X-ray Target Reconstruction for Cyber Knife Radiosurgery Assignment for CISC/CMPE 330 We will perform radiosurgery of multipole liver tumors under X-ray guidance with the Cyber Knife (CK) system. The patient underwent biopsy earlier. During biopsy, we secured an ~8-mm long metal clip in each tumor, in order to mark the location of the cancer for treatment. Now we will treat the tumor with Cyber Knife. The soft tumor is not visible in X-ray, but the implanted metal clips produces visible marks in X-ray. We will use Cyber Knife (www.accuray.com), which is an X-ray image guided robot that aims a 6MEV linear accelerator (linac) at the tumor target marker by the metal clip. In the room image below, the flat panel detectors are hidden below the white floor board. The robot, X-ray and linac have been co-registered, meaning that points localized in the coordinate frame of the X-ray are known in the coordinate frame of the robot & linear accelerator. In order to aim the linac, we must reconstruct the position of each target clip from the X-ray images. Your task is to reconstruct the location of the targets in the coordinate frame of the X-ray unit. We will irradiate a spherical region with the linac. In order to kill microscopic disease, we must radiate tissue with 5mm margin around the tumor. For this exercise, we assume that each marker is in the center of the tumor, each tumor is spherical with a diameter of 20 mm. The linac can treat a sphere of 35 mm in diameter. In the X-ray unit, the source-detector distance is SDD=200cm, the source-axis distance is SAD=100 cm. Each detector is circular with a diameter of 40cm, distortion-free flat panel detectors. +y +x Cyber Knife (CK) coordinate system
Input images & coordinate systems Assumptions In each image, the k-th target has been segmented as S k (u,v), where u and v are measured from center of the X-ray beam The beam center is at (0,0) v The (u,v) image coordinates have been converted to metric coordinates by knowing the pixel size. We know the detector s position in CK coordinate space beam center at (0,0) u Target S k (u,v). We know the source position in CK coordinate space There is no distortion in the X-ray images, we use flat panel detectors Coordinate Systems You are free to choose your coordinate systems as you like, so long they are uniquely defined right handed orthonormal systems. The convention recommend is the following: The patient is in supine position on the table +z axis points from toe to the head +x axis points toward the right hand The k-th target has been segmented as S k (u,v), where u and v are measured from center of the X-ray beam +y axis points to the ceiling The two beam central lines intersect in the center of the CK coordinate system The detector/source unit rotates about the +z axis of the CK by +/- 45 degrees The detector s u-axis and the CK s z-axis vector are the same At zero rotation, the detector s v-axis and CK x axis vectors are the same. 2
Questions and Problems maxtre Compute the clinically acceptable maximum target reconstruction error (maxtre) which still guarantees complete coverage of the tumor. Later, when a target is reconstructed with an error greater than maxtre, we will flag it as a reconstruction failure. Make a drawing, derive math, compute, explain. It is sufficient to do a manual computation, no need for MATLAB program. Workspace: Compute the radius of the spherical workspace (Rmax), the largest sphere that can be fully imaged with this device. Make a drawing, derive math, compute, explain. It is sufficient to do a manual computation, no need for MATLAB program. Correspondence: Discuss two different methods for solving the correspondence problem in X-ray target reconstruction. Explain each method step by step, discuss their merits and limitations. How can you resolve target reconstruction ambiguity in general and in Cyber Knife s X-ray imaging system? You will generate MATLAB program and modules. You are responsible for designing proper I/O for all those. Refrain from hard wiring constants such as SSD, SAD, X-ray angles in the code, make them global variables, etc. Otherwise, you design what goes in and comes out, explain in comments. Comment your code richly, add explanation step by step. RECONSTRUCTOR Design and implement a MATLAB module to reconstruct the location of a small point-like target from a pair of X-ray images. We assume that in each image, the location of the target was previously segmented. As part of the module, design and implement a suitable residual error (REM) metric to measure the quality of target reconstruction. GENERATOR Design and develop MATLAB module that generates N random target points inside the spherical workspace of the X-ray imager, with equal probability within the workspace. PROJECTOR Design and develop MATLAB module that projects a target point onto the pair of detector planes. Test the projector software by running it on a handful of simulated target points and make a 3D plot in the CK imaging coordinate system, including: CK imaging coordinate system axes, detector coordinate system axes, spherical workspace (transparent), target points, detectors, sources, beam centrals, and the projected target points. If the plot gets too busy, add switches to turn on/off some features. Rotate the scene, examine if the plot is qualitatively correct. Take a screen shots from representative views. 3
