Treatment plans optimized for intensity modulated proton therapy (IMPT) may be very sensitive to setup errors and range uncertainties. If these errors are not accounted for during treatment planning, the dose distribution realized in the patient may by strongly degraded compared to the planned dose distribution. The authors implemented the probabilistic approach to incorporate uncertainties directly into the optimization of an intensity modulated treatment plan. Following this approach, the dose distribution depends on a set of random variables which parameterize the uncertainty, as does the objective function used to optimize the treatment plan. The authors optimize the expected value of the objective function. They investigate IMPT treatment planning regarding range uncertainties and setup errors. They demonstrate that incorporating these uncertainties into the optimization yields qualitatively different treatment plans compared to conventional plans which do not account for uncertainty. The sensitivity of an IMPT plan depends on the dose contributions of individual beam directions. Roughly speaking, steep dose gradients in beam direction make treatment plans sensitive to range errors. Steep lateral dose gradients make plans sensitive to setup errors. More robust treatment plans are obtained by redistributing dose among different beam directions. This can be achieved by the probabilistic approach. In contrast, the safety margin approach as widely applied in photon therapy fails in IMPT and is neither suitable for handling range variations nor setup errors.

Treatment plans optimized for intensity modulated proton therapy (IMPT) may be sensitive to range variations. The dose distribution may deteriorate substantially when the actual range of a pencil beam does not match the assumed range. We present two treatment planning concepts for IMPT which incorporate range uncertainties into the optimization. The first method is a probabilistic approach. The range of a pencil beam is assumed to be a random variable, which makes the delivered dose and the value of the objective function a random variable too. We then propose to optimize the expectation value of the objective function. The second approach is a robust formulation that applies methods developed in the field of robust linear programming. This approach optimizes the worst case dose distribution that may occur, assuming that the ranges of the pencil beams may vary within some interval. Both methods yield treatment plans that are considerably less sensitive to range variations compared to conventional treatment plans optimized without accounting for range uncertainties. In addition, both approaches--although conceptually different--yield very similar results on a qualitative level.

Purpose We describe a treatment plan optimization method for intensity-modulated proton therapy (IMPT) that avoids high values of linear energy transfer (LET) in critical structures located within or near the target volume, while limiting degradation of the best possible physical dose distribution. Methods To allow fast optimization based on dose and LET, a GPU-based Monte-Carlo code was extended to provide dose-averaged LET in addition to dose for all pencil beams. After optimizing an initial IMPT plan based on physical dose, a prioritized optimization scheme is used to modify the LET distribution while constraining the physical dose objectives to values close to the initial plan. The LET optimization step is performed based on objective functions evaluated for the product of LET and physical dose (LETxD). To first approximation, LETxD represents a measure of the additional biological dose that is caused by high LET. Results The method is effective for treatments where serial critical structures with maximum dose constraints are located within or near the target. We report on 5 patients with intra-cranial tumors (high-grade meningiomas, base-of-skull chordomas, ependymomas) where the target volume overlaps with the brainstem and optic structures. In all cases, high LETxD in critical structures could be avoided while minimally compromising physical dose planning objectives. Conclusion LET-based reoptimization of IMPT plans represents a pragmatic approach to bridge the gap between purely physical dose-based and RBE-based planning. The method makes IMPT treatments safer by mitigating a potentially increased risk of side effects due to elevated relative biological effectiveness (RBE) of proton beams near the end of range.

