HIP
Effects of rotational acetabular osteotomy on the mechanical stress within the hip joint in patients with developmental dysplasia of the hip H. Ike, Y. Inaba, N. Kobayashi, Y. Yukizawa, Y. Hirata, M. Tomioka, T. Saito From Yokohama City University, Yokohama, Japan
H. Ike, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Inaba , MD, PhD, Orthopaedic Surgeon, Associate Professor, Department of Orthopaedic Surgery N. Kobayashi, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Yukizawa, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Hirata, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery M. Tomioka, MD, Orthopaedic Surgeon, Department of Orthopaedic Surgery T. Saito, MD, PhD, Orthopaedic Surgeon Professor, Department of Orthopaedic Surgery Yokohama City University, 3-9 Fukuura, Kanazawa-ku, Yokohama, 236-0004, Japan. Correspondence should be sent to Dr Y. Inaba; e-mail: [email protected] ©2015 The British Editorial Society of Bone & Joint Surgery doi:10.1302/0301-620X.97B4. 33736 $2.00 Bone Joint J 2015;97-B:492–7. Received 15 January 2014; Accepted after revision 4 December 2014
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A SUBJECT-SPECIFIC FINITE ELEMENT ANALYSIS In this study we used subject-specific finite element analysis to investigate the mechanical effects of rotational acetabular osteotomy (RAO) on the hip joint and analysed the correlation between various radiological measurements and mechanical stress in the hip joint. We evaluated 13 hips in 12 patients (two men and ten women, mean age at surgery 32.0 years; 19 to 46) with developmental dysplasia of the hip (DDH) who were treated by RAO. Subject-specific finite element models were constructed from CT data. The centre–edge (CE) angle, acetabular head index (AHI), acetabular angle and acetabular roof angle (ARA) were measured on anteroposterior pelvic radiographs taken before and after RAO. The relationship between equivalent stress in the hip joint and radiological measurements was analysed. The equivalent stress in the acetabulum decreased from 4.1 MPa (2.7 to 6.5) preoperatively to 2.8 MPa (1.8 to 3.6) post-operatively (p < 0.01). There was a moderate correlation between equivalent stress in the acetabulum and the radiological measurements: CE angle (R = –0.645, p < 0.01); AHI (R = –0.603, p < 0.01); acetabular angle (R = 0.484, p = 0.02); and ARA (R = 0.572, p < 0.01). The equivalent stress in the acetabulum of patients with DDH decreased after RAO. Correction of the CE angle, AHI and ARA was considered to be important in reducing the mechanical stress in the hip joint. Cite this article: Bone Joint J 2015;97-B:492–7.
Developmental dysplasia of the hip (DDH) is the most frequent cause of secondary osteoarthritis.1 The major factors thought to be responsible for this are mechanical stress and dynamic instability. Experimental and clinical studies have confirmed that patients with DDH have higher contact stresses in the hip joint than healthy subjects.2-4 Rotational acetabular osteotomy (RAO), as developed by Ninomiya and Tagawa,5 is an effective method of treating adolescents and young adults with DDH. The aim is to improve the acetabular cover and congruency of the hip joint. Its efficacy and long-term results are well documented,6 but its effect on mechanical stress in the hip joint has not been fully investigated. The extent of change in mechanical stress in the hip joint after RAO is unclear, and an accurate and quantitative means of evaluating it is required. We used a computational finite element (FE) method, which is useful in biomechanical analysis. FE analysis can handle complex geometries with precise mathematical
logic and can predict the mechanics of a joint non-invasively.7 We made the following assumptions in our FE analysis: that all elements were isotropic; that articular cartilage was a homogeneous material; and that full contact and bonding were maintained between the articular cartilage and bone. Several previous studies have described the application of FE analysis to the normal hip joint.7-9 In recent years, CT-based FE analysis has been used to evaluate stresses in the hip joint after interventional procedures. Zhao et al10 evaluated the changes in the distribution of stress after peri-acetabular osteotomy using three-dimensional (3D) FE analysis. Their DDH models showed stress concentrations at the acetabular edge and contact surface of the femoral head, with higher values than in their model of the normal hip joint. Zou et al11 developed a 3D FE model to investigate the optimum position of the acetabulum after periacetabular osteotomy and its relationship to the angle of correction, contact area, and THE BONE & JOINT JOURNAL
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Fig. 1 Diagram of cartilage layer. The articular cartilage of the femoral head was assumed to be spherical.
contact pressure between the pelvic and femoral cartilage. An understanding of the mechanical effects of RAO may help to define the indications for RAO and improve the post-operative outcome. Several epidemiological surveys have suggested that the incidence of osteoarthritis (OA) of the hip increases in patients with severe DDH.12,13 Radiological measurements, such as the centre–edge (CE) angle,14 the acetabular head index (AHI),15 acetabular angle16 and acetabular roof angle (ARA),17 are among those commonly used to assess the acetabular cover of the femoral head and lateral subluxation of the hip joint in DDH.18 Understanding the association between mechanical stress and these radiological measurements is important in the evaluation of the mechanical condition of the hip in DDH and in the pre- and post-operative evaluation of RAO. The aim of this study was to evaluate the mechanical stress in the hip joint in patients with DDH using subjectspecific FE analysis, and to examine the correlation between radiological measurements and equivalent stress in the hip joint before and after RAO.
