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) pre-operatively 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 peri-acetabular osteotomy and its relationship to the angle of correction, contact area, and 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 subject-specific 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 follow-up 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 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 al¹⁹and 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 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 step-loaded 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.

Fig. 1 Diagram of cartilage layer. The articular cartilage of the femoral head was assumed to be spherical.

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	0.001
0 < p ≤ 0.27	33900p^2.20
0.27 < p < 0.6	5307 p + 469
0.6 ≤ p	10200p^2.01

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

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) pre-operatively 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 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).

**Table II Intra-class correlation coefficients with 95% confidence intervals (CI) for the radiological measurements**
Radiological parameters		Intra-class correlation coefficients	95% CI

Acetabular roof angle	Intra-observer	0.951	0.895 to 0.978
	Inter-observer	0.932	0.855 to 0.969
Centre–edge angle	Intra-observer	0.983	0.963 to 0.992
	Inter-observer	0.958	0.894 to 0.982
Acetabular angle	Intra-observer	0.959	0.912 to 0.981
	Inter-observer	0.939	0.870 to 0.972
Acetabular head index	Intra-observer	0.976	0.947 to 0.989
	Inter-observer	0.938	0.853 to 0.973

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).

Figs. 3a - 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

Figs. 4a - 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.

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 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 long-term 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.

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 pre-operative 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 constructed 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.

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