Eur J Orthop Surg Traumatol DOI 10.1007/s00590-013-1353-4
ORIGINAL ARTICLE
A new method for the measurement of anteversion of the acetabular cup after total hip arthroplasty Mehmet Aydogan • Halil Burc¸ • Gursel Saka
Received: 5 August 2013 / Accepted: 30 October 2013 Ó Springer-Verlag France 2013
Abstract Objective Many methods of determining the anteversion of the acetabular cup have been described in the literature. The advantages and disadvantages of each of these methods are discussed in this paper. We present a new method of measuring the acetabular anteversion at the anteroposterior hip. Materials and methods The formula designed by the authors was anteversion angle (a) = arc sin |PK|/H |AK| 9 |BK|. The formula was tested using the AutoCAD software, and an experimental study was conducted to evaluate the accuracy. Three groups were created, and 16 X-ray images were taken and coded. Ten orthopaedic surgeons measured the acetabular anteversion from these X-rays using our formula. Results The results in Group 1 were closer to the actual value; in contrast, the results in Group 2 differed from the actual values. The results in Group 3 were as close to the actual anteversion values as were those in Group 1.
M. Aydogan Bosphorus Spine Center, C¸akmak Mh Tavukc¸uyolu cd Ag˘aog˘lu MY City B2 D2932 Umraniye, Istanbul, Turkey e-mail: [email protected] H. Burc¸ (&) Department of Orthopaedics and Traumatology, Faculty of Medicine, Suleyman Demirel University, 32260 C¸u¨nu¨r, Isparta, Turkey e-mail: [email protected] G. Saka Department of Orthopaedics and Traumatology, Umraniye Research and Education Hospital, Elmalıkent Mahallesi Adem ¨ mraniye, Istanbul, Turkey Yavuz Cad. No:1 U e-mail: [email protected]
Conclusion Developments in technology often bring an increase in complications. Despite newly developed surgical methods and technology, the position of the acetabular cup is still used to determine the results of a total hip arthroplasty. Our method is simple, cost-effective and achieves almost 100 % accuracy. Keywords Acetabulum Anteversion Total hip arthroplasty
Introduction The placement of the acetabular cup is the most crucial step in total hip arthroplasty (THA). Intraoperative difficulties and technical mistakes can significantly impact THA results. Accordingly, malposition of the acetabular cup results in increased risk of dislocation, limited range of motion (ROM) and impingement [1–7]. The acetabular cup position after THA has been analysed since the procedure was first performed. Complications such as dislocation, early aseptic loosening and the position of the acetabular component have always been of interest. Charnley was the first to place a cerclage wire around the cup to determine the position of the acetabular component, thereby allowing analysis of the anteversion on post-operative X-rays based on the ellipse formed by the cerclage wire [1]. In recent years, many methods of determining cup anteversion, such as tomography or radiography imaging, have been described [2–8]. However, clinical usage of these radiography-based methods is limited due to their disadvantages. In this study, we present a new method of measuring the acetabular anteversion at the anteroposterior (AP) hip using radiography and to explore the accuracy of this method
123
Eur J Orthop Surg Traumatol
using mathematics analysis.
and
software
(AutoCAD)-based
Materials and methods The formula designed by the authors was as follows: anteversion angle (a) = arc sin |PK|/H |AK| 9 |BK| ‘‘Appendix’’. The ABCD ellipse in Fig. 1 represents the ellipse formed by the wire around the cup. Point A is any point on the ellipse, which is clearly visible (Figs. 2, 3). The circle in Fig. 4a of 50 mm in diameter represents the cerclage wire around the cup that was formed in the AutoCAD 2000 (Ó2000 Autodesk Inc., USA) software. This circle, representing the inclination in the acetabular cup, was 45° and was visible as a straight line when viewed from the side (Fig. 4a, b). An ellipse was formed when the circle was 8° anteverted (Fig. 5a). According to the formula, when the necessary measurement is taken from any of the most visible points of the ellipse, since a = arc sin PK / HAK. BK
PK ¼ 3:19 mm AK ¼ 15 mm: BK = 35 mm when these values are placed in the formula, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ arc sin 3:19= 15 35 ¼ arc sin 3:19=22:91 ¼ arc sin 0:139240 ¼ 8:0039 : The circle was anteverted 20° (Fig. 5b). When the measurements were taken on the figure and applied to the formula, a ¼ arc sin 7:84=22:91 ¼ arc sin 0:342208 ¼ 20:011 : When the circle was anteverted 32°, the ellipse appeared slightly wider (Fig. 5c). When the measurements made here were applied to the formula, a ¼ arc sin 12:14=22:91 ¼ arc sin 0:529899 ¼ 31:9986 : An experimental radiological study was designed to demonstrate the clinical usability of the method, and an experimental model was prepared. Preparation of the materials The pelvic bone was located anterior to a radiolucent platform with the pelvic plane parallel to the ground. The distance between the centre of the acetabulum and the X-ray cassette was set at 10 cm. A water gauge was used to ensure that the anterior pelvic plane was parallel to the ground (Fig. 6a). In this experimental set-up, a 52-mm polyethylene cup, a 48-mm cementless metal-backed acetabular cup and a 28-mm head and femoral component were placed in the known acetabular anteversions. Experimental study There were three variables in this experimental set-up:
Fig. 1 The model explanation of the formula that was the subject of our study
Fig. 2 Creation of the acetabular anteversion model in the AutoCAD software for mathematical explanation of the formula
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1. 2.
