A Robotic C-arm Fluoroscope

Transcription

1 A Robotic C-arm Fluoroscope Norbert Binder, Lars Matthäus, Rainer Burgkart, Achim Schweikard Institute for Robotics and Cognitive Systems, University of Lübeck Ratzeburger Allee 160, Lübeck, Germany Klinik für Orthopädie, Klinikum rechts der Isar der TU München, Ismaninger Str. 22, München {binder matthaeus Abstract Fluoroscopic C-arms are common devices for acquiring images during surgery. Manual positioning is timeconsuming and requires considerable experience. Trained users must often take several images to find the best viewing direction. If a second image must be taken from the same position, e.g. for post operative control, the C- arm must be moved to the exact same position. Without guidance, this is often difficult to accomplish. We developed the idea to completely robotize a standard C-arm, i. e. to equip all joints with motors and encoders. A software environment provides for intelligent control. To archive this goal a complete kinematic analysis of the fluoroscope was necessary. On the basis of this analysis a number of clinical applications have been developed: (1) simplified positioning via cartesian control; (2) automatic acquisition of panoramic images; (3) 3D CT with arbitrary viewing angles; (4) 4D intraoperative CT with/without respiration triggering; (5) automated anatomy-oriented positioning. The goal of this research is thus three-fold: Minimize radiation exposure of the OR staff, reduce positioning time and offer enhanced imaging capability. Keywords: Robot-assisted surgery, medical robotics, intra-surgical imaging, robotized C-arm, 3D flouroscope, C-arm kinematics I. INTRODUCTION MEDICAL Robots have been the subject of research for over a decade. Two large catagories of robotic systems can be distinguished: The first category are master-slave type robots. Such systems are designed to reduce tremor, perform complex manipulation tasks in tight environments, and down-scale movements [1]. The second category are robots for positioning surgical instruments [2], [3]. In this way, heavy instrumentation (such as radiation sources) can be moved with high precision, or pre-operative planning data can be transferred to the OR. The system presented here does not fall into either category. Instead, we propose to optimize the intraoperative image acquisition workflow. Thereby, we attempt to reduce operation time, radiation dose and infection risk, and provide better intra-operative images. When using a standard C-arm fluoroscope (fig. 1), two problems occur: First, it is often desired to obtain several images from the same viewing angle during the operation. If the C-arm was moved in the meantime, the old position and orientation must be found again. Second, if another image from a different position is required, more than one joint must be adjusted in general. This is due to the rather complex kinematic construction of standard C-arms. At the moment this is done manually and without guidance, which often leads to wrong positioning. Even basic movements, such as straight line (translational) movements in the image plane are difficult to perform, due to the fact that three of the joints are rotational. Similarly, pure rotations, if desired, are cumbersome, since several joints are translational.

2 Fig. 1. Ziehm Vario 3D C-arm. We developed the idea to completely robotize the C-arm, i. e. to equip all joints of the device with motors and encoders and to establish an intelligent control environment for positioning the fluoroscope. This would not only allow for simplified positioning and repositioning, but also for completely new applications: isocentric movements with non-isocenter C-arms in arbitrary planes and variable distance between the region of interest (ROI) and the image generator. cartesian movements in the world- or image coordinate system adjusting the center of an image long-bone- or poster-images extraction of 3D information and best-position calculation automatic image collection for intraoperative CT (3D, 4D and respiration-triggered) A complete kinematic analysis is the basis of all applications and is sketched in section II. The analysis is done for a standard commercial C-arm ZIEHM Vision 3D widely used in many clinics. We derive the direct kinematics based on the Denavit-Hartenberg-rules and describe some difficulties when finding a solution for the inverse kinematic problem. A survey of our implementation of the robotized C-arm is given in section III. Section IV discusses the applications mentioned above in some more detail. The paper concludes with a discussion of the results and future work. II. THE C-ARM KINEMATICS A. The Direct Problem The C-arm used for our experiments has five independent joints as shown in figure 2 and hence processes five degrees of freedom (DOF). Movements of the single joints result in the following movements of the C-arm: Joint 1 Linear movement along z 0 which modifies the height of the C. Parameter: length d 1. Joint 2 Rotation around z 0, also called wig-wag, parallel to the x-y-plane of the base coordinate system. Parameter: angle 2. Joint 3 Linear movement to adjust the arm length. Parameter: length d 3. Joint 4 Rotation of the C around the center of the arm (angulation). Parameter: angle 4. Joint 5 Orbital movement to rotate the C in plane. Parameter: angle 5. Fig. 2. Mechanical axes of a standard C-arm fluoroscope. We performed the analysis of the kinematics according to the Denavit-Hartenberg (DH) rules and with respect to the mechanical limitations [4]: For each arm i we define a coordinate system i = (x i, y i, z i) and derive the homogeneous matrices i-1 A i describing the transformation from coordinate system i-1 to i. Finally, the complete transformation 0 A 5 given by 0 A 5 = i-1 A i is calculated. This completely solves the forward kinematics. With the joint parameters (d 1, 2, d 3, 4, 5) given, the position and orientation of the X-ray beam and the image generator is

