Minimax optimization for handling range and setup uncertainties in proton therapy

Abstract

Purpose: Intensity modulated proton therapy (IMPT) is sensitive to errors, mainly due to high density dependency and steep beam dose gradients. Conventional margins are often insufficient to ensure robustness of the plans. In this paper, a method is developed that takes the uncertainties into account during the plan optimization. Methods: Dose contributions for a number of range and setup errors are calculated and a minimax optimization is performed. The minimax optimization aims at minimizing the penalty of the worst case scenario. Any optimization function from conventional treatment planning can be utilized in the method. By considering only scenarios that are physically realizable, the unnecessary conservativeness of other robust optimization methods is avoided. Minimax optimization is related to stochastic programming by the more general minimax stochastic programming formulation, which enables accounting for uncertainties in the probability distributions of the errors. Results: The minimax optimization method is applied to a lung case, a paraspinal case, and a prostate case. It is compared to conventional methods that use margins, single field uniform dose (SFUD), and material override (MO) to handle the uncertainties. For the lung case, the minimax method and the SFUD with MO method yield robust target coverage. The minimax method yields better sparing of the lung than the other methods. For the paraspinal case, the minimax method yields more robust target coverage and better sparing of the spinal cord than the other methods. For the prostate case, the minimax method and the SFUD method yield robust target coverage and the minimax method yields better sparing of the rectum than the other methods. Conclusions: Minimax optimization provides robust target coverage without sacrificing the sparing of healthy tissues, even in the presence of low density lung tissue and high density titanium implants. Conventional methods using margins, SFUD, and MO do not utilize the full potential of IMPT and deliver unnecessarily high doses to healthy tissues. *

Robust optimization in lung treatment plans accounting for geometric uncertainty

“…The minimax method does not minimize the worst of all possible scenarios, but the worst scenario within some predefined range. It considers only scenarios that are physically reliable; with unnecessary conservative case scenarios being avoided 3, 4. The range of patient setup error specified by the user was 0.5 cm in LR, 1.0 cm in IS, and 0.5 cm in AP direction for this study.…”

“…Position uncertainties come from two sources: tumor motion and variations in tumor shapes, and patient setup uncertainties. One way to approach these uncertainties is to use minimax optimization 3. Instead of expanding the internal target volume (ITV) with a fixed margin to create the planning target volume (PTV), robust optimization allows entering the setup uncertainties into the planning computer and discretizes them into multiple scenarios (shifts within the margin bounds).…”

Efficacy of robust optimization plan with partial‐arc VMAT for photon volumetric‐modulated arc therapy: A phantom study

“…The RayStation system offers minimax optimization, in which the optimization functions selected to be robust are considered under the worst‐case scenario 8. The interfractional patient‐setup uncertainties are considered to be random; they are incorporated by shifting the isocenter of the patient in the anterior‐posterior (A‐P), superior‐inferior (S‐I), and right‐left (R‐L) directions by the same margin as those used for defining the PTV.…”

“…In proton therapy, setup errors, density errors, and organ motion can lead to differences in dose distributions when comparing the planned and delivered doses. Several authors have previously reported that stochastic programming and robust optimization in IMPT have minimized this problem 5, 6, 7, 8, 9, 10, 11, 12. Presently, RayStation (RaySearch Medical Laboratories AB, Stockholm, Sweden) offers one of the robust optimization methods used to address these demands.…”

Robust optimization of VMAT for lung cancer: Dosimetric implications of motion compensation techniques

“…This ensures a minimum level of plan quality, but results in a dependence on limitations of uncertainty and the potential for the system to over optimize low probability scenarios at the cost of plan quality of higher probability scenarios. In a paper by Fredriksson,53 in which the formalism was introduced, the method was shown to provide robust plans with increased lung sparing over PTV expansions for intensity modulated proton therapy, whilst work by Byrne et al45 has demonstrated its potential in IMRT planning. The implementation of min‐max optimization by the vendor is provided in two options; specified 3‐dimensional offsets set by the user or planning over a range of patient scans (Fig.…”