Advanced Treatment Planning

Transcription

1 Advanced Treatment Planning Minna Wedenberg a) RaySearch Laboratories, Stockholm, Sweden Chris Beltran Division of Medical Physics, Department of Radiation Oncology, Mayo Clinic, Rochester, MN, USA Andrea Mairani Heidelberg Ion Therapy Center (HIT), Heidelberg University Hospital, Heidelberg, Germany National Center for Radiation Research in Oncology (NCRO) Heidelberg Institute for Radiation Oncology (HIRO), Heidelberg, Germany The National Centre for Oncological Hadrontherapy (CNAO), Pavia, Italy Markus Alber The National Centre for Oncological Hadrontherapy (CNAO), Pavia, Italy Section for Medical Physics, Department of Radiation Oncology, Heidelberg University Hospital, Heidelberg, Germany (Received 17 November 2017; revised 22 March 2018; accepted for publication 22 April 2018; published 13 November 2018) Treatment planning for protons and heavier ions is adapting technologies originally developed for photon dose optimization, but also has to meet its particular challenges. Since the quality of the applied dose is more sensitive to geometric uncertainties, treatment plan robust optimization has a much more prominent role in particle therapy. This has led to specific planning tools, approaches, and research into new formulations of the robust optimization problems. Tools for solution space navigation and automatic planning are also being adapted to particle therapy. These challenges become even greater when detailed models of relative biological effectiveness (RBE) are included into dose optimization, as is required for heavier ions American Association of Physicists in Medicine [ Key words: automated plan generation, multicriteria optimization, particle therapy, proton therapy, realiative biological effectiveness, robust optimization, treatment planning 1. INTRODUCTION Treatment planning in particle therapy used to have a lot in common with photon treatment planning, but is now increasingly developing along its own track due to the specific challenges that have moved into focus with spot-scanning dose delivery and heavier ions. Initially, (intensity-modulated) photon dose optimization had been somewhat in the lead of the development, because it is arguably much harder to arrive at deliverable, truly clinically optimal treatment plans. In terms of mathematical complexity of treatment delivery, particle dose optimization could be conceived as a much simpler problem. Nowadays, the true development challenges lie especially in dealing with treatment-related uncertainties, giving a boost to the field of robust optimization. 1,2 Developments that had initially been suggested for photon treatment planning are being assimilated quickly into particle therapy, especially in the fields of automatic planning, plan adaptation, and multicriteria optimization. Here, we give an overview of these active developments with special focus on proton spot-scanning delivery. The specific terminology used in proton dose optimization is shown in Table I. Details of the optimization algorithms are touched upon only to the extent necessary to give a basis for the more in-depth treatment of specific topics. Dose computation algorithms and relative biological effectiveness (RBE) computation will be referred to generically, as detailed descriptions are given in other chapters. This chapter starts with a summary of the state of the art in intensity-modulated proton therapy (IMPT) planning and gives a cursory outlook into what developments may be expected. The following sections give in-depth treatments of multicriteria optimization (MCO), automated plan generation for ab-initio planning and plan adaptation, and robust optimization, initially restricted to their application to proton therapy. The final sections are concerned with questions about the inclusion of biological aspects into treatment planning, and how the above concepts translate to treatment planning for heavier particles than protons. 1.A. State of the art Up until recently, proton treatment planning systems (TPS) showed their origin in photon treatment planning in many ways that appear natural today, but are particular choices and may become redundant in the future. Typically, the optimization operates on a single patient model that is constructed from a computed tomography (CT) dataset, and one set of contours that are unique for the entire treatment plan. Treatment-related uncertainties are dealt with a common PTV, or beam-individual PTVs. The optimization goals are defined by dose-dependent cost functions that communicate the treatment intention to the software. The optimization process can be e1011 Med. Phys. 45 (11), November /2018/45(11)/e1011/ American Association of Physicists in Medicine e1011