3 fully defined. B. The Inverse Kinematics Most applications require a certain position and orientation relative to the base of the C-arm. To obtain the joint parameters leading to this position and orientation, we use inverse kinematics. Placing the image plane freely in three-dimensional space requires six degrees of freedom (DOF). The C-arm has only five joints and thus can only reach five DOFs. The missing degree of freedom is the rotation of the image around its center, i.e. the center-axis of the X-ray beam cone. As we have circular radiographs, no information is lost when ignoring the rotation of the image in plane. With the target position given in homogeneous matrix form on one side and the symbolic transformation matrix of the direct kinematics on the other side, we can derive an equation system. When including the knowledge about image rotation and mechanical design of the C-arm, we can solve this system and compute the joint parameters. A description of the mathematical details is beyond the scope of this paper and will be published separately. III. TECHNICAL REALIZATION Our goal is a fully motorized C-arm, which can be positioned by an external PC. The only limitations are those of the mechanical workspace, which is equivalent to the original manual C-arm. A. Control-Unit A Profibus system is used to control all five joints. This gives access to their parameters and monitors correct functioning. A C++-library offering high-level commands for the essential C-arm functions was developed B. C-Arm Lift The vertical lift of the C-arm is motorized in the commercial standard version and had originally been controlled by the up- and down-buttons on the C-arm base only. It can now be activated by the control unit, too. The position is measured by an incremental cable-actuated encoder. C. Wig-Wag The horizontal twist of the arm, also called wig-wag is driven by belt transmission (Fig. 3). Due to the high masses of the moving parts, a high gear-reduction must be used. Fig. 3. Wig-wag. D. Horizontal Stretch The length of the arm is adjusted by a motor with included encoder. This axis had already been modified in former experiments and was slightly adapted to our needs. E. Angulation The C can be tilted sideways by a high resolving motor-gear-combination mounted at the opposite end of the arm (Fig. 4). Due to high masses, a high gear reduction was selected. This reduction currently forbids manual motion of this joint. An emergency coupler was included. Force-torque sensors allow for a servo driven manual mode

4 comparable to common manual positioning. Fig. 4. Angulation axis. F. Orbital Movement The orbital movement (Fig. 5) of the C is activated by a belt drive. The motor and gear were designed to allow for manual handling. Due to the weight of the moving parts, a high gear reduction was applied here as well. Again, manual handling is assured by force-torque sensor controlled movement and an emergency-coupler for powerfailure. Fig. 5. Orbital Axis. G. First Results The robotized C-arm allows for automated positioning via PC and opens new perspectives for intra-surgical imaging. Nevertheless, there are still some aspects which have to be improved. Moving big masses requires high gear reduction which blocks manual handling. However, manual handling is necessary for compatibility reasons or initial positioning, and especially for emergency situations during surgery. Therefore switches, motor-encoders, and force-torque sensors are used to recognize the user s intention, and then activate the drives accordingly. This will also allow for weight compensation. The C-arm joints must be controllable during power-failures which is ensured by couplers. Safety issues such as collision detection are discussed with our clinical and industrial partners and have to be subject of all future steps. IV. APPLICATIONS A robotized C-arm offers numerous applications. As a tool to develop and test new ideas we implemented a computer simulation of the device including a patient model and the ability to take radiograph pictures [5]. Most of the images shown in this section are taken from this simulator.

