Calculation of the Beam-Modulation Effect of the Lung in Carbon Ion and Proton Therapy With Deterministic Pencil Beam Algorithms

Ion beams passing through lung tissue show more pronounced energy straggling than expected for solid materials of the same thickness. Energy straggling in active scanning particle therapy can enlarge the pencil beam Bragg peaks in-depth as well as displace them, deteriorating the dose coverage of a target within the lung. While this is not yet considered in any known treatment planning system, we implement a mathematical model to be used for treatment planning using TRiP98, which relies on a deterministic pencil beam algorithm. Through a randomization process based on a continuous Poisson probability distribution, the HU values of lung voxels are replaced with a modified value in succesive iterations. The beam-modulation effect of the lung can thus be taken into account in treatment planning by recalculating the dose n times for n randomized CTs using the raster scan file of a plan which was optimized on the nonmodulated CT. The evaluation follows by averaging the resulting n dose distributions and comparing to the corresponding nonmodulated dose distribution attending at dosimetric indices and dose-volume histograms. In this work, the functionality of these routines was tested for proton and carbon ion plans for two selected lung cancer patient cases with deep-seated tumors, showing that with existing standard tools it is possible to calculate the beam-modulation effect of the lung in TRiP98 in a transparent way. Variable model parameters such as modulation power, voxel size and density voxel selection range were evaluated. Furthermore, a systematic study for spherical geometries in a lung tissue CT cube is presented to investigate general trends.