optimization of gamma knife radiosurgery michael ferris university of wisconsin, computer sciences...

Optimization of Gamma Knife Radiosurgery

Michael FerrisUniversity of Wisconsin, Computer Sciences

David ShepardUniversity 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

mints;xs;ys

Dose(NonTarget)

subject to Dose(i; j ) =X

s2S

tsD(xs;ys; i; j )

1ô Dose(Target) ô 2ts õ 0Sj j ô N

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

1à m1 erf ( û1

xà r1) à m2 erf ( û2

xà r2)

8mm shot

Nonlinear ApproachLet xs;ys bevariable locations

s = 1;2;. . .;ND(xs;ys; i; j ) is nasty nonlinear function

What width shot touseat xs;ys?

s;w =1 if shot s is width w0 else

ú

T s;w ô ts;w ô T s;wPw s;w ô 1

Two-stage approach

• Approximate via “arctan”

• First, solve with approximation, then fix shot widths and reoptimize

-30 -20 -10 0 10 20 30-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

8s 2 SPwarctan(ts;w) ô 2

ù

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