Distance between the X-ray tube and object; Distance between the centre of the X-ray beams and the centre of the acetabulum;
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beam was set to the centre of the acetabulum. The only variable to be examined was the anteversion of the cup (Fig. 7a, b, c). In total, eight X-rays were taken and coded with cemented and cementless cups at different anteversion angles. Group 2 The distance between the X-ray tube and the object (100 cm) and the cup position was fixed, and the X-ray beams were focused on the symphysis pubis and the mid-point between the symphysis pubis and the centre of the acetabulum. Four X-rays were taken and coded (Fig. 8).
Fig. 3 Creation of the acetabular anteversion model in the AutoCAD software for mathematical explanation of the formula according to the X-ray beam direction
Group 3 X-ray beams were focused on the centre of the acetabulum, and the position of the cup was fixed. The distances between the X-ray tube and the object were 110 and 75 cm, and four X-rays were taken and coded. On 16 X-rays, 10 orthopaedic surgeons made anteversion measurements using the formula obtained in this study and the results were recorded. All measurements were taken using a standard pencil and goniometer, and the calculations were performed using a basic calculator. Statistical analysis The Statistical Package for the Social Sciences (SPSS) software was used for statistical analysis. P \ 0.05 was accepted as the level of significance. Data were expressed as mean and standard deviation. The one-sample t test was used.
Fig. 4 The frontal and 0° visual model of the acetabulum
Results 3.
The anteversion of the acetabular cup.
Three groups were created to examine each variable; the other two remained fixed. Group 1 The distance between the X-ray tube and the object was fixed at 100 cm, and the centre of the X-ray
The anteversion values determined in a computer-based environment could be calculated correctly by replacing the measurement results in the formula. Small deviations can be explained by the fact that no more than two digits after the comma were considered.
Fig. 5 Acetabular anteversion models of 8°, 20° and 32°
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Fig. 6 Preparation of the experimental model
Fig. 7 The X-ray imaging method
As can be understood from the formula, point P was selected as the optimum point, which was not superimposed by the head and neck of the femoral component. It is evident that the placement of this reference point did not affect the result. The fact that it was possible to make a measurement from one half of the ellipse made it unnecessary to complete the other half, which was not the case in cementless cups or in areas superimposed by the head.
The mean values in Group 2 were different from the actual values (P \ 0.05). The mean values in Group 3 were as close to the actual anteversion values as those in Group 1. Mean acetabular anteversion values measured by observers were not statistically significantly different from the actual values. Since magnification mathematically changes the numerator and denominator in the formula at the same rate, this did not affect the result.
Experimental study results
Discussion
The results of the experiment groups are stated in Tables 1, 2 and 3. The results in Group 1 were closer to the actual value. Mean acetabular anteversion values measured by observers are not statistically significantly different from the actual values.
In many clinics, the inclination of the acetabular cup is measured after THA, but not the anteversion, which is not typically measured unless complications arise; these include dislocation, early aseptic loosening or early polyethylene corrosion.
