Reoptimization of IMPT plans based on linear energy transfer

Figure 6 illustrates the simplified RBE model (equation 3) used in this work. Figure 6a shows 9 the physical dose di for 10 9 protons for a single pencil beam, delivering approximately 4.5 10 Gy at the Bragg peak, which is located at the distal edge of the target volume. Figure 6b 11 shows the additional biological dose c L̄idi in Gy for c = 0.04 μm/keV. The sum of c L̄idi and 12 di yields the RBE-weighted dose in Figure 6c. The RBE (Figure 6d) is the ratio of RBE13 weighted dose and physical dose, which becomes ill-defined where the dose goes to zero. For 14 our model, RBE essentially represents dose-averaged LET. For c = 0.04 μm/keV, c L̄idi adds 15 another 1.5 Gy to the physical dose near the Bragg peak, resulting in an RBE of approximately 16 1.3. In the falloff region distal to the Bragg peak the RBE increases to values around 1.5 to 1.6. 17