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

Abstract

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.

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

“…In another study [11] the effects on clinical treatment plans in proton beams were investigated using an analytical approach: Instead of using sets of modulated DICOM images and Monte Carlo tools, the pristine proton BPs were convolved using the MatRad toolkit [12] with several superimposed normal distributions of sigma values defined by certain modulation power values of the lung tissue. The underdosage of the target volumes was comparable to the results from Baumann [6]. However, to the best of our knowledge, there are no studies investigating the modulation effects for treatment planning with carbon ion beams.…”

“…The presented concept follows Baumann et al [6] but is done in a fully automated and integrated environment and works for a standard pencil beam algorithm.…”

“…Due to the porous nature of the lung, ion beams passing through a lung (or lung substitute material) show a more pronounced energy straggling than for solid materials [3,4]. A substantial broadening of the BP shape has been found when irradiating lung tissue [5,6]. So far, current treatment planning systems (TPS) assume no additional BP broadening due to tissue heterogeneities.…”

“…Through the use of a 3D printed binary voxel model (the voxels in the geometry are either composed by air or by the printing plastic material) the BP degradation of lung irradiation for protons has been shown to cause for initial beam energies of 140 and 200 MeV an increase of up to 60% for the 80-20% distal beam fall-off as compared to the unperturbed reference curve [5]. Using a similar binary voxel model, a mathematical method for estimating the broadening effect of a porous material has been developed [4,6,8]. The degree of this broadening depends on the average size of the microscopic structures as well as on the material density and thickness.…”

“…Flatten et al [9] investigated the effects of the BP degradation in proton beams by using CT phantoms with spherical targets of variable sizes placed at different depths in the lung. The lung modulation has been implemented in the TOPAS Monte Carlo tool [6] using sets of modulated DICOM images. It was shown that the underdosage of the target volume, due to the BP degradation, increases with an increasing depth of the tumor in lung and a decreasing tumor volume.…”