An efficient method to predict and include Bragg curve degradation due to lung-equivalent materials in Monte Carlo codes by applying a density modulation

Sub-millimetre-sized heterogeneities such as lung parenchyma cause Bragg peak degradation which can lead to an underdose of the tumor and an overdose of healthy tissue when not accounted for in treatment planning. Since commonly used treatment-planning CTs do not resolve the fine structure of lungs, this degradation can hardly be considered. We present a mathematical model capable of predicting and describing Bragg peak degradation due to a lung-equivalent geometry consisting of sub-millimetre voxels filled with either lung tissue or air. The material characteristic 'modulation power' is introduced to quantify the Bragg peak degradation. A strategy was developed to transfer the modulating effects of such fine structures to rougher structures such as 2 mm thick CT voxels, which is the resolution of typically used CTs. This is done by using the modulation power to derive a density distribution applicable to these voxels. By replacing the previously used sub-millimetre voxels by 2 mm thick voxels filled with lung tissue and modulating the lung tissue's density in each voxel individually, we were able to reproduce the Bragg peak degradation. Hence a solution is found to include Bragg curve degradation due to lung-equivalent materials in Monte Carlo-based treatment-planning systems.