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Computer-Assisted Optimization of the Acetabular Rotation in Periacetabular Osteotomy Using Patient’s Anatomy-Specific Finite Element Analysis

Computer-Assisted Optimization of the Acetabular Rotation in Periacetabular Osteotomy Using... Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 9730525, 11 pages https://doi.org/10.1155/2018/9730525 Research Article Computer-Assisted Optimization of the Acetabular Rotation in Periacetabular Osteotomy Using Patient’s Anatomy-Specific Finite Element Analysis 1 2 3 4 5 Sung-Jae Park , Sung-Jae Lee , Wen-Ming Chen, Jung-Hong Park, Yong-Soo Cho, 1 6 Taejin Shin, and Soon-Yong Kwon Central R&D Center, Corentec Co. Ltd., Banpo-dong, Seocho-gu, Seoul 06541, Republic of Korea Department of Biomedical Engineering, Inje University, Obang-dong, Gimhae 50834, Republic of Korea Department of Biomedical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China R&D Institute, YM Yangsan Machinery Ltd., Jeonggwan-eup, Gijang-gun, Busan 46027, Republic of Korea Department of Orthopaedic Surgery, St. Mary’s Hospital, Catholic University, Yeouido-dong, Yeoungdeungpo-gu, Seoul 07345, Republic of Korea Department of Orthopaedic Surgery, St. Paul’s Hospital, Catholic University, Jeonnong-dong, Dongdaemun-gu, Seoul 02559, Republic of Korea Correspondence should be addressed to Sung-Jae Lee; sjl@bme.inje.ac.kr and Soon-Yong Kwon; sykwon@catholic.ac.kr Received 22 June 2017; Revised 5 October 2017; Accepted 12 November 2017; Published 4 February 2018 Academic Editor: Laurence Cheze Copyright © 2018 Sung-Jae Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Periacetabular osteotomy (PAO) is a complex surgical procedure to restore acetabular coverage in the dysplastic hip, and the amount of acetabular rotation during PAO plays a key role. Using computational simulations, this study assessed the optimal direction and amount of the acetabular rotation in three dimensions for a patient undergoing PAO. Anatomy-specific finite element (FE) models of the hip were constructed based on clinical CT images. The calculated acetabular rotation during PAO ° ° ° were 9.7 ,18 , and 4.3 in sagittal, coronal, and transverse planes, respectively. Based on the actual acetabular rotations, twelve postoperative FE models were generated. An optimal position was found by gradually varying the amount of the acetabular rotations in each anatomical plane. The coronal plane was found to be the principal rotational plane, which showed the strongest effects on joint contact pressure compared to other planes. It is suggested that rotation in the coronal plane of the osteotomized acetabulum is one of the primary surgical parameters to achieve the optimal clinical outcome for a given patient. 1. Introduction Periacetabular osteotomy (PAO) is one of the preferred joint-preserving techniques known to correct multiaxial hip deformities in DDH patients [5–7]. A PAO involves osteot- Developmental dysplasia of the hip (DDH) manifests various omy at the periphery of the ilium and the ischium and morphological abnormalities including acetabular dysplasia, followed by rotation of the acetabulum in three dimensions. decreased acetabular coverage of the femoral head, excessive femoral anteversion, increased neck-shaft angle, and short- Studies have shown that PAO could effectively reduce the joint load and relieve abductor muscle forces through the ened femoral neck [1]. Patients with DDH are usually adoles- cents or young adults with congenital deformities. When left medial translation of the hip joint center [8]. To achieve the optimal surgical outcome, joint congru- untreated, DDH can cause secondary osteoarthritis due to ency between the femoral head and the acetabulum must be prolonged exposure to increased contact stresses on the artic- ular cartilage in the hip joint [2–4]. established. Normally, preoperative (Pre-OP) information 2 Applied Bionics and Biomechanics including the location of the osteotomy and subsequent rota- Set of reference points (n = 3) on the pelvis and 3-D tions of the acetabulum in terms of the direction and the congruency of the pelvis through superposition amount have to be determined [9]. Clinical studies showed that individualized Pre-OP planning of PAO could improve surgical outcomes [10–17]. Unfortunately, quantitative Calculation of Bryant angle (𝛼, 𝛽, and 𝛾) to evaluate information regarding the optimal rotational parameters the kinematic changes of the acetabulum during PAO remain unclear. As a result, surgical planning still largely relies on the experience and decision of the clinicians. Fur- Set of virtual markers (n =3) ther, Pre-OP planning and postoperative (Post-OP) assess- of the acetabulum before and aer P ft AO ment usually depend on the radiographic X-ray imaging which are essential in two dimensions, as opposed to the three-dimensional orientation and acetabular rotations for Assessment on repeatability (n =6) hip realignment during the surgery. regarding the location of anatomic landmarks Pre-OP planning was first introduced by Langlotz et al. [10], which generally involves measurement of morpholog- ical parameters such as center-edge (CE) angle in X-ray Development of local coordinate system images [11–13]. In contrast, recent development of Pre- of the acetabulum before and aer P ft AO OP planning based on biomechanical modelling permits a more quantitative solution. Biomechanical information, such as tissue stresses, contact area, and contact pressure Representation of transformation matrix in the hip joint, can be predicted through computational regarding global coordinate simulations, such as finite element (FE) analysis [12, 15, 16]. Zou et al. [15] constructed hip FE models for five patients with DDH to investigate the optimal location of Calculation of the acetabular rotation in planes (sagittal, the acetabulum in PAO in relation to CE angle. Zhao coronal, and transverse planes) using Bryant angle et al. [16] investigated the effect of PAO on von Mises stresses on the cortical bone of the acetabulum. The above Figure 1: Flow chart for three-dimensional rotational calculation of studies, however, only considered the two-dimensional the osteotomized acetabulum during PAO. acetabulum rotations. In a recent study [17], we constructed an anatomy- specific FE model based on computed tomography (CT) who was diagnosed with DDH and underwent PAO surgery images collected from a patient who underwent PAO sur- at Fukuoka University Hospital (Fukuoka, Japan). The Pre- gery. In that study, we quantitatively determined the bio- OP scan was performed for the hip and the pelvis of the mechanical parameters, including hip joint contact area, patient using a clinical scanner (Aquilion 64, Toshiba Medi- contact pressure, and peak von Mises stress, before and cal System Corp., Japan) at a resolution of 0.398 mm and a after the PAO surgery. However, our previous model used slice spacing of 2.0 mm. The Post-OP images were obtained a simplified approach by limiting the acetabular rotation 2 months after the surgery from the same patient using the in a single anatomical plane, and the actual acetabular same scanning parameters. rotations during the surgery which are in three dimen- The focus in this paper is twofold: first, based on the sions were not considered. Thus, the effects of acetabular Pre- and Post-OP CT images to calculate the amount of rotation in different anatomical planes on joint contact actual acetabular rotation (ACR) during the PAO and sec- mechanics remain unclear. ond, based on the actual ACR to guide the development of This study aims to investigate the principal axes of rota- a series of Post-OP computational models of the dysplastic tion of the acetabulum and to assess the optimal amount of hip following various acetabular rotations in three dimen- the acetabular rotation in three dimensions in a dysplastic sions. Using FE analysis, the biomechanical responses hip model. To this end, a range of rotation of the osteoto- obtained from the Post-OP models including peak contact mized acetabulum during PAO was calculated using the pressure and contact area were compared to the Pre-OP patient’s anatomy-specific FE models [17]. A series of FE model to determine the efficacy of acetabular rotations analyses were performed based on the measured anatomical along different axis during PAO. angles and changes in the joint coverage areas, and contact stresses were evaluated due to incremental rotation of the 2.1. Three-Dimensional Rotations of the Acetabulum due to osteotomized acetabulum in three dimensions. PAO. We implemented an image registration method for the calculation of three-dimensional rotations of the osteoto- mized acetabulum during PAO. The detailed procedures 2. Materials and Methods were performed as described in Figure 1. While the Pre- and Post-OP CT images were collected at Hip dysplasia is known to affect the structural geometry of the femoral head and the acetabulum. To capture the real- the same resolution, the scanning position was changed. To istic geometry of a diseased hip, CT images were collected ensure congruency, the Pre- and Post-OP images were rea- from a 42-year-old female patient (body weight of 52 kg) ligned such that the pelvis (excluding the acetabulum) before Applied Bionics and Biomechanics 3 Marker number 1 (X , Y , Z ) 11 11 11 Marker number 2 (X1 , Y , Z ) 12 12 12 Z Marker number 3 (X , Y , Z ) 13 13 13 < Pre-Op > Marker number 1 (X , Y , Z ) 21 21 21 Marker number 2 (X , Y , Z ) 22 22 22 z X Pre-Op Marker number 3 Post-Op (X , Y , Z ) 23 23 23 Post-Op Post-Op < Post-Op > X X Pre-Op Pre-Op Global coordinate system (a) (b) Figure 2: Reconstructed solid models of the pelvis based on the Pre- and Post-OP CT scans. The extent of osteotomy of the acetabulum was shown with a dotted line. (a) Locations of the anatomic landmarks in Pre- and Post-OP models in a lateral view (mark number 1 for acetabular fossa; mark number 2, and mark number 3 for the acetabular anterior and inferior sites, resp.); (b) the global coordinate system (X, Y, and Z; sagittal, coronal, and transverse planes) were shown. Three-dimensional rotations of the acetabulum were described by three Bryant angles along each axis. and after PAO was registered by superposition in the Euclidean distances commercial image-processing software Mimics (Materialise, 2 2 Louvain, Belgium). Using the built-in image registration = X − X + Y − Y + Z − Z ij ij ij ij ij ij function, the spatial position and orientation of the pelvis in Pre- and Post-OP CT images were realigned. Among the most common parameters used to describe To calculate the amount of acetabular rotations during the angular orientation of a body in three dimensions are PAO, two geometrical models, that is, solid models, were Euler angles [19]. Using Euler angles, the angular orientation built based on reconstruction of the two sets of realigned of a given body-fixed (i.e., local) coordinate system can be Pre- and Post-OP images using a previously established envisioned to be the result of three successive rotations. How- protocol [17]. Virtual markers (n =3) were set at the end ever, in the body-fixed coordinate system, the sequence of of acetabular fossa (marker number 1), inferior (marker rotations used to define the final orientation of the coordinate number 2), and anterior sites (marker number 3), which were system is to some extent arbitrary. For example, the Euler clearly identifiable in both Pre- and Post-OP models angles which act as a set of three independent body-fixed (Figure 2). To increase the accuracy in placing these markers, coordinates are altered as the initial body-fixed coordinate three-dimensional geometrical objects, that is, spheres with system changes during body’s three-dimensional rotations. radius of 3.0 mm, were used to locate the anatomic land- Therefore, we calculated the angular orientation relative marks of the acetabulum. Three-dimensional coordinates to the global coordinate system, which is defined as Bryant at the center of sphere in the Pre- and Post-OP models angles [19]. A local coordinate system was first defined for were extracted to indicate the spatial location of these ease of description of the calculation. The vector connecting anatomic landmarks. marker number 1 and marker number 2 defined the x-axis To evaluate the repeatability of individual marker of local coordinate system. The vector connecting marker placement, the interobserver variability was assessed in six number 2 and marker number 3 determined vector q. Cross independent observers. Repeatability between each landmark product of vectors x and q determined vector of z-axis by was evaluated [18] by repeatedly using coordinates of land- applying the right-handed rule. Likewise, the y-axis vector marks set (X , Y , and Z : i refers to before and after PAO, ij ij ij of local coordinate was determined by applying the cross i = 1 and 2; j denotes to anatomic landmark, j = 1, 2, and 3) products of vectors x and z, as shown in placed by the observers (X , Y , and Z ) using (1). This ij ij ij equation calculates the Euclidean distance between two x × q = z , 2 landmarks in the three-dimensional space. The interclass x × z = y correlation coefficient (ICC) on position of the virtual markers was also measured and assessed to confirm inter- By assuming rigid body motion, a transformation matrix observer variations using statistical software (SPSS 22, SPSS T [20] for the local coordinate system in describing acetabu- Inc., USA). lum rotation before and after surgery reads as follows: 4 Applied Bionics and Biomechanics R R R cos β cos β cos α sin β sin γ − sin α cos γ cos α sin β cos γ − sin α sin γ 11 12 13 T = R R R = sin α cos β sin α sin β sin γ − cos α cos γ −sin α cos β , 21 22 23 R R R −cos α sin β cos γ − sin β sin γ cos α sin β sin γ − sin α cos γ cos α cos β 31 32 33 where each column in matrix indicates the unit vector on A simulated osteotomy was performed at the periphery of x-, y-, and z-axis. And three-dimensional movement of the the acetabulum in the baseline model to mimic actual surgi- acetabulum was expressed in Bryant angle (α, β, and γ) cal procedure (Figure 4) [22]. Virtual cutting was done to and cosine, sine function with regard to global coordinate simulate osteotomy due to PAO using Mimics software with system [20]. The Bryant angles describes flexion (x-axis), a sphere (radius of 45 mm) located around the right hip cen- adduction (y-axis), and external rotation (z-axis) of the hip ter to separate the ilium, the ischium, and the pubis from the movement. Thus, the relative acetabular rotation (R) could pelvis. The position of the central point of the sphere was be obtained by multiplying the inverse transformation matrix matched with the central point made by geometry of the ace- −1 T as follows: tabular rim. The radius of the sphere was determined to include the whole regions of osteotomized acetabulum based pre −1 G R= T × R, 4 on overlapped patient’s CT images before and after PAO. post post Theoretically, the “osteotomized” acetabulum could be where G represents to global coordinate system; pre and post reoriented to any desirable angles around the hip joint center. denote to before and after surgery, respectively. Based on In this study, Post-OP FE models were generated, such that matrix components (as in (3)), Bryant angle of the osteoto- the amounts of the acetabulum rotations were varied accord- mized acetabular rotation about three orthogonal planes ing to the calculated actual acetabular rotation (ACR) during was calculated using arctangent function as follows: the surgery. In addition, the range of rotation of the osteoto- mized acetabulum by the surgery with respect to each axis was calculated based on Pre- and Post-OP patient’sCT α = arctan , images. The preoperative FE model was rotated by 1/3 ACR 1/2 in each axis incrementally up to 4/3 ACR. A total of twelve 13 2 β = arctan + R , 5 models were constructed by simulating incremental increase in the amount of the acetabular rotation (at an increment of 1/3 ACR) in each anatomical plane from 1/3 to 4/3 ACR. In γ = arctan − other words, when incremental increasing of the acetabular angle through a single axis, rotating through the other axes was held constant. All Post-OP models were prepared using 2.2. Construction of Post-OP FE Models. A previously con- FE preprocessing software Patran (Version 2010, MSC structed Pre-OP FE model was unitized to provide the base- Corp., USA). line geometry of a dysplastic hip [17]. This Pre-OP model accurately captures the geometry of the diseased bone- cartilage interface. Bone tissues were differentiated from soft 2.3. Loading and Boundary Conditions. A finite-sliding tissues in relation to the threshold in grey scale value which is surface-to-surface contact condition was defined at the joint equivalent of 226~3017 Hounsfield units (HU). Further- interface between the femoral head and acetabulum. Contact more, subdivision between the cortical and cancellous bones constraints were enforced at articular surfaces based on the penalty method (ABAQUS 6.13, Simulia, RI, USA). The fric- of the proximal femur was made based on the threshold value for the cortical bone (662–1988 HU). As the boundaries for tion coefficient, μ, was set to 0.02 for simulating low-friction the articular cartilage was not clearly identifiable from the physiological condition in the presence of the synovial fluid CT images, it was assumed that the joint interface between [23]. In Post-OP models, the reoriented acetabulum was the femoral head and the acetabulum was covered with a uni- reconnected to the pelvis through tied contact to suggest complete bony union after the surgery. form cartilage thickness of 1.0 mm [21]. The pelvis and prox- imal femur were meshed by tetrahedral and hexahedral Load conditions corresponding to those arising from a elements consisted of 475,530 and 4920 elements (677,907 single-leg stance were simulated. A distributed load of and 115,274 nodes), respectively. The cartilage was meshed 1177 N (231% of the body weight of the patient, 52 kg) was by hexahedral elements, and number of nodes and elements imparted to the distal end of the femoral shaft, while the superior region of the ilium and the symphysis pubis was were 2594 and 1220, respectively. An automatic calculation for global element edge length was used for mesh generation. fixed in all directions. Such loading and boundary conditions To ensure numerical stability, linearly elastic hexahedral ele- were assumed with abductor muscles counterbalancing the ments were used to mesh the cartilage layers (Figure 3). The body weight as suggested by Bergmann et al. [24]. FE material properties for the bone tissues and the cartilage were analysis was performed using a general-purpose FE solver ABAQUS (Simulia). Changes in the anatomical angles obtained from the literature (Table 1). Applied Bionics and Biomechanics 5 images confirmed that the osteotomized acetabular rotation occurred in three dimensions. The actual ACR during PAO for a given patient expressed in Bryant angles was 9.7 in sag- ° ° ittal plane, 18 in coronal plane, and 4.3 in transverse plane. 3.2. Changes in Acetabulum Anatomical Angles. Anatomical Cartilage layer covers angles were measured as acetabulum rotates (Table 2). In the femoral head the coronal plane (rotation along y-axis), CE angle was grad- ually increased due to incremental increase in acetabulum ° ° rotations (from 12.5 to 26.7 ), while the acetabular abduc- Pelvic cartilage tion was decreased as similar trend of changes of CE angle ° ° (from 47.4 to 29.7 ). These parameters were restored to be Figure 3: A cutaway view of the FE model illustrating interior within the normal range from the 18 rotation in the coronal mesh for the layers of articular cartilage covering the femoral head plane. An analysis of changes in the acetabular anteversion and acetabulum. was found not to be significant. Table 1: Material properties used in the hip FE models. 