, MD, Bologna, Italy
The aim of this work was to present an in vivo protocol to estimate the carrying angle of the elbow in full extension. Forty-four arms were measured by using an electrogoniometer to acquire 3-dimensional coordinates of the landmarks. An algorithm based on the Cardan decomposition method was used to compute the carrying angle and the flexion and pronation angles of the elbow. The mean carrying angle was 12.42 6 4.06 , in agreement with the literature and with values obtained by a standard goniometer (r ¼ 0.46; P ¼ .000). Our protocol provided excellent repeatability (interclass correlation coefficient [ICC] ¼ 0.85), greater than a goniometer (ICC ¼ 0.76), and a standard error of measurement of only 1.62 . Flexion was a significant factor (P ¼ .01) in carrying angle estimation. This study suggests that the carrying angle cannot be estimated independently by the flexion angle, even when measured in apparently full extension, and it could be useful in elbow disorders, such as fractures or epicondylar disease management and evaluation of elbow reconstruction. (J Shoulder Elbow Surg 2008;17:106-112.)
T
he elbow joint is a complex structure that performs an important function as the mechanical link in the upper extremity between the hand, wrist, and shoulder. The functions of the elbow include making fine movements of the hand in space, powerful grasping, and acting as a fulcrum for the forearm. It is important to recognize the unique anatomy of the elbow.11 It has a bony geometry, articulation, and soft tissue structures, and the amount of force transmitted across the joint depends on the loading configurations and the angular orientation of the joint.21 Our particular interest was focused on the angle between the arm and the forearm in the frontal From the Biomechanics Laboratory, Rizzoli Orthopaedic Institute. Reprint requests: Maria Luisa Zampagni, Laboratorio di Biomeccanica, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy (E-mail: [email protected]). Copyright ª 2008 by Journal of Shoulder and Elbow Surgery Board of Trustees. 1058-2746/2008/$34.00 doi:10.1016/j.jse.2007.03.028
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plane,1,2,3,7,12,20,17,23,24,27,36,31 called the carrying angle, which has an important role when carrying loads.31 This angle is most apparent and best seen when the shoulder is externally rotated, the elbow is completely extended, and the forearm is supinated.26 In this position, the forearm is not in line with the arm but is deviated laterally.1 Anatomically, this valgus angulation is present because the trochlea extends farther distally than does the capitellum.37 Several authors have tried to provide information about the basal values of the carrying angle in specific age groups5,4,29,23,15 or distinguish it by sex or by side of the body.23,29,35 It appears to be strongly influenced by individual changes, and attempts to identify a correlation with age or physical characteristics have proved controversial.4,15 In clinical practice, the carrying angle is generally measured in full extension, and an increase in its value, compared with the contralateral elbow, may be attributed to previous trauma or developmental abnormality.6 However, in throwing athletes, it is not uncommon to find increased valgus in the throwing elbow due to adaptive changes to repetitive stress.6,16 Information about the carrying angle and its pathologic variations are important in the etiopathogenesis of various types of fractures seen around the elbow,15 in the diagnosis of diseases of the lateral (tennis elbow) and medial (golf elbow) epicondyles, and especially in the management of elbow fractures.9,10,13 Flynn et al9 developed criteria to grade the adequacy of reduction of supracondylar fractures of the humerus based on the evaluation of the carrying angle and total elbow range of motion loss after reduction by comparing the injured elbow with the healthy one. These criteria have been recently used to compare different fixation methods in supracondylar fractures of the humerus10 and to compare radial head resection with open reduction and internal fixation in patients with a comminuted radial head fracture.13 The carrying angle is generally estimated by the orthopedist by radiographs or a standard goniometer. In light of these efforts and in an attempt to solve the controversy in the literature, we calculated the carrying angle in vivo by using the theory of general rigid body motion to isolate the 3-dimensional (3D) rotation occurring at the elbow joint as suggested by Chao
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et al20 in their in vitro studies. By adopting this approach, they demonstrated that the carrying angle linearly decreases with flexion. Such a decrease is important as the carrying angle changes from more than 10 of valgus with the elbow fully extended to varus with the elbow fully flexed,6,20,30,31 Most controversy about the carrying angle is the result of differences in methodology and definition,3,17,31 but there may also be some disagreement about the exact flexion angle at which the carrying angle is measured. When the carrying angle is assessed on radiographs or by a goniometer, the true degree of flexion is not available. Our study presents a noninvasive method for evaluating the carrying angle in an in vivo setup that uses an electrogoniometer8,18,19,22 that digitizes the 3D coordinates of the anatomic landmarks and a numeric algorithm that gives the 3 components of the angle at the elbow joint carrying angle, flexion angle, and pronation angle. Reliability of the method was assessed, and carrying angle values were compared with those of the literature and measures obtained by a goniometer generally adopted in clinical settings.14,25,35
MATERIALS AND METHODS The right and left arms of 28 adults (15 men and 13 women) with a mean age 59 6 10 years (range, 41-81 years) were measured twice by a skilled operator. A total of 88 measurements were obtained because the data of 5 right arms and 7 left arms were lost. The right arm was dominant in all subjects. All participants were healthy, fit, and had no symptoms or signs of pathologies affecting the shoulder, elbow, or wrist joints. We obtained approval from the local ethics committee and written informed consent from all participants. The FaroArm Model Bronze18,19 (FARO Technologies Inc, Lake Mary, FL, http://www.faro.com) was used for measurements. The FaroArm is digital electrogoniometer with 6 of freedom and an anthropometric structure with 3 revolute links at the wrist, 1 at the elbow, and 2 at the shoulder (Figure 1). It can acquire data continuously at a rate of 50 Hz or point-by-point at the user’s request, with 0.3 mm/0.3 accuracy in a spherical workspace of 1.8-m diameter around its base. The FaroArm sensor is light, about 4 kg, and flexible, but it is mounted on a heavy and stable clamping base used to attach the sensor rigidly onto the experimental desktop and move it easily, when necessary, to fit the environmental obstacles. The FaroArm was used as a digitized device equipped with a point end effector. For in vivo investigation, the test was divided into 2 steps: First, the anatomic landmarks were identified through palpation and were marked with a pen to highlight them. Second, these points were digitized with the subjects seated on a fixed chair in front of a table where the FaroArm was placed, with each acquisition taking less than 1 minute. Measurements were made by placing the arm of the subject on the right of the device, with the forearm maintained fixed, fully extended, and supinated. Five anatomic points were
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Figure 1 Setup of measurement acquisition with the FaroArm Model Bronze (FARO Technologies, Lake Mary, FL).