2 e1012 Wedenberg et al.: Advanced treatment planning e1012 steered usually by means of individual priority weights for each cost function. The cost functions can be selected from a set of mostly generic criteria, such as minimum and maximum dose penalties, dose volume penalties, or mean dose; the use of biologically inspired cost functions is still an exception. 3 Specific models of variable RBE are not commercially available for protons but are standard in carbon ion radiotherapy. From a user perspective, treatment planning is a highly interactive process requiring training and experience. The latest generation of TPS provides some optimization features that are specific for IMPT, for example, beam direction specific planning target volumes (owing to the fact that geometric uncertainties and therefore safety margins around targets are greater in beam direction than perpendicular to it) and robust optimization (because margins do not perform well in the presence of density heterogeneities). Also, proton-specific workflows like SFUD have become available without work-arounds. At its core, SFUD is itself a work-around as it is intended to achieve a homogeneous dose distribution per beam to avoid dose matching issues that could arise if very irregular dose distributions from different angles had to click into each other like a 3D jigsaw puzzle. Delivery uncertainties between different beams would rapidly decrease target dose homogeneity if their dose distributions were highly heterogeneous. The same effect as with separate optimization of beam doses via SFUD could be achieved if the objective of plan robustness against intrafractional anatomical changes was made an explicit optimization constraint, for example, by limiting the dose heterogeneity per beam in MFO. Technically, such secondary optimization goals are termed regularization, and have been applied to great benefit in photon dose optimization. The limitations of SFUD for heavier ions are discussed in Section 5. From a dogmatic point of view, a dose optimization problem should be formulated comprehensively, i.e., the algorithm can produce a result that requires no manual modification. The request for, and availability of, spot weight editing tools, auxiliary planning volumes and other means of interference with the dose optimization betrays the lack of such a comprehensive problem formulation. Aside from the difficulties of finding a mathematical expression for an otherwise intuitive planning goal, e.g., avoiding high-let spots in front of organs at risk, these additional secondary objectives may complicate the numerical solution of the optimization problem. While manual interference with the optimizing algorithm is merely an inconvenience for normal routine, it may become problematic for developments that require highly automated treatment planning, such as multicriteria optimization, automatic plan adaptation or automatic plan generation, for example, for plan libraries. Although there has been a large number of publications on the topic of beam angle optimization, commercial tools are rare to date. Putatively, this stems from the fact that beam angles have to be preferable with respect to good organ sparing and target coverage, both for the nominal planning geometry and also in case of geometrical uncertainties (i.e., the beam directions need to be inherently robust). In combination, formulating an efficient cost function becomes a rather tough problem and requires a definition of a set of geometric uncertainty scenarios. Finally, proton TPS do not regularly apply dose- and/or LET-dependent RBE models, but operate with a constant scaling factor, typically RBE = 1.1. Variable RBE models for protons have become available and usually require the computation of the dose-weighted LET d. While analytical dose computation algorithms are still the mainstay of clinical application, they do not regularly compute this quantity, so that variable RBE models would require modifications to dose computation and ultimately optimization algorithms, as discussed in Section 5. TABLE I. Terminology in proton dose optimization. Acronym Term Meaning SSPT Spot-scanning proton therapy A irradiation technique whereby a narrow proton spot beam is swept across the target volume by magnetical deflection in two lateral dimensions, and with a constant energy for a large number of spot positions before the energy is changed by a discrete step IMPT Intensity-modulated proton therapy Application of SSPT such that each spot weight (the number of protons per spot position and energy setting) can be chosen freely. IMPT also refers to an optimization problem wherein which the multitude of all proton spot weights from all angles of incidence is optimized simultaneously and independently SFO Single-field-optimization A method of IMPT optimization whereby the spot weights of each angle of incidence are optimized separately, and the resultant doses of all angles of incidence added in the end MFO Multi-field-optimization A method of IMPT optimization whereby all spot weights are optimized simultaneously. The term IMPT often implies MFO SFUD Single-field-uniform-dose A SFO whereby the optimization goal for the target dose is maximum homogeneity SFIB Single-field-integrated-boost A SFO whereby the optimization goal for the target is a heterogeneous dose distribution with multiple prescribed discrete dose levels TPS Treatment planning system Software for treatment planning, including dose optimization algorithms RBE Relative biological effectiveness Factor that scales the particle dose to the biologically equivalent megavoltage photon dose LET Linear energy transfer Kinetic energy deposited per unit length by a charged particle traversing matter. RBE depends nonlinearly on LET

