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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

- 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 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?

- 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 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.

- 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

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

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))]

Without the „momentum term”

With the „momentum term”

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

Δwjk+1 = –η δQ/δwjk+ α Δwjk

Initialization

Mean square error Q calc.

Weights change

NO

Q < tolerance ?

Derivative δQ/δw calc.

YES

Results

Depth dose [%]

Depth [mm]

Difference<1%

~1 MeV

Relative contribution to PDD

Relative difference [%]

Energy [MeV]

Depth [mm]

- 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).

Fitted spectra

Known spectrum

Relative contribution to PDD

Energy [MeV]

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.

- 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.

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

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

Measured dose higher than it arises form MC simulations!

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.

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