acquired to identify the relative reference systems on the arm and forearm: Scapula AH: gap between acromion and humerus Humerus EM: most caudal point on medial epicondyle EL: most caudal point on lateral epicondyle Forearm US: most caudal-medial point on the ulnar styloid RS: most caudal-medial point on the radial styloid The landmarks EL, EM, US, and RS were chosen according to the 2005 International Society of Biomechanics recommendations.34 AH was chosen because it represents a more accessible point with respect to GH to identify the humeral axis32,33 and is more suitable for clinical and practical applications. The 3D coordinates of the digitized points were used to compute the reference systems relevant to the arm and forearm. The arm reference system was constructed by defining the Y-axis as the long axis of the humerus (a line connecting AH and the mid point of EL and EM, pointing to AH). The X-axis was the line perpendicular to the plane formed by EL, EM, and Y, pointing forward. The Z-axis was the line perpendicular to the Y- and X-axes. The forearm reference system was defined by unified segments on the radius and ulna. The y-axis was the line connecting the midpoint of RS and US and the midpoint between EL and EM. The x-axis was the line perpendicular to the plane through US and RS and the y-axis. The z-axis was the line perpendicular to y- and x-axes (Figure 2). The transformation matrix from the forearm reference system to the arm reference system was computed and used to obtain Cardan angles in the sequence Z-X-Y. The rotation around the floating z-axis corresponded to flexion-extension; the carrying angle was defined as the rotation around x-axis corresponding to the abduction-adduction, and the rotation around y-axis corresponded to pronation-supination. Carrying angle measures were also taken by a standard goniometer that is usually used in clinical and rehabilitation settings (Figure 3).
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Figure 3 Setup of measurement acquisition with the standard goniometer as it is usually used in clinical applications.
Data analysis Our reliability analysis included comparison between carrying angle values obtained by the FaroArm electrogoniometer and Cardan decomposition algorithm and by a standard goniometer, in addition to the analysis of repeatability of both the methods and comparison with literature values. After verifying normal distribution of data, differences between the methods were evaluated by paired samples Student tests and by calculating Pearson correlation coefficients. To estimate the repeatability of the methods, 2 repeated acquisitions in each arm (intraobserver) were compared, and significant differences were tested by the paired samples Student test. Interclass correlation coefficient (ICC) and standard error of measurement were also calculated. For the interpretation of the ICC, the criteria suggested by Cincchetti and Sparrow28 were used. Sex differences and side differences were evaluated by performing independent samples Student test and paired samples Student test, respectively. Finally, to verify the influence of the flexion and pronation angles on the carrying angle, the analysis of variance (ANOVA) was performed, and correlations between variations in the carrying angle and variations in the flexion angle (between repeated measures) were also calculated. The significance level was set at P ¼ .05 in all cases. Statistical analysis was done using SPSS 13.0 software (SPSS Inc, Chicago, IL).
RESULTS
Figure 2 Anatomic landmark points (AH, EL, EM, UR, US) and reference axis. X, Y, and Z identify the reference system of the arm, and x, y, z, identify the reference system of the forearm.
A mean carrying angle of 12.42 6 4.06 was found by adopting the FaroArm electrogoniometer. The mean degree of flexion at which the carrying angle was measured was 26.11 6 7.13 , and the mean pronation angle was 4.08 6 2.86 . The difference between these values and values obtained by a standard goniometer was 0.97 6 3.64, which was not significant (P ¼ .47), and the correlation between the methods was fair (r ¼ 0.46 with
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DISCUSSION The purpose of this study was to estimate carrying angle values in full extension using a noninvasive protocol able to give all of the 3 components of the angle formed at the elbow joint (carrying angle, flexion angle and pronation angle) based on the digitazation of easily identifiable landmark points and the Cardan decomposition algorithm. Our main findings were: 1.
Carrying angle values obtained by the proposed method have values similar to those
CARRYING ANGLE (degrees) by FARO ARM and by STANDARD GONIOMETER 25 Carrying angle (degrees) by STANDARD GONIOMETER
P ¼ .000), thus indicating reasonable agreement between the two approaches (Figure 4). With the FaroArm, the mean difference between repeated measures on the same subject was not statistically significant (0.56 , P ¼.27), with a standard error of measurements of 1.62 (Table I). The repeatability of the measures was excellent (ICC ¼ 0.85; P ¼ .000; Figure 5). The ANOVA test indicated that the flexion angle was a significant factor on carrying angle values (F ¼ 7.037; P ¼ .01) unlike the pronation angle (F ¼ 0.051; P ¼.823). In addition, variations between trial 1 and trial 2 of the carrying angle were significantly correlated with variations in the flexion angles (r ¼ 0.40; P ¼ .003). With the standard goniometer, the repeatability was good (ICC ¼ 0.76, P ¼ .000), and the mean difference of 0.23 between repeated measures was not significant (P ¼ .47; Figure 6). Sex differences were not significant with either method, although women showed slightly greater values than men (Table II). By the Cardan decomposition method, we obtained a mean carrying angle of 11.95 6 3.92 in men and 12.92 6 4.19 in women (P ¼ .265). An interesting finding was that the mean flexion angle of 5.26 in women was significantly smaller (P ¼ .000) than in men, indicating that women reach a greater natural physiologic extension than men. By the standard goniometer, a mean carrying angle of 11.24 6 3.36 was found in men and 11.79 6 2.68 in women (P ¼ .40). Side-of-the-body differences were not significant with either of our methods or a standard goniometer (Table III). By the Cardan decomposition method, the mean carrying angle values were 12.72 6 3.51 for the right (dominant) arm and 12.08 6 4.60 for the left arm (P ¼ .464), respectively. The mean flexion angle in the right arm was 2.98 smaller (P ¼.10) than in the left arm. By standard goniometer, the mean carrying angle values were 11.20 6 2.89 for the right arm (dominant arm) and 11.83 6 3.22 for the left arm (P ¼ .331).
109
20
15
r = 0.46 p<0.001
10
5
0 0
5
10
15
20
25
Carrying angle (degrees) by FARO ARM
Figure 4 Correlation between carrying angle values ( ) obtained by FaroArm (FARO Technologies Inc, Lake Mary, FL) and by standard goniometer.
