Automated Preoperative Planning of Femoral ... - Springer Link

Automated Preoperative Planning of Femoral Component for Total Hip Arthroplasty (THA) from 3D CT Images Itaru Otomaru1 , Masahiko Nakamoto2 , Masaki Takao2 , Nobuhiko Sugano2 , Yoshiyuki Kagiyama1, Hideki Yoshikawa2, Yukio Tada1 , and Yoshinobu Sato2 1

Graduate School of Engineering, Kobe University, Kobe, Japan Graduate School of Medicine, Osaka University, Suita, Japan

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Abstract. This paper describes a method for 3D automated preoperative planning of the femoral stem in total hip arthroplasty (THA). The stem planning is formulated as a problem to determine the optimal position, rotation, and size, on the 3D surface model of femur reconstructed from CT images. We obtain the parameters that maximize the fitness between the femoral canal and stem surfaces subject to the positional and rotational constraints. The maximization is performed by local optimization from multiple initial positions. The proposed method was experimentally evaluated by the difference from planning results of an experienced surgeon in 7 cases. The average positional and rotational differences were 1.9 mm and 2.5 deg., respectively, and there was size difference only in 1 case for the proposed method while these differences were 2.8 mm, 5.0 deg., and 5 cases for an existing method. The proposed method showed better performance than the existing method. Keywords: computer assisted surgery, stem fitness, anteversion angle, orthopaedic implant.

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Introduction

Recently, surgical navigation and robotic systems have been developed for total hip arthroplasty (THA) for the purpose of accurate placement of the orthopaedic implants in preoperatively determined 3D position and orientation [1-3]. This fact means that preoperative planning is becoming important because the preoperative plan can be accurately executed using these systems. In preoperative planning of THA, anatomical compatibility of each implant component with host bone is essential for stable fixation and good clinical results. Especially, the fit and fill of the cementless femoral component (stem) in the femoral canal are important factors for component stability [4-6]. Recently, CT-based interactive systems for preoperative 3D planning have been developed in order to quantitatively visualize the fit and fill [7]. However the interactive 3D planning is subjective as well as involves time-consuming, which limit its clinical use. T. Dohi, I. Sakuma, and H. Liao (Eds.): MIAR 2008, LNCS 5128, pp. 40–49, 2008. c Springer-Verlag Berlin Heidelberg 2008

Automated Preoperative Planning of Femoral Component for THA

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In order to solve these problems, we have been developing the automated preoperative planning system for THA, which automatically select optimal size, position, and orientation of the stem. In our previous work, we have defined the objective function which describes the “fitness” value of the stem from surgeon’s expertise and his planning results. And we have determined the solution by one-by-one search at the interval of 1.0 mm and 1.0 deg. in each axis [8-9]. However, this procedure of search is not appropriate because there is a possibility that the system overlook the solution which maximizes the fitness. On the other hand, related to our efforts, Viceconti et al. proposed the use of volume registration between the femoral canal and stem [10] for automated placement of the stem. However, image matching criteria used in volume registration were not derived from stem fitness criteria used by the experienced surgeon. In this study, we propose an automated preoperative planning system of the femoral stem using 3D CT data. We use the definition of the “fitness” which we have used in previous work. In addition, we propose the constraints which describes the surgeon’s expertise of the positional relation of the stem and the femur, and the optimization procedure to maximize the fitness. To evaluate the performance of the proposed system, we apply our method and the existing method [10] to 7 cases, and measure the difference between automated planning results and those of the experienced surgeon.

2 2.1

Methods Preconditions

Block diagram of proposed system is shown in Fig. 1. As the patient information, we assume that 3D CT image of hip joint of the patient is given. The 3D model of the femoral canal is reconstructed from CT images, and the femoral coordinate system and the anatomical feature points are determined on its 3D models. As the implant information, we assume that the 3D shape models of all the variations in the femoral stems are given. Outputs of this system is the set of parameters (z = [t, r, s]), of the position t, orientation r, and size s of stem. The femur coordinate system is defined as Fig. 2. In specification of the femur coordinate system, we use the table top plane of the femur and the peak of the lesser trochanter. The z-axis of femur coordinate system is defined as the canal long axis estimated from the 3D model of femoral canal. The x-axis is orthogonal to the z-axis, and parallel to the table top plane. The y-axis is defined as the axis orthogonal to both x and z-axes. The origin is defined as the intersection point between the z-axis and the line which is perpendicular to the z-axis and passes through the peak of the lesser trochanter (Fig. 2, sagittal view). 2.2

