Bio-Medical Materials and Engineering 24 (2014) 511–518 DOI 10.3233/BME-130837 IOS Press
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Projective invariant biplanar registration of a compact modular orthopaedic robot Sheng Luana, Lei Sunb, Lei Huc, Aimin Haoa, Changsheng Lic, Peifu Tangd,∗, Lihai Zhangd, Hailong Dud a
School of Computer Science and Engineering, Beihang University, Beijing, China Traumatology and Orthopaedics Institute, Beijing Jishuitan Hospital, Beijing, China c School of Mechanical Engineering and Automation, Beihang University, Beijing, China d Department of Orthopaedics, Chinese PLA General Hospital, Beijing, China b
Abstract. This paper presents a compact orthopedic robot designed with modular concept. The layout of the modular configuration is adaptive to various conditions such as surgical workspace and targeting path. A biplanar algorithm is adopted for the mapping from the fluoroscopic image to the robot, while the former affine based method is satisfactory only when the projection rays are basically perpendicular to the reference coordinate planes. This paper introduces the area cross-ratio as a projective invariant to improve the registration accuracy for non-orthogonal orientations, so that the robotic system could be applied to more orthopedic procedures under various C-Arm orientation conditions. The system configurations for femoral neck screw and sacroiliac screw fixation are presented. The accuracy of the robotic system and its efficacy for the two typical applications are validated by experiments. Keywords: Medical robotics, projective invariant, modular design
1. Introduction Freehand targeting under fluoroscopic guidance is routine in current orthopedic practice. There are high cumulative radiation exposures due to the trial and error approach. Computerized navigation systems have helped to increase the targeting accuracy and decrease exposure time [1–3], whereas manual placement of guide wires or screws practically still demands much skill and experience of surgeons. Therefore robotic systems are introduced because they could produce more repeatable and reliable outcomes, and also minimize the X-ray exposure time [4,5]. Currently, several robotic systems have been developed for orthopedic navigation [6–9]. These robotic systems are mostly suitable for one certain clinical task, and not easy to be applied to different indications. A compact modular robot providing intraoperative guidance has been developed. The robotic system was first applied to distal locking of intramedullary nails [10]. The robot is designed with the modular concept to facilitate disinfection and packaging. During surgery, its modular units are combined to form a parallel frame, so that the robotic navigation system could provide a stable ∗ Corresponding author. [email protected] 0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
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platform. A biplanar positioning algorithm is adopted to establish the transformation between the robot coordinate and C-Arm images. The biplanar method requires that the C-Arm views are nearly perpendicular to the robot reference planes defined by markers to secure the required localizing precision. Under this condition, both the AP (anterior-posterior) and lateral views are basically orthogonal to the respective robot reference plane. Owing to the modular design concept of the robotic system, different combinations of the modular units can be made to form various layouts. Therefore, the robot configuration is adaptable to specific requirements of various indications. While for some orthopedic procedures, such as femoral neck screw or sacroiliac screw fixation, the PRR angle (angle between projection rays and the robot reference plane) could be rather large under different working conditions, and the localization accuracy of the former affine-based biplanar method is not satisfactory. Therefore, projective invariant is introduced in this paper to improve the registration accuracy. In this paper, first the modular robot configuration for various surgical applications is described, then area based cross-ratio is introduced and a projective invariant registration method for the robotic navigation system is presented. Finally, experiments and results are provided to validate the accuracy and efficacy of the robotic system in femoral neck screw and sacroiliac joint screw fixation. 2. Modular layout of the robotic system The compact robotic system comprises a modular assembly and a marker component. The first part, the modular assembly is composed of four linear-motion units (Fig. 1a), which are two horizontal and two vertical units. During surgery, the units are joined together to form two positioning modules, and installed on a mounting base to form a parallel structure. The target path is determined by two localization points on the two positioning modules respectively. The second part, the marker component is used for registration, and is also designed to be a removable unit to facilitate surgeon's operation. Two groups of radiopaque markers are embedded in the marker component with a regular pattern, and their positions are fixed with regard to the robot coordinate.
a) Modular units
b) Centered layout
c) One-sided layout
Fig. 1 Modular robot layout
Various layouts can be achieved with different combinations of the modular units. The modular layout can be divided into two types, centered layout and one-sided layout, according to the fracture site, required workspace, targeting path and marker arrangement, etc. For the centered layout, the injured body part is placed between the two positioning modules, as is shown in Fig.1b. While for the one-sided layout, the positioning modules are placed on the same side of the body, as is shown in Fig. 1c.
