Tracked surgical drill calibration

Transcription

1 Tracked surgical drill calibration An acetabular fracture is a break in the socket portion of the "ball-and-socket" hip joint. The majority of acetabular fractures are caused by some type of highenergy impact, such as a car collision or motorcycle accident. Treatment for acetabular fractures often involves surgery to restore the normal anatomy of the hip and stabilize the hip joint. The x-ray shows an acetabular fracture fixated with screws and plates. Watch a video of the surgery as executed by an experienced orthopedic trauma surgeon here: The success of the surgery, to a large degree, depends on the accuracy of the placement of the screws. We will use a tracked surgical navigation system assist in the drilling. We will instrument an electric bone drill with reflective beads for tracking. The beads are tracked in real-time with an optical stereo camera connected to a computer. We will use this drill to create pilots holes for the bone screws, navigated in real-time with respect to the CT images. F d When we attach the markers to the drill, we do not know exactly where the markers are relative to the drill tip and drill axis. So we must calibrate the tracked drill before using it in the operating room. During calibration, we will assign a drill coordinate system (F d ) to the markers and experimentally determine the position of tool tip T d and the direction vector of the drill axis v d in the F d drill coordinate system. T d You will design, develop and test methods and software for the calibration of a tracked drill. This is considered a fundamental skill in computer-integrated surgery. v d 1

2 1. Navigation coordinate system transformations Prior to surgery, we drill a post into the pelvis and attach multimodal markers that are visible in CT and can be tracked by an infrared camera in the OR. We also track the drill as explained previously. In the OR during surgery, we want to draw in real-time a simple model of the drill bit (tip and axis) over the fractured bone reconstructed from CT, in order to guide the surgeon in the drilling process. This requires computing the drill tip and drill axis in CT coordinates. Annotate the figure below with the requisite coordinate frame transformations, explain and write up the math to compute the drill tip and drill axis vector in CT coordinates. Submit your drawings and writing. (10 pts) COMPUTER SCREEN F m OPERATING ROOM FT Drill bit F m F d T CT v CT F CT 2

3 2. Calibrator We bring the assembled drill to the lab for calibration. The drill is fully operational and a disposable sharp-point drill bit is secured in the drill head. You can use only the following tools for the calibration process: Tracked drill, Optical tracker & coordinate measurements from the tracker; Thick wooden bench top that you can scratch, cut, or drill holes into; Computer with MATLAB. NOTES: We discussed the tracked tool calibration process in class. We discussed the constrained motions for both tool tip and axis calibration. We discussed the resulting trajectories on which the markers travel during these constrained motions. We discussed how one can reconstruct these trajectories from measured marker positions in tracker frame (i.e. measurement space). We discussed how one can compute the calibration parameters from these, by transforming the reconstructed drill tip and drill axis vector from tracker space to marker space. We discussed redundancies present in the setup and how to take advantage of that; we discussed how we detect if the constraints fail. Drill Tip Calibrator: Design and implement a suitable calibration process for the drill tip. (20 pts) 1. Explain the calibration process step by step with using figures, sketches, words, block diagram, etc. anything that you find appropriate to convey your thinking. Explain the nature of the constrained motion you chose and why you chose it and how you will model these constrained motions mathematically. (4pt) 2. Explain how you would detect if the enforcement of the constraint failed. (You do not have to implement it.) (2 pts) 3. Explain how you would detect if there was excessive error in tracking of the markers. (You do not have to implement it.) (2 pts) 4. Implement the calibration software in MATLAB. Input: array of (A,B,C) markers. Output: T d (12 pts) Drill Axis Calibrator: Design and implement a calibration process for the drill axis. (20 pts) Repeat the same steps as above for the drill axis. Input: array of (A,B,C) markers. Output: v d 3

4 3. Simulator DRILL MODEL: Below is a model of a tracked bone drill for simulation. (In reality, the placement of markers is unknown, which is why the drill must be calibrated.) Let the center of the model coordinate system (F mod ) be in the drill tip, the z axis be in the drill axis pointing from drill tip to drill base. A, B, and C are the marker locations in cm units. (Also note that in real life, we would not allow A,B,C to be an isosceles triangle, but such a little simplification is permissible here.) Compute Drill Frame (F d ): You are free to fix F d anywhere relative to (A,B,C), so long it is a unique orthonormal coordinate system. Input: (A,B,C). Output: Ctr d and base vectors (x d y d z d. ). Compute these and draw the result in the figure below. (5 pts). Compute Ground Truth: Use this model to compute the ground truth calibration parameters in the F d coordinate system, v d for drill axis and T d for drill tip. Compute these and draw the result in the figure below. These will be your ground truth in testing the calibrator. (5 pts). z mod F mod C (5, 0, 26) B (11,0, 20) A (5,0, 20 ) y mod x mod In the simulator, you are free place the F t tracker coordinate system anywhere with respect to the F mod drill model coordinate system. For convenience, I recommend that you place F t to coincide with the F mod. Drill Tip Simulator: Design and implement software to generate calibration poses that satisfy the requirements of your drill tip calibration module developed earlier. Design the number, range and distribution of calibration poses, explain your choices by generously commenting your code. The output is a series of (A t,b t,c t ) markers, representing simulated marker positions in F t tracker coordinate system. (5 pts) Drill Axis Simulator: Design and implement software to generate calibration poses that satisfy the requirements of your drill axis calibration module developed earlier. Design the number, range and distribution of calibration poses, explain your choices by generously commenting your code. The output is a series of (A t,b t,c t ) markers, representing simulated marker positions in F t tracker coordinate system. (5 pts) 4

5 4. Calibration Ground Truth Test Drill Tip Calibration Test: Run the Drill Tip Simulator and feed the simulated poses to the Drill Tip Calibrator, and ascertain that it the resulting T m and the ground truth are practically identical. (5 pts) Drill Axis Calibration Test: Run the Drill Axis Simulator and feed the simulated poses to the Drill Axis Calibrator, ascertain that it the resulting v m and the ground truth are practically identical. (5 pts) 5. Calibration Accuracy Analysis Acetabular fracture fixation is a delicate procedure in which the required drill calibration accuracy is 1 mm for the drill tip and 2 degrees for the drill axis. Run your simulators to generate marker positions for drill tip and axis calibration. Blend a random error of maximum E trac on the simulated marker positions. Make the direction of the error vector random and its magnitude constant E trac. Feed the simulated poses to the calibrator and compute T m, v m ; and do this by gradually increasing E trac from 0, in 1mm steps. (10 pts) Make graphs between E trac and the calibration errors both tip and axis. Determine the level of maximum tracking error (E trac ) when the calibration is no longer clinically satisfactory. (10 pts) General Rules As before... Read the online syllabus for general instructions on the submission of assignments.. 5