Motion Planning in Stereotaxic

RadiosurgeryA. Schweikard, J.R. Adler, and J.C. Latombe

Presented by Vijay Pradeep

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

Radiosurgery Methods – Single Beam

Radiation

Single Beam:- High Power along entire cylinder- Damages lots of brain tissue

Dose from multiple beams is additive

Radiosurgery Methods – Multiple Beams

- Intersection of beams is spherical- Energy is highest at tumor

Radiation

LINAC System

• 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

Obstacle Representation

Similar to Trapezoidal Decomposition

- Represent with half-sphere- Project obstacles onto surface- Find criticality points- Draw arcs

Criteria• ω – Minimum spacing between arcs• N – Number of great circle arcs• K – Minimum free length of each arc

Path Planning

0 2ππGreat Circle Plane Angle

Free

Length

s1

s2

s3

s4

s5

s6

K

Criteria• ω – Minimum spacing between arcs• N – Number of great circle arcs• K – Minimum free length of each arc

Path Planning

0 2ππGreat Circle Plane Angle

s1

s2

s3

s4

s5

s6

K

ω ω ω

p1

p2

p3 p4

p6

Free

Length

Results

Manually Planned Automatically Planned

Non-Spherical Tumors

Approximated by multiple independent spherical targets

Plan for each spherical tumor is computed and executed independently.

• 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