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The biplanar robotic system can be applied to various surgical navigation and positioning tasks. For the centered layout, the system could be used in intramedullary nailing or pelvic ring fracture with suitable spans between the two positioning modules. Under these situations, the localization path is mostly perpendicular to the longitude axis of the limb or the body. Therefore, the two modules are generally juxtaposed. The one-sided layout is suitable for fracture sites at one side of the body, such as femoral neck fracture. The positioning modules are staggered to provide a large targeting path angle with less occupied space by the robot. Herein, two typical applications for the two robot layouts are studied in this paper. The first one is sacroiliac joint screw fixation. It is a well established treatment option for pelvic ring fracture fixation [11]. Due to the complexity of the bony anatomy and close proximity of neurovascular structures, inaccurate surgical operation may cause serious complications, and screw insertion into the safety zone can be technically challenging [12]. Often the repetitive X-ray exposure is required to locate the screw path. Therefore, there is a need for accurate screw placement with minimum of X-ray exposure. For pelvic fractures, the centered layout is adopted and the marker component is designed to have a double-layered structure, and the pelvis is situated between the two layers. Generally, inlet and outlet views are used for pelvic guidance. Since it is difficult to utilize the marker component with orthogonal reference planes, two groups of markers corresponding to the two views are embedded in both layers. The robotic system configuration for this application is shown in Fig. 2. The second one is cannulated screw fixation. It is an accepted method in treating femoral neck fractures [13]. Three cannulated screws are placed in the femoral neck to fix the fracture. The cross sectional area of the femoral neck is rather small for three screws. There is a risk that the screws may penetrate the joint. And the screws should be properly distributed, such as parallel to each other [14], to obtain the best biomechanical stability. However, in practice, it is difficult to achieve this goal with high reliability. For femoral neck fractures, one-sided layout is adopted and the marker component is designed to make the AP markers placed over and below the femoral head, and the lateral markers staggered near the femoral head in accordance with the lateral view for femoral neck fixation. This robot configuration is shown in Fig. 3. Thus in summary, different combinations can be made with this modular configuration so as to provide optimal layouts for various applications.
Fig. 2 System configuration for sacroiliac screw fixation
Fig. 3 System configuration for femoral neck screw fixation
3. Area cross-ratio based biplanar registration The biplane model was first proposed by Martins et al. [15] and has been used in neurosurgical applications [16,17]. This method also requires two unparallel views to reconstruct a 3D point, while it
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is not an explicit form of calibration method which needs estimation of camera parameters [18]. There are two steps for the biplanar registration process. First, identify the reference markers and the target point in X-ray images, and then locate the target point in the reference plane for each view. Second, determine the 3D position by virtually drawing two line-of-sight rays corresponding to the two views, and take the intersection point as the target point in the robot coordinate. Affine based interpolation is used in its previous applications [19]. However, there is perpendicularity limitation for C-Arm orientation angles. Therefore, the projective invariant is introduced to enhance the biplanar registration method for conditions with large PRR angles. Geometrical invariants are used widely in computer vision technique [20], and the cross-ratio of four points along a line has been used in surgical navigation systems [21,22]. However, it is difficult to know the error distribution all over the reference plane with collinear markers. The area cross-ratio is an expansion of linear cross-ratio[23,24]. Five coplanar points (not three collinear points) are used to define the area cross-ratio. Two area cross-ratios are needed to solve the target position on a 2D plane. Thus six marker points are adopted to define a local coordinate, and four chosen marker points and the target point are used for each area cross-ratio. The markers are selected based on the principle that they should be evenly distributed and cover the region to the greatest extent possible.