5 Fig. 6. The simulator is based on a real C-arm and offers the same functionality including the aquisation of radiographs. The underlying idea for all applications is to express the desired movement or desired position of the C-arm not in terms of joint parameters, but in terms of ROI-coordinates (denoted as p) and beam or viewing direction (denoted as z). For example a cartesian movement in direction d would lead to a new ROI p new = p old + t d, where t > 0 denotes the step size, while preserving the beam direction z new = z old. With the help of the inverse kinematics of section II-B the joint parameters (d 1, 2, d 3, 4, 5) are calculated to achieve (p new, z new). Now the robot can be moved easily to the new position. A. User Controlled Movements 1) Cartesian Movements: When operating the standard mechanical C-arm by hand, joint parameters were changed one after the other. The non-trivial architecture of the fluoroscope leads to complex changes of the region of interest and the viewing direction when moving a joint. Thus it is difficult to set the parameters of the C-arm for a certain region of interest. Using the inverse kinematics, movements along cartesian axes can be performed easily. Those motions are much easier to visualize by humans than rotational movements and allow for faster positioning. Here it makes no difference which coordinate system is used. Possible choices are the base (world) coordinate system or an image-based coordinate system. The latter allows for shifts in the image plane, e. g. for reasons of recentering (coordinates x and y ) or a closer view (coordinate z ). To make positioning even easier, a simulation of the new image based on previous pictures can be presented to the OR staff on the computer screen. 2) Isocentric Rotation: As already noted, common C-arm designs were not optimized for robotic movements. Therefore most fluoroscopes are non-isocentric, i. e. when moving joints four and/or five, the image center will change. This complicates image acquisation of a ROI from different viewing angles. Using the inverse kinematics we can easily rotate the C-arm with a user specified distance around an arbitrary point and in an arbitrary plane. All the surgeon has to do, is to define the center of the rotation, either by marking a point in an image (fast, but somewhat inaccurate way) or by marking the same landmark in two different images to allow for the extraction of 3D-coordinates of the desired fixed point (exact way). The plane of the rotation can be defined by the plane of the C of the fluoroscope or by defining any two linearly independent vectors centered on a fixed point. Another application based on this isocentric rotation is described in section IV-C.2. B. Automatic Positioning 1) Re-centering: Placing the C-arm in such a way that a given ROI will be imaged is often difficult and requires experience, especially when the patient is corpulent. Thus it might be desired to obtain an image with the femur head center in the image center. If an image is not centered properly and the ROI is on the edge of the radiograph, important information might be missing. But the picture can still be used to obtain a corrected image. After marking the desired center in the old image, the robotic C-arm can automatically reposition itself such that the desired region is mapped to the center. The viewing angle can either be corrected before taking the new image or be kept from the old image (compare section IV-A.1). An example of the repositioning application on our C-arm is shown in Fig. 7.

6 Fig. 7. Original image (left) and after re-centering (right). 2) Standard Images: Many radiographs are views of standard planes e. g. anterior-posteriory, lateral, medial etc. A motorized C-arm can be moved easily to these positions. In order to enable the robotic C-arm to move to the desired position, the surgeon identifies several landmarks on two pictures of the ROI taken from different angles. The 3D-coordinates of the landmarks are calculated internally and the correct image center and image direction are calculated based on the inverse kinematics. The latter one relies on marking special landmarks from which to get the right anatomical position for the image. E. g. for a-p-images of the spine the surgeon would mark the left and right transverse process and the spine of the vertebra to define the region of interest as well as the a-p-direction. An example can be found in Fig. 8. It should be mentioned that other image modalities can be included into the set of standard images easily by defining the number of points to be marked and the algorithm describing the ROI p and beam direction z in terms of the marked points. Fig. 8. In the two pictures on the left corresponding anatomical landmarks are identified. The 3D-coordinates of them are computed and the correct position for an a-p-image of the spine is adapted automatically by the robot. C. Image Sequences One of the most interesting perspectives for a motorized C-arm are applications which need the input of more than one image. These applications require an exact calibration of the generated image [6], [7] and compensation of the mechanical deformations caused by the masses of the source and the detector. 1) Longbone And Poster Images: Some structures in the human body are bigger than the field of view of the fluoroscope. In orthopaedics sometimes images of the whole femur are useful. Neurosurgeons may have to scan the whole spine to find the vertebra of interest. Images of the entire thorax or pelvis are important in emergency rooms or surgery. Currently the field of view of the standard C-arm is very limited (typical is a 17 cm diameter circular image). Our idea is to acquire several images and compose a single image by automatically repositioning with robot C-am between images. By marking the starting point on two images from different angles its position in space can be calculated. After defining a target point in the same way, the angle of view (a-p, lateral or userdefined) is set. Depending on the length of the distance between start- and end-point, the C-arm will take a series of radiographs and aligning them to one single longbone-image. Our longbone-application offers user-interactive image aquisation. The radiographs are combined according to their position and orientation (Fig. 9).