Definition of Objective Function of Stem Fitness

We formulate the preoperative planning of the stem as the optimization problem that obtain the parameter z that maximizes the stem fitness evaluate function. The criteria in stem planning are defined as follows:

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Fig. 1. Block diagram of proposed system

Fig. 2. Definition of the femur coordinate system ((1) Sagittal view, (2) Coronal view, (3) Axial view, (4) 3D view))


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1. Overlap of the femoral canal and the stem surface is prohibited for the whole stem area. 2. Strong contact with the host bone in specific area of the stem is desirable. 3. Keep the positional and rotational relation with the femur. 4. Select the largest stem size unless the stem is not overlapped with the canal. In proposed method, we use the distance from the femoral canal and the stem surface to describe these criteria. When the distance value is negative, the femoral canal and the stem surface is overlapped, and when the distance value is positive, there is a gap between the canal and the stem surface. Especially, when the gap is small, we consider that there is a strong fixation. At the same time, we define the positional and rotational constraints derived from anatomical compatibility between the host bone and the stem other than the stem fitness. In determination of the automated plan, first we obtain the candidates of parameters in each stem size, and then select the maximum size. In our formulation, first we describe the t and r of the z as the transformation matrix of position and rotation T. In addition, t and r are collectively described as the 6 parameters vector q = [tx , ty , tz , rx , ry , rz ]. We determine the parameters T in stem size s, which maximizes the objective function of stem fitness F (T), and then select the maximum stem size. The derivation of the optimal T is defined as the following optimization problem maximize : F (T) = S f (±|C − Tx|)dS, (x = [x, y, z]) subject to : ±|C − Tx| ≥ 0, ∀x q0 − qr ≤ q ≤ q0 + qr where S describes the stem surface, and C describes the femoral canal. x is the coordinates of the stem surface point, and Tx is the coordinates of x when the position and orientation of the stem is T. ±|C − Tx| describes the shortest distance between the C and the Tx, where negative values apply when the Tx is internal to the host bone. The first expression of the constraints describes the constraint of the prohibiting of the overlap for the whole stem area. q0 is the central position and rotation of the range of limitation, and the range of limitation is described as qr . To define the function f , we divide the stem surface into three regions. The proximal region of surface is named as zone 1, and the distal region is named as zone 2 (Fig. 3)D Zone 1 is the specific area that the strong contact with the host bone is demanded. Both zone 1 and zone 2 are demanded not to be overlapped with the femoral canal. On the other hand, Other parts of stem surface are not evaluated. In objective function, the fitness value is maximized when the gap is smaller than the constant value, and if the gap is larger than the constant, the fitness value decreases according to the distance. The objective function is defined as (Fig. 4) 1 (0 ≤ d < cth ) , (d = ±|C − Tx|) f (d) = (d−cth )2 − exp{− 2σ2 } (cth ≤ d)

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where cth is the threshold of distance whose fitness value is maximized, and σ is the parameter of the Gaussian function which describes the decreasing of fitness if the distance is larger than cth . 2.3

Definition of the Constraints

The positional and rotational constraints used in stem planning are the height of the stem position and the anteversion angle. The height of the stem position affects the difference of leg length between before and after the surgery. This change of the height should be small. The change of the height is defined as the difference between the height of the femoral head center and the height of the tip of the stem neck. Anteversion angle is the angle of the femoral neck against the body of femur. This angle affects the range of motion (ROM) of the hip joint After the surgery, femoral neck is removed, and replaced by the stem neck. Therefore, the anteversion angle after the surgery is redefined using the stem neck. This change of the angle should be minimum. To define the constraints parameters q0 and qr , we refer the conventional study of the prediction of the height of the femoral head center and anteversion angle. In the prediction of the femoral head center, it is not appropriate to apply the sphere fitting to the deformed femoral head such as intended in our study. Therefore, we use the height of femoral neck saddle instead, and limit the range as 8.3 mm of the height difference from femoral neck saddle by referring the conventional study (Fig. 6)[11]. Anteversion angle is defined as the angle of of the femoral neck axis against the table top plane when the femur is put on ground (Fig. 5)[12], and we fix this angle during the automated planning. In proposed method, the initial position q0 is defined as whose height accords with that of stem neck, and whose anteversion angle accords with that before the surgery. In our definition of the coordinate axes, the height corresponds to the translation along the z axis, and anteversion angle corresponds to the rotation around the z axis. Using criteria of the range of limitation in each axis around q0 , qr is defined as qr = [∞, ∞, 8.3[mm], ∞, ∞, 0]T 2.4