2. 3. 4. 5.
reported in the literature, adopting the same definition of carrying angle.7 Measures obtained by our method were in reasonable agreement with measures taken by a standard goniometer on our sample. The repeatability of the measures obtained by the proposed method was higher than that found by the standard goniometer. Our method gave reasonable values of flexion and pronation. Degrees of flexion were a significant factor on carrying angle estimation.
The carrying angle value is greatly variable as reported in the literature, but several authors reported a range between 11 and 14 .2,20,30,23 Within this range, some authors found differences between the sexes and arm side.23,31,35 Our sample showed neither sex nor arm side differences with the electrogoniometer or the standard goniometer. This could be explained in 2 ways: First, great individual variability of carrying angle31 might determine differences between the samples. Second, Beals5 explained apparent differences between the sexes by the increased joint laxity in women, which, permitting a greater degree of extension, should determine larger carrying angles. This consideration could be extended to arm side differences and was confirmed by the great degree of extension found in our sample in women and in right arms.
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Table I Carrying angle (and relative flexion angle) by FaroArm* and carrying angle by standard goniometer in 2 trials Trial, mean ± SD ( ) Method FaroArm Goniometer
Measure
Sample, No.
1
2
SEM ( )
ICC
Carrying angle Flexion angle Carrying angle
44 44 44
12.69 6 4.30 26.05 6 6.80 11.38 6 2.99
12.13 6 3.83 26.16 6 7.50 11.61 6 3.14
1.62 4.42 1.49
0.85y 0.62y 0.76y
SEM, Standard error of measurements; ICC, intraclass correlation coefficients. *FARO Technologies Inc, Lake Mary, FL. y P < .001.
CARRYING ANGLE (degrees) by FARO ARM repeated measures 25
Identity line
Trial 2 (degrees)
20
r=0.85 p<0.001
15
10
5
0
0
5
10 15 Trial 1 (degrees)
20
25
Figure 5 Correlation between carrying angle values ( ) obtained by FaroArm (FARO Technologies Inc, Lake Mary, FL) in trial 1 and trial 2.
We, however, studied athletes who, using mainly the upper extremity in their sports activity for more than 10 years, might present reduced joint laxity with respect to the nonathletic population, thus leading to the lack of significance of sex and side differences. Probable adaptive changes due to repetitive sport activity have already been found.6,16 Nevertheless, these results need to be confirmed by future studies. Bearing this in mind, the carrying angle cannot be estimated independently by the flexion angle, even when measured in apparent full extension position, because individual and adaptive changes in joint laxity might produce a misleading carrying angle assessment. This is supported by the fact that flexion was a significant factor (P ¼ .01) in the carrying angle estimation as well as correlation between variation in the carrying angle and variation in the flexion
Figure 6 Correlation between carrying angle values ( ) obtained by standard goniometer in trial 1 and trial 2.
angle on the same subject being significant (r ¼ 0.40; P ¼ .003). A comment is needed on the different standard deviation values between measures taken on right and left side (Table III). We observed that despite comparable mean values, the standard deviation was greater in the left arm. This could be due to the placement of the FaroArm device on the right side of the body. This error could easily be avoided in future acquisitions by placing the FaroArm device on the center of the table. By further comparison of values obtained by our method and measures taken on our sample by a standard goniometer, our protocol was more repeatable, particularly considering that our measurements were calculated in a blinded fashion without being influenced by the visualization of the value, which is immediately available after the acquisition. However,
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Table II Carrying angle and flexion angle values by FaroArm* and carrying angle by standard goniometer in male and female arms Method FaroArm Goniometer
Measure
Men (n ¼ 46), mean ± SD ( )
Women (n ¼ 42), mean ± SD ( )
Difference ( )
Carrying angle Flexion angle Carrying angle
11.95 6 3.92 28.61 6 6.54 11.24 6 3.36
12.92 6 4.19 23.35 6 6.76 11.79 6 2.68
0.97 5.26y 0.55
*FARO Technologies Inc, Lake Mary, FL. y P < .001.
Table III Carrying angle and flexion angle values by FaroArm* and carrying angle by standard goniometer in right and left arms Method FaroArm Goniometer
Measure
Right (n ¼ 46), mean ± SD ( )
Left (n ¼ 42), mean ± SD ( )
Difference ( )
Carrying angle Flexion angle Carrying angle
12.72 6 3.51 24.68 6 6.07 11.20 6 2.89
12.08 6 4.60 27.66 6 7.90 11.83 6 3.22
0.64 2.98 0.63
*FARO Technologies Inc, Lake Mary, FL.
a part of the reliability of this method could be also attributed to the skilled user, who was able to determine the correct position of the anatomic landmark points, which might be an important source of error when not performed accurately. In fact, the reference system of the humerus and forearm is determined by correct position of the sensor on the landmarks.28 In conclusion, this study shows that the carrying angle evaluation by the FaroArm and the Cardan algorithm provides more reliable results than other methods. The setup is comfortable for the subject, and acquisition is fast and takes about a minute, including software elaboration of the result. In addition to better repeatability compared with standard methods, the important clinical implication of the proposed noninvasive method to assess the carrying angle by 3D digitization of anatomic landmarks is the ability to evaluate the alignment of the elbow joint by obtaining flexion, pronation, and carrying angle values simultaneously at any elbow position. A great advantage in the application of this approach is that it can help to quantify the functional impairment associated with elbow pathologies in patients presenting with a reduced full extension capability. Therefore, this method could be useful to estimate pathologic variations of the carrying angle along with flexion and pronation angles after epicondylar diseases or to grade the adequacy of reduction of supracondylar fractures of the humerus. Other applications could include evaluation of adaptive changes due to repetitive stresses at the elbow joint in athletes or to help with monitoring during an elbow rehabilitation program. The described method in which digitized landmarks are used for carrying angle assessment also al-
lows easy inclusion in new computer technologies for assisted elbow surgery by graphic display and qualification of anatomic and functional features of the joint. We thank Silvia Bassini for her valuable help in graphic design. We also thank Dott. Zaffagnini Stefano and Giampaolo Bernagozzi for their contributions.