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Eur J Orthop Surg Traumatol Table 2 Results of Group 2 X-ray code
Actual anteversion
Mean ± SD
Difference
CI 95 %
P value
AOS01
10
5.22 ± 0.6
-4.7
-6.3 to -3.1
0.006
AOS02
33
26.7 ± 0.8
-6.2
-8.4 to -4.1
0.006
AOU01
10
7.2 ± 0.3
-2.7
-3.6 to -1.8
0.005
AOU02
33
28.1 ± 0.5
-4.8
-6.3 to -3.4
0.004
Table 3 Results of Group 3
Fig. 8 Demonstration of how the X-ray beam was focused in Group 2
Table 1 Results of Group 1 X-ray code
Actual anteversion
Mean ± SD
Difference
CI 95 %
P value
AC ¸ 01
8
8.5 ± 0.4
0.5
0.6 to 1.7
0.1
AS02
10
10 ± 0.5
0.05
-1.2 to 1.3
0.8
AC ¸ 03
15
16.1 ± 0.9
1.1
-1.2 to 3.6
0.1
AS04
20
20.6 ± 1.2
0.6
-2.4 to 3.8
0.4
AC ¸ 05
26
26.6 ± 0.55
0.6
-0.7 to 2
0.1
AS06
30
30.5 ± 0.4
0.5
-0.4 to 1.6
0.1
AC ¸ 07
35
34.3 ± 1.23
AC ¸ 08
43
43.8 ± 1.7
-0.6
-3.7 to 2.3
0.4
0.8
-3.4 to 5.2
0.4
McLaren et al. [9] developed a conversion table by proportioning the major axis with the minor axis of the ellipse. Next, Ghelman and Schneider independently attempted to determine anteversion using fluoroscopy [10, 11]. These methods are not widely used, as they are timeconsuming, expensive and required high rates of radiation exposure [12]. Visser and Ko¨nig [13] explained a complex trigonometry formula using a system, in which they used Cartesian points in the ellipse, which was viewed radiographically. However, the effectiveness of the method was not stated. Ackland et al. [14] developed software to prevent mistakes while completing the ellipse to measure its minor axis. They developed a wide conversion table to determine anteversion. They did not provide information about the formula used or the software. Yao et al. [15] stated that the anteversion could be determined using axiolateral graphs and showed that it was possible to differentiate the anteversion and retroversion on the same graph. However, this method requires the use of a
X-ray code
Actual anteversion
AMF01
10
AMF02
Mean ± SD
Difference
CI 95 %
P value
9.6 ± 0.5
-0.3
-1.6 to 0.9
0.3
26
25.5 ± 0.4
-0.4
-1.4 to 0.5
0.1
AMN01
10
10.3 ± 0.7
-0.3
-1.5 to 2.2
0.5
AMN02
34
34.1 ± 0.4
0.1
-0.9 to 1.2
0.6
conversion table to convert the axiolateral anteversion angle to the actual anteversion angle; there is also the problem of radiography standardisation. Hassan et al. [16] developed a complex mathematical formula for measurement of acetabular anteversion on AP radiography and assessed its intraobserver reliability. As is the case for the others, this method requires complex calculations and a conversion table. In a study by Mian et al. [17], the acetabular anteversion was measured using computed tomography. Computer software was used to prevent the appearance of metal reflections after THA. However, this method was not widely used since it requires specialised software, exposes patients to excessive radiation and is expensive and time-consuming. In post-operative radiographs, as part of the ellipse is covered by the femoral head and neck in cemented prostheses and half of the ellipse can not be seen in uncemented ones, there are problems related to the clinical application of all of the formulae. Therefore, the authors preferred to complete the invisible part of the ellipse using relative lines. However, it is important to draw the lines correctly while completing this part. At this stage, even minor mistakes can cause considerable angular changes. Lewinnek et al. [12] attempted to complete the invisible part of the cup using a Draughtsman’s French curve. However, this led to mistakes due to changes in cup dimensions and a change in the curvature of the anteversion angles. Most of the methods described lead to mistakes and inadequate evaluation of the anteversion in cementless
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cups. Though methods such as measuring half of the ellipse and doubling it are currently used, they are prone to human error. Haenle et al. [18] selected the modified method of Pettersson et al. and compared it with the methods of Ackland, Pradhan and Hassan et al. The modified method of Pettersson et al. exhibited greater inter/intraobserver reliability. They used 28-mm metal and ceramic heads in their experimental model and stated that this method allows better visibility of landmarks and facilitates completing the ellipse since the ceramic head is radiolucent. Our method differs because the point selected is not important, and there is no need to complete the ellipse. Importantly, although the observers used different points of reference, they all arrived at similar results, which did not differ between cementless and cemented cups. In addition, it is essential to standardise X-rays to ensure accurate measurements. The anterior pelvic plane of the patient must be parallel to the cassette, and the rays must be perpendicular to both of these planes and focused on the cup centre. Otherwise, false results are unavoidable. In this study, a new formula for accurate determination of acetabular anteversion using post-operative AP radiographs was developed. The mathematical explanations and accuracy were investigated in the software environment. The focus of the X-rays, magnification and changing anteversion angles were investigated independently; the magnification did not affect the measurements, but focusing the X-rays on a point other than the centre of the acetabulum caused errors in measurements. Zheng et al. [19] described a method of measuring the acetabulum anteversion after THA along with the 2D/3D reconstruction method, which they performed directly from the graph using a computer. However, unlike our study, that method requires additional equipment and software support and reconstruction, which is a disadvantage. To identify the most reliable acetabulum anteversion measurement method, Tiberi et al. [20] compared the Einzel-Bild-Roentgen-Analyse (EBRA), and Woo and Morrey and ischio-lateral methods. Although the ischiolateral method was found to be more reliable and rapid, they also mentioned a number of limitations to their study. They stated that at least three radiographs should be taken in the post-operative phase and serial measurements should be performed, assuming that the acetabular component does not move. They also mentioned that one should be aware of increasing the radiation exposure due to performance of additional radiographs. Criticisms of the EBRA method included that it was time-consuming and required specialised software. The Moo and Morrey method was associated with a high error rate. With regard to their own method, they felt that the ischium should be completely visible in the Danelius–Miller lateral graph, which is a
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special position; otherwise, the measurements can be inaccurate. Therefore, determining the acetabular anteversion after THA is vital for identifying the aetiology of complications in patient follow-up. Additionally, our method is simple, cost-effective and yields almost 100 % accuracy. A limitation of the current study is the lack of clinical trials, which are needed to demonstrate the effectiveness of the formula after THA. Conflict of interest
None.
