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