REFERENCES
1. Aebi H. Der elbogenwinkel, seine beziehungen zu geschlect, Korperbau and Huftbrite. (Inaug Diss, Basel 1947) Acta Anat 1947; 3:229-64. 2. Amis AA, Miller JH. The elbow. Clin Rheumatol Dis 1982;8: 571-93. 3. An KN, Morrey BF, Chao EYS. Carrying angle of the human elbow joint. J Orthop Res 1984:369-78. 4. Balasubramanian P, Madhuri V, Muliyil J. Carrying angle in children: a normative study. J Pediatr Orthop B 2006;15:37-40. 5. Beals RK. The normal carrying angle of the elbow. A radiographic study of 422 patients. Clin Orthop Relat Res 1976;119:194-6. 6. Cain EL Jr, Dugas JR, Wolf RS, Andrews JR. Elbow injuries in throwing athletes: a current concepts review. Am J Sports Med 2003; 31:621-35. 7. Chao EY, Morrey BF. Three-dimensional rotation of the elbow joint. J Biomech 1978;11:57-73. 8. Feathers DJ, Paquet V, Drury CG. Measurement consistency and three-dimensional electromechanical anthropometry. Int J Indust Ergon 2004;33:181-90. 9. Flynn JC, Matthews JG, Benoit RL. Blind pinning of displaced supracondylar fractures of the humerus in children. Sixteen years’ experience with long-term follow-up. J Bone Joint Surg Am 1974;56: 263-72. 10. Foead A, Penafort R, Saw A, Sengupta S. Comparison of two methods of percutaneous pin fixation in displaced supracondylar fractures of the humerus in children. J Orthop Surg 2004;12: 76-82. 11. Fornalski S, Gupta R, Lee TQ. Anatomy and biomechanics of the elbow joint. Tech Hand Up Extrem Surg 2003;7:168-78.
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12. Goto A, Moritomo H, Murase T, et al. In vivo elbow biomechanical analysis during flexion: Three-dimensional motion analysis using magnetic resonance imaging. J Shoulder Elbow Surg 2004; 13:441-7. 13. Ikeda M, Sugiyama K, Kang C, Takagaki T, Oka Y. Comminuted fractures of the radial head: comparison of resection and internal fixation. J Bone Joint Surg Am 2006;88(1 suppl 1):11-23. 14. Karagiannopoulos C, Sitler M, Michlovitz S. Reliability of 2 functional goniometric methods for measuring forearm pronation and supination active range of motion. J Orthop Sports Phys Ther 2003;33:523-31. 15. Khare GN, Goel SC, Saraf SK, Singh G, Mohanty C. New observations on carrying angle. Indian J Med Sci 1999;53:61-7. 16. King JW, Brelsford HJ, Tullos HS. Analysis of the pitching arm of the professional baseball pitcher. Clin Orthop 1969;767:116-23. 17. London JT. Kinematics of the elbow. J Bone Joint Surg Am 1981; 63:529-35. 18. Martelli S. New method for simultaneous anatomical and functional studies of articular joints and its application to the human knee. Comput Methods Programs Biomed 2003;70:223-40. 19. Martelli S, Zaffagnini S, Falcioni B, Marcacci M. Intraoperative kinematic protocol for knee joint evaluation. Comput Methods Programs Biomed 2000;62:77-86. 20. Morrey BF, Chao EY. Passive motion of the elbow joint. J Bone Joint Surg 1976;54:501-8. 21. Morrey BF. Applied anatomy and biomechanics of the elbow joint. Instr Course Lect 1986;35:59-68. 22. Paquet V, Feathers D. An anthropometric study of manual and powered wheelchair users. Int J Indust Ergon 2004;33:191-204. 23. Paraskevas G, Papadopoulos A, Papaziogas B, Spanidou S, Argiriadou H, Gigis J. Study of the carrying angle of the human elbow joint in full extension: a morphometric analysis. Surg Radiol Anat 2004;26:19-23. 24. Potter HP. The obliquity of the arm of the female in extension. The relationship of the forearm with the upper arm in flexion. J Anat 1985;29:488-93. 25. Ruotolo C, Price E, Panchal. Loss of total arc of motion in collegiate baseball players. J Shoulder Elbow Surg 2006;15:67-71.
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26. Smith L. Deformity following supracondylar fractures of the humerus. Am J Orthop 1960;42:235-52. 27. Shiba R, Sorbie C, Siu DW, Bryant JT, Cooke D, Wevers HW. Geometry of the humeroulnar joint. J Orthop Res 1988;6: 897-906. 28. Stokdijk M, Biegstraaten M, Ormel W, de Boer YA, Veeger HE, Rozing PM. Determining the optimal flexion-extension axis of the elbow in vivo - a study of interobserver and intraobserver reliability. J Biomech 2000;33:1139-45. 29. Tu¨kenmez M, Demirel H, Perc¸in S, Tezeren G. Measurement of the carrying angle of the elbow in 2,000 children at ages six and fourteen years. Acta Orthop Traumatol Turc 2004;38:274-6. 30. Van Roy P, Van Gheluwe B, Hebbelinck M, Van Holst I. An in-vivo arthrokinematic investigation of the carrying angle of the elbow. J Biomechan 1993;26:791. 31. Van Roy P, Baeyens JP, Fauvart D, Lanssiers R, Clarijs JP. Arthrokinematics of the elbow: study of the carrying angle. Ergonomics 2005;48:1645-56. 32. Veeger HEJ, Van der Helm FCT, Rozendal RH. Orientation of the scapula in a simulated wheelchair push. Clin Biomech 1993;8: 81-90. 33. Veeger HEJ, Yu B, An KN, Rozendal RH. Parameters for modelling the upper extremity. J Biomech 1997;30:647-52. 34. Wu G, Van der Helm FC, Veeger HE, et al. 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. J Biomech 2005;38:981-92. 35. Yilmaz E, Karakurt L, Belhan O, Bulut M, Serin E, Avci M. Variation of carrying angle with age, sex, and special reference to side. Orthopedics 2005;28:1360-3. 36. Youm Y, Dryer RF, Thambyrajah K, Flatt AE, Sprague BL. Biomechanical analyses of forearm pronation-supination and elbow flexion-extension. J Biomech 1979;12:245-55. 37. Zuckerman JD, Matsen FA 3rd. Biomechanics of the elbow. In: Nordon M, Frankel VH, editors. Basic biomechanics of the musculoskeletal system. Philadelphia, PA: Williams & Wilkins: Media; 1989. p. 249-60.