Fig. 4 Area cross-ratio of markers
Two chosen marker point sets are {1, 2, 4, 5, m} and {6, 5, 3, 1, m}, and the area cross-ratios are .
ξ1 =
S (1,4,5) ⋅ S (1,2, m) S (1,2,5) ⋅ S (1,4, m)
ξ2 =
S (6,5,1) ⋅ S (6,3, m) S (6,3,1) ⋅ S (6,5, m)
where S (i, j , k ) is used to describe the area of the triangle defined by points Pi, Pj, Pk. When all positions in the image plane are collected, the target point can be located in the reference plane by calculating the invariants above. Then in the second step, the two virtual rays for the two views are generated. Practically, they may not intersect at one point due to errors, so the midpoint of the common perpendicular line of the two rays is taken as the target point in robot coordinate. A simulation experiment is conducted to investigate the performance of the registration method. The marker points are regularly arranged forming 50mm squares on an 80mm cube. The target points are eight vertexes of the cube, and the registration error is their average. The deformation of C-Arm images is taken into account by using gridded distortion data collected beforehand. The former affine method is also tested as a comparison. Only the 1,3,5 markers are used to define a local coordinate and the distance ratios along its local axes are taken as invariants. There are generally three types of CArm orientations, namely, horizontal panning, pivot rotation and orbital rotation. Specifically, experiments are conducted for conventional views in the two aforementioned applications which
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involve large PRR angles. First, for horizontal panning common in occasions such as the cannulated screw fixation, the AP view remains unchanged, while the lateral view has a panning angle ranging from -60° to 60° with a 10° step. The result is shown in Fig. 5a. It shows that for the affine method, the error increases greatly when panning is significant; while for the area cross-ratio method, the error is 0.3~0.4mm at the possible range for femoral neck screw fixation. Second, as for pivot and orbital rotations, they can be treated with similar settings in simulation. Thus only pivot rotation common in occasions such as the sacroiliac joint screw fixation is tested. Inlet/outlet views are used and the pivot angles of the two views are set equal relative to the reference plane for demonstration. The angle between them is set ranging from 50° to 130° with a 10° step. The result for pivoting rotation is shown in Fig. 5b. It shows that the registration error is reduced as a whole with the area cross-ratio method. The error is 0.7~0.8mm at the possible angle range for the sacroiliac joint screw fixation. In both cases, the error at the centered range is reduced since more markers are involved in calculation. In conclusion, the biplane method based on the area cross-ratio invariant can improve the positioning accuracy at large PRR angles.
a) Panning orientation
b) Pivot rotation
Fig. 5 Registration error at various C-Arm angles
4. Experiments of the robotic system Experiments are conducted to validate the accuracy of the biplanar robotic navigation system and its efficacy in screw fixation procedures of the two typical applications with large PRR angles, i.e. femoral neck screw and sacroiliac joint screw fixation. A Philips Libra BV C-Arm was used for intraoperative imaging in these experiments. 4.1. Accuracy test of the robotic system The steps of the positioning accuracy test are as follows: install the biplanar robot onto a polymethyl methacrylate base, and fix two 3 mm Kirschner wires on the same base. Their tips A and B are taken as the target points. Acquire the C-Arm images, making sure that the two tips are both distinct in the
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images. The surgical plan is made by identifying the target tips and assuming the horizontal orientation to provide a consistent measurement. Then run the robot to the corresponding localizing position for tip A and maintain the path with the guiding sleeve. Finally, insert another Kirschner wire along the guiding sleeve to the planned position. The deviation of these two wire tips is measured using feeler gauges and taken as the positioning error. Then repeat the robot localization and measurement procedures for tip B. Two groups of test are conducted for the femoral neck screw and the sacroiliac screw targeting, with the corresponding system layout and specific C-Arm orientation settings. Ten tests are performed for each typical application, and the positioning errors for the two groups are listed in Table 1 and Table 2, respectively. Table 1 Positioning error for femoral neck screw targeting (mm) 1
