1. The Use of Equivalent Uniform Dose constraints in IMRT Thomas Bortfeld 1 , Christian Thieke 1,2 , Yair Censor 3 1 Department of Radiation Oncology, Massachusetts General Hospital, Boston, USA 2 Department of Medical Physics, Deutsches Krebsforschungszentrum, Heidelberg, Germany, 3 Department of Mathematics, University of Haifa, Israel

3. Maximum dose constraint Volume Dose D max

4. "Positivity projector": penalty (weight) dose at voxel i in OAR k tolerance dose Penalty function: Constraints: Maximum (tolerance) doses "The spinal cord should get less than 40 Gy."

5. Small penalty ( w ) Volume Dose d max Large penalty ( w ) DVH Volume d max Dose DVH

6. Constraints: Minimum and tolerance doses

7. Volume Dose DVH d max d min

8. Non-intensity-modulated (4 beams, non-coplanar, MLC) Intensity-modulated (9 beams, coplanar) Brainstem Brainstem Target Target Example: Clivus chordoma

9. NTCP = 7% NTCP = 0.7% Example: Clivus chordoma Non-intensity-modulated (4 beams, non-coplanar, MLC) Intensity-modulated (9 beams, coplanar) Brainstem

10. Target volume Lungs Spinal cord Transversal view Target Spinal cord Lung Lung Technique: 9 beams, coplanar, intensity-modulated Example: Thyroid

11. Example: Thyroid

12. Volume Dose DVH d max V max

13. Constraints: Dose-volume constraints "No more than 1/3 of the lung should get more than 15 Gy."

14. Why are DVH constraints non-convex? Critical structure consisting of 2 voxels d 1 d 2 Not more than 50% of the volume (1 voxel) should get more than 30 Gy 30 Gy 30 Gy feasible region d 1 d 2

16. Violation of DVH constraint Volume Dose DVH d max V max  d

17. Modified penalty function: Interval constraint projector: Constraints: Dose-volume constraints Bortfeld et al., ICCR 1997

19. Example: Thyroid

21. Volume effect Whole lung: 18 Gy 50% of lung: 35 Gy

22. Volume effect Power-law relationship for tolerance dose (TD): n small: small “volume effect” n large: large “volume effect”

23. Arbitrary (not 0/1) dose distributions 0 25 50 75 100 0 20 40 60 Volume [%] Dose [Gy] 80 100 EUD = The homogeneous dose that gives the same clinical effect Lung: EUD = 25 Gy Spinal Cord: EUD = 52 Gy

26. Volume effect -> EUD, Power-Law (a-norm) Model “ a -norm” (a=1/n) Mohan et al., Med. Phys. 19(4), 933-944, 1992 Kwa et al., Radiother. Oncol. 48(1), 61-69, 1998 Niemierko, Med. Phys. 26(6), 1100, 1999 Examples:

28. POCS – Projection onto convex set x x d 2 d 1 D Convex set D‘

29. EUD constraint II Volume Dose

30. EUD constraint II Volume Dose

32. EUD projector: Lagrange multiplier

35. Initialization Organ Constraint d pres ({organ}) = ... d pres ({organ}) = ... d pres ({organ}) = ... all organs processed? Adjoint dose calculation Dose calculation Calc. objective function converged ? End Max/min DVH EUD no yes no yes

36. POCS – Example Serial Organ

37. POCS – Example Serial/Parallel Organ

38. POCS – Example Target

39. Example: Head and neck case Brainstem Spinal Cord Parotis

40. Results 58.8 61.0 13.1 Max=13.0 Parotis Min=60.0 Max=61 Target 25.5 Max=25.5 Spinal Cord 23 Max=23 Brainstem EUD (Gy) EUD-Constraint (Gy) Organ

41. Results

43. Pre-calculated D ij matrix Voxel i Bixel j Source Patient

45. POCS, Censor & Elfving: Scaled gradient projection (TBNN):

46. Physical dose only, Patient 1

47. Physical dose only, Patient 2

48. EUD only, Patient 1

49. EUD only, Patient 2

51. Conclusions

52. Optimization Iteration 1

53. Optimization Iteration 1

54. Optimization Iteration 1

55. Optimization Iteration 1

56. Optimization Iteration 1

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58. Optimization Iteration 2

59. Optimization Iteration 2

60. Optimization Iteration 2

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62. Optimization Iteration 2

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65. Optimization Iteration 2

66. Optimization Iteration 2

67. Optimization Iteration 3

68. Optimization Iteration 3

69. Optimization Iteration 3

70. Optimization Iteration 3