1. Pencil-Beam Redefinition Algorithm Robert Boyd, Ph.D.

2. Pencil Beam Algorithms
central axis of
broad beam (Z) X
pixel bounding pencil beams
(2x2 mm2 at isocenter) Y Z
X-Y plane normal to beam axis (Z)

3. Pencil Beam RedefinitionDX Z
Z+DZ
X-Y planes are spaced 5 mm apart on Z axis

4. PBRA Physics Primary electron transport only
delta-rays not modeled
Multiple Coulomb scattering approximated with a Gaussian distribution
large-angle scattering not modeled
Mean collisional energy loss only
catastrophic energy losses not modeled

5. PBRA Physics Approximations
PBRA requires measured central-axis depth dose curve
PBRA uses an energy-dependent correction factor C(E) to match calculated and measured central axis depth dose curve

6. Polyenergetic Spectrum

7. PBRA Correction Factor C(E)
Solid Line: Monoenergetic PBRA C(E)
Dashed Line: Polyenergetic PBRA C(E)

8. Polyenergetic PBRA

9. 20-MeV Horizontal Bone Slab
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

10. 20-MeV Horizontal Bone Slab
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

11. 20-MeV Horizontal Air Slab
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

12. 20-MeV Vertical Air Slab
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

13. 20-MeV Vertical Air Slab Off-axis profile at 4.5 cm depth
Varian Clinac 2100, 15x15-cm2 open applicator, 102 cm SSD

14. 20-MeV Nose Surface
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

15. 9-MeV Nose Surface Off-axis profile at 1 cm depth
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

16. PBRA Evaluation with Measured Data Set - Results
PBRA was not able to achieve 4% or 2 mm dose calculation accuracy for all data points

17. Beam Modeling electron source SADvir custom beam collimation L0
isocenter
patient

18. Dual-Source Beam Modeling
primary electron
source
secondary electron
source
custom beam
collimation
isocenter
patient

19. Dual-Source Model - 100 cm SSD
Varian Clinac 1800, 9 MeV, 6x6-cm2 open applicator

20. Dual-Source Model - 110 cm SSD
Varian Clinac 1800, 9 MeV, 6x6-cm2 open applicator

21. IMC - Transverse Plane
Varian 2100, 16 MeV, 15x15-cm2 applicator, 105 cm SSD

22. IMC - Transverse Plane
Varian 2100, 16 MeV, 15x15-cm2 applicator, 105 cm SSD

23. IMC - Sagittal Plane
Varian 2100, 16 MeV, 15x15-cm2 applicator, 105 cm SSD

24. IMC - Sagittal Plane
Varian 2100, 16 MeV, 15x15-cm2 applicator, 105 cm SSD

25. Parotid Gland - Transverse View
Varian 2100, 16 MeV, 15x15-cm2 applicator, 100 cm SSD

26. Parotid Gland - Transverse View
Varian 2100, 16 MeV, 15x15-cm2 applicator, 100 cm SSD

27. Ethmoid Sinuses - Transverse Plane
Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

28. Ethmoid Sinus - Transverse Plane
Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

29. Ethmoid Sinus - Profile at Y = 13.0 cm
Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

30. Clinical Evaluation - Results
Accuracy criteria was not achieved for entire irradiated volume, albeit only a small volume (< 3.5%) had dose differences greater than 4% and greater than 2 mm DTA.
PBRA showed good agreement with Monte Carlo in matching isodose lines.
Better modeling of physics will improve the accuracy of PBRA-calculated dose.

31. Custom Bolus / Skin Collimation

32. Custom Bolus / Skin Collimation

33. Custom Bolus / Skin Collimation

34. Custom Bolus / Skin Collimation

35. Electron Arc Therapy

36. Skin Collimation

37. Arc Therapy with Skin Collimation

38. Pencil-Beam Divergence Current PBRA
virtual source distance is equal to distance to broad beam virtual source
mathematics assume “parallel”point beams
integration performed over projected area
svir Dx Dz

39. Pencil-Beam Divergence divPBRA
virtual source distance is a pencil beam-specific parameter
mathematics assume divergent point beams
integration performed over normal pixel width
svir Dx Dz

40. Local Pencil-Beam Divergence

41. 20-MeV Horizontal Air Slab
Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

42. Pencil-Beam Divergence Results
divPBRA was more accurate than PBRA for most data points
divPBRA was not able to achieve 4% or 2 mm accuracy for all data points
Calculation times were approximately 30% longer

43. Arc Beam Modeling

44. Future Work Dosimetry studies using PBRA
Tomotherapy vs. conventional electron therapy
Field matching for chest wall treatments
Electron arc therapy planning using divPBRA
Realistic dose deposition kernels using Monte Carlo
Automated custom bolus/skin collimation planning using PBRA
Translating PBRA to commercial system

45. Acknowledgements Kenneth Hogstrom, Ph.D. Almon Shiu, Ph.D.
Dennis Leavitt, Ph.D.
Mitch Price, M.S.
Melinda Chi, M.S
Paul Alderson, B.S.