Patients and Methods This study was approved by the Institutional Review Board of Yokohama City University. Between January 2007 and January 2010, 25 consecutive RAOs were undertaken. A total of 12 could not be fully assessed because the patients could not undergo pre- or post-operative CT scans as consent was not obtained. We therefore evaluated 13 hips in 12 patients (two men and ten women). The mean age of the patients at the time of the surgery was 32.0 years (19 to 46) and the mean clinical followup was 2.6 years (between 1.3 and 4.3). The indications for RAO were: a CE angle < 15° on an AP radiograph; age < 50 years; good congruency of the VOL. 97-B, No. 4, APRIL 2015
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joint and cover of the femoral head in maximum abduction and progressive pain in the hip during daily activities. RAO was performed according to the method of Tagawa and Ninomiya.5 The line of the proximal osteotomy was approximately 20 mm from the joint: this was confirmed with an image intensifier. The acetabular fragment was displaced anteriorly and laterally to improve the cover of the femoral head. Post-operatively, range of movement exercises were started with the patient in bed. On the seventh post-operative day patients were allowed to transfer from bed to a wheelchair without bearing weight on the operated side, and were mobilised non-weight-bearing on crutches after two weeks. Partial weight-bearing was permitted three weeks after surgery, and full weight-bearing after eight weeks. The CE angle, AHI, acetabular angle and ARA were measured on AP radiographs pre-operatively and at the final follow-up. In addition, CT scans (Sensation 16; Siemens AG, Erlangen, Germany) of the pelvis and femur were taken pre- and > 12 months post-operatively. The scanner settings were approximately 140 kV, 300 mA, with a slice thickness of 2 mm, a 512 × 512 pixel resolution and a 0.70 mm × 0.70 mm × 2 mm voxel size. FE models of the femur and pelvis were generated from pre- and post-operative CT data by Mechanical Finder version 6.0 (Research Centre for Computational Mechanics Inc., Tokyo, Japan). This creates an FE model which shows the shape of the individual bone and the distribution of its density;19 it also implements the FE method for solving linear algebraic equations using the displacement method. With this software, FE mesh models are generated using Ansys ICEM CFD version 11.0 (Ansys Inc., Canonsburg, Pennsylvania). We generated FE models of the femur using the methods described by Bessho et al19 and applied their methods to the pelvis. The model with 2 mm mesh size could not be solved because of the limited capacity of our computer. Five models with different sizes of mesh were created to perform the sensitivity test: 2 mm to 4 mm; 2.5 mm to 5 mm; 3 mm to 6 mm; 3.5 mm to 7 mm and 4 mm to 8 mm. The sensitivity test was used to calculate the total strain energy of the whole model. The percentage change of the total strain energy between the 2 mm to 4 mm model and the 2.5 mm to 5 mm model was 1.1%. The percentage changes between the 2 mm to 4 mm and the 3 mm to 6 mm model, the 2 mm to 4 mm and the 3.5 mm to 7 mm model, and the 2 mm to 4 mm and the 4 mm to 8 mm model were 12.0%, 25.7% and 49.8%, respectively. The model with the 2 mm to 4 mm mesh was the finest of the five models and was therefore used in this study. 3D FE models were constructed for each patient. These had 2 mm to 4 mm tetrahedral elements for the trabecular and inner cortical bone and three-nodal point shell elements with a thickness of 0.4 mm for the outer surface of the cortical bone. Articular cartilage was modelled as a homogeneous isotropic material (Fig. 1). The articular cartilage of the femoral head was assumed to be spherical and
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Fig. 2 Diagram of loading and restriction conditions. The distal portions of the femoral shafts were fully restrained, and a load of 1800 N was applied vertically to the lumbar spine. Table I. Equations used to calculate the elastic modulus of the bone* Bone density
Elastic modulus (MPa)
P=0 0 < p ≤ 0.27 0.27 < p < 0.6 0.6 ≤ p
0.001 33900p2.20 5307 p + 469 10200p2.01
The elastic modulus of the bone is based on computed tomography density values, using the equations proposed by Keyak et al21 p (g/cm3) = (H. U. + 1.4246) × 0.001/1.058 (H. U. > -1) = 0.0 (H. U. ≤ -1) H. U., Hounsfield units
that of the femoral head and acetabulum to have a mean thickness of 2 mm.10,20 FE models of the pelvis consisted of approximately 600 000 elements, and those of the femur a further 200 000 elements. The elastic modulus of the bone was determined from CT density values using the equations proposed by Keyak et al21 (Table I). The Poisson’s ratio of the bone was 0.40. The cartilage had an elastic modulus of 10.35 MPa and a Poisson’s ratio of 0.40. The models assumed completely bonded interfaces between cartilage and bone. The applied loading condition was based on the study by Macirowski et al.22 The acetabulum was steploaded to 900 N using an instrumented femoral prosthesis. The distal parts of the femoral shafts were fully restrained and a load of 1800 N was applied vertically to the lumbar spine (Fig. 2). The Drucker–Prager equivalent stress was used. The mean equivalent stress in a sphere with a radius of 3 mm, the centre of which was located at the element generating the peak equivalent stress, was measured for the acetabulum and the femoral head and compared with the radiological measurements. Statistical analysis. Intraclass correlation coefficients (ICCs) were used to assess the intra- and inter-observer (two observers) reliability of measurements of the CE angle, the AHI,
acetabular angle and ARA. The values of ICC can range from 0 to 1, with a higher value indicating better reliability. ICC values were analysed in accordance with a previously described semi-quantitative scale (between 0 and 0.20 slight agreement; 0.21 to 0.40 fair; 0.41 to 0.60 moderate; 0.61 to 0.80 substantial; and 0.81 to 1.0 almost perfect).23 The paired t-test was used to analyse the changes in equivalent stress and radiological measurements. The correlation between equivalent stress and radiological measurements was analysed by Pearson’s product-moment correlation coefficient. All data were analysed using SPSS 16.0 Japanese for Windows (SPSS Japan Inc., Tokyo, Japan). Results with p < 0.05 were considered significant. All data were expressed as means with ranges.
