Optimisation of Irradiation Directions   in IMRT Planning Rick Johnston Matthias Ehrgott Department of Engineering Science...
What is Radiotherapy?
<ul><li>Intensity modulation -  improves treatment quality  </li></ul><ul><li>Inverse planning problem -  conflicting obje...
Model Formulation <ul><li>Discretisation of Body and Beam </li></ul>Voxels Bixels gantry
Angle Discretisation <ul><li>Linearises the problem </li></ul><ul><li>A number of LPs to be solved  </li></ul><ul><li>Repl...
MOMIP Model <ul><li>Data </li></ul><ul><li>L 1   =   lower bound in tumour </li></ul><ul><li>U k   =   upper bound in orga...
<ul><li>min (T 1 ,...,T K ) </li></ul><ul><li>D 1  = P 1 x    (L 1  - T 1 ) 1   </li></ul><ul><li>D k  = P k x    (U k  ...
Solution Methods   <ul><li>Two-phase Methods </li></ul><ul><li>3. Set Covering </li></ul><ul><li>4. LP Relaxation </li></u...
Integrated Methods <ul><li>CPLEX 7.0 </li></ul><ul><li>If  R  increases problem becomes easier, objective value improves <...
<ul><li>Optimal solution of MIP problem </li></ul>Isodose curve pictures obtained with prototype software developed at ITW...
Integrated Methods <ul><li>Alter each gantry position in turn to find better angles </li></ul><ul><li>Steepest descent wit...
Local Search Movie
Two-phase Methods <ul><li>Intuitive </li></ul><ul><li>Considers all angles </li></ul><ul><li>Relatively quick </li></ul>Fu...
<ul><li>min  C 1 y 1 +...+ C S y S </li></ul><ul><li>Ay      1 </li></ul><ul><li>y    {0,1} </li></ul><ul><li>a ij =1 if...
<ul><li>Cost coefficients   </li></ul>
<ul><li>Set Covering Solution </li></ul><ul><li>MIP Solution </li></ul>
Two-Phase Methods <ul><li>LP RELAXATION </li></ul>4 Optimal solution of LP relaxation 10-40 beams used
 
Results <ul><li>All methods were successful in generating good treatment plans in a reasonable timeframe (10 min) </li></u...
<ul><li>Solution with equidistant beams </li></ul><ul><li>Solution with optimised beams </li></ul>
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 Proble...
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  ...
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  • Welcome. Name, supervisor, conjunction with Auckland Hospital.
  • Contrary public opinion, radiotherapy nothing do with radios. Three Treatments for cancer, local to area. Successful 60%, non-metastastised localised cancers. What going talk about today
  • Starship Enterprise. Machine, bed interaction. Gantry turns. Number of Irradiation Directions. Auckland Hospital; welcome! Long setup times.
  • Represents 2-d version what just saw. Bixels – intensity across the beam. Voxels, break up body into homogeneous segments. LP formulation, specify maximum dose to healthy organs, min dose tumour
  • Creates linear problem from high-dimensional multi-extremal non-linear optimisation. (CLICK) Number of positions used picked by planners (say three). Large no. of LPs. Better approach than other papers in field.
  • Two main approaches.
  • MIP: each possible angle has a boo var associated. Allow only fixed number of boo variables be ‘on’ then solve. Problems. Very slow improve on initial solution. Failed find feasible integer solution in difficult problems. Priority list, improved search techniques (no time)
  • Set is the volume of the tumour, aim to cover tumour with radiation. Aim: replicate planner decision strategies. Aim for gaps. Results: good for low number of insertion points. Generalised SC and Distribution methods.
  • Phase 1: allow irradiation from any number of directions Phase 2: use heuristics to consider only a few of these directions. Includes Local Search
  • Imrt