2
3
4
5
6
7
8
9
10
Tip A
0.79
0.61
0.88
0.68
0.79
0.59
0.86
0.71
0.93
0.62
Tip B
0.56
0.87
0.65
0.93
0.57
0.78
0.64
0.89
0.70
0.82
Table 2 Positioning error for sacroiliac screw targeting (mm) 1
2
3
4
5
6
7
8
9
10
Tip A
1.49
1.27
1.45
1.24
1.49
1.25
1.55
1.32
1.45
1.27
Tip B
1.55
1.03
1.62
0.95
1.25
1.07
1.38
1.56
1.29
0.98
The average errors for the femoral neck screw and the sacroiliac screw fixation are (0.74 ± 0.13) mm and (1.32 ± 0.20) mm, which are acceptable for respective screw fixation procedures [25,26]. Therefore, the biplanar navigation system has sufficient positioning accuracy for the two typical applications. 4.2. Screw fixation experiment Screw fixation test is conducted using Synbone to validate the efficacy of the robot assisted procedures. Some steps are the same as above, and the primary difference is the surgical plan. After registration, the path is determined. Following the running step, the robot is locked for safety. A guide wire is inserted and the X-ray images are taken by surgeons to validate the surgical path, and finally the screws are implanted. The path planning procedure is different for the two typical applications. As for the femoral neck fixation, the plan involves marking out the femoral neck axis and three screw paths on the fluoroscopic images. The robot localization procedure involves three repetitive steps for the three screws. Four femoral models are used. No penetration is found and the parallelism of three screws is satisfactory, as is shown in Fig. 6. The total radiation exposure time is 1.8 ~ 2.5s. While for the sacroiliac screw fixation, the plan involves primarily identifying the marker points and setting the screw paths. After registration, remove only the upper marker plate to facilitate manual drilling. Four femoral bone models are used in this experiment. Drilling is processed precisely according to the planned trajectories and the screws are all within the safety zone, as is shown in Fig. 7. The total radiation exposure time is 2.2 ~ 3.5s.
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Fig. 6 Femoral neck screw fixation experiment
517
Fig. 7 Sacroiliac screw fixation experiment
5. Conclusions The robot is designed to have a parallelized structure with enhanced stiffness. It is able to provide a steady mechanical guide to maintain the surgical tool. Therefore, misguidance due to unstable freehand targeting and guide pin bending can be avoided, the positioning stability and reliability can be greatly improved. The X-ray radiation exposure for both surgeons and patients could also be reduced. Compared with the extrinsic calibration method in most fluoroscopic navigation systems, the biplanar method does not need a correction and calibration step beforehand. With the area based projective invariant method, the positioning accuracy of the robotic system is satisfactory at more working conditions of C-Arm views. Due to its modular design and the enhanced biplanar registration method, this robotic system is capable of fulfilling multiple surgical navigation tasks. It can provide guidance for various applications by modifying its layout. The clinical adaptability of the robot system is validated by experiments in femoral neck screw and sacroiliac joint screw fixation, and also in intramedullary nailing previously. Compared with most orthopedic robots having limited adaptability due to their mechanical structure, this modularized robotic system has improved versatility and cost performance, which is advantageous for its extensive clinical application. Future research will focus on applying the system to a broader range of applications, and thorough clinical studies to investigate the clinical outcome of this system. 6. Acknowledgements This work is supported by the National Key Technology R&D Program (NO. 2011BAF01B02 and NO. 2012BAI14B02), the National High-tech R&D Program of China (NO. 2012AA041604) and also the Project Data Modeling and Interactive Virtual Surgery of Digital Human Organs supported by NSFC (NO.61190125).
