1. Studies of optimization methods for dose delivery with a beam scanning system Alexei Trofimov, Thomas Bortfeld Northeast Proton Therapy Center MGH, Boston

2. Alexei Trofimov XXXVI PTCOG Beam scanning at the NPTC First tests have been conducted in collaboration with IBA last week Use the IBA scanning system for delivery Inverse treatment planning with KonRad (DKFZ)

3. Alexei Trofimov XXXVI PTCOG Treatment planning and delivery For each layer w/in target, treatment planning system generates a discrete beam weight map for regularly spaced pencil beam spots Scanning within a layer is continuous Fluence variation along the path is achieved by simultaneously varying the beam current and scanning speed

4. Alexei Trofimov XXXVI PTCOG Example: plan for a NPTC patient (medulloblastoma, 3D plan with 2cm-FWHM beam) boost sp.cord target hypoth. cochlea

5. Alexei Trofimov XXXVI PTCOG Example: plan for a NPTC patient (RPO field, spot spacing  =  = 8.5 mm) beam weight map dose distribution at B.p. range

6. Alexei Trofimov XXXVI PTCOG Converting a discrete spectrum into a continuous one  vector approximation Triangular approximation

7. Alexei Trofimov XXXVI PTCOG Difference between planned and delivered doses Along a scanning path element, delivered dose has pseudo-gaussian profile, different from the planned gaussian spot

8. Alexei Trofimov XXXVI PTCOG Calculated dose difference (  vector approximation)

9. Alexei Trofimov XXXVI PTCOG Difference between the planned and delivered doses The discrepancy is maximal in the regions of sharp dose gradient (rim of the target, boost) Size of the discrepancy depends on TPS spot spacing ( , range of variation in the weight map, scanning path. Generally, smaller for finer  /  values

10. Alexei Trofimov XXXVI PTCOG Spot weight optimization Planned dose (conv. of TPS weight map with a gaussian) D TPS = W TPS  g(  ) I teration #i: Delivered dose (convolution with a pseudo-gaussian) D i = W i  [ g(  )  f(  ) ]; f= or Optimized beam weight map for spots at (x,y) : W i+1 (x,y) = W i (x,y) * [ D TPS (x,y) / D i (x,y) ]

11. Alexei Trofimov XXXVI PTCOG Results of the optimization start1 iteration 10 iterations 100 iterations

12. Alexei Trofimov XXXVI PTCOG Results of the optimization f(i)   =  (x,y) [ ( D i - D TPS  ) 2 / D TPS ]

13. Alexei Trofimov XXXVI PTCOG Optimization for a quasi-continuous path: W 0 = W TPS  f(  ); f = or Iteration # i: Delivered dose: D i = W i  g(  ) Optimized beam weight for a quasi-continuous set of points (x,y) along the scanning path : W i+1 (x,y) = W i (x,y) * [ D TPS (x,y) / D i (x,y) ]

14. Alexei Trofimov XXXVI PTCOG Results of the optimization For a quasi-continuous weight variation along the path 20 iterations start

15. Alexei Trofimov XXXVI PTCOG Optimization results for one scanning line

16. Alexei Trofimov XXXVI PTCOG Another example: PA field  -vector approximation optimized (100 iterations)

17. Alexei Trofimov XXXVI PTCOG Another example: LPO field  -vector approximation optimized (100 iterations)

18. Alexei Trofimov XXXVI PTCOG Another example: spacing  1.5 *   -vector approximation optimized (100 iterations)

19. Alexei Trofimov XXXVI PTCOG Results of the optimization Spot spacing (  ) Maximal dose difference (%) Before optimization Optimized on targetpenumbra 0.5 *  < 1 0.10.3 0.75 *  1.5 0.30.7 1.0 *  2.50.51.2 1.25 *  3.5 12.5 1.5 *  61.54 2.0 *  1048

20. Alexei Trofimov XXXVI PTCOG Summary Simulation shows that a good dose conformity can be achieved by optimizing the TPS beam weight maps discrepancy reduced 3-fold on the target, 2-fold in the penumbra (from 1-6%) no need to use finer grid Plan to verify the results with the beam