Questions and Problems (continued) SIMULATOR Note that for the purpose of testing the Reconstructor, we do not need to create actual images; it is sufficient to generate the segmented target locations in each image (that you will feed to the Reconstructor). This this end, develop the SIMULATOR module to generate a pair of segmented target locations in each image from a target point give in the CK coordinate system. To this end, use your Projector, then transform the projected target points from CK coordinates to detector coordinates to create target image points on each detector. Then add target image points a random image segmentation error of maximum Emax. Adding this error will simulate imperfection in picking the location of the marker in the X-ray images, which is the primary source of reconstruction error in the CK imaging system. ANALYZER Design and implement a MATLAB module to analyze the performance of target reconstruction on the synthetic data. The Analyzer should call the Simulator and Reconstructor; compute the target reconstruction error (TRE) for each target as the distance between the simulated and reconstructed target positions and compute the failure rate (FR) as the ratio of the number of unacceptably erroneous reconstructions over the number of target points. We must choose a suitable N for the number of simulated target points. N needs to be sufficiently large to have enough statistical power, but sufficiently small for MATLAB to handle the problem conveniently in terms of runtime and array sizes. N=50 appears to be sufficient for our purpose. Run the Generator, Simulator and Reconstructor with Emax=0, which simulates geometrically perfect input data. Ascertain that targets are reconstructed perfectly with REM 0 and TRE 0 for all simulated targets. Run the Simulator, Reconstructor and Analyzer with Emax = (0,1, 2, 3.. ) in 1.0 mm steps, until you start receiving large reconstruction failure rates. Because in real life in an operating room we will not have ground truth TRE, the only way to flag a failed target reconstruction is by REM. Hence we must examine if/how REM is able to estimate TRE and to flag a unacceptably erroneous reconstructions. Plot avgrem, avgtre and FR as function of Emax. Analyze the trends and explain your findings. For each target across the range of Emax (0,1,2,3 mm), plot the TRE as a function of REM, mark the maxtre value in the graph. Analyze the graph and determine if/how and with what limitations you could use REM to estimate TRE and, crucially importantly, to flag unacceptably erroneous reconstructions. 4
General Instructions Always explain how you solve a problem. Use drawings, math formulas, text, block diagram, pseudo code - anything that you find them appropriate to convey your ideas. I must know that you understand what you are doing and I must be able to follow your reasoning. Depending on the quality and depth of your reasoning and discussion or results you may pick (or lose) lots of points. Write proper header and richly comment your code. There is no such thing as too much comment. Good style and neatness will earn you valuable points. The lack of these will cause reduction. Consider the validity (or deformity) of the input data, incomplete testing will lead to deduction of marks. Test each module, construct several test cases with known ground-truth answer. Write a testing m file(s) for each module or problem. Capture the output, to show that your program does what it is supposed to do. Make plots and tables when requested or when they makes sense. Add explanation text as you see it useful. Use decimal digits sensibly and consider what is precision is practical for the given problem. Generally, resolution finer than 0.1 millimeter is not practically achievable in such a surgical navigation system, so this should be your limit. Use decimal floating point format in your outputs. Do not use exponential number format. Create MATLAB functions for recurring tasks Submit the m files and the captured output file, as well as any drawing, or supplemental information you feel relevant. Also to remember: Submit all in one zip file named LastName_hw2.zip Put all.m files in the same folder Always include a main.m that calls all other files in order to test. Do not expect me ort the TA punch in parameters from the command line. Cleary identify the input and output. Always include a PDF report answering all questions and providing the required analysis of the results. (No long essays are needed, all questions can be answered in a couple of sentences.) If you include images, please limit their size 5
X-ray Target Reconstruction for Cyber Knife Radiosurgery MaxTRE drawing, math, compute 5 Total 5 Workspace drawing, math, compute 5 Total 5 Correspondence Explain method 1, with merits and limits 4 Explain method 1, with merits and limits 4 Ambiguity 2 Total 10 RECONSTRUCTOR Transform from detector to CK coordinates 5 Construct back projector lines 5 Compute intersection 5 Compoute REM 5 Total 20 Generator PROJECTOR SIMULATOR ANALYZER design and implement in MATLAB 5 Total 5 project to detectrors 5 testing plots 15 Total 20 transform from CK to detector 5 Add random image segmentation error 5 Total 10 Implement analyzer w/ TRE and FR 5 Run & test with Emax=0 2 Run with Emax = (0,1, 2, 3.. ) 4 Plot avgrem, avgtre, FR vs Emax 3 Analyze & explain 3 Plot TRE vs REM 3 Analyze & explain 5 Total 25 TOTAL 100