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

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

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

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

5. LINAC System

6. Problem Statement Goal: Parameters: Tumor Critical
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
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Critical
Tumor

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

8. Great Circle Plane Angle
Path Planning
Criteria
ω – Minimum spacing between arcs
N – Number of great circle arcs
K – Minimum free length of each arc s1 s2 s3 s4 s5 s6
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Free Length π 2π
Great Circle Plane Angle

9. Great Circle Plane Angle
Path Planning
Criteria
ω – Minimum spacing between arcs
N – Number of great circle arcs
K – Minimum free length of each arc s1 s2 s3 s4 s5 s6
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Free Length ω ω ω π 2π
Great Circle Plane Angle

10. Automatically Planned
Results
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Manually Planned
Automatically 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
Take Aways
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