The aim of this work was to present an in vivo protocol to estimate the carrying angle of the elbow in full extension. Forty-four arms were measured by using an electrogoniometer to acquire 3-dimensional coordinates of the landmarks. An algorithm based on the Cardan decomposition method was used to compute the carrying angle and the flexion and pronation angles of the elbow. The mean carrying angle was 12.42 6 4.06 , in agreement with the literature and with values obtained by a standard goniometer (r ¼ 0.46; P ¼ .000). Our protocol provided excellent repeatability (interclass correlation coefficient [ICC] ¼ 0.85), greater than a goniometer (ICC ¼ 0.76), and a standard error of measurement of only 1.62 . Flexion was a significant factor (P ¼ .01) in carrying angle estimation. This study suggests that the carrying angle cannot be estimated independently by the flexion angle, even when measured in apparently full extension, and it could be useful in elbow disorders, such as fractures or epicondylar disease management and evaluation of elbow reconstruction. (J Shoulder Elbow Surg 2008;17:106-112.)
T
he elbow joint is a complex structure that performs an important function as the mechanical link in the upper extremity between the hand, wrist, and shoulder. The functions of the elbow include making fine movements of the hand in space, powerful grasping, and acting as a fulcrum for the forearm. It is important to recognize the unique anatomy of the elbow.11 It has a bony geometry, articulation, and soft tissue structures, and the amount of force transmitted across the joint depends on the loading configurations and the angular orientation of the joint.21 Our particular interest was focused on the angle between the arm and the forearm in the frontal From the Biomechanics Laboratory, Rizzoli Orthopaedic Institute. Reprint requests: Maria Luisa Zampagni, Laboratorio di Biomeccanica, Istituti Ortopedici Rizzoli, Via di Barbiano 1/10, 40136 Bologna, Italy (E-mail: [email protected]). Copyright ª 2008 by Journal of Shoulder and Elbow Surgery Board of Trustees. 1058-2746/2008/$34.00 doi:10.1016/j.jse.2007.03.028
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plane,1,2,3,7,12,20,17,23,24,27,36,31 called the carrying angle, which has an important role when carrying loads.31 This angle is most apparent and best seen when the shoulder is externally rotated, the elbow is completely extended, and the forearm is supinated.26 In this position, the forearm is not in line with the arm but is deviated laterally.1 Anatomically, this valgus angulation is present because the trochlea extends farther distally than does the capitellum.37 Several authors have tried to provide information about the basal values of the carrying angle in specific age groups5,4,29,23,15 or distinguish it by sex or by side of the body.23,29,35 It appears to be strongly influenced by individual changes, and attempts to identify a correlation with age or physical characteristics have proved controversial.4,15 In clinical practice, the carrying angle is generally measured in full extension, and an increase in its value, compared with the contralateral elbow, may be attributed to previous trauma or developmental abnormality.6 However, in throwing athletes, it is not uncommon to find increased valgus in the throwing elbow due to adaptive changes to repetitive stress.6,16 Information about the carrying angle and its pathologic variations are important in the etiopathogenesis of various types of fractures seen around the elbow,15 in the diagnosis of diseases of the lateral (tennis elbow) and medial (golf elbow) epicondyles, and especially in the management of elbow fractures.9,10,13 Flynn et al9 developed criteria to grade the adequacy of reduction of supracondylar fractures of the humerus based on the evaluation of the carrying angle and total elbow range of motion loss after reduction by comparing the injured elbow with the healthy one. These criteria have been recently used to compare different fixation methods in supracondylar fractures of the humerus10 and to compare radial head resection with open reduction and internal fixation in patients with a comminuted radial head fracture.13 The carrying angle is generally estimated by the orthopedist by radiographs or a standard goniometer. In light of these efforts and in an attempt to solve the controversy in the literature, we calculated the carrying angle in vivo by using the theory of general rigid body motion to isolate the 3-dimensional (3D) rotation occurring at the elbow joint as suggested by Chao
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et al20 in their in vitro studies. By adopting this approach, they demonstrated that the carrying angle linearly decreases with flexion. Such a decrease is important as the carrying angle changes from more than 10 of valgus with the elbow fully extended to varus with the elbow fully flexed,6,20,30,31 Most controversy about the carrying angle is the result of differences in methodology and definition,3,17,31 but there may also be some disagreement about the exact flexion angle at which the carrying angle is measured. When the carrying angle is assessed on radiographs or by a goniometer, the true degree of flexion is not available. Our study presents a noninvasive method for evaluating the carrying angle in an in vivo setup that uses an electrogoniometer8,18,19,22 that digitizes the 3D coordinates of the anatomic landmarks and a numeric algorithm that gives the 3 components of the angle at the elbow joint carrying angle, flexion angle, and pronation angle. Reliability of the method was assessed, and carrying angle values were compared with those of the literature and measures obtained by a goniometer generally adopted in clinical settings.14,25,35
MATERIALS AND METHODS The right and left arms of 28 adults (15 men and 13 women) with a mean age 59 6 10 years (range, 41-81 years) were measured twice by a skilled operator. A total of 88 measurements were obtained because the data of 5 right arms and 7 left arms were lost. The right arm was dominant in all subjects. All participants were healthy, fit, and had no symptoms or signs of pathologies affecting the shoulder, elbow, or wrist joints. We obtained approval from the local ethics committee and written informed consent from all participants. The FaroArm Model Bronze18,19 (FARO Technologies Inc, Lake Mary, FL, http://www.faro.com) was used for measurements. The FaroArm is digital electrogoniometer with 6 of freedom and an anthropometric structure with 3 revolute links at the wrist, 1 at the elbow, and 2 at the shoulder (Figure 1). It can acquire data continuously at a rate of 50 Hz or point-by-point at the user’s request, with 0.3 mm/0.3 accuracy in a spherical workspace of 1.8-m diameter around its base. The FaroArm sensor is light, about 4 kg, and flexible, but it is mounted on a heavy and stable clamping base used to attach the sensor rigidly onto the experimental desktop and move it easily, when necessary, to fit the environmental obstacles. The FaroArm was used as a digitized device equipped with a point end effector. For in vivo investigation, the test was divided into 2 steps: First, the anatomic landmarks were identified through palpation and were marked with a pen to highlight them. Second, these points were digitized with the subjects seated on a fixed chair in front of a table where the FaroArm was placed, with each acquisition taking less than 1 minute. Measurements were made by placing the arm of the subject on the right of the device, with the forearm maintained fixed, fully extended, and supinated. Five anatomic points were
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Figure 1 Setup of measurement acquisition with the FaroArm Model Bronze (FARO Technologies, Lake Mary, FL).
