Keywords

12.1 Introduction

Developmental dysplasia of the hip joint is a prearthrotic deformity resulting in osteoarthritis at a very young age. Periacetabular osteotomy (PAO) is an effective approach for surgical treatment of painful dysplasia of the hip in younger patients [1]. The aim of PAO is to increase acetabular coverage of the femoral head and to reduce contact pressures by realigning the hip joint [2, 3]. However, insufficient reorientation leads to continued instability, while excessive reorientation correction would result in femoroacetabular impingement (FAI) [4, 5]. Therefore, a main important factor for clinical outcome and long-term success of PAO is to achieve an optimal acetabular reorientation [6]. The application of computer-assisted planning and navigation in PAO opens such an opportunity by showing its potential to improve surgical outcomes in PAO. Abraham et al. [7] reported an experimental cadaveric study to investigate the feasibility of preoperative 3D osteotomy planning and acetabular fragment repositioning in performing intraoperatively navigated PAOs. Hsieh et al. [8] assessed the efficacy of the navigated PAO procedure in 36 clinical cases using a commercially available navigation application for total hip arthroplasty (THA) (VectorVision, BrainLab Inc., Westchester, IL). Langlotz et al. [9] developed the first customized navigation system for PAO and applied it in 14 clinical cases. However, this system is only limited to intraoperative navigation and does not incorporate the preoperative planning module. More recently, Murphy et al. [10] developed a computer-assisted biomechanical guidance system (BGS) for performing PAO. The system combines geometric and biomechanical feedback with intraoperative tracking to guide the surgeon through the PAO procedure. In this paper, we present a validation study of a novel computer-assisted diagnosis, planning, simulation, and navigation system for PAO. It is hypothesized that the preoperative plan done with our system can be achieved by the navigated PAO procedure with a reasonable accuracy.

12.2 Materials and Methods

12.2.1 System Workflow

The computer-assisted diagnosis, planning, simulation, and navigation system for PAO consists of three modules as shown in Fig. 12.1.

  • Model generation module. 3D surface models of the femur and the pelvis are generated by fully automatic segmentation of the preoperatively acquired CT data.

  • Computer-assisted diagnosis, planning, and simulation module. The aim of this module is first to quantify the 3D hip joint morphology for a computer-assisted diagnosis of hip dysplasia and then to plan and simulate the reorientation procedure using the surface models generated from the model generation module. It starts with a fully automatic detection of the acetabular rim, which allows for computing important information quantifying the acetabular morphology such as femoral head coverage (FHC), femoral head extrusion index (EI), lateral center-edge (LCE) angle, version, and inclination. This module then provides a graphical user interface allowing the surgeon to conduct a virtual osteotomy and to further reorient the acetabular fragment until an optimal realignment is achieved.

  • Intraoperative navigation module. Based on an optical tracking technique, this module aims for providing intraoperative visual feedback during acetabular fragment osteotomy and reorientation until the preoperatively planned orientation is achieved.

Fig. 12.1
figure 1

Schematic view of our computer-assisted planning and navigation system for PAO

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12.2.2 Fully Automatic Segmentation of Hip

In our study, given an unseen hip CT image of the target patient, the associated pelvic surface model and a set of acetabular rim points are obtained by using an in-house developed fully automatic hip CT segmentation method MASCG [11]. More specifically, in the first step, a multi-atlas fusion scheme is used to get an initial segmentation of the pelvis. Each atlas consists of a CT volume, manual segmentation of pelvis, and a set of predefined acetabular rim points. By performing registrations between the atlases and the target image using a hybrid registration method as described in [11], all the atlases can be aligned to the target image space. The initial segmentation of the pelvis is then obtained by deforming and fusing the manual segmentation of a selected subset of atlases. Similarly, the acetabular rim points are obtained by transforming and fusing the predefined rim point of these selected atlases. In the second step, by using a graph-cut constrained graph-search method, the initial segmentation of the pelvis is further modified, and from the modified binary segmentation, we generate the associated pelvic surface model which is used in the following study. Each acetabular rim point is also refined by replacing itself with the associated closet point on the generated pelvic surface model. For more details, we refer to [11].

