USING CONE BEAM RECONSTRUCTION AND SIMULATION TECHNIQUES
Захариас Камарианакис, Иван Булиев Резюме: Използването на интрамедуларни импланти е често срещана техника за лекуване на счупвания на фемурата и тибията. Най-критичната стъпка в подобна процедура е прецизното насочване и поставяне на подържащите. В настоящето изследване, с помощта на симулирани флуороскопски изображения от С-конзола, се прави опит да бъде намерен начин за идентифицирането на положението и посоката на отворите. Подобна информация може да се използва от робот, който автоматично да подходи и закрепи винтовете. В обкръжение на Matlab, върху две от проекциите, потребителя интерактивно посочва положението на отворите, на базата на което координатите на краищата на отворите се изчислява в 3D. Направена е реконструкция на импланта, която в последствие може да се използва за донастройване на ориентацията на оста на завинтване
Ключови думи: Томография с коничен профил на лъчите, интрамедуларни гвоздеи, визуално-насочвана хирургия
Abstract: Closed intramedullary nailing is the common technique for treatment of femur and tibia fractures. The most challenging step in this procedure is the precise placement of the lateral screws that stabilize the fragmented bone. In the present work, using fluoroscopic images from a common mobile C-arm, we try to accurately identify in 3-D space the axis that connects the nail holes. This information can be further used to guide a robot for drilling the bone along the nail openings. A software tool was constructed in Matlab. The user interactively selects with the mouse the points of interest in projection images. Then the simulation program provides the 3-D reconstruction of these points and marks the location found on the 3-D nail. Verification of the procedure described above was performed using FDKRC, an in-house software tool that reconstructed the intramedullary nail based on the well known FDK algorithm
Ключови думи: Cone beam reconstruction, intramedullary nail, image-guided surgery
Many non-CIS(Computer Integrated Surgery) devices have been developed for distal locking [2, 5]. Between others, proximally mounted targeting devices, mechanical guides, stereo fluoroscopy and optical and electro-magnetic navigation systems help in the location of the center of the distal locking nail holes. Moreover, fluoroscopy-based computer-assisted surgery (CAS) navigation systems try to help surgeon in aligning the drill axis with the distal locking nail hole axis. Robot-based CAS systems are designed to assist the surgeon in implementing a preoperative plan by mechanically positioning or sometimes executing the surgical action itself. Most of the above mentioned systems involve an optical or magnetic tracking unit for usually real-time relating the different coordinate systems referred in the procedures.
In this work we investigate a simpler procedure of nail holes identification using X-ray projections. We consider the intramedullary nail as a 3-D object and we try to accurately locate the axes of the screw holes, using at least two projection images.
II. MATERIALS AND METHODS Intramedullary nail and x-ray projections
The intramedullary nails used in healing tibial fractures have typical diameters of 8-12mm as the openings for the locking screws are placed in various locations and directions all around it. A 3D model of a nail, in the shape of a voxel matrix, with two aligned screw holes, was created and used during the simulations. The intramedullary nail was voxelized into a 190x190x190 array with a pixel size and slice thickness of 1 mm. Cone beam projections were generated using Simphan, an in-house a software tool for radiographic imaging investigations. This investigative software tool can be used to simulate the entire radiological process, including the imaged object, imaging modalities, operating parameters, beam transport. It provides sufficient accuracy and flexibility to allow its use in a wide range of approaches, being of particular help in the design of an experiment and conducting first level trials. The simulated x-ray projections were acquired considering C-arm with the source-to-isocenter and source-to-detector distances 1000 mm and 1300 mm, respectively. 360 uniformly distributed projections of 400x400 pixels were acquired at 10 spacing.
FDK Cone Beam Reconstruction algorithm
The main advantage of cone beam algorithms is the reduction in data collection time. With a single source, ray integrals are measured through every point in the object in the time it takes to measure a single slice in a conventional two-dimensional scanner. The projection data Rβ(t, r) are a function of the source angle β , and the horizontal and vertical positions on the detector plane, t and r. A filtered backprojection algorithm was used, based on analyses presented in .The reconstruction is based on filtering and backprojecting a single plane within the cone for each elevation along the z – axis. The final three-dimensional reconstruction is obtained by summing the contribution to the object from all the tilted fan beams . An in-house software tool was used to reconstruct the intramedullary nail from a set of 360 projections, based on the well known FDK algorithm. This tool (FDKRC) was used mainly for the verification of the procedure described above. We present below the cone beam reconstruction algorithm FDK  that has been implemented in C++ in the core of FDKRC software tool.