Results Inter- and intra-observer reliabilities were almost perfect for the CE angle, AHI, acetabular angle and ARA (Table II). The cover of the femoral head improved after RAO. The mean CE angle increased from -4 (between -36 and 14) preoperatively to 26 (between 8 and 41) post-operatively (p < 0.01), and the mean AHI from 47% (15% to 66%) to 80% (60% to 95%) (p < 0.01). The mean acetabular angle THE BONE & JOINT JOURNAL
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Table II. Intra-class correlation coefficients with 95% confidence intervals (CI) for the radiological measurements Radiological parameters Acetabular roof angle Centre–edge angle Acetabular angle Acetabular head index
Intra-observer Inter-observer Intra-observer Inter-observer Intra-observer Inter-observer Intra-observer Inter-observer
Fig. 3a
Intra-class correlation coefficients
95% CI
0.951 0.932 0.983 0.958 0.959 0.939 0.976 0.938
0.895 to 0.978 0.855 to 0.969 0.963 to 0.992 0.894 to 0.982 0.912 to 0.981 0.870 to 0.972 0.947 to 0.989 0.853 to 0.973
Fig. 3b
Images showing equivalent stress in the acetabulum a) before and b) after rotational acetabular osteotomy. The concentration of stress in the load bearing area was confirmed
decreased after surgery from 53 (45 to 64) to 42 (28 to 52) (p < 0.01), and the mean ARA from 31 (20 to 47) to 11 (1 to 24) (p < 0.01). The equivalent stress in the acetabulum decreased from 4.1 MPa (2.7 to 6.5) pre-operatively to 2.8 MPa (1.8 to 3.6) post-operatively (p < 0.01) (Fig. 3). The equivalent stress in the femoral head decreased from 3.4 MPa (1.2 to 6.0) to 2.9 MPa (1.7 to 4.0), but this change was not statistically significant (p = 0.29). Moderate correlations were observed between equivalent stress in the acetabulum and radiological measurements: CE angle (R = –0.645, p < 0.01), AHI (R = –0.603, p < 0.01), acetabular angle (R = 0.484, p = 0.02), and ARA (R = 0.572, p < 0.01) (Fig. 4).
Discussion Although the primary purpose of RAO for patients with DDH is to increase the contact area within the joint and reduce the excessive load on the hip joint, the extent of the decrease in mechanical stress remains unclear. In this study we investigated the change in mechanical stress in the hip joint after RAO using a subject-specific FE analysis. Several studies have reported mathematical models, such as the HIPSTRESS method, and FE models for the analysis and quantification of the effects of pelvic osteotomy.2,10,11,24 In the HIPSTRESS method, measurements of the hips and VOL. 97-B, No. 4, APRIL 2015
pelvis were taken from AP radiographs. Zupanc et al25 claimed that this radiologically based model accords well with a CT-based model. For our study, we performed FE analysis using 3D reconstructed CT models because we believed that 3D information was needed to perform the biomechanical evaluation of RAO. We also investigated bone heterogeneity using the equations proposed by Keyak21 so that we could construct subject-specific FE models. A number of factors have been said to influence the longterm results of RAO, including AHI, CE angle, the stage of OA26 and post-operative congruency.27 Recnik et al28 showed that greater contact hip stress is associated with a need for arthroplasty at a younger age, and suggested that it may have a deleterious role in the progression of OA of the hip. In patients with DDH, the characteristic shallow acetabulum results in increased stress on the cartilage matrix.29 Although this mechanism is not fully understood, we consider it important to reduce the stress across the hip joint before the articular cartilage and subchondral bone are severely damaged. Our results show that the equivalent stress in the acetabulum decreased significantly after RAO, and that this correlated significantly with the CE angle, the AHI, the acetabular angle and the ARA.
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7
p < 0.01
7
p < 0.01
R = 0.572
6
R = -0.645
5 4 3 2
Pre-operative Post-operative
1
5
Equivalent stress in acetabulum (MPa)
Equivalent stress in acetabulum (MPa)
6
4 3 2
0
0 0
10
20
30
40
50
-40
-20
Acetabular roof angle (°)
0
20
40
60
Centre edge angle (°)
Fig. 4a
Fig. 4b
7
p = 0.02
7
p < 0.01
6
R = 0.484
6
R = -0.603
Equivalent stress in acetabulum (MPa)
Equivalent stress in acetabulum (MPa)
Pre-operative Post-operative
1
5 4 3 2 Pre-operative Post-operative
1
5 4 3 2 Pre-operative Post-operative
1 0
0 0
20
40
60
80
Acetabular angle (°) Fig. 4c
0
20
40
60
80
100
Acetabular head index (%) Fig. 4d
Graphs showing the relationship between a) equivalent stress in the acetabulum and acetabular roof angle, b) equivalent stress in the acetabulum and centre-edge angle, c) equivalent stress in the acetabulum and acetabular angle and d) equivalent stress in the acetabulum and acetabular head index.
To the best of our knowledge, this is the first study to investigate the relationship between radiological measurements and the distribution of stress using a subject-specific FE method. Our results indicate that these radiological measurements may be used to evaluate the mechanical condition before and after RAO in order to develop a preoperative plan, and to establish whether the RAO has achieved the desired outcome. Furthermore, we made the assumption that measurement of stress across the hip joint using FE may be a more precise way of evaluating a RAO, however, further studies will be needed to clarify their usefulness. It is difficult to establish the correct amount bywhich the acetabular fragment should be rotated. Tsumura et al30 reported on computer simulations of RAO and used peak pressure to evaluate the effect of the osteotomy. The lowest peak pressure was achieved with between 15 and 25 of anterior and 15 to 20 of lateral rotation. Zou et al11 used FE to investigate the best position for the acetabulum after a Ganz peri-acetabular osteotomy and claimed that it depended on the patient and did not always correspond to what would be considered a normal CE angle. Although
anterior and lateral rotation of the acetabular fragment increases the weight-bearing area of the acetabulum, overcorrection can cause secondary impingement.31 Ziebarth et al32 reported a high rate of clinical signs of femoroacetabular impingement after peri-acetabular osteotomy, despite achieving normal cover. Femoroacetabular impingement can lead to secondary arthritis of the hip. Theoretically, FE analysis might detect excessive distribution of stress caused by overcorrection after RAO. In our study the maximum value of post-operative AHI was 95%, and no excessive equivalent stress of the acetabulum could be detected. Prospective longitudinal cohort studies are needed to determine the best position for the rotated acetabular fragment. This study has several limitations. First, all analyses were undertaken using only one static loading condition. Therefore, the stress and the instability of the hip joint during gait could not be evaluated. Secondly, the articular cartilage was modelled artificially based on the anatomy of a typical femoral head and acetabulum. Our models did not include the labrum, as neither cartilage nor labrum was visible on the CT images. Thirdly, we could not evaluate the cartilage contact pressures in the hip joint. Our models were conTHE BONE & JOINT JOURNAL
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structed from clinical CT images with a coarse resolution for the thickness of articular cartilage. Therefore, the cartilage of the femoral head and acetabulum were not separated in our FE models. A possible effect of modelling the cartilage as a single entity is an overestimation of stress near the cartilage, as force is transmitted across the cartilage– cartilage interface without generating shear stress. This assumption could also change the shape of mesh elements of the cartilage and the direction of the stress at the bone– cartilage interface. The sample size for this study was relatively small, and finally, we did not perform experimental validation tests. However, mesh sensitivity tests were performed to verify mesh refinement. Our pre-operative models showed a concentration of stress in the upper part of the acetabulum, similar to that reported by Zou et al.11 In addition, our post-operative models showed a reduction in the concentration of stress, which is also consistent with a previous study by Zhao et al.10 These results support the validity of our models. In conclusion, the equivalent stress in the acetabulum of patients with DDH decreased after RAO. Correction of the CE angle, AHI and ARA was considered important to reduce the mechanical stress in the hip joint. Author contributions H. Ike: Data collection; Data analysis, Writing the paper. Y. Inaba: Performed surgeries, Data analysis, Writing the paper, Formulation of the study design. N. Kobayashi: Performed surgeries. Y. Yukizawa: Data collection, Data analysis. Y. Hirata: Data collection, Data analysis. M. Tomioka: Data collection, Data analysis. T. Saito: Writing the paper, Formulation of the study design. No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article.