acquired to identify the relative reference systems on the arm and forearm: Scapula AH: gap between acromion and humerus Humerus EM: most caudal point on medial epicondyle EL: most caudal point on lateral epicondyle Forearm US: most caudal-medial point on the ulnar styloid RS: most caudal-medial point on the radial styloid The landmarks EL, EM, US, and RS were chosen according to the 2005 International Society of Biomechanics recommendations.34 AH was chosen because it represents a more accessible point with respect to GH to identify the humeral axis32,33 and is more suitable for clinical and practical applications. The 3D coordinates of the digitized points were used to compute the reference systems relevant to the arm and forearm. The arm reference system was constructed by defining the Y-axis as the long axis of the humerus (a line connecting AH and the mid point of EL and EM, pointing to AH). The X-axis was the line perpendicular to the plane formed by EL, EM, and Y, pointing forward. The Z-axis was the line perpendicular to the Y- and X-axes. The forearm reference system was defined by unified segments on the radius and ulna. The y-axis was the line connecting the midpoint of RS and US and the midpoint between EL and EM. The x-axis was the line perpendicular to the plane through US and RS and the y-axis. The z-axis was the line perpendicular to y- and x-axes (Figure 2). The transformation matrix from the forearm reference system to the arm reference system was computed and used to obtain Cardan angles in the sequence Z-X-Y. The rotation around the floating z-axis corresponded to flexion-extension; the carrying angle was defined as the rotation around x-axis corresponding to the abduction-adduction, and the rotation around y-axis corresponded to pronation-supination. Carrying angle measures were also taken by a standard goniometer that is usually used in clinical and rehabilitation settings (Figure 3).
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Figure 3 Setup of measurement acquisition with the standard goniometer as it is usually used in clinical applications.
Data analysis Our reliability analysis included comparison between carrying angle values obtained by the FaroArm electrogoniometer and Cardan decomposition algorithm and by a standard goniometer, in addition to the analysis of repeatability of both the methods and comparison with literature values. After verifying normal distribution of data, differences between the methods were evaluated by paired samples Student tests and by calculating Pearson correlation coefficients. To estimate the repeatability of the methods, 2 repeated acquisitions in each arm (intraobserver) were compared, and significant differences were tested by the paired samples Student test. Interclass correlation coefficient (ICC) and standard error of measurement were also calculated. For the interpretation of the ICC, the criteria suggested by Cincchetti and Sparrow28 were used. Sex differences and side differences were evaluated by performing independent samples Student test and paired samples Student test, respectively. Finally, to verify the influence of the flexion and pronation angles on the carrying angle, the analysis of variance (ANOVA) was performed, and correlations between variations in the carrying angle and variations in the flexion angle (between repeated measures) were also calculated. The significance level was set at P ¼ .05 in all cases. Statistical analysis was done using SPSS 13.0 software (SPSS Inc, Chicago, IL).
RESULTS
Figure 2 Anatomic landmark points (AH, EL, EM, UR, US) and reference axis. X, Y, and Z identify the reference system of the arm, and x, y, z, identify the reference system of the forearm.
A mean carrying angle of 12.42 6 4.06 was found by adopting the FaroArm electrogoniometer. The mean degree of flexion at which the carrying angle was measured was 26.11 6 7.13 , and the mean pronation angle was 4.08 6 2.86 . The difference between these values and values obtained by a standard goniometer was 0.97 6 3.64, which was not significant (P ¼ .47), and the correlation between the methods was fair (r ¼ 0.46 with
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DISCUSSION The purpose of this study was to estimate carrying angle values in full extension using a noninvasive protocol able to give all of the 3 components of the angle formed at the elbow joint (carrying angle, flexion angle and pronation angle) based on the digitazation of easily identifiable landmark points and the Cardan decomposition algorithm. Our main findings were: 1.
Carrying angle values obtained by the proposed method have values similar to those
CARRYING ANGLE (degrees) by FARO ARM and by STANDARD GONIOMETER 25 Carrying angle (degrees) by STANDARD GONIOMETER
P ¼ .000), thus indicating reasonable agreement between the two approaches (Figure 4). With the FaroArm, the mean difference between repeated measures on the same subject was not statistically significant (0.56 , P ¼.27), with a standard error of measurements of 1.62 (Table I). The repeatability of the measures was excellent (ICC ¼ 0.85; P ¼ .000; Figure 5). The ANOVA test indicated that the flexion angle was a significant factor on carrying angle values (F ¼ 7.037; P ¼ .01) unlike the pronation angle (F ¼ 0.051; P ¼.823). In addition, variations between trial 1 and trial 2 of the carrying angle were significantly correlated with variations in the flexion angles (r ¼ 0.40; P ¼ .003). With the standard goniometer, the repeatability was good (ICC ¼ 0.76, P ¼ .000), and the mean difference of 0.23 between repeated measures was not significant (P ¼ .47; Figure 6). Sex differences were not significant with either method, although women showed slightly greater values than men (Table II). By the Cardan decomposition method, we obtained a mean carrying angle of 11.95 6 3.92 in men and 12.92 6 4.19 in women (P ¼ .265). An interesting finding was that the mean flexion angle of 5.26 in women was significantly smaller (P ¼ .000) than in men, indicating that women reach a greater natural physiologic extension than men. By the standard goniometer, a mean carrying angle of 11.24 6 3.36 was found in men and 11.79 6 2.68 in women (P ¼ .40). Side-of-the-body differences were not significant with either of our methods or a standard goniometer (Table III). By the Cardan decomposition method, the mean carrying angle values were 12.72 6 3.51 for the right (dominant) arm and 12.08 6 4.60 for the left arm (P ¼ .464), respectively. The mean flexion angle in the right arm was 2.98 smaller (P ¼.10) than in the left arm. By standard goniometer, the mean carrying angle values were 11.20 6 2.89 for the right arm (dominant arm) and 11.83 6 3.22 for the left arm (P ¼ .331).
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20
15
r = 0.46 p<0.001
10
5
0 0
5
10
15
20
25
Carrying angle (degrees) by FARO ARM
Figure 4 Correlation between carrying angle values ( ) obtained by FaroArm (FARO Technologies Inc, Lake Mary, FL) and by standard goniometer.
