Proton Dose Calculation Algorithm

Jinsung Kim, Ph.D jinsung.k@gmail.com

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Dose Modeling?

• 우리가  가진  방사선원에  대한  특징을    • 정확히  모사할  수  있는  Simulation  Tool!  !

• 일반적으로  MC가  가장  정확하다고  알려져있지만,  • 속도에  대한  부분이  해결이  어렵기  때문에  • 필요한  가정(!!)들을  포함하여  • 간단+정확한  모델로  만들어서    • 환자  체내의  선량을  계산해  내는  수식(?)  만들기!    • 필요에  따라  변수들  조절

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Proton Dose!

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SMC NozzleQuadrupole

magnet

Wobbling magnet

Dose monitor 2D monitor

MLC

Block

He gas duct

Quadrupole magnet

Wobbling magnet

Dose monitor 2D monitor Dose monitor

2D monitor

Quadrupole magnet

Scanning magnet

Scatterer

Ridge filter

MLC

Block

Compensator Block

Wobbling (scattering) Scanning Scanning

MultiPurpose Nozzle (G1)

PBS dedicated Nozzle (G2)

Proton Dose Modeling• Passive Scattering • Scanning • Monte-Carlo Simulation

6http://vimeo.com/aapm/343

Reference• Hong L, Goitein M, Bucciolini M, Comiskey R, Gottschalk B, Rosenthal S, Serago C

and Urie M 1996 A pencil beam algorithm for proton dose calculations Phys. Med. Biol. 41 1305–30

• B. Schaffner, E. Pedroni, and A. Lomax, “Dose calculation models for pro- ton treatment planning using a dynamic beam delivery system: An attempt to include density heterogeneity effects in the analytical dose calculation,” Phys. Med. Biol. 44, 27–41 (1999)

• M. Soukup, M. Fippel, and M. Alber, “A pencil beam algorithm for in- tensity modulated proton therapy derived from Monte Carlo simulations,” Phys. Med. Biol. 50, 5089–5104 (2005)

• Kimstrand P, Traneus E, Ahnesjo ̈A, Grusell E, Glimelius B and Tilly N 2007 A beam source model for scanned proton beams Phys. Med. Biol. 52 3151–68

• Y. Li, X. R. Zhu, N. Sahoo, A. Anand, and X. Zhang, “Beyond Gaussians: A study of single-spot modeling for scanning proton dose calculation,” Phys. Med. Biol. 57, 983–997 (2012)

• Zhu XR1, Poenisch F, Lii M, Sawakuchi GO, “Commissioning dose computation models for spot scanning proton beams in water for a commercially available treatment planning system,” Med Phys. 2013 Apr;40(4):041723.

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Proton Scanning Modeling

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Depth Dose + Lateral Dosehttp://vimeo.com/aapm/343

Pencil Beam Algorithm

• Fluence(x,y,z) of Ek x Beamlet (x,y,d(z))

10Med Phys. 2013 Apr;40(4):041723

Pencil Beam’s Beamlet

• Interactions • Primary Proton

• elastic interaction with electron

• elastic proton-nucleus scattering

• Secondary Proton • nonelastic nuclear interaction

• secondary proton, other fragments

11Med Phys. 2013 Apr;40(4):041723

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• Stopping Power • Lateral distribution • Klat,pp : Multiple Coulomb Scattering • Molière theory

• is approximated by the sum of two Gaussian functions representing the scattering angles probability

• 2nd Gaussian describes the tail of the scattering distribution due to large angle scattering, which accounts for only 4% of the contributions

• Klat,sp : “Halo” dose • lateral dose distribution of the 2nd particles for the beamlet

and is represented by the 3rd Gaussian functionMed Phys. 2013 Apr;40(4):041723

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Sigma?

Definition of Sigma!

• 68-95-99.7 rule?

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2D Gaussian

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Double Gaussian Tuning!

• A, B, C for1st Gaussian • Sigma + Fitting

• A, B, C for 2nd Gaussian • Empirical

1. increase w2 to improve the agreements between measured and calculated FSFs for 3E (Low, Intermediate, High E)

2.A, B, C adjustment to match FSFs for 3E at 2 depth (2cm, proximal)

3.w2 was linearly interpolated for 17E & step 2 was repeated 4.w2 & A, B, C were linearly interpolated for 74E

• Not large enough to predict the FSFs18

Med Phys. 2013 Apr;40(4):041723

What’s Double Gaussian?

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• Y. Li, X. R. Zhu, N. Sahoo, A. Anand, and X. Zhang, “Beyond Gaussians: A study of single-spot modeling for scanning proton dose calculation,” Phys. Med. Biol. 57, 983–997 (2012)

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• Y. Li, X. R. Zhu, N. Sahoo, A. Anand, and X. Zhang, “Beyond Gaussians: A study of single-spot modeling for scanning proton dose calculation,” Phys. Med. Biol. 57, 983–997 (2012)

Lateral profiles of individual scanning spots modeled at various depths using the double- Gaussian functions and Cauchy–Lorentz component (solid lines) and double-Gaussian functions only (dashed lines). The measured lateral profiles at shallow, medium and deep depths are indicated by the circle, triangle and square markers, respectively. In the top plot (221.8 MeV), the red (gray) circles, green (gray) triangles, blue (dark) squares and the corresponding solid and dashed lines correspond to depths of 2, 19 and 30 cm, respectively. In the middle plot (181.1 MeV), the red circles, green triangles, blue squares and the corresponding lines correspond to depths of 2, 10 and 20 cm, respectively. In the bottom plot (72.5 MeV), the red circles, blue squares and the corresponding solid and dashed lines represent depths of 2 and 4 cm, respectively

PBS’s Beam Data ComparisonXio RayStation

IDDCs Min-Max 5~10 MeV step

Min-Max 1-2cm spacing

MUDose @ E same as IDDCs

2cm depth FS 10x10 (8x8), 2.5mm spacing

Dose @ E same as IDDCs Depth is between 1cm and one half

of the bragg peak max

VSAD Profiles @ least 3 planes

Spot 2D array or film In air, for E same as IDDCs

In air 5 planes recommendation(min:3)Profiles @ isocenter plane

Divergence @ isocenter, +-10 cm

With beam modifiers

Range shifter, ridge filter @ 3 planes (min, middle, max)

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RayStation’s PBS

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To Be Continue

오늘은 여기까지…

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