Appendix: The mathematical explanation of the formula When the hemisphere in Fig. 2a is an acetabular cup and the M plane beneath that is an X-ray cassette, the open surface of acetabular cup will only appear as a straight line. When the acetabular cup in Fig. 2a is anteverted at an angle, this straight line will appear as an ellipse (Fig. 2b). The reflection of this ellipse on the X-ray will be seen as the hatched area in Fig. 2c. Now, when we consider that the X-ray beams come from the arrow mark direction as shown in Fig. 3: OA ¼ OB ¼ OE ¼ r OP1 ¼ OP2 ¼ r When the AP1B circle turns around AB as much as AP2B, the turning angle will be P1OP2 = a. While the view of AP1B circle AB line, the view (projection) of AP2BP3 circle ACBD ellipse. OP1P2E ? AB ¼ OP1 ? AB; OP2 ? AB; OP1==P2C and CP2O angle ¼ a
OP1 ? OE
P2C ? OE ðprojectionÞ so OC ¼ b OP2 ¼ r
In OP2C right triangle, sin a = OC/OP2 = b/r. Ellipse equation x2/a2 ? y2/b2 = 1 here; OA = a = r, OC = b. PK and KA are measurable lengths, and PK = y, OK = x = OA-AK = r-l. x2 =a2 þ y2 =b2 ¼ 1 a2 b2 b2 x2 þ a2 y2 ¼ a2 b2 b2 x2 a2 b2 ¼ a2 y2 ð 1Þ b2 a2 x 2 ¼ a2 y 2 p b2 ¼ a2 y2 =a2 x2 b ¼ ay= a2 x2 a ¼ r; x ¼ ðr lÞ to find b: x2 ¼ r 2 2rl þ l2 p p sin a ¼ b=a ¼ y= r 2 r 2 þ 2rl l2 ¼ y= 2rl l2 p p ¼ PK= 2r AKAK2 ¼ PK= AKð2r AKÞ Since 2r-AK = BK, Sin a = PK/HAKBK.
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References 1. Charnley J (1961) Arthroplasty of the hip: a new operation. Lancet 1(7187):1129–1132 2. DiGioia AM, Jaramaz B, Blackwell M et al (1998) Image guided navigation system to measure intraoperatively acetabular implant alignment. Clin Orthop 355:8–22 3. DiGioia AM, Jaramaz B, Plakseychuk AY et al (2002) Comparison of a mechanical acetabular alignment guide with computer placement of the socket. J Arthroplast 17:359–364 4. D’Lima DD, Urquhart AG, Buehler KO et al (2000) The effect of the orientation of the acetabular and femoral components on the range of motion of the hip at different head–neck ratios. J Bone Joint Surg 82A:315–321 5. Kennedy JG, Roger WB, Suffe KE et al (1998) Effect of acetabular component orientation on recurrent dislocation. J Arthroplast 13:530 6. Maruyama M, Feinberg JR, Capello WN, D’Antonio JA (2001) Morphologic features of the acetabulum and femur. Clin Orthop 393:52–65 7. Mc Collum DE, Gray WJ (1990) Dislocation of total hip arthroplasty: causes and prevention. Clin Orthop 261:159 8. Vendittolli PA, Duval N, Stitson DJ, Masse B (2002) Vertical acetabular positioning with an inclinometer in total hip arthroplasty. J Arthroplast 17:936–941 9. Mc Laren RH (1973) Prosthetic hip angulations. Radiology 107:705–706 10. Ghelman B (1979) Radiographic localization of the acetabular component of a hip prosthesis. Radiology 130:540–542 11. Schneider R, Freiberger RH, Ghelman B, Ranawat CS (1982) Radiologic evaluations of painful joint prosthesis. Clin Orthop 170:156–168
12. Pradhan R (1999) Planar anteversion of the acetabular cup as determined from plain anteroposterior radiographs. J Bone Joint Surg Br 81(3):431–435 13. Visser JD, Ko¨nings JG (1981) A new method for measuring angels after total hip arthroplasty: a study of the acetabular cup and femoral component. J Bone Joint Surg 68B:409–413 14. Ackland MK, Bourne WB, Uhthoff HK (1986) Anteversion of the acetabular cup measurement of angle after total hip replacement. J Bone Joint Surg 68B:409–413 15. Yao L, Yao J, Gold RH (1995) Measurement of acetabular version on the axiolateral radiograph. Clin Orthop 316:106–111 16. Hassan DM, Johnston GH, Dust WN, Watson G, Dolovich AT (1998) Accuracy of intraoperative assessment of acetabular prosthesis placement. J Arthroplast 13:80–84 17. Mian SW, Truchly G, Pflum FA (1992) Computed tomography measurement of acetabular cup anteversion and retroversion in total hip arthroplasty. Clin Orthop 276:206–209 18. Haenle M, Mittelmeier W, Barbano R, Wo¨rtler K, Scholz R, Bader R (2010) Accuracy and reliability of different methods to evaluate the acetabular cup version from plain radiographs. Surg Radiol Anat 32:725–730 19. Zheng G, von Recum J, Nolte LP, Gru¨tzner PA, Steppacher SD, Franke J (2012) Validation of a statistical shape model-based 2D/ 3D reconstruction method for determination of cup orientation after THA. Int J Comput Assist Radiol Surg 7:225–231 20. Tiberi JV, Pulos N, Kertzner M, Schmlazried TP (2012) A more reliable method to assess acetabular component position. Clin Orthop Relat Res 470:471–476