3 e1013 Wedenberg et al.: Advanced treatment planning e B. Future developments Future developments with regard to robust optimization and automation will be treated in the following sections. Developments in more generic optimization questions could include: (a) acceleration up to real-time interactive optimization, (b) constrained optimization as a facilitator of automation, (c) regularization to improve plan robustness and delivery speed, (d) beam direction optimization, and (e) MRbased treatment planning. Compared to photon dose optimization, SSPT optimization has several inherent speed advantages. Firstly, the optimization of a deliverable treatment plan is straightforward and does not require the inclusion of complicated delivery machine constraints; secondly, the dose distributions of each beam spot cover a relatively smaller volume than photon beamlets. The latter is important because every iteration of the dose optimizer requires two distinct volume integrals over all spot/beamlet dose distributions. The bottleneck of SSPT is currently high-quality dose computation, which can be parallelized trivially. Hence, it is currently only a question of optimizing the code for high-performance hardware to accelerate it to real-time performance. The remaining challenges of (deformable) image registration and automatic contouring are currently a hot research focus of radiotherapy in general, not in the least boosted by the advent of the MR-Linac, a device essentially built for real-time plan generation. Another prerequisite of fast, highly automated dose optimization is a subtle shift in the optimization setup. The manual adjustment of priority weights for cost functions is very time-consuming and has been addressed by multicriteria visualization tools. Constrained optimization, on the other hand, replaces priority weights with constraints on the cost function values that must be obeyed by the optimizer. The optimization can then become fully automated if either the correct constraints are known (in case of plan reoptimization) or can be found according to a set of rules (in case of the lexicographic ordering approach). Constrained optimization also ties in with knowledge-based plan prediction. These issues will be treated in more depth in Section 2. Very early in the development of photon dose optimization, it was realized that the problem was ill-posed and that a large amount of the beam modulation was due to numerical instabilities. The introduction of regularization terms that smoothed the beam profiles lead to a significant acceleration of delivery. The situation is similar in SSPT, which is also an ill-posed problem, but has a different structure and also different factors that affect beam delivery time. However, delivery speed is essential for efficient motion mitigation, such as volume repainting. Energy layer changing, being the slowest of the three axes of the spot-scanning system, makes optimum energy step spacing the highest priority. 4,5 Depending on details of the delivery system, the range of spot weights per energy layer may also need to be limited by removing spots with low weight. 6 Including all in the overall cost function may come at a cost, especially for single beam dose homogeneity, so it is best accompanied by another secondary optimization goal that ensures this. Photon dose optimization systems have very intimate knowledge of the various linac models which helped to accelerate the delivery times by roughly an order of magnitude in the last decade. It is reasonable to assume that this could be achieved for IMPT, but to a somewhat lesser extent. Furthermore, regularization schemes could make SFO approaches redundant in the long run and thereby make the full potential of IMPT available. It has also been shown that regularization can improve plan robustness. 7,8 The full extent of the benefit of regularization in MFO still needs to be explored. Speedier delivery, enabling more beam directions, faster optimization and robust optimization methods will also affect the issue of beam direction optimization, which is more aptly named selection. In contrast to photon dose optimization, the coupling between individual beams is much weaker, especially given the preference of homogeneous individual beam doses. Hence, the overall merit of each beam could be determined individually and the set of the best n beams compiled. Selection of beams on the basis of their (biological) dose and robustness quality should be superior to geometric substitute measures. The number of beams also has implications on uncertainties associated with estimates of RBE, which could be alleviated by increasing their number. The reason for this lies in the fact that superposition of dose distributions from different directions almost always decreases the doseweighted LET, and therefore the RBE of the composite treatment plan. Thus, no challenge in dose optimization, especially for high-let irradiation, can be dealt with in isolation, calling for a more comprehensive approach to optimization. SSPT planning may not require the full extent of the sophistication of dose optimization for heavier ions, but it may derive some input from the latter. Robust optimization is only one application where the traditional static patient model of treatment planning begins to blur. An increasing amount of image information is attached to this model, ranging from functional imaging to