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9. Anderson AE, Ellis BJ, Maas SA, Weiss JA. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech 2010;43:1351–1357. 10. Zhao X, Chosa E, Totoribe K, Deng G. Effect of periacetabular osteotomy for acetabular dysplasia clarified by three-dimensional finite element analysis. J Orthop Sci 2010;15:632–640. 11. Zou Z, Chávez-Arreola A, Mandal P, Board TN, Alonso-Rasgado T. Optimization of the position of the acetabulum in a ganz periacetabular osteotomy by finite element analysis. J Orthop Res 2013;31:472–479. 12. Jacobsen S, Sonne-Holm S. Hip dysplasia: a significant risk factor for the development of hip osteoarthritis. A cross-sectional survey. Rheumatology (Oxford) 2005;44:211–218. 13. Reijman M, Hazes JM, Pols HA, Koes BW, Bierma-Zeinstra SM. Acetabular dysplasia predicts incident osteoarthritis of the hip: the Rotterdam study. Arthritis Rheum 2005;52:787–793. 14. Cooperman D. What is the evidence to support acetabular dysplasia as a cause of osteoarthritis? J Pediatr Orthop 2013;33(Suppl1):S2–S7. 15. Heyman CH, Herndon CH. Legg-Perthes disease; a method for the measurement of the roentgenographic result. :J Bone Joint Surg [Am] 1950;32-A:767–778. 16. Sharp IK. Acetabular dysplasia; the acetabular angle. :J Bone Joint Surg [Br] 1961;43-B:268–272. 17. Massie WK, Howorth MB. Congenital dislocation of the hip. Part I. Method of grading results. J Bone Joint Surg [Am] 1950;32-A:519–531. 18. Kosuge D, Cordier T, Solomon LB, Howie DW. Dilemmas in imaging for peri-acetabular osteotomy: the influence of patient position and imaging technique on the radiological features of hip dysplasia. Bone Joint J 2014;96-B:1155–1160. 19. Bessho M, Ohnishi I, Matsuyama J, et al. Prediction of strength and strain of the proximal femur by a CT-based finite element method. J Biomech 2007;40:1745–1753. 20. Anderson AE, Peters CL, Tuttle BD, Weiss JA. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J Biomech Eng 2005;127:364–373. 21. Keyak JH, Rossi SA, Jones KA, Skinner HB. Prediction of femoral fracture load using automated finite element modeling. J Biomech 1998;31:125–133. 22. Macirowski T, Tepic S, Mann RW. Cartilage stresses in the human hip joint. J Biomech Eng 1994;116:10–18. 23. Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics 1977;33:159–174. 24. Vukasinovic Z, Spasovski D, Kralj-Iglic V, et al. Impact of triple pelvic osteotomy on contact stress pressure distribution in the hip joint. Int Orthop 2013;37:95–98.
This article was primary edited by A. C. Ross and first proof edited by J. Scott.
25. Zupanc O, Antolic V, Iglic A, et al. The assessment of contact stress in the hip joint after operative treatment for severe slipped capital femoral epiphysis. Int Orthop 2001;25:9–12.
References
26. Nakamura S, Ninomiya S, Takatori Y, Morimoto S, Umeyama T. Long-term outcome of rotational acetabular osteotomy: 145 hips followed for 10–23 years. Acta Orthop Scand 1998;69:259–265.
1. Aronson J. Osteoarthritis of the young adult hip: etiology and treatment. Instr Course Lect 1986;35:119–128. 2. Mavcic B, Pompe B, Antolic V, et al. Mathematical estimation of stress distribution in normal and dysplastic human hips. J Orthop Res 2002;20:1025–1030. 3. Michaeli DA, Murphy SB, Hipp JA. Comparison of predicted and measured contact pressures in normal and dysplastic hips. Med Eng Phys 1997;19:180–186. 4. Nakahara I, Takao M, Sakai T, et al. Three-dimensional morphology and bony range of movement in hip joints in patients with hip dysplasia. Bone Joint J 2014;96B:580–589. 5. Ninomiya S, Tagawa H. Rotational acetabular osteotomy for the dysplastic hip. J Bone Joint Surg [Am] 1984;66-A:430–436. 6. Yasunaga Y, Ochi M, Shimogaki K, Yamamoto S, Iwamori H. Rotational acetabular osteotomy for hip dysplasia: 61 hips followed for 8-15 years. Acta Orthop Scand 2004;75:10–15. 7. Anderson AE, Ellis BJ, Maas SA, Peters CL, Weiss JA. Validation of finite element predictions of cartilage contact pressure in the human hip joint. J Biomech Eng 2008;130:051008. 8. Dalstra M, Huiskes R, van Erning L. Development and validation of a three-dimensional finite element model of the pelvic bone. J Biomech Eng 1995;117:272–278.
