Studies of optimization methods for dose delivery with a beam scanning system

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

2. 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) Alexei Trofimov XXXVI PTCOG

3. 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 Alexei Trofimov XXXVI PTCOG

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

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

6. Converting a discrete spectrum into a continuous one • d-vector approximation • Triangular approximation Alexei Trofimov XXXVI PTCOG

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

8. Calculated dose difference (d-vector approximation) Alexei Trofimov XXXVI PTCOG

9. 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 (D), range of variation in the weight map, scanning path. • Generally, smaller for finer D/s values Alexei Trofimov XXXVI PTCOG

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

11. start 1 iteration 100 iterations 10 iterations Results of the optimization Alexei Trofimov XXXVI PTCOG

12. Results of the optimization f(i)= S(x,y) [ ( Di - DTPS)2 / DTPS ] Alexei Trofimov XXXVI PTCOG

13. Optimization for a quasi-continuous path: W0 = WTPS f(D); f = or Iteration # i: Delivered dose:Di = Wi g(s) Optimized beam weight for a quasi-continuous set of points (x,y) along the scanning path: Wi+1 (x,y) = Wi(x,y)*[DTPS(x,y)/Di(x,y)] Alexei Trofimov XXXVI PTCOG

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

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

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

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

18. Another example: spacing D = 1.5*s d-vector approximation optimized (100 iterations) Alexei Trofimov XXXVI PTCOG

19. Results of the optimization Alexei Trofimov XXXVI PTCOG

20. 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 Alexei Trofimov XXXVI PTCOG