Optimisation of Irradiation Directions in IMRT Planning Rick Johnston Matthias Ehrgott Department of...
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Transcript of Optimisation of Irradiation Directions in IMRT Planning Rick Johnston Matthias Ehrgott Department of...
Optimisation of Optimisation of Irradiation DirectionsIrradiation Directions
in IMRT Planningin IMRT Planning
Rick JohnstonRick JohnstonMatthias EhrgottMatthias EhrgottDepartment of Engineering ScienceDepartment of Engineering ScienceUniversity of AucklandUniversity of Auckland M. Ehrgott, R. Johnston Optimisation of M. Ehrgott, R. Johnston Optimisation of
Irradiation Directions in IMRT Planning, OR Irradiation Directions in IMRT Planning, OR Spectrum 25(2):251-264, 2003Spectrum 25(2):251-264, 2003
What is Radiotherapy?What is Radiotherapy?
Intensity modulation - Intensity modulation - improves treatment improves treatment quality quality
Inverse planning problem - Inverse planning problem - conflicting conflicting
objectives toobjectives to irradiate tumour without damage to irradiate tumour without damage to healthy organshealthy organs
IMRTIMRT
Model FormulationModel Formulation
Discretisation of Body and BeamDiscretisation of Body and Beam
gantry
VoxelsVoxels
BixelsBixels
Angle DiscretisationAngle Discretisation
Linearises the Linearises the problemproblem
A number of LPs A number of LPs to be solved to be solved
Replicates Replicates physical setupphysical setup
MOMIP ModelMOMIP Model
DataData LL11 == lower bound in tumourlower bound in tumour UUkk == upper bound in organ upper bound in organ kk RR = number of directions to be used = number of directions to be used
Variables and functionsVariables and functions Intensity vector Intensity vector x = (xx = (x1111,...,x,...,xHNHN)) Direction choice vector Direction choice vector y = (yy = (y11,...,y,...,yHH)) Deviation vector Deviation vector T = (TT = (T11,...,T,...,TKK)) Dose distribution vectors Dose distribution vectors DDkk = (D = (Dk1k1,...,D,...,DkMkkMk))
min (Tmin (T11,...,T,...,TKK))
DD11 = P = P11x x (L (L1 1 - T- T11))11
DDk k = P= Pkkx x (U (Uk k + T+ Tkk))11, k=2,...,K, k=2,...,K xxhihi My Myhh, h=1,…,H, i=1,…,N, h=1,…,H, i=1,…,N
yy11+ ...+y+ ...+yHH R R
yyh h {0,1} h=1,...,H {0,1} h=1,...,H
T, x T, x 00
To study effect of direction optimisation consider To study effect of direction optimisation consider weighted sum min weighted sum min 11TT11+ + 22TT22 + ... + + ... + KKTTKK
Extension of multicriteria model by Hamacher/KüferExtension of multicriteria model by Hamacher/Küfer
Solution MethodsSolution Methods
Two-phase MethodsTwo-phase Methods
3. Set Covering3. Set Covering
4. LP Relaxation4. LP Relaxation
Integrated MethodsIntegrated Methods
1. Mixed Integer 1. Mixed Integer FormulationFormulation
2. Local Search 2. Local Search Heuristics Heuristics
Integrated MethodsIntegrated Methods
CPLEX 7.0CPLEX 7.0 If If RR increases problem becomes increases problem becomes
easier, objective value improveseasier, objective value improves For small For small RR and small angle and small angle
discretisation often no feasible discretisation often no feasible solution foundsolution found
MIP SOLVER1
Optimal solution of MIP problemOptimal solution of MIP problem
Isodose curve pictures obtained with Isodose curve pictures obtained with prototype software developed at prototype software developed at ITWM, KaiserslauternITWM, Kaiserslautern
Integrated MethodsIntegrated Methods
Alter each gantry position in turn to find Alter each gantry position in turn to find better anglesbetter angles
Steepest descent with randomised starting Steepest descent with randomised starting anglesangles
Solve LP for each selection of anglesSolve LP for each selection of angles
LOCAL SEARCH2
Local Search MovieLocal Search Movie
Two-phase MethodsTwo-phase Methods
IntuitiveIntuitive Considers all anglesConsiders all angles Relatively quickRelatively quick
Fully irradiate every voxel in the tumour
Avoid damage to healthy organs
Benefits:Benefits:
SET COVERING3
min min CC11yy11+...++...+CCSSyySS
AyAy 11
yy {0,1}{0,1}
aaijij=1 if and only if =1 if and only if beam beam jj hits voxel hits voxel i i
Weighted angle methodWeighted angle method
CCjj is sum of is sum of kk/U/Ukk over all organs over all organs at risk and voxels in beam at risk and voxels in beam jj
Dose deposition methodDose deposition method
CCjj is sum of is sum of kkPPkk(i,j)/U(i,j)/Ukk over all over all voxels and all organs at riskvoxels and all organs at risk
Cost coefficientsCost coefficients
Com parison of Cost Coefficients
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340
An gle (degrees)
Cost(WeightedAngle)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Cost(DoseDeposition)
W eighted Angle M ethod
Dose Deposition M ethod
Set Covering SolutionSet Covering Solution MIP SolutionMIP Solution
4 Two-Phase MethodsTwo-Phase MethodsLP RELAXATIONLP RELAXATION
Optimal solution ofOptimal solution ofLP relaxationLP relaxation10-40 beams used10-40 beams used
ResultsResults
All methods were successful in All methods were successful in generating good treatment plans in a generating good treatment plans in a reasonable timeframe (10 min)reasonable timeframe (10 min)
Optimal beams were Optimal beams were often counterintuitiveoften counterintuitive
Angle optimisation is Angle optimisation is important if few beams important if few beams to be usedto be used
Solution with Solution with equidistant beamsequidistant beams
Solution with Solution with optimised beamsoptimised beams
ComparisonComparisonO
bje
ctiv
e
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Problem 1 3 heads Problem 1 4 heads Problem 2 3 heads Problem 2 4 heads Problem 3 3 heads
Set CoveringLP relaxationLocal SearchMixed Integer
Objective vs. TimeObjective vs. TimeO
bje
ctiv
e
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 2000 4000 6000 8000 10000 12000
Time (s)
Local search improvement
Set Covering
Local Search
LP relaxation
Mixed Integer