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Derivation of initial electron beam energy spectrum Janusz Harasimowicz Establishment for Nuclear Equipment http://www.zdaj.com

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Electron beams Range of electrons depends on the energy. Percentage depth dose curve shape depends on contribution of particular energies of particles directed onto the water phantom surface.

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Electron beam energy Electron beam mean energy at phantom surface can be derived, ex. IAEA TRS 381: E 0 [MeV] = 0.818 + 1.935 R J 50 + 0.040 (R J 50 ) 2 [cm] However, direct measurement of full energy distribution of the beam is difficult and accelerator time consuming. Cannot be performed in oncology department. Is it possible to get information about initial electron beam energy spectrum from the water phantom measurements?

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Energy spectrum derivation Proposed method: PDD measurement. Simulation of dose distribution for mono- energetic beams (Monte Carlo method). Derivation of each simulated beam contribution to measured PDD curve shape (error backpropagation algorithm). Calculated weights of particular simulated PDD curves should give information about real energy spectrum distribution.

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Measurements Measurements were performed for Coline 15 accelerator (Establishment for Nuclear Equipment ZdAJ, Poland) for ”12 MeV” (nominal) electron beam. To minimize energy losses, scattering foils and applicator were removed and jaws were set for 40 cm x 40 cm field. Water phantom RFA-300 (Scanditronix) and plane-parallel ionization chamber NACP-02 (Scanditronix) were used.

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Monte Carlo BEAMnrc Monte Carlo code was used: Modified Coline 15 treatment head model. Radiation source: parallel circular electron beam with 2D Gaussian XY distribution (2 mm FWHM) directed onto the exit vacuum window. Water phantom at SSD=100 cm. Depth dose curves calculated for monoenergetic beams in energy range from 1 MeV to 15 MeV with 250 keV interval. Weighted sum of simulated PDDs was fitted to measured PDD curve (inverse Monte Carlo). Rogers DWO, Faddegon BA, Ding GX, Ma C-M, Wei J, Mackie TR. BEAM: A Monte Carlo code to simulate radiotherapy treatment units. Medical Physics 1995 22:503-524

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Error backpropagation algorithm Used error backpropagation algorithm is based on minimization of difference between measured and simulated values as stated by equation: Q = 0.5 Σ i [m i – Σ j (w j c i j )] 2 m i → depth dose measured at the i-th point c i j → depth dose calculated at the i-th point for the j-th energy bin w j → weight of the j-th energy bin

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Error backpropagation algorithm Q = 0.5 Σ i [m i – Σ j (w j c i j )] 2 δQ/δw j = Σ i [–c i j (m i – Σ j (w j c i j ))] Δw j = –η δQ/δw j Δw j = η Σ i [c i j (m i – Σ j (w j c i j ))]

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Error backpropagation algorithm To speed up the fitting procedure, a „momentum term” was added: Δw j k+1 = –η δQ/δw j k + α Δw j k Without the „momentum term” With the „momentum term”

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Fitting procedure Initialization Mean square error Q calc. Derivative δQ/δw calc.Q < tolerance ? Weights change Results YES NO

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Results Difference <1% ~1 MeV Depth dose [%] Depth [mm] Relative contribution to PDD Energy [MeV]Depth [mm] Relative difference [%]

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Results NOTICE NOTICE: Difference in PDDs <1% is not equal to method uncertainty! Derivation of fitted energy uncertainty for any complicated case is rather difficult. However, one can try to estimate uncertainty by analysing matched simulated beams to the known results (ex. for monoenergetic spectrum).

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Uncertainty analysis Known spectrum Fitted spectra

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Uncertainty analysis Energy [MeV] Relative contribution to PDD

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Other results Source: Source: Deng J, Jiang SB, Pawlicki T, Li J, Ma C-M. Derivation of electron and photon energy spectra from electron beam central axis depth dose curves. Phys. Med. Biol. 46 (2001) Random creep algorithm used but more advanced method adapted: Four-source model for beam phase-space reconstruction. Separation of photons and electrons contribution to dose distribution. Would be interesting to check the method with error backpropagation algorithm.

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Conclusions It seems to be possible to derive energy from depth dose measurements in water phantom. But with what accuracy? Derived energy spectrum of Coline 15 is rather wide. Possible explanations: Large energy intervals (250 keV). Energy slit filter (located in the deflection system) has not been optimized yet (and perhaps too wide energy spectrum is getting to the exit vacuum window). Wrong source definition. Set up and measurement errors. Further studies are needed.

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Conclusions Scheme of Coline 15 energy slit filter (located in the deflection system)

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Appendix: Build-up region Measured dose higher than it arises form MC simulations! Difference in the build-up region: 2-4%

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Appendix: Build-up region Bruce Faddegon (UCSF Comprehensive Cancer Center, San Francisco) found similar differences of 2-4% in parallel- plate and simulated surface dose for 6-21 MeV electron beams delivered with a Siemens Primus accelerator with the jaws wide open and no applicator. Agreement was much better with diode measurements.

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Appendix: Build-up region Source: Source: Faddegon B, Schreiber E, Ding X. Monte Carlo simulation of large electron fields. Phys. Med. Biol. 50 (2005)

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