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511
Projective invariant biplanar registration of a compact modular orthopaedic robot Sheng Luana, Lei Sunb, Lei Huc, Aimin Haoa, Changsheng Lic, Peifu Tangd,∗, Lihai Zhangd, Hailong Dud a
School of Computer Science and Engineering, Beihang University, Beijing, China Traumatology and Orthopaedics Institute, Beijing Jishuitan Hospital, Beijing, China c School of Mechanical Engineering and Automation, Beihang University, Beijing, China d Department of Orthopaedics, Chinese PLA General Hospital, Beijing, China b
Abstract. This paper presents a compact orthopedic robot designed with modular concept. The layout of the modular configuration is adaptive to various conditions such as surgical workspace and targeting path. A biplanar algorithm is adopted for the mapping from the fluoroscopic image to the robot, while the former affine based method is satisfactory only when the projection rays are basically perpendicular to the reference coordinate planes. This paper introduces the area cross-ratio as a projective invariant to improve the registration accuracy for non-orthogonal orientations, so that the robotic system could be applied to more orthopedic procedures under various C-Arm orientation conditions. The system configurations for femoral neck screw and sacroiliac screw fixation are presented. The accuracy of the robotic system and its efficacy for the two typical applications are validated by experiments. Keywords: Medical robotics, projective invariant, modular design
1. Introduction Freehand targeting under fluoroscopic guidance is routine in current orthopedic practice. There are high cumulative radiation exposures due to the trial and error approach. Computerized navigation systems have helped to increase the targeting accuracy and decrease exposure time [1–3], whereas manual placement of guide wires or screws practically still demands much skill and experience of surgeons. Therefore robotic systems are introduced because they could produce more repeatable and reliable outcomes, and also minimize the X-ray exposure time [4,5]. Currently, several robotic systems have been developed for orthopedic navigation [6–9]. These robotic systems are mostly suitable for one certain clinical task, and not easy to be applied to different indications. A compact modular robot providing intraoperative guidance has been developed. The robotic system was first applied to distal locking of intramedullary nails [10]. The robot is designed with the modular concept to facilitate disinfection and packaging. During surgery, its modular units are combined to form a parallel frame, so that the robotic navigation system could provide a stable ∗ Corresponding author. [email protected] 0959-2989/14/$27.50 © 2014 – IOS Press and the authors. All rights reserved
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platform. A biplanar positioning algorithm is adopted to establish the transformation between the robot coordinate and C-Arm images. The biplanar method requires that the C-Arm views are nearly perpendicular to the robot reference planes defined by markers to secure the required localizing precision. Under this condition, both the AP (anterior-posterior) and lateral views are basically orthogonal to the respective robot reference plane. Owing to the modular design concept of the robotic system, different combinations of the modular units can be made to form various layouts. Therefore, the robot configuration is adaptable to specific requirements of various indications. While for some orthopedic procedures, such as femoral neck screw or sacroiliac screw fixation, the PRR angle (angle between projection rays and the robot reference plane) could be rather large under different working conditions, and the localization accuracy of the former affine-based biplanar method is not satisfactory. Therefore, projective invariant is introduced in this paper to improve the registration accuracy. In this paper, first the modular robot configuration for various surgical applications is described, then area based cross-ratio is introduced and a projective invariant registration method for the robotic navigation system is presented. Finally, experiments and results are provided to validate the accuracy and efficacy of the robotic system in femoral neck screw and sacroiliac joint screw fixation. 2. Modular layout of the robotic system The compact robotic system comprises a modular assembly and a marker component. The first part, the modular assembly is composed of four linear-motion units (Fig. 1a), which are two horizontal and two vertical units. During surgery, the units are joined together to form two positioning modules, and installed on a mounting base to form a parallel structure. The target path is determined by two localization points on the two positioning modules respectively. The second part, the marker component is used for registration, and is also designed to be a removable unit to facilitate surgeon's operation. Two groups of radiopaque markers are embedded in the marker component with a regular pattern, and their positions are fixed with regard to the robot coordinate.
a) Modular units
b) Centered layout
c) One-sided layout
Fig. 1 Modular robot layout
Various layouts can be achieved with different combinations of the modular units. The modular layout can be divided into two types, centered layout and one-sided layout, according to the fracture site, required workspace, targeting path and marker arrangement, etc. For the centered layout, the injured body part is placed between the two positioning modules, as is shown in Fig.1b. While for the one-sided layout, the positioning modules are placed on the same side of the body, as is shown in Fig. 1c.