12.2.3 Computer-Assisted Diagnosis of Hip Dysplasia

Accurate assessment of acetabular morphology and its relationship to the femoral head is essential for hip dysplasia diagnosis and PAO planning. After pelvic and femoral surface models are input to our system, the pelvic local coordinate systems is established using anatomical landmarks extracted from the CT data which is defined on the anterior pelvic plane (APP) using the bilateral anterior superior iliac spines (ASISs) and the bilateral pubic tubercles [12]. After local coordinate system is established, a fully automatic detection of the acetabular rim is conducted using an aforementioned method [26] (see Fig. 12.2a). As soon as acetabular rim points are extracted, least-squares fitting is used to fit a plane to these points (see Fig. 12.2b). The normal of the fitted plane is defined as the orientation of acetabulum \( {\protect\overrightarrow{n}}_{CT} \).The fitted plane then allows for computing acetabular inclination and anteversion [13] (see Fig. 12.2c, d). Additional hip morphological parameters such as the 3D LCE angle, the 3D femoral head EI, the FHC, the anterior coverage of femoral head (AC), and posterior coverage of femoral head (PC) are computed as well (see Fig. 12.2e–i). LCE is depicted as an angle formed by a line parallel to the longitudinal pelvic axis defined on the APP and by the line connecting the center of the femoral head with the lateral edge of the acetabulum according to Wiberg [14]. Femoral head EI is defined as the percentage of uncovered femoral head in comparison to the total horizontal head diameter according to Murphy et al. [15]. FHC is defined to be a ratio between the area of the upper femoral head surface covered by the acetabulum and the area of the complete upper femoral head surface from the weight-bearing point of view [16]. The 3D measurements of FHC used in this system are adapted from our previous method reported in [17]. The difference is that our current method [18] is based on native geometry of the femoral head. In contrast, our previous work assumed that the femoral head is ideally spherical [17]. In normal hips the assumption is valid since the femoral head is spherical or nearly so. However, in dysplastic hips, the femoral head may be elliptical or deformed [19]. Thus the method [18] used in this system is more accurate than the method that we introduced in [17]. Here the FHC is calculated with following algorithm. The inputs to this algorithm are femoral surface model, acetabular rim points, and the axial plane which is perpendicular to the APP and passes through the femoral head center.

  • Step 1: Only the superior weight-bearing surface of the femoral head is used to estimate coverage as shown in Fig. 12.3a. The cranial rim points of the acetabulum and the superior hemisphere are both projected on to the axial plane to produce a circle and a curved line (the projected acetabular rim contour) cutting across it (Fig. 12.3b).

  • Step 2: A topographical image is generated on the axial plane which represents the total femoral head. The covered and uncovered areas are separated by the projected acetabular rim contour. The green and white areas represent covered and uncovered parts, respectively, (Fig. 12.3c).

  • Step 3: The percentage of FHC is calculated as a ratio between the area of covered part and the area of the total femoral head (see Fig. 3d for details).

Fig. 12.2
figure 2

Computing 3D morphological parameters of the hip joint. (a) Fully automatic acetabular rim detection; (b) least-squares fitting plane of acetabular rim and the orientation of acetabulum \( {\protect\overrightarrow{n}}_{CT} \); (c) acetabular inclination; (d) acetabular anteversion; (e) lateral center-edge angle (LCE); (f) femoral head extrusion index (EI); (g) femoral head coverage (FHC); (h) anterior coverage of femoral head (AC); (i) posterior coverage of femoral head (PC)

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Fig. 12.3
figure 3

3D measurement of the FHC. (a) The superior surface of the native femoral head (approximated with blue triangle meshes) and the opposing acetabular surface are major weight-bearing areas; (b) cranial rim points of the acetabulum and the superior hemisphere are projected onto the axial plane to produce a circle and a curved line (the projected acetabular rim contour) cutting across it; (c) a topographical image on the axial plane represents the femoral head with its covered (green area) and uncovered (white area) parts; (d) the percentage of FHC is calculated as a ratio between the green area and the sum of the green and the white areas on the femoral head

