1. Motion Planning in Stereotaxic Radiosurgery A. Schweikard, J.R. Adler, and J.C. Latombe Presented by Vijay Pradeep

2. Tumor = bad Brain = good Critical Section = good & sensitive Minimally invasive procedure that uses an intense, focused beam of radiation as an ablative surgical instrument to destroy tumors Radiosurgery Problem

3. Radiosurgery Methods – Single Beam Radiation Single Beam: - High Power along entire cylinder - Damages lots of brain tissue

4. Dose from multiple beams is additive Radiosurgery Methods – Multiple Beams - Intersection of beams is spherical - Energy is highest at tumor Radiation

5. LINAC System

6. Goal: –Determine a set of beam configurations that will destroy a tumor by cross firing at it Parameters: –Assume Spherical Tumor –LINAC Kinematics (Only Vertical Great-Circle Arcs) –Minimum angle of separation between arcs –Min # Of Arcs Critical Tumor Problem Statement

7. Obstacle Representation Similar to Trapezoidal Decomposition - Represent with half-sphere - Project obstacles onto surface - Find criticality points - Draw arcs

8. Criteria ω – Minimum spacing between arcs N – Number of great circle arcs K – Minimum free length of each arc Path Planning 0 2π2ππ Great Circle Plane Angle Free Length s1s1 s2s2 s3s3 s4s4 s5s5 s6s6 K

9. Criteria ω – Minimum spacing between arcs N – Number of great circle arcs K – Minimum free length of each arc Path Planning 0 2π2ππ Great Circle Plane Angle s1s1 s2s2 s3s3 s4s4 s5s5 s6s6 K ωωω p1p1 p2p2 p3p3 p4p4 p6p6 Free Length

10. Results Manually PlannedAutomatically Planned

11. Non-Spherical Tumors Approximated by multiple independent spherical targets Plan for each spherical tumor is computed and executed independently.

12. Takes advantage of structure/simplicity –Uses idea of criticality on obstacles vertices –Constrained to Vertical Great-Circle Arcs –Assumes independent spherical tumors –Plans for feasibility, not optimality Elegant, but not necessarily easiest –Actually samples 128 points and chooses the best under constraints Take Aways