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27. Okano K, Enomoto H, Osaki M, Shindo H. Joint congruency as an indication for rotational acetabular osteotomy. Clin Orthop Relat Res 2009;467:894–900. 28. Recnik G, Vengust R, Kralj-Iglic V, et al. Association between sub-clinical acetabular dysplasia and a younger age at hip arthroplasty in idiopathic osteoarthritis. J Int Med Res 2009;37:1620–1625. 29. Jessel RH, Zurakowski D, Zilkens C, et al. Radiographic and patient factors associated with pre-radiographic osteoarthritis in hip dysplasia. J Bone Joint Surg [Am] 2009;91-A:1120–1129. 30. Tsumura H, Kaku N, Ikeda S, Torisu T. A computer simulation of rotational acetabular osteotomy for dysplastic hip joint: does the optimal transposition of the acetabular fragment exist? J Orthop Sci 2005;10:145–151. 31. Clohisy JC, Nunley RM, Carlisle JC, Schoenecker PL. Incidence and characteristics of femoral deformities in the dysplastic hip. Clin Orthop Relat Res 2009;467:128–134. 32. Ziebarth K, Balakumar J, Domayer S, Kim YJ, Millis MB. Bernese periacetabular osteotomy in males: is there an increased risk of femoroacetabular impingement (FAI) after Bernese periacetabular osteotomy? Clin Orthop Relat Res 2011;469:447– 453.
Effects of rotational acetabular osteotomy on the mechanical stress within the hip joint in patients with developmental dysplasia of the hip H. Ike, Y. Inaba, N. Kobayashi, Y. Yukizawa, Y. Hirata, M. Tomioka, T. Saito From Yokohama City University, Yokohama, Japan
H. Ike, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Inaba , MD, PhD, Orthopaedic Surgeon, Associate Professor, Department of Orthopaedic Surgery N. Kobayashi, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Yukizawa, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery Y. Hirata, MD, PhD, Orthopaedic Surgeon, Department of Orthopaedic Surgery M. Tomioka, MD, Orthopaedic Surgeon, Department of Orthopaedic Surgery T. Saito, MD, PhD, Orthopaedic Surgeon Professor, Department of Orthopaedic Surgery Yokohama City University, 3-9 Fukuura, Kanazawa-ku, Yokohama, 236-0004, Japan. Correspondence should be sent to Dr Y. Inaba; e-mail: [email protected] ©2015 The British Editorial Society of Bone & Joint Surgery doi:10.1302/0301-620X.97B4. 33736 $2.00 Bone Joint J 2015;97-B:492–7. Received 15 January 2014; Accepted after revision 4 December 2014
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A SUBJECT-SPECIFIC FINITE ELEMENT ANALYSIS In this study we used subject-specific finite element analysis to investigate the mechanical effects of rotational acetabular osteotomy (RAO) on the hip joint and analysed the correlation between various radiological measurements and mechanical stress in the hip joint. We evaluated 13 hips in 12 patients (two men and ten women, mean age at surgery 32.0 years; 19 to 46) with developmental dysplasia of the hip (DDH) who were treated by RAO. Subject-specific finite element models were constructed from CT data. The centre–edge (CE) angle, acetabular head index (AHI), acetabular angle and acetabular roof angle (ARA) were measured on anteroposterior pelvic radiographs taken before and after RAO. The relationship between equivalent stress in the hip joint and radiological measurements was analysed. The equivalent stress in the acetabulum decreased from 4.1 MPa (2.7 to 6.5) preoperatively to 2.8 MPa (1.8 to 3.6) post-operatively (p < 0.01). There was a moderate correlation between equivalent stress in the acetabulum and the radiological measurements: CE angle (R = –0.645, p < 0.01); AHI (R = –0.603, p < 0.01); acetabular angle (R = 0.484, p = 0.02); and ARA (R = 0.572, p < 0.01). The equivalent stress in the acetabulum of patients with DDH decreased after RAO. Correction of the CE angle, AHI and ARA was considered to be important in reducing the mechanical stress in the hip joint. Cite this article: Bone Joint J 2015;97-B:492–7.
Developmental dysplasia of the hip (DDH) is the most frequent cause of secondary osteoarthritis.1 The major factors thought to be responsible for this are mechanical stress and dynamic instability. Experimental and clinical studies have confirmed that patients with DDH have higher contact stresses in the hip joint than healthy subjects.2-4 Rotational acetabular osteotomy (RAO), as developed by Ninomiya and Tagawa,5 is an effective method of treating adolescents and young adults with DDH. The aim is to improve the acetabular cover and congruency of the hip joint. Its efficacy and long-term results are well documented,6 but its effect on mechanical stress in the hip joint has not been fully investigated. The extent of change in mechanical stress in the hip joint after RAO is unclear, and an accurate and quantitative means of evaluating it is required. We used a computational finite element (FE) method, which is useful in biomechanical analysis. FE analysis can handle complex geometries with precise mathematical
logic and can predict the mechanics of a joint non-invasively.7 We made the following assumptions in our FE analysis: that all elements were isotropic; that articular cartilage was a homogeneous material; and that full contact and bonding were maintained between the articular cartilage and bone. Several previous studies have described the application of FE analysis to the normal hip joint.7-9 In recent years, CT-based FE analysis has been used to evaluate stresses in the hip joint after interventional procedures. Zhao et al10 evaluated the changes in the distribution of stress after peri-acetabular osteotomy using three-dimensional (3D) FE analysis. Their DDH models showed stress concentrations at the acetabular edge and contact surface of the femoral head, with higher values than in their model of the normal hip joint. Zou et al11 developed a 3D FE model to investigate the optimum position of the acetabulum after periacetabular osteotomy and its relationship to the angle of correction, contact area, and THE BONE & JOINT JOURNAL
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Fig. 1 Diagram of cartilage layer. The articular cartilage of the femoral head was assumed to be spherical.
contact pressure between the pelvic and femoral cartilage. An understanding of the mechanical effects of RAO may help to define the indications for RAO and improve the post-operative outcome. Several epidemiological surveys have suggested that the incidence of osteoarthritis (OA) of the hip increases in patients with severe DDH.12,13 Radiological measurements, such as the centre–edge (CE) angle,14 the acetabular head index (AHI),15 acetabular angle16 and acetabular roof angle (ARA),17 are among those commonly used to assess the acetabular cover of the femoral head and lateral subluxation of the hip joint in DDH.18 Understanding the association between mechanical stress and these radiological measurements is important in the evaluation of the mechanical condition of the hip in DDH and in the pre- and post-operative evaluation of RAO. The aim of this study was to evaluate the mechanical stress in the hip joint in patients with DDH using subjectspecific FE analysis, and to examine the correlation between radiological measurements and equivalent stress in the hip joint before and after RAO.