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12.2.4 Computer-Assisted Planning and Simulation of PAO Treatment

An in silico PAO procedure is conducted with our system as follows. First, since the actual osteotomies don’t need to be planned as an exact trajectory, a sphere is used to simulate osteotomy operation. More specifically, the center of femoral head is taken as the center of the sphere whose radius and position can be interactively adjusted along lateral/medial, caudal/cranial, and dorsal/ventral directions, respectively, in order to approximate actual osteotomy operation (see Fig. 12.4a). After that, the in silico PAO procedure is conducted by interactively changing the inclination and the anteversion of the acetabulum fragment (see Fig. 12.4b). During the acetabulum fragment reorientation, 3D LCE angle, EI, FHC, AC, and PC are computed in real time based on the reoriented acetabulum fragment and showed at the bottom of the screen (see Fig. 12.4b). Once the morphological parameters of normal hip are achieved (inclination, 45° ± 4°, [37°–54°] [20]; anteversion, 17° ± 8°, [1°–31°] [20]; LCE > 25° [21]; FHC, 73% ± 4% [66–81%] [20]), the planned morphological parameters are stored and subsequently transferred to the navigation module as explained in details in the following section.

Fig. 12.4
figure 4

In silico PAO surgical procedure in our PAO planning system. (a) Virtual osteotomy operation is done with a sphere, whose radius and position can be interactively adjusted; (b) virtual reorientation operation is done by interactively adjusting anteversion and inclination angle of the acetabulum fragment. The hip morphological parameters (inclination, anteversion, LCE, EI, FHC, AC, and PC) are then computed based on the reoriented acetabulum fragment and showed at the bottom of the screen

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12.2.5 Intraoperative Surgical Navigation

Navigated PAO surgical intervention is described as follows: Before the acetabular fragment is osteotomized, the pelvis is attached with a dynamic reference base (DRB) in order to register the surgical anatomy to the pelvis surface model generated from a preoperatively acquired CT data (see Fig. 12.5a, b). After that, CT-patient registration based on a so-called restricted surface matching (RSM) algorithm [22] is conducted, which mainly consists of a paired point matching followed by a surface matching (see Fig. 12.5b). Specifically, the paired point matching is based on the alignment process of pairs of anatomical landmarks. In a preoperative step, four anatomical landmarks (bilateral ASISs and the bilateral pubic tubercles) are determined on the pelvic model segmented from CT data. Intraoperatively, the corresponding landmarks on the patient are digitized using a tracked probe. The digitized points are defined in the coordinate system of the DRB, which is rigidly fixed onto the pelvis. Then the surface matching computes the registration transformation based on 20–30 scattered points around the accessible surgical site that is matched onto a surface of a pelvic model (see Fig. 12.5b). After registration, the osteotomes are calibrated using a multi-tools calibration unit in order to determine the size and orientation of the blade plane (see Fig. 12.5c). The tip of the osteotome is shown in relation to the virtual bone model, axial, sagittal, and coronal views of the actual CT dataset. The cutting trajectory is visualized in real time by prolongation of the blade plane of the osteotome. Thus the osteotomies can be performed in a controlled manner, and complications such as intraarticular penetration and accidental transection of the posterior column can be avoided [2] (see Fig. 12.5d). After the acetabular fragment is mobilized from the pelvis, another DRB is anchored to the acetabulum area for intraoperative tracking, thereby the acetabular reorientation can be supported by the navigation module. The navigation system can provide interactive measurements of acetabular morphological parameters and image-guidance information, which instantaneously updates the virtual display, current position and orientation parameters of the acetabulum, and the planned situation (inclination and anteversion angles) derived from the preoperative planning module. The surgeon repositions the acetabulum by controlling its inclination and anteversion angle in order to determine whether the current position achieves the preoperatively planned position or further adjustment is required (see Fig. 12.5e). After successful repositioning, preliminary K-wire fixation and finally definitive screw fixation are conducted [23]. In this sawbone model study, a 3D articulated arm (Fisso 3D Articulated Gaging Arms, Switzerland) is employed to anchor the fragment for navigation accuracy validation (see Fig. 12.5a).