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ORIGINAL ARTICLE
A new method for the measurement of anteversion of the acetabular cup after total hip arthroplasty Mehmet Aydogan • Halil Burc¸ • Gursel Saka
Received: 5 August 2013 / Accepted: 30 October 2013 Ó Springer-Verlag France 2013
Abstract Objective Many methods of determining the anteversion of the acetabular cup have been described in the literature. The advantages and disadvantages of each of these methods are discussed in this paper. We present a new method of measuring the acetabular anteversion at the anteroposterior hip. Materials and methods The formula designed by the authors was anteversion angle (a) = arc sin |PK|/H |AK| 9 |BK|. The formula was tested using the AutoCAD software, and an experimental study was conducted to evaluate the accuracy. Three groups were created, and 16 X-ray images were taken and coded. Ten orthopaedic surgeons measured the acetabular anteversion from these X-rays using our formula. Results The results in Group 1 were closer to the actual value; in contrast, the results in Group 2 differed from the actual values. The results in Group 3 were as close to the actual anteversion values as were those in Group 1.
M. Aydogan Bosphorus Spine Center, C¸akmak Mh Tavukc¸uyolu cd Ag˘aog˘lu MY City B2 D2932 Umraniye, Istanbul, Turkey e-mail: [email protected] H. Burc¸ (&) Department of Orthopaedics and Traumatology, Faculty of Medicine, Suleyman Demirel University, 32260 C¸u¨nu¨r, Isparta, Turkey e-mail: [email protected] G. Saka Department of Orthopaedics and Traumatology, Umraniye Research and Education Hospital, Elmalıkent Mahallesi Adem ¨ mraniye, Istanbul, Turkey Yavuz Cad. No:1 U e-mail: [email protected]
Conclusion Developments in technology often bring an increase in complications. Despite newly developed surgical methods and technology, the position of the acetabular cup is still used to determine the results of a total hip arthroplasty. Our method is simple, cost-effective and achieves almost 100 % accuracy. Keywords Acetabulum Anteversion Total hip arthroplasty
Introduction The placement of the acetabular cup is the most crucial step in total hip arthroplasty (THA). Intraoperative difficulties and technical mistakes can significantly impact THA results. Accordingly, malposition of the acetabular cup results in increased risk of dislocation, limited range of motion (ROM) and impingement [1–7]. The acetabular cup position after THA has been analysed since the procedure was first performed. Complications such as dislocation, early aseptic loosening and the position of the acetabular component have always been of interest. Charnley was the first to place a cerclage wire around the cup to determine the position of the acetabular component, thereby allowing analysis of the anteversion on post-operative X-rays based on the ellipse formed by the cerclage wire [1]. In recent years, many methods of determining cup anteversion, such as tomography or radiography imaging, have been described [2–8]. However, clinical usage of these radiography-based methods is limited due to their disadvantages. In this study, we present a new method of measuring the acetabular anteversion at the anteroposterior (AP) hip using radiography and to explore the accuracy of this method
123
Eur J Orthop Surg Traumatol
using mathematics analysis.
