Robust optimization of intensity modulated proton therapy

Abstract

Purpose: Intensity modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT optimized based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. In this paper, a method that takes the uncertainties into account during plan optimization is used to mitigate the influence of uncertainties in IMPT.

Methods: The authors use the so-called "worst-case robust optimization" to render IMPT plans robust in the face of uncertainties. For each iteration, nine different dose distributions are computed-one each for ± setup uncertainties along anteroposterior (A-P), lateral (R-L) and superior-inferior (S-I) directions, for ± range uncertainty, and the nominal dose distribution. The worst-case dose distribution is obtained by assigning the lowest dose among the nine doses to each voxel in the clinical target volume (CTV) and the highest dose to each voxel outside the CTV. Conceptually, the use of worst-case dose distribution is similar to the dose distribution achieved based on the use of PTV in traditional planning. The objective function value for a given iteration is computed using this worst-case dose distribution. The objective function used has been extended to further constrain the target dose inhomogeneity.

Results: The worst-case robust optimization method is applied to a lung case, a skull base case, and a prostate case. Compared with IMPT plans optimized using conventional methods based on the PTV, our method yields plans that are considerably less sensitive to range and setup uncertainties. An interesting finding of the work presented here is that, in addition to reducing sensitivity to uncertainties, robust optimization also leads to improved optimality of treatment plans compared to the PTV-based optimization. This is reflected in reduction in plan scores and in the lower normal tissue doses for the same coverage of the target volume when subjected to uncertainties.

Conclusions: The authors find that the worst-case robust optimization provides robust target coverage without sacrificing, and possibly even improving, the sparing of normal tissues. Our results demonstrate the importance of robust optimization. The authors assert that all IMPT plans should be robustly optimized.

Figure 1

Color wash represents the DVH bands for dose distributions covering all setup and proton range uncertainties for CTV and various organs for the robustly optimized plan (right column) and the PTV-based plan (left) for the NSCLC case. The solid lines are the DVHs for the nominal dose distribution (i.e., without consideration of uncertainties). The narrowness of CTV band for the robustly optimized plan indicates improved robustness. At the same time, the sparing for the esophagus, spinal cord, and normal lung is perceptibly improved.

Figure 2

DVH bands for dose distributions covering all setup and proton range uncertainties for CTV and various organs for the robustly optimized plan (right column) and the PTV-based plan (left) for the base-of-skull case. As for the lung case, the solid lines are DVHs for the nominal dose distribution, and it is apparent that the CTV coverage for the robustly optimized plans is less sensitive to uncertainties and the normal tissue sparing is improved.

Figure 3

DVH bands for dose distributions for the prostate case with the solid lines indicating the nominal dose distribution. Robustness of prosate dose distribution and the sparing of the bladder and rectum are improved.

Figure 4

Comparison of base-of-skull case CTV, brainstem, whole brain, optic chiasm, left temporal lobe, and right temporal lobe DVHs for the robustly optimized plan with constraint on the maximum dose in each target voxel [solid lines, Eq. 2b] vs without maximum dose constraint [dashed lines, Eq. 2a]. The constraint makes CTV dose distribution more homogenous but at the cost of reduced normal tissue sparing.

Figure 5

Dose distributions in the transverse plane for the lung case illustrating that robustly optimized plan is relatively insensitive to range uncertainty. Left panels: PTV-based plans. Right panels: robustly optimized plans. Top row: with nominal range. Bottom row: with 3.5% higher range. CTV: green color wash; spinal cord: purple color wash.

Figure 6

Dose distributions in the transverse plane for the base-of-skull case illustrating that robustly optimized plan is relatively insensitive to set-up uncertainty. Left panels: PTV-based plans. Right panels: robustly optimized plans. Top row: nominal position. Bottom row: with patient shifted inferiorly by 3 mm. CTV: green color wash; brainstem: purple color wash.

Figure 7

Panel (a) is the nominal dose distribution for the PTV-based prostate plan. The remaining panels are the dose distributions for the robustly optimized plan: (b) nominal, (c) with patient shifted posteriorly by 5 mm, (d) shifted to the right by 5 mm, and (e) with beam range decreased by 3.5%. Red is the prescription isodose contour lines (76 Gy), green line is the PTV and blue line is the CTV. Letters O and O’ indicate original and shifted positions of the isocenter. Comparison of panel (a) with other panels illustrates that the prescription isodose surface encloses a larger volume for the PTV-based optimization vs robust optimization. At the same time, the CTV remains covered with the prescription dose in the face of uncertainties.