Fig. 12.5
figure 5

Intraoperative PAO surgical navigation. (a) Setup of the navigated PAO surgery where two dynamic reference bases (DRBs) with reflective spheres are attached to both the iliac crest and the acetabular fragment; (b) the areas of the pelvis acquired with the tracked probe to perform the RSM registration; (c) osteotome calibration where the green part represents the blade plane of the osteotome and the yellow part represents the prolongation of the blade plane; (d) screenshot of CT-based osteotomy guidance where the tip of the osteotome is displayed on axial, sagittal, and coronal views of the CT dataset, and a cutting trajectory is displayed on the bony model; (e) screenshot of navigated reorientation procedure

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12.3 Study Design

In order to validate this newly developed planning and navigation system for PAO, two validation studies were designed and conducted on four sawbone models. The purpose of the first study is to evaluate the intraoperative accuracy and reliability of navigation system. The second study is designed to evaluate whether the acetabulum repositioning based on navigated PAO procedure can achieve the preoperative planned situation by comparing the measured acetabular orientation parameters between preoperative and postoperative CT data.

In the first study, preoperative planning was conducted with the PAO planning module. Subsequently the intraoperative navigation module was used to track acetabular and pelvic fragments, supporting and guiding the surgeon to adjust the inclination and anteversion angles of acetabulum interactively. Acetabular reorientation measured by the inclination and anterversion angles can be planned preoperatively and subsequently realized intraoperatively without significant difference. In order to assess the error difference between the preoperatively planned and the intraoperatively achieved acetabular orientation, we compared the decomposed rotation components derived from the acetabular fragment reorientation between the planned and intraoperative situations.

In the following, all related coordinate systems are first defined (see Fig. 12.6 for details) before the details about how to compute decomposed rotation components will be presented. During preoperative planning stage, the Ref_CT represents the preoperative CT data coordinate system, and the (Ref_APP) Pre represents the local coordinate system defined on the APP that is extracted from the preoperative CT data. During intraoperative navigation stage, the Ref_P represents the intraoperative patient coordinate system defined on the pelvic DRB, the Ref_A represents the intraoperative acetabulum coordinate system defined on acetabular DRB, and the (Ref_APP) Intra represents the local coordinate system defined on the intraoperative APP (see Fig. 12.6 for details). Following the definition of all related coordinate systems, details about how to compute decomposed rotation components are described below.

  • Step 1:

Fig. 12.6
figure 6

Schematic representation of precise estimation of orientation change of acetabulum fragment after reorientation. (a) Estimation of orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^0 \) at the 0′ moment before reorientation procedure; (b) estimation of orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^t \) at the t’ moment during reorientation procedure

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In order to register Ref_CT to Ref_P, the DRBs are fixated and a RSM algorithm [22] is applied before the osteotomies and the acetabular fragment tracking (see Fig. 12.6a). The transformation \( {\left({T}_P^{APP}\right)}_{Intra} \) between the Ref_P and the (Ref_APP) Intra can be calculated by Eq.(12.1).

$$ {\left({T}_P^{APP}\right)}_{Intra}={\left({T}_{CT}^{APP}\right)}_{\Pr e}\cdot {T}_P^{CT} $$
(12.1)

where \( {T}_P^{CT} \) is the rigid transformation between the Ref_P and the Ref_CT and \( {\left({T}_{CT}^{APP}\right)}_{\Pr e} \) is the transformation between the Ref_CT and the (Ref_APP) Pre.

  • Step 2:

Before the fragment is moved, a snapshot of the neutral positional relationship \( {\left({T}_A^p\right)}_0 \) between Ref_A and the Ref_P is recorded (Fig. 12.6a). At this moment, the orientation of the acetabulum \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^0 \) with respect to the (Ref_APP) Intra can be estimated by the following equation (see Fig. 12.6a):

$$ \begin{array}{llll} {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^0&=&{\left({T}_P^{APP}\right)}_{Intra}\cdot {\left({\protect\overrightarrow{n}}_P\right)}_0\nonumber\\ &=&{\left({T}_P^{APP}\right)}_{Intra}\cdot {\left({T}_A^P\right)}_0\cdot {\left({T}_P^A\right)}_0\nonumber\\ &&\cdot {T}_{CT}^P\cdot {\protect\overrightarrow{n}}_{CT}\nonumber\\ \end{array} $$
(12.2)

where \( \setcounter{equation}{1} {\protect\overrightarrow{n}}_{CT} \) denotes the orientation of acetabulum measured in the Ref_CT preoperatively. Equation (12.2) indicates that one can first compute the orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_P\right)}_0 \) with respect to the Ref_P and then transform it to the (Ref_APP) Intra through a transformation train.