3.3. Changes in Joint Contact Areas. Joint contact area due to incremental increase in acetabulum rotations showed the Components Young’s modulus (MPa) Poisson’s ratio Ref. changes of −2.9%, 4.4%, 9.4%, and −1.2% in the sagittal plane Cortical bone 17,000 0.3 (rotation along x-axis) and 0.9%, 4.2%, 23.5%, and 8.1% in [19] Cancellous bone 100 0.2 the coronal plane (rotation along y-axis), respectively. In Cartilage 12 0.45 [20] the transverse plane (rotation along z-axis), contact area and pressure remained relatively unchanged (differences less than ±1%). The above results were plotted in Figure 5. Max- (CE angle, acetabular abduction, and acetabular anteversion) imum contact area was achieved for the sagittal plane and the and the joint contact area, rate of changes in contact area, the coronal plane rotations. A most favourable increase of 23.5% contact pressure (95th percentile value) in relation to the 2 2 in contact area (from 344.7 mm to 425.5 mm ) was seen for directions, and amount of the rotations were assessed. All ° the 18 rotation in the coronal plane. An analysis of rate of results were compared to the Pre-OP condition to determine changes in contact area showed the highest sensitivity of the consequences of varied acetabulum rotations in three 2 4.5 mm /degree for the coronal plane (Figure 6). dimensions. For clarity, the difference was marked positive, if it indicated an increase in contact area/pressure, and nega- 3.4. Changes in Contact Pressures (95th Percentile Value). tive if it indicated a decrease. There was clear trend in reduction in contact pressure as ace- tabulum rotates (Figure 7). Before PAO, contact pressure dis- 2.4. Sensitivity Analysis. Sensitivity analysis was performed to tributions showed stress concentrations on the superolateral investigate changes of Pre-OP FE model’s contact predictions regions of the femoral cartilage (Figure 8). Acetabular rota- due to variability in cartilage material properties and loading tions resulted in increased contact area thus reduced pressure conditions. The baseline Young’s modulus of the cartilage values. Contact pressure reached the lowest value in the was altered by ±1 SD while the Poisson’s ratio was kept con- model where the applied rotation of the acetabulum matched stant. Then, Young’s modulus was kept constant and the the actual acetabular rotation (ACR) during PAO. Similarly, Poisson’s ratio was deceased to 0.42 [25] and increased to the maximum pressure reduction was 53.2% (from 10.4 MPa 0.49 (with an assumption of cartilage incompressibility). to 4.9 MPa) found for the 18 acetabulum rotations in the The contact pressure (95th percentile value), mean contact coronal plane. A reduction of 19.2% in pressure was observed pressure, and contact area were predicted for three different during acetabulum rotations in the transverse plane. The rate loading conditions [21], consisting of single-leg stance, of change in contact pressure (95th percentile value) showed normal walking, and stair climbing. A total of 15 models the highest sensitivity (0.3 MPa/degree) for acetabular rota- were evaluated for the sensitivity analysis. tions in the coronal plane. 3. Results 3.5. Sensitivity Analysis. Alterations of Young’s modulus of 3.1. Acetabular Rotations during PAO Surgery. The Euclidean cartilage resulted in approximately changes of contact pres- distance between individual landmarks had a mean ± stan- sure and mean contact pressure by ±7.1% and ±4.5%, respec- dard deviation of 0.59 ± 0.15 mm, which confirmed the high tively, and changes in contact area were about ±2% repeatability in virtual marker placement, and the ICC (Figure 9). When the Poisson’s ratio was altered, contact pressure varied from −10.9 to 30.1%, and changes in contact was found to be 1.0 (p <0 05) which is extremely high reliability. Our results provide evidence of position reliabil- area were approximately ±12.6%, while changes in mean ity between the observers. The calculated actual acetabular contact pressure were less than 6%. Average RMS differences rotation (ACR) based on Pre- and Post-OP patient’sCT as compared to the baseline model were only about 3%. 6 Applied Bionics and Biomechanics 45 mm Hip joint center Pelvis 3-D reconstruction Placement sphere for osteotomy (a) (b) Virtual osteotomy model Post-OP FE model generation (c) (d) Figure 4: Procedure of the virtual PAO surgery: (a) 3-D reconstruction of the patient’s pelvis, (b) superposition of the sphere (r =45mm)on the periphery of the acetabulum for osteotomy, (c) Boolean process to cut the pelvis and the acetabulum, and (d) 3-D rotation of the osteotomized acetabulum. Table 2: Changes in anatomical angles of Post-OP models due to incremental increase in acetabulum rotations. The “ ” sign indicated to be within the normal range. Rotation axis Incremental ROM of acetabulum CE angle Acetabular abduction Acetabular anteversion ° ° ° Pre-OP model 12.2 48.1 10.8 Post-OP models ° ° ° 1/3 9.7 51 13.5 ° ° ° 2/3 10.5 51.3 14.6 Sagittal plane (x-axis) ° ° ° 3/3 11.7 49.4 15.6 ° ° ° 4/3 10.9 48.5 16.2 ° ° ° 1/3 12.5 47.4 15 ° ° ° 2/3 15.9 41.9 10.5 Coronal plane (y-axis) ° ° ° ∗ ∗ 3/3 20.9 36.2 10.7 ° ° ° 4/3 26.7 29.7 8.5 ° ° ° 1/3 9 50.4 12.1 ° ° ° 2/3 9.8 50.6 11.5 Transverse plane (z-axis) ° ° ° 3/3 10 51.4 11.5 ° ° ° 4/3 11.9 49.5 13.5 ` Applied Bionics and Biomechanics 7 Changes in the contact area Changes in the contact pressure (95th percentile value) 23.5% Pre-OP (10.4 MPa) 53.2% 350 Pre-OP (344.7mm ) 1/3 2/3 3/3 4/3 1/3 2/3 3/3 4/3 Incremental ROM of the acetabulum Incremental ROM of the acetabulum x-axis rotation x-axis rotation y-axis rotation y-axis rotation z-axis rotation z-axis rotation Figure 7: Changes in the contact pressure (95th percentile value) as Figure 5: Changes in the contact area as a function of incremental a function of incremental increased rotations of the acetabulum as increased rotations of the acetabulum as compared to the Pre-OP compared to the Pre-OP condition. The “ ” sign indicates the condition. The “ ” sign indicates the actual acetabular rotation actual acetabular rotation (ACR) during the surgery. (ACR) during the surgery. out the most dominant factor regarding direction of the Rate of changes in the contact area rotation due to incremental rotation of the osteotomized 4.5 mm /degree acetabulum in each axis. The effectiveness according to the three-dimensional rotations of the acetabulum was deter- mined in terms of the contact stresses and the coverage area of the hip. The results obtained at different angles (joint realignments) provide quantitative information related to 0 acetabular rotations to achieve the optimal outcome of the −1 PAO surgical procedure. In this study, virtual anatomic landmarks were created in −2 the Pre- and Post-OP models in order to apply Bryant angles −3 for calculating kinematic changes of the acetabulum. We −4 verified the procedure of the landmark placement to ensure −5 1/3 2/3 3/3 4/3 the repeatability of our method. Three landmarks of the pel- Incremental ROM of the acetabulum vis were chosen, as suggested by Lycett and von Cramon- Taubadel [18], due to their clearly identifiable morphological x-axis rotation features in CT images. Similar to the Lycett’s approach [18], y-axis rotation we quantified errors associated with anatomical landmark z-axis rotation placement by applying Euclidean distance equation based Figure 6: Rate of change in the contact area as a function of on coordinates of the landmarks manually picked by six incremental increased rotations of the acetabulum. The negative independent observers. The repeatability on anatomic land- sign indicates a decrease in contact area. The “ ” sign indicates the marks set could be confirmed since Euclidean distance of less actual acetabular rotation (ACR) during the surgery. than 1.0 mm was calculated for individual landmarks. Various studies on optimization of PAO have been reported [10–17]. Most studies have investigated the bio- 4. Discussion mechanical effectiveness of PAO in relation to acetabular Computational simulations using patient’s anatomy-specific rotation. More specifically, the 3-D FE simulation-based models offer an attractive approach for prediction of key bio- optimal reorientation planning method was introduced by mechanical parameters, such as hip joint contact patterns, Liu et al. [11]. The study was performed subject-specificFE before the PAO surgery. Currently, the clinical outcomes of simulation for 4 subjects who underwent PAO surgery and the PAO remain controversial mainly because the procedure evaluated biomechanical effect of the reorientation planning. involves highly complex multiaxial rotations of the acetabu- However, the direction and amount of the acetabular rota- lum while the optimal rotational parameters were unclear. tion and the most dominantly affecting direction of the ace- tabular rotation during the actual PAO surgery have not While the osteotomy and rotation take place in three dimen- sions, but its pre- or intra-OP rotation depends on the been investigated. Therefore, using a kinematic analysis method, we determined the Bryant angle of the osteotomized experience and decision of the surgeon. In particular limited information on clinical and biomechanical efficacies in acetabular rotation during PAO. Our results indicated that ° ° relation to amount and directions for rotation of the osteoto- Bryant angles were 9.7 in the sagittal plane, 18 in the coro- mized acetabulum was reported. Therefore, we aimed to find nal plane, and 4.3 in the transverse plane. The results Contact area (mm ) Rate of changes in the contact area (mm /degree) Contact pressure (MPa) 8 Applied Bionics and Biomechanics (MPa) +1.407e +01 +1.407e +01 +1.289e +01 +1.172e +01 Incremental increased rotations of the acetabulum +1.055e +01 +9.377e +00 + +8.205 8.205ee + +0 00 0 + +7.033 7.033ee + +0 00 0 + +5.861 5.861ee + +0 00 0 +4. +4.689 689ee + +0 00 0 + +3.516 3.516ee + +0 00 0 x-axis rotation +2 +2.344 .344ee + +0 00 0 (sagittal plane) + +1.172 1.172ee + +0 00 0 +0.00 +0.000 0ee + +0 00 0 y-axis rotation (coronal plane) z-axis rotation (transverse plane) P Pr re-O e-OP mo P model del Figure 8: Contact pressure distributions of the Pre-OP model and twelve Post-OP models due to rotations of the osteotomized acetabulum in three anatomical planes. ° ° ° suggested that acetabulum rotated in three dimensions dur- reported CE angles after PAO were 29.6 ± 6 (from 21 to 48 ) ° ° ° ing the surgery. While the major component of acetabular [28] and 36.4 ± 6.5 (from 21 to 50 ) [29], respectively. The ° ° rotations was in the coronal plane, rotations in other ana- reported acetabular abduction was 39.6 ± 3.9 (from 31 to tomical planes were also significant. 