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Med Phys. 2012 Nov;39(11):6726-37. doi: 10.1118/1.4757578.

A pencil beam algorithm for helium ion beam therapy.

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  • 1Christian Doppler Laboratory for Medical Radiation Research for Radiation Oncology, Medical University of Vienna, Vienna, Austria.



To develop a flexible pencil beam algorithm for helium ion beam therapy. Dose distributions were calculated using the newly developed pencil beam algorithm and validated using Monte Carlo (MC) methods.


The algorithm was based on the established theory of fluence weighted elemental pencil beam (PB) kernels. Using a new real-time splitting approach, a minimization routine selects the optimal shape for each sub-beam. Dose depositions along the beam path were determined using a look-up table (LUT). Data for LUT generation were derived from MC simulations in water using GATE 6.1. For materials other than water, dose depositions were calculated by the algorithm using water-equivalent depth scaling. Lateral beam spreading caused by multiple scattering has been accounted for by implementing a non-local scattering formula developed by Gottschalk. A new nuclear correction was modelled using a Voigt function and implemented by a LUT approach. Validation simulations have been performed using a phantom filled with homogeneous materials or heterogeneous slabs of up to 3 cm. The beams were incident perpendicular to the phantoms surface with initial particle energies ranging from 50 to 250 MeV/A with a total number of 10(7) ions per beam. For comparison a special evaluation software was developed calculating the gamma indices for dose distributions.


In homogeneous phantoms, maximum range deviations between PB and MC of less than 1.1% and differences in the width of the distal energy fall off of the Bragg-Peak from 80% to 20% of less than 0.1 mm were found. Heterogeneous phantoms using layered slabs satisfied a γ-index criterion of 2%/2mm of the local value except for some single voxels. For more complex phantoms using laterally arranged bone-air slabs, the γ-index criterion was exceeded in some areas giving a maximum γ-index of 1.75 and 4.9% of the voxels showed γ-index values larger than one. The calculation precision of the presented algorithm was considered to be sufficient for clinical practice. Although only data for helium beams was presented, the performance of the pencil beam algorithm for proton beams was comparable.


The pencil beam algorithm developed for helium ions presents a suitable tool for dose calculations. Its calculation speed was evaluated to be similar to other published pencil beam algorithms. The flexible design allows easy customization of measured depth-dose distributions and use of varying beam profiles, thus making it a promising candidate for integration into future treatment planning systems. Current work in progress deals with RBE effects of helium ions to complete the model.

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