  • Step 3:

Fragment mobility is measured by the navigation system, which records the instantaneous positional relationship \( {\left({T}_A^P\right)}_t \) between the Ref_A and the Ref_P. The neutral positional relationship \( {\left({T}_A^P\right)}_0 \) obtained from Step 2 is used to calculate the orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_P\right)}_t \) with respect to the Ref_P during motion. The instantaneous orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^t \) with respect to the (Ref_APP) Intra can be calculated by the following equation (see Fig. 12.6b):

$$ \setcounter{equation}{2}\begin{array}{llll} {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^t&=&{\left({T}_P^{APP}\right)}_{Intra}\cdot \nonumber\\ {\left({\protect\overrightarrow{n}}_P\right)}_t&=&{\left({T}_P^{APP}\right)}_{Intra}\cdot {\left({T}_A^P\right)}_t \cdot {\left({T}_P^A\right)}_0\nonumber\\ &&\cdot {T}_{CT}^P\cdot {\protect\overrightarrow{n}}_{CT} \end{array} $$
(12.3)

Equation (12.3) indicates that one can first compute the instantaneous orientation of acetabulum \( {\left({\protect\overrightarrow{n}}_P\right)}_t \) with respect to the Ref_P and then transform it to the (Ref_APP) Intra through a transformation train.

  • Step 4:

The \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^0 \) and \( {\left({\protect\overrightarrow{n}}_{APP}\right)}_{Intra}^t \) can then be decomposed into three motion components (flexion/extension, external rotation/internal rotation, and abduction/adduction) along x, y, and z axis of the (Ref_APP) Intra. The differences of respective decomposed rotation components were compared quantitatively between preoperative planned and intraoperative navigation situations in order to evaluate reorientation misalignment.

In the second study, we evaluated postoperatively the repositioning of the acetabular fragment and compared this with the preoperative planned acetabular orientation parameters. Specifically, the acetabular rim points after reorientation were digitized and transformed to preoperative CT space based on the aforementioned registration transformation \( {T}_{CT}^P \). The transformed acetabular rim points were then imported into the computer-assisted PAO diagnosis module to quantify acetabular orientation parameters (inclination and anteversion) and compared them with the preoperatively planned acetabular orientation parameters.

12.4 Results

In the first intraoperative evaluation study, the decomposed rotation components of the acetabular fragment between the preoperatively planned situation and the intraoperatively achieved situation were compared. According to Tables 12.1, eight groups of acetabular reorientation data were obtained. It can be seen that the average errors along three motion components (flexion/extension, abduction/adduction, and external rotation/internal rotation) are 0.6° ± 0.3°, 0.3° ± 0.2°, and 1.1° ± 1.1°, respectively.

Table 12.1 The difference (°) of decomposed motion components between preoperative planning and intraoperative navigation situations
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In the second postoperative evaluation study, the morphological parameters of hip joint between the preoperatively planned situation and postoperatively repositioned situation were compared. The results are shown in Table 12.2. From this table, it can be seen that the average errors of acetabular orientation parameters (inclination and anteversion angles) are 0.9° ± 0.3° and 0.9° ± 0.7°, respectively. The results are accurate enough from a clinical point of view for PAO surgical intervention and verify the hypothesis that the preoperatively planned situation can be achieved by navigated PAO procedure with reasonable accuracy.