48 ) [29]. In our FE analysis, the optimal CE angle (rotating In our investigation, anatomical angles were assessed from the initial adduction at 18 ) and acetabular abduction due to incremental adjustment of the acetabular rotations. angle (from the initial acetabulum rotations in the coronal ° ° ° CE angles were increased due to incremental increase in ace- plane at 18 ) were 20.9 and 36.2 , respectively, which were tabulum rotations in the coronal plane and restored to be comparable with the measured clinical outcomes. While within the normal range (CE angle more than 20 ) from it appears that the CE angle has fallen slightly out of the adduction of 18 rotation [26]. In the same rotation, acetabular lower bound of the reported angular range, this could be abduction also restored of normal range (35 ≤ acetabular attributed to the fact that only acetabular rotations were abduction ≤ 45 ) [27]. The acetabular anteversion of the simulated in the study. If realistic translations of osteoto- dysplastic hip was reported because it was not significantly mized acetabular during actual PAO surgery were applied, different from that of normal hips. In addition, the weight- the accuracy of our biomechanical simulation results may be bearing surface of the acetabulum is almost perpendicular improved. However, such analysis involves surgical simula- to a vertical line in the standing position. Therefore, ana- tions of the acetabular motions in six degrees of freedom, tomical planes perpendicular to it are optimal for direct which would require significant more efforts thus time for visualization and measurement of the surface and acetabular model preprocessing [8]. coverage; in practices, these are the coronal and sagittal From FE analysis, we showed that adduction of 18 planes [26]. The finding of changes in anatomical angles (the ACR in the coronal plane along y-axis) resulted in a was compared with studies of long-term clinical outcome most significant increase in contact area by 23.5% (from of PAO to improve clinical evidence of our study. Rela- 344.7 to 425.5 mm ) compared to Pre-OP condition. Due to tively few long-term outcome studies of PAO are available increased contact area, the corresponding contact pressure [2, 28–31]. In two long-term clinical studies (>10 years), the (95th percentile value) was reduced by 53.2% (from 10.4 to Applied Bionics and Biomechanics 9 40 40 30 30 20 20 10 10 0 0 −10 −10 −20 −20 E = 11 MPa E = 13 MPa ν = 0.42 ν = 0.49 Young’s modulus Poisson’s ratio Contact pressure (95th percentile value) Contact pressure (95th percentile value) Mean contact pressure Mean contact pressure Contact area Contact area (a) (b) Figure 9: Percent changes in contact pressure (95th percentile value), mean contact pressure and contact area due to alterations in cartilage material properties, Young’s modulus (a) and Poisson’s ratio (b). Error bars indicate standard deviations over the three loading conditions evaluated. 4.9 MPa). Especially, peak contact pressure in Pre-OP model and contact pressure (4.4–5.0 MPa) measured in Anderson’s was concentrated on the superolateral regions of cartilage. experimental study [21]. Due to the poor acetabular cover- However, contact pressures were reduced and evenly distrib- age, the contact pressure (95th percentile value) predicted uted around the superior regions of the cartilage due to incre- by our Pre-OP dysplastic hip model was 10.4 MPa, which mental adjustment of the acetabular rotation in the coronal were higher than those measured in normal hips. Unfortu- plane. While contact distributions of rotation in the sagittal nately, the experimental data on joint contact pressures at and transverse planes were relatively unchanged (Figure 8), the dysplastic hip model is still significantly lacking. Never- these changes improved contact area and peak contact pres- theless, Russell et al. conducted the FE analysis on a dys- sure to the level close to the normal range [32–34]. Sensitivity plastic hip model and the predicted peak contact pressure of contact area and peak contact pressure according to the was 9.9 MPa [25]. However, due to the variations in acetab- rotation direction of the acetabulum also showed the highest ular coverage between different patients, direct comparison value (4.5 mm between the models may be difficult. The model predic- /degree and 0.3 MPa/degree) at adduction of 18 . Thus, the coronal plane (adduction) turned out to be tions, in terms of joint contact pressure and contact area, the most important rotation plane that strongly affects hip compared favourably with those previous studies. In addi- contact mechanics as compared to other planes (sagittal tion, since our study focused on evaluating relative perfor- plane, x-axis; transverse plane, z-axis) for a given patient. In mance of the same model and only relative changes were made for different hip alignment angles, the simulation clinical scenarios, the actual amount of acetabulum rotations during PAO is mainly determined by surgeons. Our results results presented in this study should be thus considered seem to suggest that, to ensure clinical benefits of the proce- clinically meaningful. dure, acetabulum rotations in the coronal plane are of critical The cartilage Young’s modulus alternations did not importance during the PAO. significantly affect the FE results of contact pressure (95th The FE models used in this study were constructed percentile value), mean contact pressure, and contact area based on CT images of a patient who underwent the PAO (±7.1%, ±4.5%, and ±2%, resp.) from the baseline case. When surgery. FE analysis requires robust validation process. Poisson’s ratio decreased from 0.45 to 0.42, the peak pressure We carefully compared our model results against Ander- was decreased by 10.9% due to an increased contact area by son’s cadaveric experimental study on a normal hip joint about 12.4%. However, as the Poisson’s ratio increased to [21] and Russell’s FE analysis on a dysplastic hip model nearly incompressible materials (ν =0 49), contact pressure [25]. The contact area predicted by our Post-OP FE model was remarkably increased by approximately 30.1%; however, was 428.8 mm and peak contact pressure 4.6 MPa, which the mean contact pressure was only changed by 6%. These agreed with the average contact area (321.9–425.1 mm ) results suggested that the proper choice for Poisson’s ratio Percent change Percent change 10 Applied Bionics and Biomechanics is more critical for accurate prediction of peak contact pres- 5. Conclusions sure, as compared to the mean contact pressure. In addition, The results of our study show that the acetabulum rotation in a decrease in mean contact pressure was considered to be the coronal plane (adduction) had the strongest effects on indicative of a general decrease in joint contact stresses, contact pressure and contact pressure compared to rotations which is aligned with clinical goal of the PAO surgery. Simi- in other planes. In particular, the osteotomized acetabulum lar approaches have been adopted in FE analysis performed rotation with adduction of 18 is considered to be the most for the understanding of the hip and elbow joint contact effective angle for the given patient. Although this study mechanics [21, 35]. was limited to a single patient, the methodology developed A number of modelling assumptions were also made to in this study could contribute to the preoperative planning facilitate FE analysis in the study. Firstly, linear-elastic, that determines the optimal direction and amount of rota- homogeneous material properties were used to model bone tion of the osteotomized acetabulum in three dimensions and cartilage tissues. In most FE simulation studies of PAO during PAO. [12, 15, 16], the bony structure and cartilage were modeled as the linear-elastic, homogeneous materials. It was reported that the effects of using linear-elastic, homogeneous material Conflicts of Interest properties on predicted cartilage stresses were negligible [36]. The authors declare that there is no conflict of interest While the cartilage is reported as a biphasic material with regarding the publication of this paper. time-dependent mechanical behavior, the frequency for walking loads is in the order of 1 Hz. Thus, time-dependent Authors’ Contributions response of the cartilage can be neglected [37]. Secondly, the cartilages were not clearly identifiable from the CT Sung-Jae Lee Park and Wen-Ming Chen contributed equally images (using the clinical CT scanner), and a constant thick- to this work. ness of 1.0 mm was assumed for articulating surfaces of the acetabulum and the femoral head. This enabled us to evaluate References contact mechanisms on the cartilage in DDH patients similar to a previous study [32]. Modeling subject’s anatomy-specific [1] M. Fujii, Y. Nakashima, T. Yamamoto et al., “Acetabular retro- cartilage layer seems to be essential for our FE analysis. How- version in developmental dysplasia of the hip,” The Journal of ever, it has been reported that the predicted optimal align- Bone and Joint Surgery. American Volume, vol. 92, no. 4, ment of the acetabulum was not significantly sensitive to pp. 895–903, 2010. the change of the cartilage thickness distribution during [2] S. D. Steppacher, M. Tannast, R. Ganz, and Siebenrock K a., PAO [14]. 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Ramachandran, “Management of developmental dysplasia of the hip in young adults: current concepts,” The Bone & Joint acknowledged that CT scan was performed in the supine Journal, vol. 95, no. B, pp. 732–737, 2013. position and the FE models simulated a single-leg stance sce- [5] A. Troelsen, B. Elmengaard, and K. Søballe, “Medium-term nario [24]. Niknafs et al. [14] found no significant difference outcome of periacetabular osteotomy and predictors of con- between the contact pressure in the single-leg stance refer- version to total hip replacement,” The Journal of Bone and ence frame and those in the supine reference frame. Lastly, Joint Surgery. American Volume, vol. 91, no. 9, pp. 2169– we performed anatomical-specific FE analysis for only one 2179, 2009. patient. For providing clinical evidence, our finding of [6] M. Fu, S. Xiang, Z. 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Computer-Assisted Optimization of the Acetabular Rotation in Periacetabular Osteotomy Using Patient’s Anatomy-Specific Finite Element Analysis