Patients and Methods This study was approved by the Institutional Review Board of Yokohama City University. Between January 2007 and January 2010, 25 consecutive RAOs were undertaken. A total of 12 could not be fully assessed because the patients could not undergo pre- or post-operative CT scans as consent was not obtained. We therefore evaluated 13 hips in 12 patients (two men and ten women). The mean age of the patients at the time of the surgery was 32.0 years (19 to 46) and the mean clinical followup was 2.6 years (between 1.3 and 4.3). The indications for RAO were: a CE angle < 15° on an AP radiograph; age < 50 years; good congruency of the VOL. 97-B, No. 4, APRIL 2015
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joint and cover of the femoral head in maximum abduction and progressive pain in the hip during daily activities. RAO was performed according to the method of Tagawa and Ninomiya.5 The line of the proximal osteotomy was approximately 20 mm from the joint: this was confirmed with an image intensifier. The acetabular fragment was displaced anteriorly and laterally to improve the cover of the femoral head. Post-operatively, range of movement exercises were started with the patient in bed. On the seventh post-operative day patients were allowed to transfer from bed to a wheelchair without bearing weight on the operated side, and were mobilised non-weight-bearing on crutches after two weeks. Partial weight-bearing was permitted three weeks after surgery, and full weight-bearing after eight weeks. The CE angle, AHI, acetabular angle and ARA were measured on AP radiographs pre-operatively and at the final follow-up. In addition, CT scans (Sensation 16; Siemens AG, Erlangen, Germany) of the pelvis and femur were taken pre- and > 12 months post-operatively. The scanner settings were approximately 140 kV, 300 mA, with a slice thickness of 2 mm, a 512 × 512 pixel resolution and a 0.70 mm × 0.70 mm × 2 mm voxel size. FE models of the femur and pelvis were generated from pre- and post-operative CT data by Mechanical Finder version 6.0 (Research Centre for Computational Mechanics Inc., Tokyo, Japan). This creates an FE model which shows the shape of the individual bone and the distribution of its density;19 it also implements the FE method for solving linear algebraic equations using the displacement method. With this software, FE mesh models are generated using Ansys ICEM CFD version 11.0 (Ansys Inc., Canonsburg, Pennsylvania). We generated FE models of the femur using the methods described by Bessho et al19 and applied their methods to the pelvis. The model with 2 mm mesh size could not be solved because of the limited capacity of our computer. Five models with different sizes of mesh were created to perform the sensitivity test: 2 mm to 4 mm; 2.5 mm to 5 mm; 3 mm to 6 mm; 3.5 mm to 7 mm and 4 mm to 8 mm. The sensitivity test was used to calculate the total strain energy of the whole model. The percentage change of the total strain energy between the 2 mm to 4 mm model and the 2.5 mm to 5 mm model was 1.1%. The percentage changes between the 2 mm to 4 mm and the 3 mm to 6 mm model, the 2 mm to 4 mm and the 3.5 mm to 7 mm model, and the 2 mm to 4 mm and the 4 mm to 8 mm model were 12.0%, 25.7% and 49.8%, respectively. The model with the 2 mm to 4 mm mesh was the finest of the five models and was therefore used in this study. 3D FE models were constructed for each patient. These had 2 mm to 4 mm tetrahedral elements for the trabecular and inner cortical bone and three-nodal point shell elements with a thickness of 0.4 mm for the outer surface of the cortical bone. Articular cartilage was modelled as a homogeneous isotropic material (Fig. 1). The articular cartilage of the femoral head was assumed to be spherical and
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Fig. 2 Diagram of loading and restriction conditions. The distal portions of the femoral shafts were fully restrained, and a load of 1800 N was applied vertically to the lumbar spine. Table I. Equations used to calculate the elastic modulus of the bone* Bone density
Elastic modulus (MPa)
P=0 0 < p ≤ 0.27 0.27 < p < 0.6 0.6 ≤ p
0.001 33900p2.20 5307 p + 469 10200p2.01
The elastic modulus of the bone is based on computed tomography density values, using the equations proposed by Keyak et al21 p (g/cm3) = (H. U. + 1.4246) × 0.001/1.058 (H. U. > -1) = 0.0 (H. U. ≤ -1) H. U., Hounsfield units
that of the femoral head and acetabulum to have a mean thickness of 2 mm.10,20 FE models of the pelvis consisted of approximately 600 000 elements, and those of the femur a further 200 000 elements. The elastic modulus of the bone was determined from CT density values using the equations proposed by Keyak et al21 (Table I). The Poisson’s ratio of the bone was 0.40. The cartilage had an elastic modulus of 10.35 MPa and a Poisson’s ratio of 0.40. The models assumed completely bonded interfaces between cartilage and bone. The applied loading condition was based on the study by Macirowski et al.22 The acetabulum was steploaded to 900 N using an instrumented femoral prosthesis. The distal parts of the femoral shafts were fully restrained and a load of 1800 N was applied vertically to the lumbar spine (Fig. 2). The Drucker–Prager equivalent stress was used. The mean equivalent stress in a sphere with a radius of 3 mm, the centre of which was located at the element generating the peak equivalent stress, was measured for the acetabulum and the femoral head and compared with the radiological measurements. Statistical analysis. Intraclass correlation coefficients (ICCs) were used to assess the intra- and inter-observer (two observers) reliability of measurements of the CE angle, the AHI,
acetabular angle and ARA. The values of ICC can range from 0 to 1, with a higher value indicating better reliability. ICC values were analysed in accordance with a previously described semi-quantitative scale (between 0 and 0.20 slight agreement; 0.21 to 0.40 fair; 0.41 to 0.60 moderate; 0.61 to 0.80 substantial; and 0.81 to 1.0 almost perfect).23 The paired t-test was used to analyse the changes in equivalent stress and radiological measurements. The correlation between equivalent stress and radiological measurements was analysed by Pearson’s product-moment correlation coefficient. All data were analysed using SPSS 16.0 Japanese for Windows (SPSS Japan Inc., Tokyo, Japan). Results with p < 0.05 were considered significant. All data were expressed as means with ranges.
