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

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

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)

Pencil Beam Redefinition
DX Z Z+DZ X-Y planes are spaced 5 mm apart on Z axis

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

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

Polyenergetic Spectrum

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

Polyenergetic PBRA

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

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

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

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

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

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

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

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

Beam Modeling electron source SADvir custom beam collimation L0
isocenter patient

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

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

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

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

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

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

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

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

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

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

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

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

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.

Custom Bolus / Skin Collimation

Custom Bolus / Skin Collimation

Custom Bolus / Skin Collimation

Custom Bolus / Skin Collimation

Electron Arc Therapy

Skin Collimation

Arc Therapy with Skin Collimation

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

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

Local Pencil-Beam Divergence

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

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

Arc Beam Modeling

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

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.