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Hindawi Applied Bionics and Biomechanics Volume 2018, Article ID 9730525, 11 pages https://doi.org/10.1155/2018/9730525 Research Article Computer-Assisted Optimization of the Acetabular Rotation in Periacetabular Osteotomy Using Patient’s Anatomy-Specific Finite Element Analysis 1 2 3 4 5 Sung-Jae Park , Sung-Jae Lee , Wen-Ming Chen, Jung-Hong Park, Yong-Soo Cho, 1 6 Taejin Shin, and Soon-Yong Kwon Central R&D Center, Corentec Co. Ltd., Banpo-dong, Seocho-gu, Seoul 06541, Republic of Korea Department of Biomedical Engineering, Inje University, Obang-dong, Gimhae 50834, Republic of Korea Department of Biomedical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China R&D Institute, YM Yangsan Machinery Ltd., Jeonggwan-eup, Gijang-gun, Busan 46027, Republic of Korea Department of Orthopaedic Surgery, St. Mary’s Hospital, Catholic University, Yeouido-dong, Yeoungdeungpo-gu, Seoul 07345, Republic of Korea Department of Orthopaedic Surgery, St. Paul’s Hospital, Catholic University, Jeonnong-dong, Dongdaemun-gu, Seoul 02559, Republic of Korea Correspondence should be addressed to Sung-Jae Lee; sjl@bme.inje.ac.kr and Soon-Yong Kwon; sykwon@catholic.ac.kr Received 22 June 2017; Revised 5 October 2017; Accepted 12 November 2017; Published 4 February 2018 Academic Editor: Laurence Cheze Copyright © 2018 Sung-Jae Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Periacetabular osteotomy (PAO) is a complex surgical procedure to restore acetabular coverage in the dysplastic hip, and the amount of acetabular rotation during PAO plays a key role. Using computational simulations, this study assessed the optimal direction and amount of the acetabular rotation in three dimensions for a patient undergoing PAO. Anatomy-specific finite element (FE) models of the hip were constructed based on clinical CT images. The calculated acetabular rotation during PAO ° ° ° were 9.7 ,18 , and 4.3 in sagittal, coronal, and transverse planes, respectively. Based on the actual acetabular rotations, twelve postoperative FE models were generated. An optimal position was found by gradually varying the amount of the acetabular rotations in each anatomical plane. The coronal plane was found to be the principal rotational plane, which showed the strongest effects on joint contact pressure compared to other planes. It is suggested that rotation in the coronal plane of the osteotomized acetabulum is one of the primary surgical parameters to achieve the optimal clinical outcome for a given patient. 1. Introduction Periacetabular osteotomy (PAO) is one of the preferred joint-preserving techniques known to correct multiaxial hip deformities in DDH patients [5–7]. A PAO involves osteot- Developmental dysplasia of the hip (DDH) manifests various omy at the periphery of the ilium and the ischium and morphological abnormalities including acetabular dysplasia, followed by rotation of the acetabulum in three dimensions. decreased acetabular coverage of the femoral head, excessive femoral anteversion, increased neck-shaft angle, and short- Studies have shown that PAO could effectively reduce the joint load and relieve abductor muscle forces through the ened femoral neck [1]. Patients with DDH are usually adoles- cents or young adults with congenital deformities. When left medial translation of the hip joint center [8]. To achieve the optimal surgical outcome, joint congru- untreated, DDH can cause secondary osteoarthritis due to ency between the femoral head and the acetabulum must be prolonged exposure to increased contact stresses on the artic- ular cartilage in the hip joint [2–4]. established. Normally, preoperative (Pre-OP) information 2 Applied Bionics and Biomechanics including the location of the osteotomy and subsequent rota- Set of reference points (n = 3) on the pelvis and 3-D tions of the acetabulum in terms of the direction and the congruency of the pelvis through superposition amount have to be determined [9]. Clinical studies showed that individualized Pre-OP planning of PAO could improve surgical outcomes [10–17]. Unfortunately, quantitative Calculation of Bryant angle (𝛼, 𝛽, and 𝛾) to evaluate information regarding the optimal rotational parameters the kinematic changes of the acetabulum during PAO remain unclear. As a result, surgical planning still largely relies on the experience and decision of the clinicians. Fur- Set of virtual markers (n =3) ther, Pre-OP planning and postoperative (Post-OP) assess- of the acetabulum before and aer P ft AO ment usually depend on the radiographic X-ray imaging which are essential in two dimensions, as opposed to the three-dimensional orientation and acetabular rotations for Assessment on repeatability (n =6) hip realignment during the surgery. regarding the location of anatomic landmarks Pre-OP planning was first introduced by Langlotz et al. [10], which generally involves measurement of morpholog- ical parameters such as center-edge (CE) angle in X-ray Development of local coordinate system images [11–13]. In contrast, recent development of Pre- of the acetabulum before and aer P ft AO OP planning based on biomechanical modelling permits a more quantitative solution. Biomechanical information, such as tissue stresses, contact area, and contact pressure Representation of transformation matrix in the hip joint, can be predicted through computational regarding global coordinate simulations, such as finite element (FE) analysis [12, 15, 16]. Zou et al. [15] constructed hip FE models for five patients with DDH to investigate the optimal location of Calculation of the acetabular rotation in planes (sagittal, the acetabulum in PAO in relation to CE angle. Zhao coronal, and transverse planes) using Bryant angle et al. [16] investigated the effect of PAO on von Mises stresses on the cortical bone of the acetabulum. The above Figure 1: Flow chart for three-dimensional rotational calculation of studies, however, only considered the two-dimensional the osteotomized acetabulum during PAO. acetabulum rotations. In a recent study [17], we constructed an anatomy- specific FE model based on computed tomography (CT) who was diagnosed with DDH and underwent PAO surgery images collected from a patient who underwent PAO sur- at Fukuoka University Hospital (Fukuoka, Japan). The Pre- gery. In that study, we quantitatively determined the bio- OP scan was performed for the hip and the pelvis of the mechanical parameters, including hip joint contact area, patient using a clinical scanner (Aquilion 64, Toshiba Medi- contact pressure, and peak von Mises stress, before and cal System Corp., Japan) at a resolution of 0.398 mm and a after the PAO surgery. However, our previous model used slice spacing of 2.0 mm. The Post-OP images were obtained a simplified approach by limiting the acetabular rotation 2 months after the surgery from the same patient using the in a single anatomical plane, and the actual acetabular same scanning parameters. rotations during the surgery which are in three dimen- The focus in this paper is twofold: first, based on the sions were not considered. Thus, the effects of acetabular Pre- and Post-OP CT images to calculate the amount of rotation in different anatomical planes on joint contact actual acetabular rotation (ACR) during the PAO and sec- mechanics remain unclear. ond, based on the actual ACR to guide the development of This study aims to investigate the principal axes of rota- a series of Post-OP computational models of the dysplastic tion of the acetabulum and to assess the optimal amount of hip following various acetabular rotations in three dimen- the acetabular rotation in three dimensions in a dysplastic sions. Using FE analysis, the biomechanical responses hip model. To this end, a range of rotation of the osteoto- obtained from the Post-OP models including peak contact mized acetabulum during PAO was calculated using the pressure and contact area were compared to the Pre-OP patient’s anatomy-specific FE models [17]. A series of FE model to determine the efficacy of acetabular rotations analyses were performed based on the measured anatomical along different axis during PAO. angles and changes in the joint coverage areas, and contact stresses were evaluated due to incremental rotation of the 2.1. Three-Dimensional Rotations of the Acetabulum due to osteotomized acetabulum in three dimensions. PAO. We implemented an image registration method for the calculation of three-dimensional rotations of the osteoto- mized acetabulum during PAO. The detailed procedures 2. Materials and Methods were performed as described in Figure 1. While the Pre- and Post-OP CT images were collected at Hip dysplasia is known to affect the structural geometry of the femoral head and the acetabulum. To capture the real- the same resolution, the scanning position was changed. To istic geometry of a diseased hip, CT images were collected ensure congruency, the Pre- and Post-OP images were rea- from a 42-year-old female patient (body weight of 52 kg) ligned such that the pelvis (excluding the acetabulum) before Applied Bionics and Biomechanics 3 Marker number 1 (X , Y , Z ) 11 11 11 Marker number 2 (X1 , Y , Z ) 12 12 12 Z Marker number 3 (X , Y , Z ) 13 13 13 < Pre-Op > Marker number 1 (X , Y , Z ) 21 21 21 Marker number 2 (X , Y , Z ) 22 22 22 z X Pre-Op Marker number 3 Post-Op (X , Y , Z ) 23 23 23 Post-Op Post-Op < Post-Op > X X Pre-Op Pre-Op Global coordinate system (a) (b) Figure 2: Reconstructed solid models of the pelvis based on the Pre- and Post-OP CT scans. The extent of osteotomy of the acetabulum was shown with a dotted line. (a) Locations of the anatomic landmarks in Pre- and Post-OP models in a lateral view (mark number 1 for acetabular fossa; mark number 2, and mark number 3 for the acetabular anterior and inferior sites, resp.); (b) the global coordinate system (X, Y, and Z; sagittal, coronal, and transverse planes) were shown. Three-dimensional rotations of the acetabulum were described by three Bryant angles along each axis. and after PAO was registered by superposition in the Euclidean distances commercial image-processing software Mimics (Materialise, 2 2 Louvain, Belgium). Using the built-in image registration = X − X + Y − Y + Z − Z ij ij ij ij ij ij function, the spatial position and orientation of the pelvis in Pre- and Post-OP CT images were realigned. Among the most common parameters used to describe To calculate the amount of acetabular rotations during the angular orientation of a body in three dimensions are PAO, two geometrical models, that is, solid models, were Euler angles [19]. Using Euler angles, the