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

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**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)

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**Pencil Beam Redefinition**

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

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**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

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**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

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**Polyenergetic Spectrum**

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**PBRA Correction Factor C(E)**

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

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Polyenergetic PBRA

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**20-MeV Horizontal Bone Slab**

Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

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**20-MeV Horizontal Bone Slab**

Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

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**20-MeV Horizontal Air Slab**

Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

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

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**20-MeV Vertical Air Slab Off-axis profile at 4.5 cm depth**

Varian Clinac 2100, 15x15-cm2 open applicator, 102 cm SSD

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

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**9-MeV Nose Surface Off-axis profile at 1 cm depth**

Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

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**PBRA Evaluation with Measured Data Set - Results**

PBRA was not able to achieve 4% or 2 mm dose calculation accuracy for all data points

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**Beam Modeling electron source SADvir custom beam collimation L0**

isocenter patient

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**Dual-Source Beam Modeling**

primary electron source secondary electron source custom beam collimation isocenter patient

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**Dual-Source Model - 100 cm SSD**

Varian Clinac 1800, 9 MeV, 6x6-cm2 open applicator

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**Dual-Source Model - 110 cm SSD**

Varian Clinac 1800, 9 MeV, 6x6-cm2 open applicator

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

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

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

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

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**Parotid Gland - Transverse View**

Varian 2100, 16 MeV, 15x15-cm2 applicator, 100 cm SSD

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**Parotid Gland - Transverse View**

Varian 2100, 16 MeV, 15x15-cm2 applicator, 100 cm SSD

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**Ethmoid Sinuses - Transverse Plane**

Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

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**Ethmoid Sinus - Transverse Plane**

Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

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**Ethmoid Sinus - Profile at Y = 13.0 cm**

Varian 2100, 16 MeV, 10x10-cm2 applicator, 100 cm SSD

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**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.

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**Custom Bolus / Skin Collimation**

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**Custom Bolus / Skin Collimation**

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**Custom Bolus / Skin Collimation**

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**Custom Bolus / Skin Collimation**

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Electron Arc Therapy

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Skin Collimation

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**Arc Therapy with Skin Collimation**

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**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

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**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

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**Local Pencil-Beam Divergence**

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**20-MeV Horizontal Air Slab**

Varian Clinac 2100, 15x15-cm2 open applicator, 100 cm SSD

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**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

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Arc Beam Modeling

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**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

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**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.

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