    1. 1. 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
    2. 2. What is Radiotherapy?
    3. 3. <ul><li>Intensity modulation - improves treatment quality </li></ul><ul><li>Inverse planning problem - conflicting objectives to irradiate tumour without damage to healthy organs </li></ul>IMRT
    4. 4. Model Formulation <ul><li>Discretisation of Body and Beam </li></ul>Voxels Bixels gantry
    5. 5. Angle Discretisation <ul><li>Linearises the problem </li></ul><ul><li>A number of LPs to be solved </li></ul><ul><li>Replicates physical setup </li></ul>
    6. 6. MOMIP Model <ul><li>Data </li></ul><ul><li>L 1 = lower bound in tumour </li></ul><ul><li>U k = upper bound in organ k </li></ul><ul><li>R = number of directions to be used </li></ul><ul><li>Variables and functions </li></ul><ul><li>Intensity vector x = (x 11 ,...,x HN ) </li></ul><ul><li>Direction choice vector y = (y 1 ,...,y H ) </li></ul><ul><li>Deviation vector T = (T 1 ,...,T K ) </li></ul><ul><li>Dose distribution vectors D k = (D k1 ,...,D kMk ) </li></ul>
    7. 7. <ul><li>min (T 1 ,...,T K ) </li></ul><ul><li>D 1 = P 1 x  (L 1 - T 1 ) 1 </li></ul><ul><li>D k = P k x  (U k + T k ) 1 , k=2,...,K </li></ul><ul><li>x hi  My h , h=1,…,H, i=1,…,N </li></ul><ul><li>y 1 + ...+y H  R </li></ul><ul><li>y h  {0,1} h=1,...,H </li></ul><ul><li>T, x  0 </li></ul>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
    8. 8. Solution Methods <ul><li>Two-phase Methods </li></ul><ul><li>3. Set Covering </li></ul><ul><li>4. LP Relaxation </li></ul><ul><li>Integrated Methods </li></ul><ul><li>1. Mixed Integer Formulation </li></ul><ul><li>2. Local Search Heuristics </li></ul>
    9. 9. Integrated Methods <ul><li>CPLEX 7.0 </li></ul><ul><li>If R increases problem becomes easier, objective value improves </li></ul><ul><li>For small R and small angle discretisation often no feasible solution found </li></ul>MIP SOLVER 1
    10. 10. <ul><li>Optimal solution of MIP problem </li></ul>Isodose curve pictures obtained with prototype software developed at ITWM, Kaiserslautern
    11. 11. Integrated Methods <ul><li>Alter each gantry position in turn to find better angles </li></ul><ul><li>Steepest descent with randomised starting angles </li></ul><ul><li>Solve LP for each selection of angles </li></ul>LOCAL SEARCH 2
    12. 12. Local Search Movie
    13. 13. Two-phase Methods <ul><li>Intuitive </li></ul><ul><li>Considers all angles </li></ul><ul><li>Relatively quick </li></ul>Fully irradiate every voxel in the tumour Avoid damage to healthy organs Benefits: SET COVERING 3
    14. 14. <ul><li>min C 1 y 1 +...+ C S y S </li></ul><ul><li>Ay  1 </li></ul><ul><li>y  {0,1} </li></ul><ul><li>a ij =1 if and only if beam j hits voxel i </li></ul><ul><li>Weighted angle method </li></ul><ul><li>C j is sum of  k /U k over all organs at risk and voxels in beam j </li></ul><ul><li>Dose deposition method </li></ul><ul><li>C j is sum of  k P k (i,j)/U k over all voxels and all organs at risk </li></ul>
    15. 15. <ul><li>Cost coefficients </li></ul>
    16. 16. <ul><li>Set Covering Solution </li></ul><ul><li>MIP Solution </li></ul>
    17. 17. Two-Phase Methods <ul><li>LP RELAXATION </li></ul>4 Optimal solution of LP relaxation 10-40 beams used
    18. 19. Results <ul><li>All methods were successful in generating good treatment plans in a reasonable timeframe (10 min) </li></ul><ul><li>Optimal beams were often counterintuitive </li></ul><ul><li>Angle optimisation is important if few beams to be used </li></ul>
    19. 20. <ul><li>Solution with equidistant beams </li></ul><ul><li>Solution with optimised beams </li></ul>
    20. 21. 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
    21. 22. 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

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