and
software
(AutoCAD)-based
Materials and methods The formula designed by the authors was as follows: anteversion angle (a) = arc sin |PK|/H |AK| 9 |BK| ‘‘Appendix’’. The ABCD ellipse in Fig. 1 represents the ellipse formed by the wire around the cup. Point A is any point on the ellipse, which is clearly visible (Figs. 2, 3). The circle in Fig. 4a of 50 mm in diameter represents the cerclage wire around the cup that was formed in the AutoCAD 2000 (Ó2000 Autodesk Inc., USA) software. This circle, representing the inclination in the acetabular cup, was 45° and was visible as a straight line when viewed from the side (Fig. 4a, b). An ellipse was formed when the circle was 8° anteverted (Fig. 5a). According to the formula, when the necessary measurement is taken from any of the most visible points of the ellipse, since a = arc sin PK / HAK. BK
PK ¼ 3:19 mm AK ¼ 15 mm: BK = 35 mm when these values are placed in the formula, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ arc sin 3:19= 15 35 ¼ arc sin 3:19=22:91 ¼ arc sin 0:139240 ¼ 8:0039 : The circle was anteverted 20° (Fig. 5b). When the measurements were taken on the figure and applied to the formula, a ¼ arc sin 7:84=22:91 ¼ arc sin 0:342208 ¼ 20:011 : When the circle was anteverted 32°, the ellipse appeared slightly wider (Fig. 5c). When the measurements made here were applied to the formula, a ¼ arc sin 12:14=22:91 ¼ arc sin 0:529899 ¼ 31:9986 : An experimental radiological study was designed to demonstrate the clinical usability of the method, and an experimental model was prepared. Preparation of the materials The pelvic bone was located anterior to a radiolucent platform with the pelvic plane parallel to the ground. The distance between the centre of the acetabulum and the X-ray cassette was set at 10 cm. A water gauge was used to ensure that the anterior pelvic plane was parallel to the ground (Fig. 6a). In this experimental set-up, a 52-mm polyethylene cup, a 48-mm cementless metal-backed acetabular cup and a 28-mm head and femoral component were placed in the known acetabular anteversions. Experimental study There were three variables in this experimental set-up:
Fig. 1 The model explanation of the formula that was the subject of our study
Fig. 2 Creation of the acetabular anteversion model in the AutoCAD software for mathematical explanation of the formula
123
1. 2.
Distance between the X-ray tube and object; Distance between the centre of the X-ray beams and the centre of the acetabulum;
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beam was set to the centre of the acetabulum. The only variable to be examined was the anteversion of the cup (Fig. 7a, b, c). In total, eight X-rays were taken and coded with cemented and cementless cups at different anteversion angles. Group 2 The distance between the X-ray tube and the object (100 cm) and the cup position was fixed, and the X-ray beams were focused on the symphysis pubis and the mid-point between the symphysis pubis and the centre of the acetabulum. Four X-rays were taken and coded (Fig. 8).
Fig. 3 Creation of the acetabular anteversion model in the AutoCAD software for mathematical explanation of the formula according to the X-ray beam direction
Group 3 X-ray beams were focused on the centre of the acetabulum, and the position of the cup was fixed. The distances between the X-ray tube and the object were 110 and 75 cm, and four X-rays were taken and coded. On 16 X-rays, 10 orthopaedic surgeons made anteversion measurements using the formula obtained in this study and the results were recorded. All measurements were taken using a standard pencil and goniometer, and the calculations were performed using a basic calculator. Statistical analysis The Statistical Package for the Social Sciences (SPSS) software was used for statistical analysis. P \ 0.05 was accepted as the level of significance. Data were expressed as mean and standard deviation. The one-sample t test was used.
Fig. 4 The frontal and 0° visual model of the acetabulum
Results 3.
The anteversion of the acetabular cup.
Three groups were created to examine each variable; the other two remained fixed. Group 1 The distance between the X-ray tube and the object was fixed at 100 cm, and the centre of the X-ray
The anteversion values determined in a computer-based environment could be calculated correctly by replacing the measurement results in the formula. Small deviations can be explained by the fact that no more than two digits after the comma were considered.
Fig. 5 Acetabular anteversion models of 8°, 20° and 32°
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Eur J Orthop Surg Traumatol
Fig. 6 Preparation of the experimental model
Fig. 7 The X-ray imaging method
As can be understood from the formula, point P was selected as the optimum point, which was not superimposed by the head and neck of the femoral component. It is evident that the placement of this reference point did not affect the result. The fact that it was possible to make a measurement from one half of the ellipse made it unnecessary to complete the other half, which was not the case in cementless cups or in areas superimposed by the head.
