Medical Engineering and Physics 46 (2017) 112–113
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Corrigendum
Corrigendum to ‘A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty’ Medical Engineering & Physics 38 (2016) 1376–1381 Jing-Xin Zhao a,1, Xiu-Yun Su b,a,1, Ruo-Xiu Xiao c, Zhe Zhao d,a, Li-Hai Zhang a, Li-Cheng Zhang a, Pei-Fu Tang a,∗ a
Department of Orthopaedics, Chinese PLA General Hospital, Beijing, 100853, People’s Republic of China; Department of Orthopaedics, Affiliated Hospital of the Academy of Military Medical Sciences, No.8 Dongdajie Road, Beijing 100071, People’s Republic of China; c Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, 100084, People’s Republic of China; d Department of Orthopaedics, Beijing Tsinghua Chang Gung Hospital, No.1 Block Tiantongyuan North, Beijing 102218, People’s Republic of China. b
The authors would like to apologise for three errors in the above published article. We acknowledge that it is authors’ responsibility to prevent any mistakes in the manuscript prior to submission and accept full responsibility for those errors. The first mistake was that the calculation results of Tables 1 and 2 were based on the conditions that the coordinates of the center of the opening circle of the cup and the X-ray beam source were (80, 0, 125) and (0, 0, 1150) in 3D space, and the radius of the opening circle of the cup was 55. Actually, the radius of the opening circle of the cup could not be 55 in the clinical situation. Based on the conditions in the published manuscript, that the center of the opening circle of the cup and the X-ray beam source were (80, 0, 125) and (0, 0, 1250), and the diameter of the opening circle of the cup was 55, the correct Tables 1 and 2 are listed as follows. Table 1 The measured RA angles at different combinations of the true RA and RI angles True RI/deg
True RA angle/deg 5
10
15
20
25
30
35
40
45
35 40 45 50 55
2.66 2.37 2.12 1.88 1.67
7.65 7.37 7.11 6.88 6.67
12.64 12.36 12.11 11.88 11.67
17.62 17.35 17.11 16.88 16.67
22.61 22.35 22.1 21.88 21.67
27.6 27.34 27.09 26.87 26.68
32.58 32.33 32.09 31.87 32.68
37.57 37.32 37.08 36.87 36.68
42.55 42.3 42.08 41.87 41.68
Table 2 The measured RI angles at different combinations of the true RI and RA angles True RI/deg
True RA angle/deg 5
10
15
20
25
30
35
40
45
35 40 45 50 55
35.15 40.13 45.11 50.1 55.07
35.45 40.4 45.36 50.31 55.27
35.74 40.68 45.61 50.54 55.48
36.05 40.96 45.87 50.78 55.69
36.37 41.26 46.14 51.03 55.91
36.71 41.57 46.43 51.29 56.14
37.08 41.92 46.75 51.57 56.39
37.48 42.29 47.09 51.88 56.66
37.95 42.72 47.48 52.23 56.97
DOI of original article: 10.1016/j.medengphy.2016.09.007 Corresponding author: Tel: 86-10-66938101; Fax: 86-10-68161218. E-mail addresses:
[email protected] (J.-X. Zhao),
[email protected] (X.-Y. Su),
[email protected] (R.-X. Xiao),
[email protected] (Z. Zhao),
[email protected] (L.-H. Zhang),
[email protected] (L.-C. Zhang),
[email protected] (P.-F. Tang). 1 These authors have contributed equally to this work. ∗
http://dx.doi.org/10.1016/j.medengphy.2017.06.014 1350-4533
J.-X. Zhao et al. / Medical Engineering and Physics 46 (2017) 112–113
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We agree with Dr. Derbyshire’s viewpoint that it’s inappropriate to use Student’s t tests to assess the values in Tables 1 and 2 in our published paper. We tried to use this way to present the statistic differences between the “measurement” results of the traditional method and the true RI and RA angles of the cup at different angles combinations in Tables 1 and 2. The second mistake was that the single example in the result section 3.2 was based on the coordinate of the X-ray beam source in 3D space, (0, 0, 1025), which also could be found in the Eq. (8) in the above published manuscript. Actually, the third parameter of the parametric equation for the oblique cone (8), 1025v, also represents the position of the X-ray beam source or the vertex of this oblique cone in 3D space. Based on Eq. (1) in our published manuscript and the calculated normal vector of the opening circle of the cup, [0.688, –0.6745, 0.2678], the true RI and RA angles were 45.5676° and 15.5322° in this case. The RI angle of 46.94° in the article was a calculation mistake. The third mistake was related with the second mistake. As Dr. Derbyshire have mentioned in his letter to Editor, the longer and shorter semi-axes should not be 61 and 13 in the case of the result section 3.2. If the longer and shorter axes are 61 and 13, according to the actual clinical situation, the ellipse’s center is still (80, 0, 0), with the inclination angle of 46.24 °, and the X-ray beam source is (0, 0, 1025), the parametric equation for the oblique cone can be established and Eq. (8) should be transformed into the following form.
{(1 − v )(21.09 cos (u ) − 4.69 sin (u ) + 80), (1 − v )(4.496 sin (u ) + 22.03 cos (u )), 1025v} Based on Eqs. (1) and (2) in the manuscript, the true RI and RA angles are 45.5668° and 15.5168° in this situation. These results are similar to the situation when the longer and shorter semi-axes are 61 and 13, respectively. Although these mistakes would not influence the calculation process and accuracy of the established model, we still emphasized that “the established formulas must be deduced and verified with caution when applied for the first time” in the end of the article. Once the mathematical model is set up, it’s very important that the calculation conditions should be set correctly before computational processing. Dr. Derbyshire mentioned that our mathematical method was used in the situation when the X-ray beam was focusing centrally on the pelvis. However, the established model of the oblique cone can connect any “3D circle” to any projected “2D ellipse” on the projection plane.