Table 12.2 The error of hip joint morphological parameters (IN inclination, AV anteversion) between preoperative planning and postoperative evaluation
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12.5 Discussion and Conclusions

In this paper, we present a computer-assisted planning, simulation, and navigation system for PAO, which allows for not only quantifying the 3D hip joint morphology with geometric parameters such as acetabular orientation (expressed as inclination and anteversion angles), LCE angle, and femoral head coverage for a computer-assisted diagnosis of hip dysplasia but also virtual PAO surgical planning and simulation. Intraoperatively navigation was performed to achieve the preoperative plan. A validation study was conducted on four sawbone models in order to evaluate the efficacy of navigated PAO intervention intraoperatively and postoperatively. The experimental results verified our hypothesis that the preoperative planned situation can be achieved intraoperatively with reasonable accuracy.

There exists a variety of studies in developing and validating PAO planning and navigation system. Langlotz et al. [9] developed the first generation of CT-based customized navigation system for PAO and applied it to 14 clinical cases. The osteotomes can be tracked and displayed on 3D pelvic model during osteotomies procedure. Acetabular reorientation can be achieved according to the angles in the sagittal, frontal, and transverse planes. However this system did not integrate the preoperative planning and the surgeon could not refer to standard parameters defining acetabular orientation (inclination and anteversion angle). Abraham et al. [7] reported an experimental cadaver study in order to prove the utility of preoperative 3D osteotomy planning and intraoperative acetabular repositioning in the navigated PAO surgery. The result of this study demonstrated considerably higher error (LCE, 4.9 ± 6° with maximum 12.4°). Moreover, in their system, in silico PAO reorientation was performed using commercially available image processing and editing software (Mimics, Materialise, Belgium). In contrast, our customized system can not only quantify the 3D hip morphology of hip dysplasia precisely but also provide virtual PAO surgical planning and simulation. Another application of CT-based navigation application for PAO was reported by Hsieh et al. [8], which has been successfully applied to 36 clinical cases. In their study they evaluated the efficiency of computer-assisted navigation in PAO by comparing with the conventional freehand approach. However, their study was conducted using a modified version of commercially available navigation program for THA (VectorVision, BrainLab Inc., Westchester, IL), with no preoperative planning function and which only allows for tool tracking of osteotomes. Once the acetabular fragment has been osteotomized and mobilized from the pelvis, the program does not allow for real-time tracking the fragment to guide the reorientation. In result, proper correction has to rely on the surgeon’s own experience to find a new optimal position. In contrast, our PAO navigation system can track both pelvic and acetabular fragments in real time and guide the surgeon during acetabulum repositioning until the preoperative planned acetabular orientation was achieved. Jäger [24] et al. introduced a clinical trial based on a CT-based navigation system allowing for control of the acetabular fragment in 3D space. However no statistical evaluation of accuracy of acetabular repositioning was reported. In contrast, we conducted sawbone model-based studies to evaluate the accuracy and efficacy of navigation-based acetabular repositioning. Intraoperatively, we used decomposed rotation components (flexion/extension, abduction/adduction, and external rotation/internal rotation) to assess difference between the preoperatively planned and the intraoperatively navigated acetabular repositioning. Our experimental results demonstrated that sub-degree accuracy was achieved for the flexion/extension and abduction/adduction directions while slightly larger than 1 º error for the external rotation/internal rotation direction. Postoperatively, we used quantitative acetabular orientation parameters to assess the error between the preoperatively planned and the postoperatively achieved acetabular repositioning. Our experimental results demonstrated that the preoperative plan done with our system can be achieved by the navigated PAO procedure with a reasonable accuracy.

However, there are still limitations in the present validation experiment. The first limitation is that the developed system is only validated on sawbone models. However, the intraoperative navigation accuracy has been previously assessed in a cadaver experiment in order to investigate the technical feasibility of the pararectus surgical approach [25]. Another limitation is that the preoperative planning is only limited to increase FHC and does not consider aspects of impingement. The argument why we adopted such a strategy is that we are aiming to evaluate navigation accuracy in this study. In order to avoid impingement following PAO, the planned situation can be optimized with impingement simulation by making a trade-off between FHC and hip range of motion (ROM) reported in our previous work [17]. In addition, the transfer of this technique to the clinical setting has not yet been performed. A clinical trial is planned to further validate the efficacy of the developed system for PAO interventions.