The mean values in Group 2 were different from the actual values (P \ 0.05). The mean values in Group 3 were as close to the actual anteversion values as those in Group 1. Mean acetabular anteversion values measured by observers were not statistically significantly different from the actual values. Since magnification mathematically changes the numerator and denominator in the formula at the same rate, this did not affect the result.
Experimental study results
Discussion
The results of the experiment groups are stated in Tables 1, 2 and 3. The results in Group 1 were closer to the actual value. Mean acetabular anteversion values measured by observers are not statistically significantly different from the actual values.
In many clinics, the inclination of the acetabular cup is measured after THA, but not the anteversion, which is not typically measured unless complications arise; these include dislocation, early aseptic loosening or early polyethylene corrosion.
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Eur J Orthop Surg Traumatol Table 2 Results of Group 2 X-ray code
Actual anteversion
Mean ± SD
Difference
CI 95 %
P value
AOS01
10
5.22 ± 0.6
-4.7
-6.3 to -3.1
0.006
AOS02
33
26.7 ± 0.8
-6.2
-8.4 to -4.1
0.006
AOU01
10
7.2 ± 0.3
-2.7
-3.6 to -1.8
0.005
AOU02
33
28.1 ± 0.5
-4.8
-6.3 to -3.4
0.004
Table 3 Results of Group 3
Fig. 8 Demonstration of how the X-ray beam was focused in Group 2
Table 1 Results of Group 1 X-ray code
Actual anteversion
Mean ± SD
Difference
CI 95 %
P value
AC ¸ 01
8
8.5 ± 0.4
0.5
0.6 to 1.7
0.1
AS02
10
10 ± 0.5
0.05
-1.2 to 1.3
0.8
AC ¸ 03
15
16.1 ± 0.9
1.1
-1.2 to 3.6
0.1
AS04
20
20.6 ± 1.2
0.6
-2.4 to 3.8
0.4
AC ¸ 05
26
26.6 ± 0.55
0.6
-0.7 to 2
0.1
AS06
30
30.5 ± 0.4
0.5
-0.4 to 1.6
0.1
AC ¸ 07
35
34.3 ± 1.23
AC ¸ 08
43
43.8 ± 1.7
-0.6
-3.7 to 2.3
0.4
0.8
-3.4 to 5.2
0.4
McLaren et al. [9] developed a conversion table by proportioning the major axis with the minor axis of the ellipse. Next, Ghelman and Schneider independently attempted to determine anteversion using fluoroscopy [10, 11]. These methods are not widely used, as they are timeconsuming, expensive and required high rates of radiation exposure [12]. Visser and Ko¨nig [13] explained a complex trigonometry formula using a system, in which they used Cartesian points in the ellipse, which was viewed radiographically. However, the effectiveness of the method was not stated. Ackland et al. [14] developed software to prevent mistakes while completing the ellipse to measure its minor axis. They developed a wide conversion table to determine anteversion. They did not provide information about the formula used or the software. Yao et al. [15] stated that the anteversion could be determined using axiolateral graphs and showed that it was possible to differentiate the anteversion and retroversion on the same graph. However, this method requires the use of a
X-ray code
Actual anteversion
AMF01
10
AMF02
Mean ± SD
Difference
CI 95 %
P value
9.6 ± 0.5
-0.3
-1.6 to 0.9
0.3
26
25.5 ± 0.4
-0.4
-1.4 to 0.5
0.1
AMN01
10
10.3 ± 0.7
-0.3
-1.5 to 2.2
0.5
AMN02
34
34.1 ± 0.4
0.1
-0.9 to 1.2
0.6
conversion table to convert the axiolateral anteversion angle to the actual anteversion angle; there is also the problem of radiography standardisation. Hassan et al. [16] developed a complex mathematical formula for measurement of acetabular anteversion on AP radiography and assessed its intraobserver reliability. As is the case for the others, this method requires complex calculations and a conversion table. In a study by Mian et al. [17], the acetabular anteversion was measured using computed tomography. Computer software was used to prevent the appearance of metal reflections after THA. However, this method was not widely used since it requires specialised software, exposes patients to excessive radiation and is expensive and time-consuming. In post-operative radiographs, as part of the ellipse is covered by the femoral head and neck in cemented prostheses and half of the ellipse can not be seen in uncemented ones, there are problems related to the clinical application of all of the formulae. Therefore, the authors preferred to complete the invisible part of the ellipse using relative lines. However, it is important to draw the lines correctly while completing this part. At this stage, even minor mistakes can cause considerable angular changes. Lewinnek et al. [12] attempted to complete the invisible part of the cup using a Draughtsman’s French curve. However, this led to mistakes due to changes in cup dimensions and a change in the curvature of the anteversion angles. Most of the methods described lead to mistakes and inadequate evaluation of the anteversion in cementless
