Modeling Variable Proton Relative Biological Effectiveness (RBE) Using Voxel-Level Image Density Change for Non-Small Cell Lung Cancer (NSCLC) Patients Treated with Passive Scattering Proton Therapy (PSPT) or Intensity Modulated Photon Therapy (IMRT)

Abstract

<h3>Purpose/Objective(s)</h3> To test the hypothesis that radiation damage measured via lung image density change is a function of variable RBE for protons with a coefficient of determination (R²) greater than 0.8. <h3>Materials/Methods</h3> Data from 61 NSCLC patients previously treated on a prospective clinical trial with PSPT (N = 24) or IMRT (N = 37) to 74 Gy(RBE) (proton RBE of 1.1) were acquired. Patients with noticeable atelectasis or pleural effusion were excluded. For each patient, a ∼5-month post-treatment PETCT was obtained to assess response and was deformed to the planning exhale phase of the 4DCT (exCT) via a biomechanical model-based image registration algorithm. Subsequently, voxel-level image density change (IDC) within the normal ipsilateral lung was obtained by subtracting the exCT from the deformed PETCT, as a signal of biological damage. IMRT dose (D_x) was recalculated on the exCT using a commercial treatment planning system while the PSPT dose (D_p) and dose-averaged linear energy transfer (LET_d) were recalculated on the exCT using a commissioned track-repeating Monte-Carlo system. The fitted variable RBE models included a linear model (RBE = 1 + λ•LET_d) and a linear-quadratic (LQ) model (RBE = 1/(2D_p)•{√[(α/β)² + 4D_p(α/β)(p₀+(p₁•LET_d)/(α/β) + 4D_p²(p₂ + p₃•√(α/β)•LET_d)] - α/β}) with α/β = 3 Gy for lung tissue. <b>RBE was modeled against the ratio between D_x and D_p at given IDC levels.</b> We adapted Lyman-Kutcher-Burman normal tissue complication probability (NTCP) model to fit the dose-IDC relationship for each cohort by averaging the dose and IDC of voxels in 5-Gy dose intervals (adaptations: n = 1, effective dose = voxel dose, and complication probability = IDC normalized against global min and max IDC). LET_d corresponding to each D_p was approximated by averaging the LET_d of voxels that received D_p with a margin of 0.001Gy. All NTCP and RBE models were fitted using non-linear least squares with the Python SciPy package. <h3>Results</h3> For NTCP fitting, min and max IDC were 2.7 HU and 136.3 HU, respectively, and TD₅₀ and m were fitted to be 31.5 Gy and 0.51 for PSPT (R² = 0.99) and 44.4 Gy and 0.40 for IMRT (R² = 0.98). The table shows the IDC levels, the corresponding LET_d (SD), and the fitted D_x and D_p. The linear model resulted in λ = 0.154 µm/keV (R² = 0.27), and the LQ model resulted in p₀ = -0.72, p₁ = 10.02, p₂ = 1.51, and p₃ = -0.08 (R² = 0.999). <h3>Conclusion</h3> The study demonstrates that voxel-level radiation damage and image changes for proton therapy are functions of dose and LET and, thus, variable RBE.