Technical note: Extraction of proton pencil beam energy spectrum from measured integral depth dose in a cyclotron...

Proton pencil beam energy spectrum is an essential parameter for calculations of dose and linear energy transfer. We extract the energy spectrum from measured integral depth dose (IDD).

A measured IDD (measIDD) in water is decomposed into many IDDs of mono-energetic pencil beams (monoIDDs) in water. A simultaneous iterative technique is used to do the decomposition that extracts the energy spectrum of protons from the measIDD. The monoIDDs are generated by our analytic random walk model-based proton dose calculation algorithm. The linear independence of the monoIDDs is considered and high spatial resolution monoIDDs are used to improve their linear independence. To validate the extraction, first we use synthesized IDDs (synIDD) with Gaussian energy spectrum and compare the extracted energy spectrum with the Gaussian; second, for the energy spectrum extracted from measIDDs, the accuracy of the extraction is validated by comparing the calculated IDD from the energy spectrum with the measIDD. The measIDDs are derived from commissioning of a cyclotron proton pencil beam system with a Bragg peak ionization chamber. The nominal energy of the pencil beams is from 70 to 245 MeV. The monoIDDs are generated for energies from 0.05 to 275 MeV in steps of 0.05 MeV with a spatial resolution of 1 mm.

The difference of the extracted and original Gaussian energy spectrum peaked at 75 and 80 MeV was <1%. As the energy decreased, the difference increased but was reduced by using 0.1-mm monoIDDs. The difference was not sensitive to the energy interval of monoIDDs when the interval increased from 0.05 to 1 MeV. For the energy spectrum extraction from measIDDs, there was a main peak near the nominal energy but the spectrum was not in Gaussian distribution. In three example cases (70, 160, and 245 MeV), the relative differences of the measIDDs and calculated IDDs were within 3.4%, 2.9%, and 4.7% of the Bragg peak value, respectively. Fitting the spectrum by Gaussian distribution, we had σ = 0.87, 1.51, and 0.86 MeV, respectively, for these three examples, and the relative differences of the resultant calculated IDDs from the measIDDs were within 4.7%, 7.4%, and 4.5%, respectively.

Our algorithm accurately extracted the energy spectrum from the synIDDs and measIDDs. High-resolution monoIDDs are necessary to extract low-energy spectrum. Energy spectrum extraction from measIDD reveals important information for beam modeling.