2. 3. 4. 5.
reported in the literature, adopting the same definition of carrying angle.7 Measures obtained by our method were in reasonable agreement with measures taken by a standard goniometer on our sample. The repeatability of the measures obtained by the proposed method was higher than that found by the standard goniometer. Our method gave reasonable values of flexion and pronation. Degrees of flexion were a significant factor on carrying angle estimation.
The carrying angle value is greatly variable as reported in the literature, but several authors reported a range between 11 and 14 .2,20,30,23 Within this range, some authors found differences between the sexes and arm side.23,31,35 Our sample showed neither sex nor arm side differences with the electrogoniometer or the standard goniometer. This could be explained in 2 ways: First, great individual variability of carrying angle31 might determine differences between the samples. Second, Beals5 explained apparent differences between the sexes by the increased joint laxity in women, which, permitting a greater degree of extension, should determine larger carrying angles. This consideration could be extended to arm side differences and was confirmed by the great degree of extension found in our sample in women and in right arms.
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Table I Carrying angle (and relative flexion angle) by FaroArm* and carrying angle by standard goniometer in 2 trials Trial, mean ± SD ( ) Method FaroArm Goniometer
Measure
Sample, No.
1
2
SEM ( )
ICC
Carrying angle Flexion angle Carrying angle
44 44 44
12.69 6 4.30 26.05 6 6.80 11.38 6 2.99
12.13 6 3.83 26.16 6 7.50 11.61 6 3.14
1.62 4.42 1.49
0.85y 0.62y 0.76y
SEM, Standard error of measurements; ICC, intraclass correlation coefficients. *FARO Technologies Inc, Lake Mary, FL. y P < .001.
CARRYING ANGLE (degrees) by FARO ARM repeated measures 25
Identity line
Trial 2 (degrees)
20
r=0.85 p<0.001
15
10
5
0
0
5
10 15 Trial 1 (degrees)
20
25
Figure 5 Correlation between carrying angle values ( ) obtained by FaroArm (FARO Technologies Inc, Lake Mary, FL) in trial 1 and trial 2.
We, however, studied athletes who, using mainly the upper extremity in their sports activity for more than 10 years, might present reduced joint laxity with respect to the nonathletic population, thus leading to the lack of significance of sex and side differences. Probable adaptive changes due to repetitive sport activity have already been found.6,16 Nevertheless, these results need to be confirmed by future studies. Bearing this in mind, the carrying angle cannot be estimated independently by the flexion angle, even when measured in apparent full extension position, because individual and adaptive changes in joint laxity might produce a misleading carrying angle assessment. This is supported by the fact that flexion was a significant factor (P ¼ .01) in the carrying angle estimation as well as correlation between variation in the carrying angle and variation in the flexion
Figure 6 Correlation between carrying angle values ( ) obtained by standard goniometer in trial 1 and trial 2.
angle on the same subject being significant (r ¼ 0.40; P ¼ .003). A comment is needed on the different standard deviation values between measures taken on right and left side (Table III). We observed that despite comparable mean values, the standard deviation was greater in the left arm. This could be due to the placement of the FaroArm device on the right side of the body. This error could easily be avoided in future acquisitions by placing the FaroArm device on the center of the table. By further comparison of values obtained by our method and measures taken on our sample by a standard goniometer, our protocol was more repeatable, particularly considering that our measurements were calculated in a blinded fashion without being influenced by the visualization of the value, which is immediately available after the acquisition. However,
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Table II Carrying angle and flexion angle values by FaroArm* and carrying angle by standard goniometer in male and female arms Method FaroArm Goniometer
Measure
Men (n ¼ 46), mean ± SD ( )
Women (n ¼ 42), mean ± SD ( )
Difference ( )
Carrying angle Flexion angle Carrying angle
11.95 6 3.92 28.61 6 6.54 11.24 6 3.36
12.92 6 4.19 23.35 6 6.76 11.79 6 2.68
0.97 5.26y 0.55
*FARO Technologies Inc, Lake Mary, FL. y P < .001.
Table III Carrying angle and flexion angle values by FaroArm* and carrying angle by standard goniometer in right and left arms Method FaroArm Goniometer
Measure
Right (n ¼ 46), mean ± SD ( )
Left (n ¼ 42), mean ± SD ( )
Difference ( )
Carrying angle Flexion angle Carrying angle
12.72 6 3.51 24.68 6 6.07 11.20 6 2.89
12.08 6 4.60 27.66 6 7.90 11.83 6 3.22
0.64 2.98 0.63
*FARO Technologies Inc, Lake Mary, FL.
a part of the reliability of this method could be also attributed to the skilled user, who was able to determine the correct position of the anatomic landmark points, which might be an important source of error when not performed accurately. In fact, the reference system of the humerus and forearm is determined by correct position of the sensor on the landmarks.28 In conclusion, this study shows that the carrying angle evaluation by the FaroArm and the Cardan algorithm provides more reliable results than other methods. The setup is comfortable for the subject, and acquisition is fast and takes about a minute, including software elaboration of the result. In addition to better repeatability compared with standard methods, the important clinical implication of the proposed noninvasive method to assess the carrying angle by 3D digitization of anatomic landmarks is the ability to evaluate the alignment of the elbow joint by obtaining flexion, pronation, and carrying angle values simultaneously at any elbow position. A great advantage in the application of this approach is that it can help to quantify the functional impairment associated with elbow pathologies in patients presenting with a reduced full extension capability. Therefore, this method could be useful to estimate pathologic variations of the carrying angle along with flexion and pronation angles after epicondylar diseases or to grade the adequacy of reduction of supracondylar fractures of the humerus. Other applications could include evaluation of adaptive changes due to repetitive stresses at the elbow joint in athletes or to help with monitoring during an elbow rehabilitation program. The described method in which digitized landmarks are used for carrying angle assessment also al-
lows easy inclusion in new computer technologies for assisted elbow surgery by graphic display and qualification of anatomic and functional features of the joint. We thank Silvia Bassini for her valuable help in graphic design. We also thank Dott. Zaffagnini Stefano and Giampaolo Bernagozzi for their contributions.
