Development and Application of a Random Lung Model for Dose Calculations in Radiotherapy.

Abstract

Radiotherapy requires accurate dose calculations in the human body, especially in disease sites with large variations of electron density in neighboring tissues, such as the lung. Currently, the lung is modeled by a voxelized geometry interpolated from computed tomography (CT) scans to various resolutions. The simplest such voxelized lung, the atomic mix model, is a homogenized whole lung with a volume averaged bulk density. However, according traditional transport theory, even the relatively fine CT voxelization of the lung is not valid, due to the extremely small mean free path (MFP) of the electrons.

The purpose of this thesis is to study the impact of the lung’s heterogeneities on dose calculations in lung treatment planning. We first extend the traditional atomic mix theory for charged particles by approximating the Boltzmann equation for electrons to its Fokker-Planck (FP) limit, and then applying a formal asymptotic analysis to the BFP equation. This analysis raises the length scale for homogenizing a heterogeneous medium from the electron mean free path (MFP) to the much larger electron transport MFP. Then, using the lung’s anatomical data and our new atomic mix theory, we build a realistic 2 1/2-D random lung model. The dose distributions for representative realizations of the random lung model are compared to those from the atomic mix approximation of the random lung model, showing that significant perturbations may occur with small field sizes and large lung structures. We also apply our random lung model to a more realistic lung phantom and investigate the effect of CT resolutions on lung treatment planning. We show that, compared to the reference 1 ×1 mm2 CT resolution, a 2 ×2 mm2 CT resolution is sufficient to voxelize the lung, while significant deviations in dose can be observed with a larger 4×4 mm2 CT resolution. We use the Monte Carlo method extensively in this thesis, to avoid systematic errors caused by inaccurate heterogeneity corrections that occur in approximate clinical dose calculation methods.

Finally, we address potential improvements for our random lung model and some possible future applications.