angular orientation built based on reconstruction of the two sets of realigned of a given body-fixed (i.e., local) coordinate system can be Pre- and Post-OP images using a previously established envisioned to be the result of three successive rotations. How- protocol [17]. Virtual markers (n =3) were set at the end ever, in the body-fixed coordinate system, the sequence of of acetabular fossa (marker number 1), inferior (marker rotations used to define the final orientation of the coordinate number 2), and anterior sites (marker number 3), which were system is to some extent arbitrary. For example, the Euler clearly identifiable in both Pre- and Post-OP models angles which act as a set of three independent body-fixed (Figure 2). To increase the accuracy in placing these markers, coordinates are altered as the initial body-fixed coordinate three-dimensional geometrical objects, that is, spheres with system changes during body’s three-dimensional rotations. radius of 3.0 mm, were used to locate the anatomic land- Therefore, we calculated the angular orientation relative marks of the acetabulum. Three-dimensional coordinates to the global coordinate system, which is defined as Bryant at the center of sphere in the Pre- and Post-OP models angles [19]. A local coordinate system was first defined for were extracted to indicate the spatial location of these ease of description of the calculation. The vector connecting anatomic landmarks. marker number 1 and marker number 2 defined the x-axis To evaluate the repeatability of individual marker of local coordinate system. The vector connecting marker placement, the interobserver variability was assessed in six number 2 and marker number 3 determined vector q. Cross independent observers. Repeatability between each landmark product of vectors x and q determined vector of z-axis by was evaluated [18] by repeatedly using coordinates of land- applying the right-handed rule. Likewise, the y-axis vector marks set (X , Y , and Z : i refers to before and after PAO, ij ij ij of local coordinate was determined by applying the cross i = 1 and 2; j denotes to anatomic landmark, j = 1, 2, and 3) products of vectors x and z, as shown in placed by the observers (X , Y , and Z ) using (1). This ij ij ij equation calculates the Euclidean distance between two x × q = z , 2 landmarks in the three-dimensional space. The interclass x × z = y correlation coefficient (ICC) on position of the virtual markers was also measured and assessed to confirm inter- By assuming rigid body motion, a transformation matrix observer variations using statistical software (SPSS 22, SPSS T [20] for the local coordinate system in describing acetabu- Inc., USA). lum rotation before and after surgery reads as follows: 4 Applied Bionics and Biomechanics R R R cos β cos β cos α sin β sin γ − sin α cos γ cos α sin β cos γ − sin α sin γ 11 12 13 T = R R R = sin α cos β sin α sin β sin γ − cos α cos γ −sin α cos β , 21 22 23 R R R −cos α sin β cos γ − sin β sin γ cos α sin β sin γ − sin α cos γ cos α cos β 31 32 33 where each column in matrix indicates the unit vector on A simulated osteotomy was performed at the periphery of x-, y-, and z-axis. And three-dimensional movement of the the acetabulum in the baseline model to mimic actual surgi- acetabulum was expressed in Bryant angle (α, β, and γ) cal procedure (Figure 4) [22]. Virtual cutting was done to and cosine, sine function with regard to global coordinate simulate osteotomy due to PAO using Mimics software with system [20]. The Bryant angles describes flexion (x-axis), a sphere (radius of 45 mm) located around the right hip cen- adduction (y-axis), and external rotation (z-axis) of the hip ter to separate the ilium, the ischium, and the pubis from the movement. Thus, the relative acetabular rotation (R) could pelvis. The position of the central point of the sphere was be obtained by multiplying the inverse transformation matrix matched with the central point made by geometry of the ace- −1 T as follows: tabular rim. The radius of the sphere was determined to include the whole regions of osteotomized acetabulum based pre −1 G R= T × R, 4 on overlapped patient’s CT images before and after PAO. post post Theoretically, the “osteotomized” acetabulum could be where G represents to global coordinate system; pre and post reoriented to any desirable angles around the hip joint center. denote to before and after surgery, respectively. Based on In this study, Post-OP FE models were generated, such that matrix components (as in (3)), Bryant angle of the osteoto- the amounts of the acetabulum rotations were varied accord- mized acetabular rotation about three orthogonal planes ing to the calculated actual acetabular rotation (ACR) during was calculated using arctangent function as follows: the surgery. In addition, the range of rotation of the osteoto- mized acetabulum by the surgery with respect to each axis was calculated based on Pre- and Post-OP patient’sCT α = arctan , images. The preoperative FE model was rotated by 1/3 ACR 1/2 in each axis incrementally up to 4/3 ACR. A total of twelve 13 2 β = arctan + R , 5 models were constructed by simulating incremental increase in the amount of the acetabular rotation (at an increment of 1/3 ACR) in each anatomical plane from 1/3 to 4/3 ACR. In γ = arctan − other words, when incremental increasing of the acetabular angle through a single axis, rotating through the other axes was held constant. All Post-OP models were prepared using 2.2. Construction of Post-OP FE Models. A previously con- FE preprocessing software Patran (Version 2010, MSC structed Pre-OP FE model was unitized to provide the base- Corp., USA). line geometry of a dysplastic hip [17]. This Pre-OP model accurately captures the geometry of the diseased bone- cartilage interface. Bone tissues were differentiated from soft 2.3. Loading and Boundary Conditions. A finite-sliding tissues in relation to the threshold in grey scale value which is surface-to-surface contact condition was defined at the joint equivalent of 226~3017 Hounsfield units (HU). Further- interface between the femoral head and acetabulum. Contact more, subdivision between the cortical and cancellous bones constraints were enforced at articular surfaces based on the penalty method (ABAQUS 6.13, Simulia, RI, USA). The fric- of the proximal femur was made based on the threshold value for the cortical bone (662–1988 HU). As the boundaries for tion coefficient, μ, was set to 0.02 for simulating low-friction the articular cartilage was not clearly identifiable from the physiological condition in the presence of the synovial fluid CT images, it was assumed that the joint interface between [23]. In Post-OP models, the reoriented acetabulum was the femoral head and the acetabulum was covered with a uni- reconnected to the pelvis through tied contact to suggest complete bony union after the surgery. form cartilage thickness of 1.0 mm [21]. The pelvis and prox- imal femur were meshed by tetrahedral and hexahedral Load conditions corresponding to those arising from a elements consisted of 475,530 and 4920 elements (677,907 single-leg stance were simulated. A distributed load of and 115,274 nodes), respectively. The cartilage was meshed 1177 N (231% of the body weight of the patient, 52 kg) was by hexahedral elements, and number of nodes and elements imparted to the distal end of the femoral shaft, while the superior region of the ilium and the symphysis pubis was were 2594 and 1220, respectively. An automatic calculation for global element edge length was used for mesh generation. fixed in all directions. Such loading and boundary conditions To ensure numerical stability, linearly elastic hexahedral ele- were assumed with abductor muscles counterbalancing the ments were used to mesh the cartilage layers (Figure 3). The body weight as suggested by Bergmann et al. [24]. FE material properties for the bone tissues and the cartilage were analysis was performed using a general-purpose FE solver ABAQUS (Simulia). Changes in the anatomical angles obtained from the literature (Table 1). Applied Bionics and Biomechanics 5 images confirmed that the osteotomized acetabular rotation occurred in three dimensions. The actual ACR during PAO for a given patient expressed in Bryant angles was 9.7 in sag- ° ° ittal plane, 18 in coronal plane, and 4.3 in transverse plane. 3.2. Changes in Acetabulum Anatomical Angles. Anatomical Cartilage layer covers angles were measured as acetabulum rotates (Table 2). In the femoral head the coronal plane (rotation along y-axis), CE angle was grad- ually increased due to incremental increase in acetabulum ° ° rotations (from 12.5 to 26.7 ), while the acetabular abduc- Pelvic cartilage tion was decreased as similar trend of changes of CE angle ° ° (from 47.4 to 29.7 ). These parameters were restored to be Figure 3: A cutaway view of the FE model illustrating interior within the normal range from the 18 rotation in the coronal mesh for the layers of articular cartilage covering the femoral head plane. An analysis of changes in the acetabular anteversion and acetabulum. was found not to be significant. Table 1: Material properties used in the hip FE models. 