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cups. Though methods such as measuring half of the ellipse and doubling it are currently used, they are prone to human error. Haenle et al. [18] selected the modified method of Pettersson et al. and compared it with the methods of Ackland, Pradhan and Hassan et al. The modified method of Pettersson et al. exhibited greater inter/intraobserver reliability. They used 28-mm metal and ceramic heads in their experimental model and stated that this method allows better visibility of landmarks and facilitates completing the ellipse since the ceramic head is radiolucent. Our method differs because the point selected is not important, and there is no need to complete the ellipse. Importantly, although the observers used different points of reference, they all arrived at similar results, which did not differ between cementless and cemented cups. In addition, it is essential to standardise X-rays to ensure accurate measurements. The anterior pelvic plane of the patient must be parallel to the cassette, and the rays must be perpendicular to both of these planes and focused on the cup centre. Otherwise, false results are unavoidable. In this study, a new formula for accurate determination of acetabular anteversion using post-operative AP radiographs was developed. The mathematical explanations and accuracy were investigated in the software environment. The focus of the X-rays, magnification and changing anteversion angles were investigated independently; the magnification did not affect the measurements, but focusing the X-rays on a point other than the centre of the acetabulum caused errors in measurements. Zheng et al. [19] described a method of measuring the acetabulum anteversion after THA along with the 2D/3D reconstruction method, which they performed directly from the graph using a computer. However, unlike our study, that method requires additional equipment and software support and reconstruction, which is a disadvantage. To identify the most reliable acetabulum anteversion measurement method, Tiberi et al. [20] compared the Einzel-Bild-Roentgen-Analyse (EBRA), and Woo and Morrey and ischio-lateral methods. Although the ischiolateral method was found to be more reliable and rapid, they also mentioned a number of limitations to their study. They stated that at least three radiographs should be taken in the post-operative phase and serial measurements should be performed, assuming that the acetabular component does not move. They also mentioned that one should be aware of increasing the radiation exposure due to performance of additional radiographs. Criticisms of the EBRA method included that it was time-consuming and required specialised software. The Moo and Morrey method was associated with a high error rate. With regard to their own method, they felt that the ischium should be completely visible in the Danelius–Miller lateral graph, which is a
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special position; otherwise, the measurements can be inaccurate. Therefore, determining the acetabular anteversion after THA is vital for identifying the aetiology of complications in patient follow-up. Additionally, our method is simple, cost-effective and yields almost 100 % accuracy. A limitation of the current study is the lack of clinical trials, which are needed to demonstrate the effectiveness of the formula after THA. Conflict of interest
None.
Appendix: The mathematical explanation of the formula When the hemisphere in Fig. 2a is an acetabular cup and the M plane beneath that is an X-ray cassette, the open surface of acetabular cup will only appear as a straight line. When the acetabular cup in Fig. 2a is anteverted at an angle, this straight line will appear as an ellipse (Fig. 2b). The reflection of this ellipse on the X-ray will be seen as the hatched area in Fig. 2c. Now, when we consider that the X-ray beams come from the arrow mark direction as shown in Fig. 3: OA ¼ OB ¼ OE ¼ r OP1 ¼ OP2 ¼ r When the AP1B circle turns around AB as much as AP2B, the turning angle will be P1OP2 = a. While the view of AP1B circle AB line, the view (projection) of AP2BP3 circle ACBD ellipse. OP1P2E ? AB ¼ OP1 ? AB; OP2 ? AB; OP1==P2C and CP2O angle ¼ a
OP1 ? OE
P2C ? OE ðprojectionÞ so OC ¼ b OP2 ¼ r
In OP2C right triangle, sin a = OC/OP2 = b/r. Ellipse equation x2/a2 ? y2/b2 = 1 here; OA = a = r, OC = b. PK and KA are measurable lengths, and PK = y, OK = x = OA-AK = r-l. x2 =a2 þ y2 =b2 ¼ 1 a2 b2 b2 x2 þ a2 y2 ¼ a2 b2 b2 x2 a2 b2 ¼ a2 y2 ð 1Þ b2 a2 x 2 ¼ a2 y 2 p b2 ¼ a2 y2 =a2 x2 b ¼ ay= a2 x2 a ¼ r; x ¼ ðr lÞ to find b: x2 ¼ r 2 2rl þ l2 p p sin a ¼ b=a ¼ y= r 2 r 2 þ 2rl l2 ¼ y= 2rl l2 p p ¼ PK= 2r AKAK2 ¼ PK= AKð2r AKÞ Since 2r-AK = BK, Sin a = PK/HAKBK.
Eur J Orthop Surg Traumatol
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