repeated anatomical scans, across a large range of modalities. It becomes questionable if the planning CT scan should really be the central pillar, or rather just another piece of information of a comprehensive patient model that starts with an anatomical representation of the patient. Magnetic resonance imaging (MRI), arguably being the method with the best soft tissue contrast, will increase its importance across radiotherapy applications to an extent that may make the vision of purely MRI-based radiotherapy a reality. This requires that the problem of pseudo-ct creation from MRI finally be solved, which could be one of the first core applications of MRI-based anatomical models Motion models, as required for robust optimization in the presence of organ motion or for motion-corrected 4D dose accumulation, would also be easier to obtain in an MR-based framework. 2. MULTICRITERIA OPTIMIZATION Multicriteria optimization (MCO) in treatment planning is a general term for a class of techniques designed to handle

4 e1014 Wedenberg et al.: Advanced treatment planning e1014 multiple conflicting goals in the construction of a treatment plan. The fundamental challenge in cancer therapy is to find the right balance between eradicating the cancer and avoiding unacceptable injury to different organs and tissues. In the design of a treatment plan, there are inherent trade-offs: more conformal dose to the target comes at a cost of higher dose to organs at risk (OAR), sparing of one OAR gives increased dose to another, and so on. The higher the number of OARs to take into account, the more combinatorically complex the planning process becomes. Traditionally, the process of finding a satisfactory treatment plan is iterative, where the planner constructs and modifies optimization functions and constraints, and executes a series of optimizations and evaluations until a plan that fulfills certain clinical goals is obtained (to a higher or lesser extent). It is generally hard to know beforehand how realistic the objectives are to fulfill, how they are correlated, how a change in the priority weights of the objectives modify the dose distribution, and if better treatment options exist for the patient. Therefore, this iterative process can be time-consuming with its manual parameter tuning and repeated optimizations, and may lead to suboptimal plans. The aim of MCO is to manage the inherent multidimensional trade-offs better, and to present these trade-offs in a transparent way. In this way, MCO enables a more efficient planning process and facilitates the decision-making. Multicriteria optimization approaches can be divided into two main categories based on the decision maker s participation (the classification is adopted from Bokrantz 12 ): In a priori methods, such as lexicographic optimization, treatment goals are stated before optimizing the plan. In a posteriori methods, such as Pareto surface navigation, the preferred plan is obtained by interpolating between precalculated Pareto optimal plans. In this way, the decision on how to prioritize between clinical goals is made a posteriori, when the tradeoffs between goals are known. for a small relaxation of the constraints since they may be so strict that there is no room for improvements in lower priority goals. For example, a minor deviation from a uniformity constraint of a PTV may enable significant sparing of an OAR. The end result is a plan optimized based on the priority of the objection functions where the goals have been fulfilled to a higher or lower extent. By explicitly incorporating priorities, the need of weighting factors is eliminated. 2.B. Pareto surface navigation With this MCO technique, the importance of specific planning objectives does not need to be stated beforehand, but the trade-offs can be interactively explored, and the navigation to a preferred trade-off is done in real-time. Pareto surface navigation relies on the principle of Pareto optimality. A multiobjective treatment plan is Pareto optimal if it is feasible with respect to all constraints and no objective function can be improved without deteriorating at least one of the other objectives. Since an improvement in one objective results in a deterioration in another, this implies that there is a trade-off between the solutions. The set of all Pareto optimal treatment plans for a patient defines the so called Pareto surface (see Fig. 1). Pareto surface navigation is typically implemented as an automated precalculation of a relevant set of treatment plans, where each plan emphasizes different treatment planning objectives, followed by an interactive exploration of combinations of these plans. It is a challenge to represent the Pareto surface with a discrete number of well-distributed Pareto optimal solutions in an effective way. Methods for generating plans so that their convex combinations are good approximations of the Pareto surface include so called sandwich methods that combine inner and outer approximation methods and thereby enclose 2.A. Lexicographic optimization In lexicographic optimization, also called lexicographic ordering, prioritized optimization, or goal programming, the decision maker sets up in advance a set of goals, related to clinical prescriptions, that are ordered with respect to importance Instead of combining