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# Imrt

## by fondas vakalis, doctor/radiation oncologist at radiotherapy department on Mar 10, 2010

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## ImrtPresentation Transcript

• Optimisation of Irradiation Directions in IMRT Planning Rick Johnston Matthias Ehrgott Department of Engineering Science University of Auckland M. Ehrgott, R. Johnston Optimisation of Irradiation Directions in IMRT Planning, OR Spectrum 25(2):251-264, 2003
• Intensity modulation - improves treatment quality
• Inverse planning problem - conflicting objectives to irradiate tumour without damage to healthy organs
IMRT
• Model Formulation
• Discretisation of Body and Beam
Voxels Bixels gantry
• Angle Discretisation
• Linearises the problem
• A number of LPs to be solved
• Replicates physical setup
• MOMIP Model
• Data
• L 1 = lower bound in tumour
• U k = upper bound in organ k
• R = number of directions to be used
• Variables and functions
• Intensity vector x = (x 11 ,...,x HN )
• Direction choice vector y = (y 1 ,...,y H )
• Deviation vector T = (T 1 ,...,T K )
• Dose distribution vectors D k = (D k1 ,...,D kMk )
• min (T 1 ,...,T K )
• D 1 = P 1 x  (L 1 - T 1 ) 1
• D k = P k x  (U k + T k ) 1 , k=2,...,K
• x hi  My h , h=1,…,H, i=1,…,N
• y 1 + ...+y H  R
• y h  {0,1} h=1,...,H
• T, x  0
To study effect of direction optimisation consider weighted sum min  1 T 1 +  2 T 2 + ... +  K T K Extension of multicriteria model by Hamacher/Küfer
• Solution Methods
• Two-phase Methods
• 3. Set Covering
• 4. LP Relaxation
• Integrated Methods
• 1. Mixed Integer Formulation
• 2. Local Search Heuristics
• Integrated Methods
• CPLEX 7.0
• If R increases problem becomes easier, objective value improves
• For small R and small angle discretisation often no feasible solution found
MIP SOLVER 1
• Optimal solution of MIP problem
Isodose curve pictures obtained with prototype software developed at ITWM, Kaiserslautern
• Integrated Methods
• Alter each gantry position in turn to find better angles
• Steepest descent with randomised starting angles
• Solve LP for each selection of angles
LOCAL SEARCH 2
• Local Search Movie
• Two-phase Methods
• Intuitive
• Considers all angles
• Relatively quick
Fully irradiate every voxel in the tumour Avoid damage to healthy organs Benefits: SET COVERING 3
• min C 1 y 1 +...+ C S y S
• Ay  1
• y  {0,1}
• a ij =1 if and only if beam j hits voxel i
• Weighted angle method
• C j is sum of  k /U k over all organs at risk and voxels in beam j
• Dose deposition method
• C j is sum of  k P k (i,j)/U k over all voxels and all organs at risk
• Cost coefficients
• Set Covering Solution
• MIP Solution
• Two-Phase Methods
• LP RELAXATION
4 Optimal solution of LP relaxation 10-40 beams used
•
• Results
• All methods were successful in generating good treatment plans in a reasonable timeframe (10 min)
• Optimal beams were often counterintuitive
• Angle optimisation is important if few beams to be used
• Solution with equidistant beams
• Solution with optimised beams
• Comparison Objective 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 Covering LP relaxation Local Search Mixed Integer
• Objective vs. Time Objective 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