Results Inter- and intra-observer reliabilities were almost perfect for the CE angle, AHI, acetabular angle and ARA (Table II). The cover of the femoral head improved after RAO. The mean CE angle increased from -4 (between -36 and 14) preoperatively to 26 (between 8 and 41) post-operatively (p < 0.01), and the mean AHI from 47% (15% to 66%) to 80% (60% to 95%) (p < 0.01). The mean acetabular angle THE BONE & JOINT JOURNAL
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Table II. Intra-class correlation coefficients with 95% confidence intervals (CI) for the radiological measurements Radiological parameters Acetabular roof angle Centre–edge angle Acetabular angle Acetabular head index
Intra-observer Inter-observer Intra-observer Inter-observer Intra-observer Inter-observer Intra-observer Inter-observer
Fig. 3a
Intra-class correlation coefficients
95% CI
0.951 0.932 0.983 0.958 0.959 0.939 0.976 0.938
0.895 to 0.978 0.855 to 0.969 0.963 to 0.992 0.894 to 0.982 0.912 to 0.981 0.870 to 0.972 0.947 to 0.989 0.853 to 0.973
Fig. 3b
Images showing equivalent stress in the acetabulum a) before and b) after rotational acetabular osteotomy. The concentration of stress in the load bearing area was confirmed
decreased after surgery from 53 (45 to 64) to 42 (28 to 52) (p < 0.01), and the mean ARA from 31 (20 to 47) to 11 (1 to 24) (p < 0.01). The equivalent stress in the acetabulum decreased from 4.1 MPa (2.7 to 6.5) pre-operatively to 2.8 MPa (1.8 to 3.6) post-operatively (p < 0.01) (Fig. 3). The equivalent stress in the femoral head decreased from 3.4 MPa (1.2 to 6.0) to 2.9 MPa (1.7 to 4.0), but this change was not statistically significant (p = 0.29). Moderate correlations were observed between equivalent stress in the acetabulum and radiological measurements: CE angle (R = –0.645, p < 0.01), AHI (R = –0.603, p < 0.01), acetabular angle (R = 0.484, p = 0.02), and ARA (R = 0.572, p < 0.01) (Fig. 4).
Discussion Although the primary purpose of RAO for patients with DDH is to increase the contact area within the joint and reduce the excessive load on the hip joint, the extent of the decrease in mechanical stress remains unclear. In this study we investigated the change in mechanical stress in the hip joint after RAO using a subject-specific FE analysis. Several studies have reported mathematical models, such as the HIPSTRESS method, and FE models for the analysis and quantification of the effects of pelvic osteotomy.2,10,11,24 In the HIPSTRESS method, measurements of the hips and VOL. 97-B, No. 4, APRIL 2015
pelvis were taken from AP radiographs. Zupanc et al25 claimed that this radiologically based model accords well with a CT-based model. For our study, we performed FE analysis using 3D reconstructed CT models because we believed that 3D information was needed to perform the biomechanical evaluation of RAO. We also investigated bone heterogeneity using the equations proposed by Keyak21 so that we could construct subject-specific FE models. A number of factors have been said to influence the longterm results of RAO, including AHI, CE angle, the stage of OA26 and post-operative congruency.27 Recnik et al28 showed that greater contact hip stress is associated with a need for arthroplasty at a younger age, and suggested that it may have a deleterious role in the progression of OA of the hip. In patients with DDH, the characteristic shallow acetabulum results in increased stress on the cartilage matrix.29 Although this mechanism is not fully understood, we consider it important to reduce the stress across the hip joint before the articular cartilage and subchondral bone are severely damaged. Our results show that the equivalent stress in the acetabulum decreased significantly after RAO, and that this correlated significantly with the CE angle, the AHI, the acetabular angle and the ARA.
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7
p < 0.01
7
p < 0.01
R = 0.572
6
R = -0.645
5 4 3 2
Pre-operative Post-operative
1
5
Equivalent stress in acetabulum (MPa)
Equivalent stress in acetabulum (MPa)
6
4 3 2
0
0 0
10
20
30
40
50
-40
-20
Acetabular roof angle (°)
0
20
40
60
Centre edge angle (°)
Fig. 4a
Fig. 4b
7
p = 0.02
7
p < 0.01
6
R = 0.484
6
R = -0.603
Equivalent stress in acetabulum (MPa)
Equivalent stress in acetabulum (MPa)
Pre-operative Post-operative
1
5 4 3 2 Pre-operative Post-operative
1
5 4 3 2 Pre-operative Post-operative
1 0
0 0
20
40
60
80
Acetabular angle (°) Fig. 4c
0
20
40
60
80
100
Acetabular head index (%) Fig. 4d
Graphs showing the relationship between a) equivalent stress in the acetabulum and acetabular roof angle, b) equivalent stress in the acetabulum and centre-edge angle, c) equivalent stress in the acetabulum and acetabular angle and d) equivalent stress in the acetabulum and acetabular head index.