Motion and uncertainty in radiotherapy is traditionally handled via margins. The clinical target volume (CTV) is expanded to a larger planning target volume (PTV), which is irradiated to the prescribed dose. However, the PTV concept has several limitations, especially in proton therapy. Therefore, robust and probabilistic optimization methods have been developed that directly incorporate motion and uncertainty into treatment plan optimization for intensity modulated radiotherapy (IMRT) and intensity modulated proton therapy (IMPT). Thereby, the explicit definition of a PTV becomes obsolete and treatment plan optimization is directly based on the CTV. Initial work focused on random and systematic setup errors in IMRT. Later, inter-fraction prostate motion and intra-fraction lung motion became a research focus. Over the past ten years, IMPT has emerged as a new application for robust planning methods. In proton therapy, range or setup errors may lead to dose degradation and misalignment of dose contributions from different beams -a problem that cannot generally be addressed by margins. Therefore, IMPT has led to the first implementations of robust planning methods in commercial planning systems, making these methods available for clinical use. This paper first summarizes the limitations of the PTV concept. Subsequently, robust optimization methods are introduced and their applications in IMRT and IMPT planning are reviewed.Abstract. Motion and uncertainty in radiotherapy is traditionally handled via 31 margins. The clinical target volume (CTV) is expanded to a larger planning target 32 volume (PTV), which is irradiated to the prescribed dose. However, the PTV 33 concept has several limitations, especially in proton therapy. Therefore, robust and 34 probabilistic optimization methods have been developed that directly incorporate 35 motion and uncertainty into treatment plan optimization for intensity modulated 36 radiotherapy (IMRT) and intensity modulated proton therapy (IMPT). Thereby, the 37 explicit definition of a PTV becomes obsolete and treatment plan optimization is 38 directly based on the CTV. Initial work focused on random and systematic setup errors 39 in IMRT. Later, inter-fraction prostate motion and intra-fraction lung motion became 40 a research focus. Over the past 10 years, IMPT has emerged as a new application for 41 robust planning methods. In proton therapy, range or setup errors may lead to dose 42 degradation and misalignment of dose contributions from different beams a problem 43 Robust radiotherapy planning 2 that cannot generally be addressed by margins. Therefore, IMPT has led to the first 44 implementations of robust planning methods in commercial planning systems, making 45 these methods available for clinical use. This paper first summarizes the limitations 46 of the PTV concept. Subsequently, robust optimization methods are introduced and 47 their applications in IMRT and IMPT planning are reviewed. 48 1. Introduction 49Radiotherapy aims at delivering curative doses of radiation ...

We present a method to include robustness into a multi-criteria optimization (MCO) framework for intensity modulated proton therapy (IMPT). The approach allows one to simultaneously explore the tradeoff between different objectives as well as the tradeoff between robustness and nominal plan quality. In MCO, a database of plans, each emphasizing different treatment planning objectives, is pre-computed to approximate the Pareto surface. An IMPT treatment plan that strikes the best balance between the different objectives can be selected by navigating on the Pareto surface. In our approach, robustness is integrated into MCO by adding robustified objectives and constraints to the MCO problem. Uncertainties (or errors) of the robust problem are modeled by pre-calculated dose-influence matrices for a nominal scenario and a number of pre-defined error scenarios (shifted patient positions, proton beam undershoot and overshoot). Objectives and constraints can be defined for the nominal scenario, thus characterizing nominal plan quality. A robustified objective represents the worst objective function value that can be realized for any of the error scenarios and thus provides a measure of plan robustness. The optimization method is based on a linear projection solver and is capable of handling large problem sizes resulting from a fine dose grid resolution, many scenarios, and a large number of proton pencil beams. A base of skull case is used to demonstrate the robust optimization method. It is demonstrated that the robust optimization method reduces the sensitivity of the treatment plan to setup and range errors to a degree that is not achieved by a safety margin approach. A chordoma case is analysed in more detail to demonstrate the involved tradeoffs between target underdose and brainstem sparing as well as robustness and nominal plan quality. The latter illustrates the advantage of MCO in the context of robust planning. For all cases examined, the robust optimization for each Pareto optimal plan takes less than 5 minutes on a standard computer, making a computationally friendly interface possible to the planner. In conclusion, the uncertainty pertinent to the IMPT procedure can be reduced during treatment planning by optimizing plans that emphasize different treatment objectives, including robustness, and then interactively seeking for a most-preferred one from the solution Pareto surface.

In this paper, we investigate an off-line strategy to incorporate inter-fraction organ motion in IMRT treatment planning. It was suggested that inverse planning could be based on a probability distribution of patient geometries instead of a single snap shot. However, this concept is connected to two intrinsic problems: first, this probability distribution has to be estimated from only a few images; and second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In the current work, we develop new concepts of inverse planning which account for these two problems.

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed. C 2015 American Association of Physicists in Medicine. [http://dx

The treatment of cancer with proton radiation therapy was first suggested in 1946 followed by the first treatments in the 1950s. As of 2020, almost 200 000 patients have been treated with proton beams worldwide and the number of operating proton therapy (PT) facilities will soon reach one hundred. PT has long moved from research institutions into hospital-based facilities that are increasingly being utilized with workflows similar to conventional radiation therapy. While PT has become mainstream and has established itself as a treatment option for many cancers, it is still an area of active research for various reasons: the advanced dose shaping capabilities of PT cause susceptibility to uncertainties, the high degrees of freedom in dose delivery offer room for further improvements, the limited experience and understanding of optimizing pencil beam scanning, and the biological effect difference compared to photon radiation. In addition to these challenges and opportunities currently being investigated, there is an economic aspect because PT treatments are, on average, still more expensive compared to conventional photon based treatment options. This roadmap highlights the current state and future direction in PT categorized into four different themes, 'improving efficiency', 'improving planning and delivery', 'improving imaging', and 'improving patient selection'.