Optimization of Gamma Knife Radiosurgery Michael Ferris University of Wisconsin, Computer Sciences David Shepard University of Maryland School of Medicine

Overview Details of machine and problem Formulation –modeling dose –shot / target optimization Results –Two-dimensional data –Real patient (three-dimensional) data

The Leksell Gamma Knife

Problem characteristics Machine has 201 radiation sources focussed on one location Very accurate dose delivery Benefits of computer solution –uniformity of treatment plan –better treatment plan –faster determination of plan

Problem outline Target volume (from MRI or CT) Maximum number of shots to use –Which size shots to use –Where to place shots –How long to deliver shot for –Conform to Target (50% isodose curve) –Real-time optimization

Two-dimensional example

Ideal Optimization

Dose calculation Measure dose at distance from shot center Fit a nonlinear curve to these measurements Functional form from literature, 6 parameters to fit via least-squares

8mm shot

18mm shot

MIP Approach A-priori fix possible shot locations

MIP Problem

Size Problem Dose(NonTarget) ~= Dose(Rind) Too many shots –Generate grid of large shots grid spacing grid offset –Small shots randomly placed nr boundary –Proportion of each?

Features of MIP Large amounts of data/integer variables Shot location on 1mm grid too restrictive Time consuming, even with restrictions and CPLEX but... have guarantee of global optimality

Nonlinear Approach

Two-stage approach Approximate via “arctan” First, solve with approximation, then fix shot widths and reoptimize

3D slice image

Slice + 3

Axial slice Manual Computer Optimized

Axial slice Manual Computer Optimized

Coronal slice Manual Computer Optimized

Sagittal slice Manual Computer Optimized

Challenges Integration into real system Reduction of optimization time What if scenarios? –Improve the objective function –Change number of shots Global versus local solutions