Optimization Procedure

The derivation of the candidate in each stem size is performed by the Powell method using initial values equally sampled within the possible solution space. We define the range of initial positions using q0 as q0 − qs ≤ qI ≤ q0 + qs , qs = [Pt Pt Pt Pr Pr 0]T where qI is the set of the initial positions, and Pt and Pr are the constant which describe the range of initial position. In proposed method, the Pt = 8.0 mm and Pt = 4.0 deg.. This range is inside the constraints, and we have already confirmed experimentally that this range includes the appropriate position and


Fig. 3. Evaluation areas

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Fig. 4. Definition of f (d) of stem fitness

Fig. 5. ConstraintsFAgreement of “anteversion angle”

Fig. 6. ConstraintsFLimitation of height of femoral neck saddle and tip of stem neck

rotation enough. We define the sample rate of initial position as 4.0 mm and 4.0 deg. We have also experimented the sample rate of 1.0 mm and 1.0 deg., and 2.0 mm and 2.0 deg., and we have confirmed that there is few risk to failed to find the optimal solution in the sample rate of initial position of 4.0 mm and 4.0 deg.

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3 3.1

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Experimental Results Experimental Conditions

We applied this method to 7 cases, and compared the results with the existing method proposed by Viceconti et al. [9]. CT slice thickness and reconstruction pitch were both 3mm, and FOV (Field of view) was 421 mm × 421 mm. The 3D model of femoral canal was segmented with a threshold of 800 Hounsfields Units (HU). We used the stem product of size 3 to 8 of Centpillar GB HA Stem (Stryker Orthopaedics, Mahwah, NJ, USA) (Fig. 7). The parameter tuning of evaluate function was cth = 2.0 [mm]C σ = 1.0. The difference of the planning result was calculated from the experienced surgeon’s plan, in position, rotation, and size selection. Surgeon’s plan was planned using the complex system of the MPR images and the 3D surface, by referring the information of distance between the canal and stem. 3.2

Results

The mean difference of the existing and proposed methods from surgeon’s plan in each case are shown in Fig. 8 - Fig. 10. The mean difference of existing

Fig. 7. Centpillar GB HA Stem (Size 3 ∼ 8)

Fig. 8. Mean difference between existing Fig. 9. Mean difference between existing methods and proposed method in each methods and proposed method in each case (distance) case (rotation)


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Fig. 10. Mean difference between existing methods and proposed method in each case (size selection)

Fig. 11. Visualization of each planning results of case 3 ((a) existing method, (b) proposed method (c) surgeon planning). The color map on stem surface indicates distance between canal and stem, corresponds to color bar.

method in 7 cases of distance was 2.8 mm, rotation was 5.0 deg., and 2 cases are matched with surgeon’s plan. On the other hand, the mean difference of proposed method of distance was 1.9 mm, rotation was 2.5 deg., and 5 cases are matched with surgeon’s plan. The planning results of case 3 is shown in Fig. 11. The color map on the stem surface indicates the distance between the canal and stem, corresponds to the color bar in the bottom of the figure. In the result of existing method (a), there was some undesirable regions of the stem surface which distance is negative.

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Fig. 12. Visualization of each planning results of case 2 ((a) existing method, (b) proposed method (c) surgeon planning). The color map on stem surface indicates distance between canal and stem, corresponds to color bar.

The difference of the proposed method in case 2 was larger than the existing method, especially the difference of rotation was 8.1 deg. The difference of the proposed method was quite large in the direction of the stem neck from the surgeon’s plan as shown in the top view (Fig. 12, right side of each figure).

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Discussions and Conclusions

We have developed the automated planning system of stem to properly determine the size, position and orientation. Difference of the planning results of the proposed methods from surgeon’s plan was smaller than the results of the existing method. The existing method does not evaluate the stem fitness, and thus unacceptable penetration occurred between the canal and stem surface. On the other hand, the proposed method measures and optimizes the fitness and thus the system is able to determine the plan which is near to the experienced surgeon’s one. And, in the size selection, difference of proposed method was smaller than the existing method. Because, the scaling factors of the femur shape which is used as criteria in size selection in existing method, does not completely correspond to the suitable size selection. On the other hand, the proposed method shows the higher performance in size selection. However, the difference in rotation of the proposed method from surgeon’s plan was quite large in case 2. From the visualization of the planning result, we found out that the difference of the anteversion angle was larger than the other axes. We consider that this result was caused by the failure of estimation of the anteversion angle which was not optimized by Powell method in the proposed method. This is the limitation of the current method.


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As future work, we will add the learning function to this system, to learn the aspects of planning due to surgeon’s trend or to automate the parameter tuning when the unknown stem model is given.

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