all optimization functions into a single composite objective function via a weighted sum as in conventional plan optimization, lexicographic optimization is performed as a stepwise sequence of constrained optimizations, starting with the highest prioritized objective function. At each iterative step, a new objective function from the list is optimized with the previous goals incorporated as constraints so that the higher prioritized goals are not deteriorated. The constraints are non-negotiable and therefore have the highest priority. Additional constraints may be included from the beginning throughout all optimization steps to prevent unacceptable plans. The feasible solution space is gradually reduced as the method proceeds with the added constraints. Sometimes a preselected slip factor allows FIG. 1. Illustration of a 3D Pareto surface. Figure courtesy of Lovisa Engberg. 7

5 e1015 Wedenberg et al.: Advanced treatment planning e1015 the Pareto surface. Efforts are made to reduce computational cost by more effective methods and parallelized algorithms After creating a set of Pareto optimal treatment plans from the discrete Pareto surface representation, an important aspect is techniques to efficiently explore and compare these plans to find the best balance between the different objectives and to select a clinical plan. Navigation of the Pareto surface is performed through continuous interpolation of the combined dose distributions of the precalculated Pareto optimal plans. By forming weighted averages of the Pareto plans, a smooth search between the trade-offs is possible. The navigation is in practice made through at set of slider bar controls corresponding to each objective function (see Fig. 2). By moving a slider, the current convex combination is updated as well as the corresponding dose distribution and DVH. The combination of all slider positions, corresponding to weighting the various Pareto plans, gives a navigated dose distribution. Adjusting the slider of an objective function will generally affect sliders of other objective functions since there is a trade-off between the clinical goals. A certain position of the slider can be clamped to constrain that objective function and thereby also limit the reachable solution space. High dimensional navigation methods include those presented by Monz et al. 22 By navigating the Pareto optimal plans, more informed decision-making is enabled since the trade-off between the different clinical goals are visually displayed in real-time. 2.C. MCO for protons MCO and robust optimization have both been explored extensively, but have rarely been combined. For IMPT, the full potential of MCO is not achieved unless robustness is included. The dosimetric advantages of IMPT come at a cost of high sensitivity to errors, and the quality of IMPT plans can be severely compromised if uncertainties are not considered in the plan creation (see Section 4 about robust optimization). Multiobjective optimization under uncertainty can be obtained by including objective functions that minimizes the worst-case dose for a set of predefined error scenarios, and/or with robust constraints. 23,24 In that way the set of Pareto optimal plans can include both robust plans and plans for the nominal scenario, and new types of trade-offs can be explored. Robustness and MCO have recently been combined for IMPT in in-house and commercial treatment planning systems. 2.D. Future The combination of MCO and robustness has not been extensively explored and different approaches and methods need to be evaluated and compared. Another adoption of MCO to particle therapy to be made is the need to take into account LET and RBE-weighted doses. Pareto surface reconstruction and plan navigation relies on the linear superposition of dose distributions. This linearity is no longer given for RBE-weighted doses, which increases the distance between the navigated dose and the truly optimum dose. Some specialization of MCO for particle therapy is thus required. 3. AUTOMATED PLAN GENERATION There are different levels of automation of the planning process requiring various degrees of human intervention and postprocessing. Automation can range from specific steps and cases to larger and more general planning processes. The aims of automating the treatment planning process include to free time, reduce workload, increase consistency, and improve plan quality. There are parts of the treatment planning process that are automated to a certain extent such as image registration, segmentation of normal tissue, and dose optimization. This section highlights a few other steps of various complexity. MCO is described separately in Section 2. 3.A. Planning based on templates, protocols, and scripting For a specific indication there may be standard ways in a clinic to set up the plan for most of these patients. For example, the clinic may have a standard number of beams with certain beam orientations, a set of structures and ROIs with consistent names that are defined and contoured, some optimization functions that usually give a good starting point, and clinical goals to which the plan is evaluated against. These types of repetitive and recurrent steps in the planning process can be automated with templates. Instead of setting FIG. 2. MCO navigation with sliders.