To the best of our knowledge, this is the first study to investigate the relationship between radiological measurements and the distribution of stress using a subject-specific FE method. Our results indicate that these radiological measurements may be used to evaluate the mechanical condition before and after RAO in order to develop a preoperative plan, and to establish whether the RAO has achieved the desired outcome. Furthermore, we made the assumption that measurement of stress across the hip joint using FE may be a more precise way of evaluating a RAO, however, further studies will be needed to clarify their usefulness. It is difficult to establish the correct amount bywhich the acetabular fragment should be rotated. Tsumura et al30 reported on computer simulations of RAO and used peak pressure to evaluate the effect of the osteotomy. The lowest peak pressure was achieved with between 15 and 25 of anterior and 15 to 20 of lateral rotation. Zou et al11 used FE to investigate the best position for the acetabulum after a Ganz peri-acetabular osteotomy and claimed that it depended on the patient and did not always correspond to what would be considered a normal CE angle. Although
anterior and lateral rotation of the acetabular fragment increases the weight-bearing area of the acetabulum, overcorrection can cause secondary impingement.31 Ziebarth et al32 reported a high rate of clinical signs of femoroacetabular impingement after peri-acetabular osteotomy, despite achieving normal cover. Femoroacetabular impingement can lead to secondary arthritis of the hip. Theoretically, FE analysis might detect excessive distribution of stress caused by overcorrection after RAO. In our study the maximum value of post-operative AHI was 95%, and no excessive equivalent stress of the acetabulum could be detected. Prospective longitudinal cohort studies are needed to determine the best position for the rotated acetabular fragment. This study has several limitations. First, all analyses were undertaken using only one static loading condition. Therefore, the stress and the instability of the hip joint during gait could not be evaluated. Secondly, the articular cartilage was modelled artificially based on the anatomy of a typical femoral head and acetabulum. Our models did not include the labrum, as neither cartilage nor labrum was visible on the CT images. Thirdly, we could not evaluate the cartilage contact pressures in the hip joint. Our models were conTHE BONE & JOINT JOURNAL
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structed from clinical CT images with a coarse resolution for the thickness of articular cartilage. Therefore, the cartilage of the femoral head and acetabulum were not separated in our FE models. A possible effect of modelling the cartilage as a single entity is an overestimation of stress near the cartilage, as force is transmitted across the cartilage– cartilage interface without generating shear stress. This assumption could also change the shape of mesh elements of the cartilage and the direction of the stress at the bone– cartilage interface. The sample size for this study was relatively small, and finally, we did not perform experimental validation tests. However, mesh sensitivity tests were performed to verify mesh refinement. Our pre-operative models showed a concentration of stress in the upper part of the acetabulum, similar to that reported by Zou et al.11 In addition, our post-operative models showed a reduction in the concentration of stress, which is also consistent with a previous study by Zhao et al.10 These results support the validity of our models. In conclusion, the equivalent stress in the acetabulum of patients with DDH decreased after RAO. Correction of the CE angle, AHI and ARA was considered important to reduce the mechanical stress in the hip joint. Author contributions H. Ike: Data collection; Data analysis, Writing the paper. Y. Inaba: Performed surgeries, Data analysis, Writing the paper, Formulation of the study design. N. Kobayashi: Performed surgeries. Y. Yukizawa: Data collection, Data analysis. Y. Hirata: Data collection, Data analysis. M. Tomioka: Data collection, Data analysis. T. Saito: Writing the paper, Formulation of the study design. No benefits in any form have been received or will be received from a commercial party related directly or indirectly to the subject of this article.
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9. Anderson AE, Ellis BJ, Maas SA, Weiss JA. Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip. J Biomech 2010;43:1351–1357. 10. Zhao X, Chosa E, Totoribe K, Deng G. Effect of periacetabular osteotomy for acetabular dysplasia clarified by three-dimensional finite element analysis. J Orthop Sci 2010;15:632–640. 11. Zou Z, Chávez-Arreola A, Mandal P, Board TN, Alonso-Rasgado T. Optimization of the position of the acetabulum in a ganz periacetabular osteotomy by finite element analysis. J Orthop Res 2013;31:472–479. 12. Jacobsen S, Sonne-Holm S. Hip dysplasia: a significant risk factor for the development of hip osteoarthritis. A cross-sectional survey. Rheumatology (Oxford) 2005;44:211–218. 13. Reijman M, Hazes JM, Pols HA, Koes BW, Bierma-Zeinstra SM. Acetabular dysplasia predicts incident osteoarthritis of the hip: the Rotterdam study. Arthritis Rheum 2005;52:787–793. 14. Cooperman D. What is the evidence to support acetabular dysplasia as a cause of osteoarthritis? J Pediatr Orthop 2013;33(Suppl1):S2–S7. 15. Heyman CH, Herndon CH. Legg-Perthes disease; a method for the measurement of the roentgenographic result. :J Bone Joint Surg [Am] 1950;32-A:767–778. 16. Sharp IK. Acetabular dysplasia; the acetabular angle. :J Bone Joint Surg [Br] 1961;43-B:268–272. 17. Massie WK, Howorth MB. Congenital dislocation of the hip. Part I. Method of grading results. J Bone Joint Surg [Am] 1950;32-A:519–531. 18. Kosuge D, Cordier T, Solomon LB, Howie DW. Dilemmas in imaging for peri-acetabular osteotomy: the influence of patient position and imaging technique on the radiological features of hip dysplasia. Bone Joint J 2014;96-B:1155–1160. 19. Bessho M, Ohnishi I, Matsuyama J, et al. Prediction of strength and strain of the proximal femur by a CT-based finite element method. J Biomech 2007;40:1745–1753. 20. Anderson AE, Peters CL, Tuttle BD, Weiss JA. Subject-specific finite element model of the pelvis: development, validation and sensitivity studies. J Biomech Eng 2005;127:364–373. 21. Keyak JH, Rossi SA, Jones KA, Skinner HB. Prediction of femoral fracture load using automated finite element modeling. J Biomech 1998;31:125–133. 22. Macirowski T, Tepic S, Mann RW. Cartilage stresses in the human hip joint. J Biomech Eng 1994;116:10–18. 23. Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics 1977;33:159–174. 24. Vukasinovic Z, Spasovski D, Kralj-Iglic V, et al. Impact of triple pelvic osteotomy on contact stress pressure distribution in the hip joint. Int Orthop 2013;37:95–98.
This article was primary edited by A. C. Ross and first proof edited by J. Scott.
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