3.3. Changes in Joint Contact Areas. Joint contact area due to incremental increase in acetabulum rotations showed the Components Young’s modulus (MPa) Poisson’s ratio Ref. changes of −2.9%, 4.4%, 9.4%, and −1.2% in the sagittal plane Cortical bone 17,000 0.3 (rotation along x-axis) and 0.9%, 4.2%, 23.5%, and 8.1% in [19] Cancellous bone 100 0.2 the coronal plane (rotation along y-axis), respectively. In Cartilage 12 0.45 [20] the transverse plane (rotation along z-axis), contact area and pressure remained relatively unchanged (differences less than ±1%). The above results were plotted in Figure 5. Max- (CE angle, acetabular abduction, and acetabular anteversion) imum contact area was achieved for the sagittal plane and the and the joint contact area, rate of changes in contact area, the coronal plane rotations. A most favourable increase of 23.5% contact pressure (95th percentile value) in relation to the 2 2 in contact area (from 344.7 mm to 425.5 mm ) was seen for directions, and amount of the rotations were assessed. All ° the 18 rotation in the coronal plane. An analysis of rate of results were compared to the Pre-OP condition to determine changes in contact area showed the highest sensitivity of the consequences of varied acetabulum rotations in three 2 4.5 mm /degree for the coronal plane (Figure 6). dimensions. For clarity, the difference was marked positive, if it indicated an increase in contact area/pressure, and nega- 3.4. Changes in Contact Pressures (95th Percentile Value). tive if it indicated a decrease. There was clear trend in reduction in contact pressure as ace- tabulum rotates (Figure 7). Before PAO, contact pressure dis- 2.4. Sensitivity Analysis. Sensitivity analysis was performed to tributions showed stress concentrations on the superolateral investigate changes of Pre-OP FE model’s contact predictions regions of the femoral cartilage (Figure 8). Acetabular rota- due to variability in cartilage material properties and loading tions resulted in increased contact area thus reduced pressure conditions. The baseline Young’s modulus of the cartilage values. Contact pressure reached the lowest value in the was altered by ±1 SD while the Poisson’s ratio was kept con- model where the applied rotation of the acetabulum matched stant. Then, Young’s modulus was kept constant and the the actual acetabular rotation (ACR) during PAO. Similarly, Poisson’s ratio was deceased to 0.42 [25] and increased to the maximum pressure reduction was 53.2% (from 10.4 MPa 0.49 (with an assumption of cartilage incompressibility). to 4.9 MPa) found for the 18 acetabulum rotations in the The contact pressure (95th percentile value), mean contact coronal plane. A reduction of 19.2% in pressure was observed pressure, and contact area were predicted for three different during acetabulum rotations in the transverse plane. The rate loading conditions [21], consisting of single-leg stance, of change in contact pressure (95th percentile value) showed normal walking, and stair climbing. A total of 15 models the highest sensitivity (0.3 MPa/degree) for acetabular rota- were evaluated for the sensitivity analysis. tions in the coronal plane. 3. Results 3.5. Sensitivity Analysis. Alterations of Young’s modulus of 3.1. Acetabular Rotations during PAO Surgery. The Euclidean cartilage resulted in approximately changes of contact pres- distance between individual landmarks had a mean ± stan- sure and mean contact pressure by ±7.1% and ±4.5%, respec- dard deviation of 0.59 ± 0.15 mm, which confirmed the high tively, and changes in contact area were about ±2% repeatability in virtual marker placement, and the ICC (Figure 9). When the Poisson’s ratio was altered, contact pressure varied from −10.9 to 30.1%, and changes in contact was found to be 1.0 (p <0 05) which is extremely high reliability. Our results provide evidence of position reliabil- area were approximately ±12.6%, while changes in mean ity between the observers. The calculated actual acetabular contact pressure were less than 6%. Average RMS differences rotation (ACR) based on Pre- and Post-OP patient’sCT as compared to the baseline model were only about 3%. 6 Applied Bionics and Biomechanics 45 mm Hip joint center Pelvis 3-D reconstruction Placement sphere for osteotomy (a) (b) Virtual osteotomy model Post-OP FE model generation (c) (d) Figure 4: Procedure of the virtual PAO surgery: (a) 3-D reconstruction of the patient’s pelvis, (b) superposition of the sphere (r =45mm)on the periphery of the acetabulum for osteotomy, (c) Boolean process to cut the pelvis and the acetabulum, and (d) 3-D rotation of the osteotomized acetabulum. Table 2: Changes in anatomical angles of Post-OP models due to incremental increase in acetabulum rotations. The “ ” sign indicated to be within the normal range. Rotation axis Incremental ROM of acetabulum CE angle Acetabular abduction Acetabular anteversion ° ° ° Pre-OP model 12.2 48.1 10.8 Post-OP models ° ° ° 1/3 9.7 51 13.5 ° ° ° 2/3 10.5 51.3 14.6 Sagittal plane (x-axis) ° ° ° 3/3 11.7 49.4 15.6 ° ° ° 4/3 10.9 48.5 16.2 ° ° ° 1/3 12.5 47.4 15 ° ° ° 2/3 15.9 41.9 10.5 Coronal plane (y-axis) ° ° ° ∗ ∗ 3/3 20.9 36.2 10.7 ° ° ° 4/3 26.7 29.7 8.5 ° ° ° 1/3 9 50.4 12.1 ° ° ° 2/3 9.8 50.6 11.5 Transverse plane (z-axis) ° ° ° 3/3 10 51.4 11.5 ° ° ° 4/3 11.9 49.5 13.5 ` Applied Bionics and Biomechanics 7 Changes in the contact area Changes in the contact pressure (95th percentile value) 23.5% Pre-OP (10.4 MPa) 53.2% 350 Pre-OP (344.7mm ) 1/3 2/3 3/3 4/3 1/3 2/3 3/3 4/3 Incremental ROM of the acetabulum Incremental ROM of the acetabulum x-axis rotation x-axis rotation y-axis rotation y-axis rotation z-axis rotation z-axis rotation Figure 7: Changes in the contact pressure (95th percentile value) as Figure 5: Changes in the contact area as a function of incremental a function of incremental increased rotations of the acetabulum as increased rotations of the acetabulum as compared to the Pre-OP compared to the Pre-OP condition. The “ ” sign indicates the condition. The “ ” sign indicates the actual acetabular rotation actual acetabular rotation (ACR) during the surgery. (ACR) during the surgery. out the most dominant factor regarding direction of the Rate of changes in the contact area rotation due to incremental rotation of the osteotomized 4.5 mm /degree acetabulum in each axis. The effectiveness according to the three-dimensional rotations of the acetabulum was deter- mined in terms of the contact stresses and the coverage area of the hip. The results obtained at different angles (joint realignments) provide quantitative information related to 0 acetabular rotations to achieve the optimal outcome of the −1 PAO surgical procedure. In this study, virtual anatomic landmarks were created in −2 the Pre- and Post-OP models in order to apply Bryant angles −3 for calculating kinematic changes of the acetabulum. We −4 verified the procedure of the landmark placement to ensure −5 1/3 2/3 3/3 4/3 the repeatability of our method. Three landmarks of the pel- Incremental ROM of the acetabulum vis were chosen, as suggested by Lycett and von Cramon- Taubadel [18], due to their clearly identifiable morphological x-axis rotation features in CT images. Similar to the Lycett’s approach [18], y-axis rotation we quantified errors associated with anatomical landmark z-axis rotation placement by applying Euclidean distance equation based Figure 6: Rate of change in the contact area as a function of on coordinates of the landmarks manually picked by six incremental increased rotations of the acetabulum. The negative independent observers. The repeatability on anatomic land- sign indicates a decrease in contact area. The “ ” sign indicates the marks set could be confirmed since Euclidean distance of less actual acetabular rotation (ACR) during the surgery. than 1.0 mm was calculated for individual landmarks. Various studies on optimization of PAO have been reported [10–17]. Most studies have investigated the bio- 4. Discussion mechanical effectiveness of PAO in relation to acetabular Computational simulations using patient’s anatomy-specific rotation. More specifically, the 3-D FE simulation-based models offer an attractive approach for prediction of key bio- optimal reorientation planning method was introduced by mechanical parameters, such as hip joint contact patterns, Liu et al. [11]. The study was performed subject-specificFE before the PAO surgery. Currently, the clinical outcomes of simulation for 4 subjects who underwent PAO surgery and the PAO remain controversial mainly because the procedure evaluated biomechanical effect of the reorientation planning. involves highly complex multiaxial rotations of the acetabu- However, the direction and amount of the acetabular rota- lum while the optimal rotational parameters were unclear. tion and the most dominantly affecting direction of the ace- tabular rotation during the actual PAO surgery have not While the osteotomy and rotation take place in three dimen- sions, but its pre- or intra-OP rotation depends on the been investigated. Therefore, using a kinematic analysis method, we determined the Bryant angle of the osteotomized experience and decision of the surgeon. In particular limited information on clinical and biomechanical efficacies in acetabular rotation during PAO. Our results indicated that ° ° relation to amount and directions for rotation of the osteoto- Bryant angles were 9.7 in the sagittal plane, 18 in the coro- mized acetabulum was reported. Therefore, we aimed to find nal plane, and 4.3 in the transverse plane. The results Contact area (mm ) Rate of changes in the contact area (mm /degree) Contact pressure (MPa) 8 Applied Bionics and Biomechanics (MPa) +1.407e +01 +1.407e +01 +1.289e +01 +1.172e +01 Incremental increased rotations of the acetabulum +1.055e +01 +9.377e +00 + +8.205 8.205ee + +0 00 0 + +7.033 7.033ee + +0 00 0 + +5.861 5.861ee + +0 00 0 +4. +4.689 689ee + +0 00 0 + +3.516 3.516ee + +0 00 0 x-axis rotation +2 +2.344 .344ee + +0 00 0 (sagittal plane) + +1.172 1.172ee + +0 00 0 +0.00 +0.000 0ee + +0 00 0 y-axis rotation (coronal plane) z-axis rotation (transverse plane) P Pr re-O e-OP mo P model del Figure 8: Contact pressure distributions of the Pre-OP model and twelve Post-OP models due to rotations of the osteotomized acetabulum in three anatomical planes. ° ° ° suggested that acetabulum rotated in three dimensions dur- reported CE angles after PAO were 29.6 ± 6 (from 21 to 48 ) ° ° ° ing the surgery. While the major component of acetabular [28] and 36.4 ± 6.5 (from 21 to 50 ) [29], respectively. The ° ° rotations was in the coronal plane, rotations in other ana- reported acetabular abduction was 39.6 ± 3.9 (from 31 to tomical planes were also significant. 