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The biplanar robotic system can be applied to various surgical navigation and positioning tasks. For the centered layout, the system could be used in intramedullary nailing or pelvic ring fracture with suitable spans between the two positioning modules. Under these situations, the localization path is mostly perpendicular to the longitude axis of the limb or the body. Therefore, the two modules are generally juxtaposed. The one-sided layout is suitable for fracture sites at one side of the body, such as femoral neck fracture. The positioning modules are staggered to provide a large targeting path angle with less occupied space by the robot. Herein, two typical applications for the two robot layouts are studied in this paper. The first one is sacroiliac joint screw fixation. It is a well established treatment option for pelvic ring fracture fixation [11]. Due to the complexity of the bony anatomy and close proximity of neurovascular structures, inaccurate surgical operation may cause serious complications, and screw insertion into the safety zone can be technically challenging [12]. Often the repetitive X-ray exposure is required to locate the screw path. Therefore, there is a need for accurate screw placement with minimum of X-ray exposure. For pelvic fractures, the centered layout is adopted and the marker component is designed to have a double-layered structure, and the pelvis is situated between the two layers. Generally, inlet and outlet views are used for pelvic guidance. Since it is difficult to utilize the marker component with orthogonal reference planes, two groups of markers corresponding to the two views are embedded in both layers. The robotic system configuration for this application is shown in Fig. 2. The second one is cannulated screw fixation. It is an accepted method in treating femoral neck fractures [13]. Three cannulated screws are placed in the femoral neck to fix the fracture. The cross sectional area of the femoral neck is rather small for three screws. There is a risk that the screws may penetrate the joint. And the screws should be properly distributed, such as parallel to each other [14], to obtain the best biomechanical stability. However, in practice, it is difficult to achieve this goal with high reliability. For femoral neck fractures, one-sided layout is adopted and the marker component is designed to make the AP markers placed over and below the femoral head, and the lateral markers staggered near the femoral head in accordance with the lateral view for femoral neck fixation. This robot configuration is shown in Fig. 3. Thus in summary, different combinations can be made with this modular configuration so as to provide optimal layouts for various applications.
Fig. 2 System configuration for sacroiliac screw fixation
Fig. 3 System configuration for femoral neck screw fixation
3. Area cross-ratio based biplanar registration The biplane model was first proposed by Martins et al. [15] and has been used in neurosurgical applications [16,17]. This method also requires two unparallel views to reconstruct a 3D point, while it
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is not an explicit form of calibration method which needs estimation of camera parameters [18]. There are two steps for the biplanar registration process. First, identify the reference markers and the target point in X-ray images, and then locate the target point in the reference plane for each view. Second, determine the 3D position by virtually drawing two line-of-sight rays corresponding to the two views, and take the intersection point as the target point in the robot coordinate. Affine based interpolation is used in its previous applications [19]. However, there is perpendicularity limitation for C-Arm orientation angles. Therefore, the projective invariant is introduced to enhance the biplanar registration method for conditions with large PRR angles. Geometrical invariants are used widely in computer vision technique [20], and the cross-ratio of four points along a line has been used in surgical navigation systems [21,22]. However, it is difficult to know the error distribution all over the reference plane with collinear markers. The area cross-ratio is an expansion of linear cross-ratio[23,24]. Five coplanar points (not three collinear points) are used to define the area cross-ratio. Two area cross-ratios are needed to solve the target position on a 2D plane. Thus six marker points are adopted to define a local coordinate, and four chosen marker points and the target point are used for each area cross-ratio. The markers are selected based on the principle that they should be evenly distributed and cover the region to the greatest extent possible.
