Derivation of initial electron beam energy spectrum
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Derivation of initial electron beam energy spectrum. Janusz Harasimowicz Establishment for Nuclear Equipment. http:// www.zdaj.com. Electron beams. Range of electrons depends on the energy.

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Derivation of initial electron beam energy spectrum

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Derivation of initial electron beam energy spectrum

Derivation of initial electron beam energy spectrum

Janusz Harasimowicz

Establishment for Nuclear Equipment

http://www.zdaj.com


Electron beams

Electron beams

  • Range of electrons depends on the energy.

  • Percentage depth dose curve shapedepends oncontribution ofparticular energies of particles directed onto the water phantom surface.


Electron beam energy

Electron beam energy

  • Electron beam mean energy at phantom surface can be derived, ex. IAEA TRS 381:

    E0 [MeV] = 0.818 + 1.935 RJ50 + 0.040 (RJ50)2 [cm]

  • However, direct measurement of full energy distribution of the beam is difficult and accelerator time consuming.Cannot be performed in oncologydepartment.

  • Is it possible to get information about initial electron beam energy spectrum from the water phantom measurements?


Energy spectrum derivation

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.


Measurements

Measurements

  • Measurements were performed forColine 15 accelerator (Establishmentfor 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.


Monte carlo

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


Error backpropagation algorithm

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 Σi[mi – Σj(wjcij)]2

mi→ depth dose measured at the i-th point

cij→ depth dose calculated at the i-th point for the j-th energy bin

wj→ weight of the j-th energy bin


Error backpropagation algorithm1

Error backpropagation algorithm

Q = 0.5 Σi[mi – Σj(wjcij)]2

δQ/δwj = Σi[–cij (mi – Σj(wjcij))]

Δwj = –η δQ/δwj

Δwj = η Σi[cij (mi – Σj(wjcij))]


Error backpropagation algorithm2

Without the „momentum term”

With the „momentum term”

Error backpropagation algorithm

To speed up the fitting procedure,a „momentum term” was added:

Δwjk+1 = –η δQ/δwjk+ α Δwjk


Fitting procedure

Fitting procedure

Initialization

Mean square error Q calc.

Weights change

NO

Q < tolerance ?

Derivative δQ/δw calc.

YES

Results


Results

Results

Depth dose [%]

Depth [mm]

Difference<1%

~1 MeV

Relative contribution to PDD

Relative difference [%]

Energy [MeV]

Depth [mm]


Results1

Results

  • 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).


Uncertainty analysis

Uncertainty analysis

Fitted spectra

Known spectrum


Uncertainty analysis1

Uncertainty analysis

Relative contribution to PDD

Energy [MeV]


Other results

Other results

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.


Conclusions

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.


Conclusions1

Conclusions

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


Appendix build up region

Appendix: Build-up region

Difference in the build-up region:2-4%

Measured dose higher than it arises form MC simulations!


Appendix build up region1

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 for6-21 MeV electron beams delivered witha Siemens Primus accelerator with the jaws wide open and no applicator.Agreement was much better with diode measurements.


Appendix build up region2

Appendix: Build-up region

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


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