REFERENCES
1. Aebi H. Der elbogenwinkel, seine beziehungen zu geschlect, Korperbau and Huftbrite. (Inaug Diss, Basel 1947) Acta Anat 1947; 3:229-64. 2. Amis AA, Miller JH. The elbow. Clin Rheumatol Dis 1982;8: 571-93. 3. An KN, Morrey BF, Chao EYS. Carrying angle of the human elbow joint. J Orthop Res 1984:369-78. 4. Balasubramanian P, Madhuri V, Muliyil J. Carrying angle in children: a normative study. J Pediatr Orthop B 2006;15:37-40. 5. Beals RK. The normal carrying angle of the elbow. A radiographic study of 422 patients. Clin Orthop Relat Res 1976;119:194-6. 6. Cain EL Jr, Dugas JR, Wolf RS, Andrews JR. Elbow injuries in throwing athletes: a current concepts review. Am J Sports Med 2003; 31:621-35. 7. Chao EY, Morrey BF. Three-dimensional rotation of the elbow joint. J Biomech 1978;11:57-73. 8. Feathers DJ, Paquet V, Drury CG. Measurement consistency and three-dimensional electromechanical anthropometry. Int J Indust Ergon 2004;33:181-90. 9. Flynn JC, Matthews JG, Benoit RL. Blind pinning of displaced supracondylar fractures of the humerus in children. Sixteen years’ experience with long-term follow-up. J Bone Joint Surg Am 1974;56: 263-72. 10. Foead A, Penafort R, Saw A, Sengupta S. Comparison of two methods of percutaneous pin fixation in displaced supracondylar fractures of the humerus in children. J Orthop Surg 2004;12: 76-82. 11. Fornalski S, Gupta R, Lee TQ. Anatomy and biomechanics of the elbow joint. Tech Hand Up Extrem Surg 2003;7:168-78.
112
Zampagni et al
12. Goto A, Moritomo H, Murase T, et al. In vivo elbow biomechanical analysis during flexion: Three-dimensional motion analysis using magnetic resonance imaging. J Shoulder Elbow Surg 2004; 13:441-7. 13. Ikeda M, Sugiyama K, Kang C, Takagaki T, Oka Y. Comminuted fractures of the radial head: comparison of resection and internal fixation. J Bone Joint Surg Am 2006;88(1 suppl 1):11-23. 14. Karagiannopoulos C, Sitler M, Michlovitz S. Reliability of 2 functional goniometric methods for measuring forearm pronation and supination active range of motion. J Orthop Sports Phys Ther 2003;33:523-31. 15. Khare GN, Goel SC, Saraf SK, Singh G, Mohanty C. New observations on carrying angle. Indian J Med Sci 1999;53:61-7. 16. King JW, Brelsford HJ, Tullos HS. Analysis of the pitching arm of the professional baseball pitcher. Clin Orthop 1969;767:116-23. 17. London JT. Kinematics of the elbow. J Bone Joint Surg Am 1981; 63:529-35. 18. Martelli S. New method for simultaneous anatomical and functional studies of articular joints and its application to the human knee. Comput Methods Programs Biomed 2003;70:223-40. 19. Martelli S, Zaffagnini S, Falcioni B, Marcacci M. Intraoperative kinematic protocol for knee joint evaluation. Comput Methods Programs Biomed 2000;62:77-86. 20. Morrey BF, Chao EY. Passive motion of the elbow joint. J Bone Joint Surg 1976;54:501-8. 21. Morrey BF. Applied anatomy and biomechanics of the elbow joint. Instr Course Lect 1986;35:59-68. 22. Paquet V, Feathers D. An anthropometric study of manual and powered wheelchair users. Int J Indust Ergon 2004;33:191-204. 23. Paraskevas G, Papadopoulos A, Papaziogas B, Spanidou S, Argiriadou H, Gigis J. Study of the carrying angle of the human elbow joint in full extension: a morphometric analysis. Surg Radiol Anat 2004;26:19-23. 24. Potter HP. The obliquity of the arm of the female in extension. The relationship of the forearm with the upper arm in flexion. J Anat 1985;29:488-93. 25. Ruotolo C, Price E, Panchal. Loss of total arc of motion in collegiate baseball players. J Shoulder Elbow Surg 2006;15:67-71.
J Shoulder Elbow Surg January/February 2008
26. Smith L. Deformity following supracondylar fractures of the humerus. Am J Orthop 1960;42:235-52. 27. Shiba R, Sorbie C, Siu DW, Bryant JT, Cooke D, Wevers HW. Geometry of the humeroulnar joint. J Orthop Res 1988;6: 897-906. 28. Stokdijk M, Biegstraaten M, Ormel W, de Boer YA, Veeger HE, Rozing PM. Determining the optimal flexion-extension axis of the elbow in vivo - a study of interobserver and intraobserver reliability. J Biomech 2000;33:1139-45. 29. Tu¨kenmez M, Demirel H, Perc¸in S, Tezeren G. Measurement of the carrying angle of the elbow in 2,000 children at ages six and fourteen years. Acta Orthop Traumatol Turc 2004;38:274-6. 30. Van Roy P, Van Gheluwe B, Hebbelinck M, Van Holst I. An in-vivo arthrokinematic investigation of the carrying angle of the elbow. J Biomechan 1993;26:791. 31. Van Roy P, Baeyens JP, Fauvart D, Lanssiers R, Clarijs JP. Arthrokinematics of the elbow: study of the carrying angle. Ergonomics 2005;48:1645-56. 32. Veeger HEJ, Van der Helm FCT, Rozendal RH. Orientation of the scapula in a simulated wheelchair push. Clin Biomech 1993;8: 81-90. 33. Veeger HEJ, Yu B, An KN, Rozendal RH. Parameters for modelling the upper extremity. J Biomech 1997;30:647-52. 34. Wu G, Van der Helm FC, Veeger HE, et al. 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. J Biomech 2005;38:981-92. 35. Yilmaz E, Karakurt L, Belhan O, Bulut M, Serin E, Avci M. Variation of carrying angle with age, sex, and special reference to side. Orthopedics 2005;28:1360-3. 36. Youm Y, Dryer RF, Thambyrajah K, Flatt AE, Sprague BL. Biomechanical analyses of forearm pronation-supination and elbow flexion-extension. J Biomech 1979;12:245-55. 37. Zuckerman JD, Matsen FA 3rd. Biomechanics of the elbow. In: Nordon M, Frankel VH, editors. Basic biomechanics of the musculoskeletal system. Philadelphia, PA: Williams & Wilkins: Media; 1989. p. 249-60.