Fig. 4 Area cross-ratio of markers
Two chosen marker point sets are {1, 2, 4, 5, m} and {6, 5, 3, 1, m}, and the area cross-ratios are .
ξ1 =
S (1,4,5) ⋅ S (1,2, m) S (1,2,5) ⋅ S (1,4, m)
ξ2 =
S (6,5,1) ⋅ S (6,3, m) S (6,3,1) ⋅ S (6,5, m)
where S (i, j , k ) is used to describe the area of the triangle defined by points Pi, Pj, Pk. When all positions in the image plane are collected, the target point can be located in the reference plane by calculating the invariants above. Then in the second step, the two virtual rays for the two views are generated. Practically, they may not intersect at one point due to errors, so the midpoint of the common perpendicular line of the two rays is taken as the target point in robot coordinate. A simulation experiment is conducted to investigate the performance of the registration method. The marker points are regularly arranged forming 50mm squares on an 80mm cube. The target points are eight vertexes of the cube, and the registration error is their average. The deformation of C-Arm images is taken into account by using gridded distortion data collected beforehand. The former affine method is also tested as a comparison. Only the 1,3,5 markers are used to define a local coordinate and the distance ratios along its local axes are taken as invariants. There are generally three types of CArm orientations, namely, horizontal panning, pivot rotation and orbital rotation. Specifically, experiments are conducted for conventional views in the two aforementioned applications which
S. Luan et al. / Projective invariant biplanar registration of a compact modular orthopaedic robot
515
involve large PRR angles. First, for horizontal panning common in occasions such as the cannulated screw fixation, the AP view remains unchanged, while the lateral view has a panning angle ranging from -60° to 60° with a 10° step. The result is shown in Fig. 5a. It shows that for the affine method, the error increases greatly when panning is significant; while for the area cross-ratio method, the error is 0.3~0.4mm at the possible range for femoral neck screw fixation. Second, as for pivot and orbital rotations, they can be treated with similar settings in simulation. Thus only pivot rotation common in occasions such as the sacroiliac joint screw fixation is tested. Inlet/outlet views are used and the pivot angles of the two views are set equal relative to the reference plane for demonstration. The angle between them is set ranging from 50° to 130° with a 10° step. The result for pivoting rotation is shown in Fig. 5b. It shows that the registration error is reduced as a whole with the area cross-ratio method. The error is 0.7~0.8mm at the possible angle range for the sacroiliac joint screw fixation. In both cases, the error at the centered range is reduced since more markers are involved in calculation. In conclusion, the biplane method based on the area cross-ratio invariant can improve the positioning accuracy at large PRR angles.
a) Panning orientation
b) Pivot rotation
Fig. 5 Registration error at various C-Arm angles
4. Experiments of the robotic system Experiments are conducted to validate the accuracy of the biplanar robotic navigation system and its efficacy in screw fixation procedures of the two typical applications with large PRR angles, i.e. femoral neck screw and sacroiliac joint screw fixation. A Philips Libra BV C-Arm was used for intraoperative imaging in these experiments. 4.1. Accuracy test of the robotic system The steps of the positioning accuracy test are as follows: install the biplanar robot onto a polymethyl methacrylate base, and fix two 3 mm Kirschner wires on the same base. Their tips A and B are taken as the target points. Acquire the C-Arm images, making sure that the two tips are both distinct in the
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images. The surgical plan is made by identifying the target tips and assuming the horizontal orientation to provide a consistent measurement. Then run the robot to the corresponding localizing position for tip A and maintain the path with the guiding sleeve. Finally, insert another Kirschner wire along the guiding sleeve to the planned position. The deviation of these two wire tips is measured using feeler gauges and taken as the positioning error. Then repeat the robot localization and measurement procedures for tip B. Two groups of test are conducted for the femoral neck screw and the sacroiliac screw targeting, with the corresponding system layout and specific C-Arm orientation settings. Ten tests are performed for each typical application, and the positioning errors for the two groups are listed in Table 1 and Table 2, respectively. Table 1 Positioning error for femoral neck screw targeting (mm) 1
