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Application of a Semi-Empirical Formula to Determine Spread Out Bragg Peak Factors and Range Shifter Factors From Measured Depth Dose Curves for Passively Scattered Proton Beams

N Sahoo*, S Dhanesar, F Poenisch, M Lii, H Li, X Zhang, R Amos, R Wu, M Gillin, X Zhu, M.D. Anderson Cancer Center, Houston, TX

SU-E-T-4 Sunday 3:00PM - 6:00PM Room: Exhibit Hall

Purpose: To apply two semi-empirical formulas to calculate the spread out Bragg peak ₍SOBP₎ factors ₍SOBPFs₎ and range shifter ₍RS₎ factors ₍RSFs₎ used for monitor unit calculation¹ of passively scattered proton beams ₍PSPB₎.

Methods:Following two recently developed² and refined formulas were used to calculate the SOBPFs and RSFs from measured depth dose curves for various options in our PSPB.
For a specific option,
SOBPF₍W₎₌PDDWr₍0₎/PDDW₍0₎.₍₍SSD+dcW₎/₍SSD+dcWr₎₎² .NSF ₍W₎.
For the same SOBP width and option, but for different RS thickness, t,
RSF ₍W, t₎ ₌ ₍₍SSD+dcWt₎/₍SSD+dcW₎₎².₍PDDW₍0₎/PDDW₍t₎₎. NSF₍W,t₎,
W is the width of the SOBP under consideration, Wr is the reference SOBP width relative to which other SOBPF are determined, SSD is the source to surface distance for the percentage depth dose ₍PDD₎ measurement, PDDWr₍0₎ and PDDW₍0₎ are PDDs at the surface, and dcW and dcWr are the depths of the centers of SOBP under consideration and reference SOBP respectively, t is the RS thickness, dcWt and dcW are the depths of the centers of SOBP under consideration with RS of thickness t and without any RS respectively, and PDDw₍t₎ and PDDw₍0₎ are the PDD at depth t and surface respectively for the SOBP width W for which the RSFs are being determined. NSF₍W₎ and NSF ₍W,t₎ accounts for the contribution of the nozzle elements including the aperture to the back scatter dose at the dose monitor.

Results:The SOBPFs and RSFs calculated using above formulas agreed within 2 percent with their respective measured values using an ionization chamber in a water tank for all of our clinically used options for PSPB.

Conclusion:The proposed formulas were found to be valid to calculate the required SOBPFs and RSFs for monitor unit calculation of PSPB fields from measured PDD curves.
¹N. Sahoo et. al, Med. Phys. 35, 5088, ₍2008₎.
²N. Sahoo et. al, IJROBP, 84₍3S₎ S849, ₍2012₎.

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