7 For emergency radiographs marking start- and endpoint in two images each will take too much time. Thus, only the start point and a direction-vector are marked in the first image and the fluoroscope moves in the indicated direction parallel to the image plane to take a specified number of radiographs. It is a non-trivial task to align single images for manual long-bone-image construction. Different methods, such as X-ray rulers were suggested for registration [8]. In our approach, position and orientation of the images in space are given and saved with the image-data (see also section II-B). Therefore it is not difficult to combine the images with a minimum effort of registration. In the example shown in Fig. 9 no registration was applied. Fig. 9. Original image series and constructed long-bone image based on position and orientation information only (no registration). An application similar to the longbone sequence is taking an image of the whole thorax. There, not only one row of images but a whole matrix of images must be taken and set together in the correct way. It is easy to see that our approach extends to this application naturally. 2) Intra-surgical CT: In some surgeries, 3D-images of bones or other body structures substantially help to get better orientation and control. Acquiring such image data in a standard OR is complicated as a CT is normally not available. With the help of the fluoroscope robot, CT-like 3D-images can now be acquired. For this, the C-arm is rotated around the ROI in small discrete steps in an isocentric movement (see section IV-A.2). In each step a radiograph is taken. The rotation plane can be selected freely within the mechanical limits of the C-arm. The algebraic reconstruction technique (ART) algorithm [9] is then able to calculate a 3D model of the ROI in reasonable time. The achieved 3D resolution is sufficient for diagnostic means. Unlike the 3D-reconstruction introduced in [10], only images are necessary to create a sufficient 3D image of the target. Furthermore, the distance between ROI and detector-screen can be varied freely and is not fixed. Fig. 10. (Semi-)automatic aquisation of images for intrasurgical CT calculation. V. DISCUSSION AND FUTURE WORK Up to now most experiments and evaluations were done in computer simulation. (see section IV). Our aim is to bring this simulation into practice. The C-arm we are working on is now equipped with actors and encoders for all

8 joints. The communication is based on a common fieldbus system. A first version of our software allows for moving the C-arm to specified positions with variable joint speeds. Recent implementation of the repositioning, longbone application (see figures 7 and 9), and CT data collection showed promising results. The latest version of our simulation program already includes an interface to the C-arm, so that the real fluoroscope can be steered from the simulator GUI. The approach we introduced here should help assist the surgeon. Therefore the human-machine-interface must be as intuitive as possible to prevent mistakes and allow for minimal stress during surgery. For the next generation, the GUI of the simulator has to be optimized for OR usage. A force-torque sensor controlled drive-mode will allow for manual positioning, smooth the movements, and achieve weight compensation for the operator. Emergency couplers have to be integrated to ensure safety and mobility in critical situations like power failures. Further safefty issues are discussed and are subject of improvement in future steps. VI. CONCLUSION In the project presented here, we have solved the inverse kinematic problem for a common fluoroscopic C-arm. This is the basis for many applications which can assist the users during everyday work. These applications aim at simplifying the workflow and reducing radiation dose. We successfully evaluated a first selection of applications on our computer simulation. Repositioning, longbone application and CT-data collection were also tested successfully in reality on our C-arm. The results were presented. Next steps will include implementation of further applications and acquisation of user feedback for improvement. ACKNOWLEDGMENT The authors would like to thank Ziehm-Imaging for the Vision 3D we use for our experiments and also for the assistance in this project. We also want to thank all surgeons involved for their ideas, advices, and feedback. REFERENCES [1] G. Muhlmann, A. Klaus, W. Kirchmayr, H. Wykypiel, A. Unger, E. Holler, H. Nehoda, F. Aigner, and H. Weiss, Davinci robotic-assisted laparoscopic bariatric surgery: is it justified in a routine setting? Obesity Surgery, vol. 13, no. 6, pp , [2] J. Pransky, Surgeon s realizations of robodoc, Industrial Robot, vol. 25, no. 2, pp , [3] J. R. Adler, A. Schweikard, M. Murphy, and S. Hancock, Image-Guided Stereotactic Radiosurgery: The Cyberknife. Barnett, G., Roberts, D., Guthrie, B. (ed.), McGraw Hill, [4] H.-J. Siegert and S. Bocionek, Robotik: Programmierung intelligenter Roboter. Springer-Verlag, [5] R. Gross, N. Binder, and A. Schweikard, Röntgen-C-Bogen Simulator, Proc. Computer-unterstützte Radiologie und Chirurgie, [6] C. Brack, H. G otte, F. Gosse, J. Moctezuma, M. Roth, and A. Schweikard, Towards Accurate X-Ray-Camera Calibration in Computer- Assisted Robotic Surgery, Proc. Int. Symp. Computer Assisted Radiology (CAR), pp , 1996, paris. [7] C. Brack, R. Burgkart, A. Czopf, H. Götte, M. Roth, B. Radig, and A. Schweikard, Radiological Navigation in Orthopaedic Surgery, Rechnergestützte Verfahren in Orthopädie und Traumatologie, pp , 1999, steinkopf-verlag. [8] Z. Yaniv and L. Joskowicz, Long bone panoramas from fluoroscopic x-ray images, IEEE Transactions on Medical Imaging, vol. 23, pp , [9] P. Toft, The Radon transform - Theory and Implementation, Ph.D. Thesis, Department of Mathematical Modelling, Section for Digital Signal Processing, Technical University of Denmark, [10] D. Ritter, M. Mitschke, and R. Graumann, Intraoberative soft tissue 3D reconstruction with a mobile c-arm, International Congress Series 1256, pp , 2003.