2
3
4
5
6
7
8
9
10
Tip A
0.79
0.61
0.88
0.68
0.79
0.59
0.86
0.71
0.93
0.62
Tip B
0.56
0.87
0.65
0.93
0.57
0.78
0.64
0.89
0.70
0.82
Table 2 Positioning error for sacroiliac screw targeting (mm) 1
2
3
4
5
6
7
8
9
10
Tip A
1.49
1.27
1.45
1.24
1.49
1.25
1.55
1.32
1.45
1.27
Tip B
1.55
1.03
1.62
0.95
1.25
1.07
1.38
1.56
1.29
0.98
The average errors for the femoral neck screw and the sacroiliac screw fixation are (0.74 ± 0.13) mm and (1.32 ± 0.20) mm, which are acceptable for respective screw fixation procedures [25,26]. Therefore, the biplanar navigation system has sufficient positioning accuracy for the two typical applications. 4.2. Screw fixation experiment Screw fixation test is conducted using Synbone to validate the efficacy of the robot assisted procedures. Some steps are the same as above, and the primary difference is the surgical plan. After registration, the path is determined. Following the running step, the robot is locked for safety. A guide wire is inserted and the X-ray images are taken by surgeons to validate the surgical path, and finally the screws are implanted. The path planning procedure is different for the two typical applications. As for the femoral neck fixation, the plan involves marking out the femoral neck axis and three screw paths on the fluoroscopic images. The robot localization procedure involves three repetitive steps for the three screws. Four femoral models are used. No penetration is found and the parallelism of three screws is satisfactory, as is shown in Fig. 6. The total radiation exposure time is 1.8 ~ 2.5s. While for the sacroiliac screw fixation, the plan involves primarily identifying the marker points and setting the screw paths. After registration, remove only the upper marker plate to facilitate manual drilling. Four femoral bone models are used in this experiment. Drilling is processed precisely according to the planned trajectories and the screws are all within the safety zone, as is shown in Fig. 7. The total radiation exposure time is 2.2 ~ 3.5s.
S. Luan et al. / Projective invariant biplanar registration of a compact modular orthopaedic robot
Fig. 6 Femoral neck screw fixation experiment
517
Fig. 7 Sacroiliac screw fixation experiment
5. Conclusions The robot is designed to have a parallelized structure with enhanced stiffness. It is able to provide a steady mechanical guide to maintain the surgical tool. Therefore, misguidance due to unstable freehand targeting and guide pin bending can be avoided, the positioning stability and reliability can be greatly improved. The X-ray radiation exposure for both surgeons and patients could also be reduced. Compared with the extrinsic calibration method in most fluoroscopic navigation systems, the biplanar method does not need a correction and calibration step beforehand. With the area based projective invariant method, the positioning accuracy of the robotic system is satisfactory at more working conditions of C-Arm views. Due to its modular design and the enhanced biplanar registration method, this robotic system is capable of fulfilling multiple surgical navigation tasks. It can provide guidance for various applications by modifying its layout. The clinical adaptability of the robot system is validated by experiments in femoral neck screw and sacroiliac joint screw fixation, and also in intramedullary nailing previously. Compared with most orthopedic robots having limited adaptability due to their mechanical structure, this modularized robotic system has improved versatility and cost performance, which is advantageous for its extensive clinical application. Future research will focus on applying the system to a broader range of applications, and thorough clinical studies to investigate the clinical outcome of this system. 6. Acknowledgements This work is supported by the National Key Technology R&D Program (NO. 2011BAF01B02 and NO. 2012BAI14B02), the National High-tech R&D Program of China (NO. 2012AA041604) and also the Project Data Modeling and Interactive Virtual Surgery of Digital Human Organs supported by NSFC (NO.61190125).
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