The user interactively selects with the mouse the points of interest in two images of his choice, from the projections set. In this paper the selected images concern projections taken at 00 and 900 where the region of interest (nail holes) clearly appeared. Then the simulation program provides the 3-D reconstruction of these points and marks the location found on the 3-D nail. The reconstruction of these points is based on the following geometric facts.
Figure 1.The couple source-detector rotated at 0 and 900.
It is considered that the two lines presented in figure 1 coincide in point Q in 3-D space. These two distinct rays generated from the source and ended to the detector’s plane come true with the following parities.
Where P1(ΧP1, YP1, ZP1) and P2(ΧP2, YP2, ZP2) are the projections of point Q for gantry angles 0 and 900 respectively, while(ΧS1, YS1, ZS1) and (ΧS2, YS2, ZS2) state for the location of the point source of the C-arm for the same gantry angles. This system of equations provides the 3-D coordinates of point Q. Let A(XA,YA,ZA) is the center of the hole A and B(XB,YB,ZB) is the center of the hole B respectively.
The target is to find the vector AB which passes from the center of the hole A and to that of B respectively. The direction of vector where i,j,k refer to the system of coordinates of the C-arm and denote the direction of each main axis. The direction cosines of vector are , and where is the vector's norm. After the calculation of the hole axis we proceed with the recostruction of the intramedullary nail using the FDKRC program. The aim is to depict slices in the same or vertical direction as the one found before.This procedure works as a verification step. Figure 2 depicts the suggested sequence of activities that was tested trough simulations.
Figure 2. Flow diagram of the performed activities.
III. Results The user interactively selects with the mouse the points of interest in the two images (red crosses in figure 3).Then the simulation program provides the 3-D reconstruction of these points and marks the location found on the 3-D nail. Figure 3 visually presents the successful identification of the nail-holes. The red crosses on the nail are marks from user’s selections on it, while in the lower side of the figure, the 3-D nail with the reconstructed points (showed with pink color are showed. Previous studies  showed that the mean error and the standard deviation of the direction of the nail-axis is 1.25 ± 0.65 degrees, after 40 interactive user interventions. Based on these facts we proceed further in this work with the incorporation of the approximate cone beam CT reconstruction algorithm, FDK
Figure 3. Interactive simulation of points of interest and 3-D marking on the nail after backprojection
Figure 4. Cone beam reconstruction of the intramedullary nail along the plane vertical to the hole axis that was calculated in figure 5.
More precisely, we reconstruct (backproject) a slice in 3-D volume that is perpendicular to the direction found from clicking to the projection images, as shown in figure 6, using the FDKRC software tool. Furthermore a slice perpendicular to the latter one was reconstructed. Figures 5 and 6 show a “small” deviation of the calculated axis and the one that exists in the reconstructed image.
Figure 6. Recostructed slice perpendicular to that showed in figure 5, showing the nail axis.
IV. Discussion and Conclusions The nail hole axis was located. The cone beam reconstruction of the intramedullary nail along the plane vertical to the hole axis showed satifactory results. It should be mentioned that the overall accuracy of the system depends on the accuracy of the points selection in the projection images as well as the accuracy of the reconstruction algorithm that is used. The user selects points until the specified location is accurately defined.
Previous study  concluded that averaging of a series of point selections (up to 40) activity improves the accuracy of axis determination. However, this is not practical since no physician will accept that. An approach that comes out of this study seems more practical. Using image processing, on nail tomograms in perpendicular to the determined axis direction, automatic hole center detection can be applied, monitored and eventually used for refinement of the position and the orientation of the axis.
V. Acknowledgments The authors would like to express their thanks to the program PENED 2003 for funding the above work.
K. Bliznakova, “Study and development of software simulation for X-ray imaging”, Ph.D. dissertation, Dept. Medical Physics, University of Patras, Greece, 2003
L.Joskowicz and R.H.Taylor, “Computers in imaging and guided surgery”, Computers in Science and Engineering, 3(5) 2001, pp 65-72.
Z.Kamarianakis, “Simulation of robotic procedure for intramedullaray nail locking”, Master Thesis, Dept. Medical Physics, Patras University, Greece, 2006
Z.Kamarianakis, Ivan Buliev, “Identification of Intramedullary nail holes for orthopedic procedures”, Proceedings of the 5th European Symposium on Biomedical Engineering Patras 2006, July 7-9 Patras.
Eric J. Hazan and L.Joskowicz, “Computer Assisted Image-Guided Intramedullary Nailing of Femoral Shaft Fractures”, Techniques in Orthopaedics, 18(2), 2003.
L.A. Feldkamp, L.C. Davis, J.W. Kress: “Practical cone-beam algorithm”, J. Opt. Soc. Am. A. 1(6): 612-619, 1984
A. C. Kak and M.Slaney, “Principles of Computerized Tomographic Imaging”, IEEE Press 1987.