48 ) [29]. In our FE analysis, the optimal CE angle (rotating In our investigation, anatomical angles were assessed from the initial adduction at 18 ) and acetabular abduction due to incremental adjustment of the acetabular rotations. angle (from the initial acetabulum rotations in the coronal ° ° ° CE angles were increased due to incremental increase in ace- plane at 18 ) were 20.9 and 36.2 , respectively, which were tabulum rotations in the coronal plane and restored to be comparable with the measured clinical outcomes. While within the normal range (CE angle more than 20 ) from it appears that the CE angle has fallen slightly out of the adduction of 18 rotation [26]. In the same rotation, acetabular lower bound of the reported angular range, this could be abduction also restored of normal range (35 ≤ acetabular attributed to the fact that only acetabular rotations were abduction ≤ 45 ) [27]. The acetabular anteversion of the simulated in the study. If realistic translations of osteoto- dysplastic hip was reported because it was not significantly mized acetabular during actual PAO surgery were applied, different from that of normal hips. In addition, the weight- the accuracy of our biomechanical simulation results may be bearing surface of the acetabulum is almost perpendicular improved. However, such analysis involves surgical simula- to a vertical line in the standing position. Therefore, ana- tions of the acetabular motions in six degrees of freedom, tomical planes perpendicular to it are optimal for direct which would require significant more efforts thus time for visualization and measurement of the surface and acetabular model preprocessing [8]. coverage; in practices, these are the coronal and sagittal From FE analysis, we showed that adduction of 18 planes [26]. The finding of changes in anatomical angles (the ACR in the coronal plane along y-axis) resulted in a was compared with studies of long-term clinical outcome most significant increase in contact area by 23.5% (from of PAO to improve clinical evidence of our study. Rela- 344.7 to 425.5 mm ) compared to Pre-OP condition. Due to tively few long-term outcome studies of PAO are available increased contact area, the corresponding contact pressure [2, 28–31]. In two long-term clinical studies (>10 years), the (95th percentile value) was reduced by 53.2% (from 10.4 to Applied Bionics and Biomechanics 9 40 40 30 30 20 20 10 10 0 0 −10 −10 −20 −20 E = 11 MPa E = 13 MPa ν = 0.42 ν = 0.49 Young’s modulus Poisson’s ratio Contact pressure (95th percentile value) Contact pressure (95th percentile value) Mean contact pressure Mean contact pressure Contact area Contact area (a) (b) Figure 9: Percent changes in contact pressure (95th percentile value), mean contact pressure and contact area due to alterations in cartilage material properties, Young’s modulus (a) and Poisson’s ratio (b). Error bars indicate standard deviations over the three loading conditions evaluated. 4.9 MPa). Especially, peak contact pressure in Pre-OP model and contact pressure (4.4–5.0 MPa) measured in Anderson’s was concentrated on the superolateral regions of cartilage. experimental study [21]. Due to the poor acetabular cover- However, contact pressures were reduced and evenly distrib- age, the contact pressure (95th percentile value) predicted uted around the superior regions of the cartilage due to incre- by our Pre-OP dysplastic hip model was 10.4 MPa, which mental adjustment of the acetabular rotation in the coronal were higher than those measured in normal hips. Unfortu- plane. While contact distributions of rotation in the sagittal nately, the experimental data on joint contact pressures at and transverse planes were relatively unchanged (Figure 8), the dysplastic hip model is still significantly lacking. Never- these changes improved contact area and peak contact pres- theless, Russell et al. conducted the FE analysis on a dys- sure to the level close to the normal range [32–34]. Sensitivity plastic hip model and the predicted peak contact pressure of contact area and peak contact pressure according to the was 9.9 MPa [25]. However, due to the variations in acetab- rotation direction of the acetabulum also showed the highest ular coverage between different patients, direct comparison value (4.5 mm between the models may be difficult. The model predic- /degree and 0.3 MPa/degree) at adduction of 18 . Thus, the coronal plane (adduction) turned out to be tions, in terms of joint contact pressure and contact area, the most important rotation plane that strongly affects hip compared favourably with those previous studies. In addi- contact mechanics as compared to other planes (sagittal tion, since our study focused on evaluating relative perfor- plane, x-axis; transverse plane, z-axis) for a given patient. In mance of the same model and only relative changes were made for different hip alignment angles, the simulation clinical scenarios, the actual amount of acetabulum rotations during PAO is mainly determined by surgeons. Our results results presented in this study should be thus considered seem to suggest that, to ensure clinical benefits of the proce- clinically meaningful. dure, acetabulum rotations in the coronal plane are of critical The cartilage Young’s modulus alternations did not importance during the PAO. significantly affect the FE results of contact pressure (95th The FE models used in this study were constructed percentile value), mean contact pressure, and contact area based on CT images of a patient who underwent the PAO (±7.1%, ±4.5%, and ±2%, resp.) from the baseline case. When surgery. FE analysis requires robust validation process. Poisson’s ratio decreased from 0.45 to 0.42, the peak pressure We carefully compared our model results against Ander- was decreased by 10.9% due to an increased contact area by son’s cadaveric experimental study on a normal hip joint about 12.4%. However, as the Poisson’s ratio increased to [21] and Russell’s FE analysis on a dysplastic hip model nearly incompressible materials (ν =0 49), contact pressure [25]. The contact area predicted by our Post-OP FE model was remarkably increased by approximately 30.1%; however, was 428.8 mm and peak contact pressure 4.6 MPa, which the mean contact pressure was only changed by 6%. These agreed with the average contact area (321.9–425.1 mm ) results suggested that the proper choice for Poisson’s ratio Percent change Percent change 10 Applied Bionics and Biomechanics is more critical for accurate prediction of peak contact pres- 5. Conclusions sure, as compared to the mean contact pressure. In addition, The results of our study show that the acetabulum rotation in a decrease in mean contact pressure was considered to be the coronal plane (adduction) had the strongest effects on indicative of a general decrease in joint contact stresses, contact pressure and contact pressure compared to rotations which is aligned with clinical goal of the PAO surgery. Simi- in other planes. In particular, the osteotomized acetabulum lar approaches have been adopted in FE analysis performed rotation with adduction of 18 is considered to be the most for the understanding of the hip and elbow joint contact effective angle for the given patient. Although this study mechanics [21, 35]. was limited to a single patient, the methodology developed A number of modelling assumptions were also made to in this study could contribute to the preoperative planning facilitate FE analysis in the study. Firstly, linear-elastic, that determines the optimal direction and amount of rota- homogeneous material properties were used to model bone tion of the osteotomized acetabulum in three dimensions and cartilage tissues. In most FE simulation studies of PAO during PAO. [12, 15, 16], the bony structure and cartilage were modeled as the linear-elastic, homogeneous materials. It was reported that the effects of using linear-elastic, homogeneous material Conflicts of Interest properties on predicted cartilage stresses were negligible [36]. The authors declare that there is no conflict of interest While the cartilage is reported as a biphasic material with regarding the publication of this paper. time-dependent mechanical behavior, the frequency for walking loads is in the order of 1 Hz. Thus, time-dependent Authors’ Contributions response of the cartilage can be neglected [37]. Secondly, the cartilages were not clearly identifiable from the CT Sung-Jae Lee Park and Wen-Ming Chen contributed equally images (using the clinical CT scanner), and a constant thick- to this work. ness of 1.0 mm was assumed for articulating surfaces of the acetabulum and the femoral head. This enabled us to evaluate References contact mechanisms on the cartilage in DDH patients similar to a previous study [32]. Modeling subject’s anatomy-specific [1] M. Fujii, Y. Nakashima, T. Yamamoto et al., “Acetabular retro- cartilage layer seems to be essential for our FE analysis. How- version in developmental dysplasia of the hip,” The Journal of ever, it has been reported that the predicted optimal align- Bone and Joint Surgery. American Volume, vol. 92, no. 4, ment of the acetabulum was not significantly sensitive to pp. 895–903, 2010. the change of the cartilage thickness distribution during [2] S. D. Steppacher, M. Tannast, R. Ganz, and Siebenrock K a., PAO [14]. Thirdly, an osteotomy gap between the osteoto- “Mean 20-year followup of Bernese periacetabular osteotomy,” mized acetabulum and the pelvis was assumed a perfect Clinical Orthopaedics and Related Research, vol. 466, no. 7, fusion after PAO [12]. Clinically, the osteotomy gap is ini- pp. 1633–1644, 2008. tially fixed with biodegradable fixation screws and then fused [3] J. C. Clohisy, A. L. Schutz, L. S. John, P. L. Schoenecker, and over a period of time [15]. Thus, our Post-OP FE models did R. W. Wright, “Periacetabular osteotomy: a systematic litera- not include the potential effects of model instability due to ture review,” Clinical Orthopaedics and Related Research, osteotomy gap and insufficient screw fixation after the sur- vol. 467, no. 8, pp. 2041–2052, 2009. gery. The effects of such model instability on joint contact [4] D. Kosuge, N. Yamada, S. Azegami, P. Achan, and interactions remain to be investigated. Fourthly, it was M. Ramachandran, “Management of developmental dysplasia of the hip in young adults: current concepts,” The Bone & Joint acknowledged that CT scan was performed in the supine Journal, vol. 95, no. B, pp. 732–737, 2013. position and the FE models simulated a single-leg stance sce- [5] A. Troelsen, B. Elmengaard, and K. Søballe, “Medium-term nario [24]. Niknafs et al. [14] found no significant difference outcome of periacetabular osteotomy and predictors of con- between the contact pressure in the single-leg stance refer- version to total hip replacement,” The Journal of Bone and ence frame and those in the supine reference frame. Lastly, Joint Surgery. American Volume, vol. 91, no. 9, pp. 2169– we performed anatomical-specific FE analysis for only one 2179, 2009. patient. For providing clinical evidence, our finding of [6] M. Fu, S. Xiang, Z. 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