6 e1016 Wedenberg et al.: Advanced treatment planning e1016 up beams or objective functions from scratch every time in the treatment planning system, a template is made once for a certain patient group and can be loaded for all those patients. In a next step, templates and some actions can be grouped together to standardize the planning. In addition to templates running consecutively in a predefined schedule, certain settings such as grid resolution, the number of fractions, and the number of optimization iterations may be set to run automatically as well as certain actions such as optimization and dose computation: 1. Create ROIs via, e.g., atlas-based or model-based segmentation 2. Set dose grid 3. Load beam configuration 4. Load objective functions 5. Load clinical goals 6. Run optimization 7. Compute final dose Another approach is to record mouse clicks and keystrokes and then play the recorded program on other cases. Scripting is an even more flexible tool. Besides automation of treatment planning, it can be used to extract data, extend and further develop functionality, communicate with other programs, etc., which can be useful for specific needs for a clinic or in research projects. 3.B. Dose mimicking Dose mimicking is a technique to automatically generate plans based on the dose distribution of a reference plan. The dose mimicking optimization can have objectives such as to mimic the dose in each voxel over the entire dose grid, or to reproduce the DVH of ROIs. The algorithm can penalize all deviations from the reference dose distribution, or accept better doses (such as lower doses in OARs). This technique is useful for generating additional alternative plans for a patient as backups when the original plan cannot be delivered, e.g., due to that the original machine becomes unavailable or is overscheduled. The key is to manually create one plan of high quality, and to let the automatic plan generator strive to mimic the optimized dose distribution with another setup. Hence, new plans with another treatment machine, a different treatment technique and/or an alternative treatment modality, can automatically be created with the aim of reproducing the dose distribution of the original reference plan. One, several or all fractions can then be delivered with the alternative plan(s). Another use of mimicking is to automatically improve an existing plan. The dose distribution of a previous plan is used as reference and a new optimization is performed with the objective to, e.g., minimize the doses to healthy structures under the constraint that the dose to each voxel or the DVH of each ROI must be at least as good as in the reference plan. 25 Mimicking can also be used to convert automatically generated dose distributions to deliverable dose distributions and clinically achievable treatment plans with modulated beams or arcs C. Prioritized clinical goal optimization For each patient, there are in principle numerous treatment options. The patient could be treated with different techniques and modalities, and for each technique the setup, such as the number of fields and beam angles, could be varied. With multiple alternative plans for each patient, it is possible to choose which option would be most beneficial. In practice, it is too cumbersome and time-consuming to manually create and evaluate more than a few alternatives. With an automatic plan generation that generates a large number of different treatment plans, the task of the planner would rather be to choose the best plan from a variety of plans for each patient than to create it. In this section, a method for automated plan generation is described that is inspired from lexicographic principles and driven by prioritized clinical goals (see Section 2.A.). A set of clinical goals are listed and ordered in terms of importance, where several goals can have the same Yes START: Priori zed clinical goals Create objec ve func ons for target(s) and OARs with highest priority Op mize Areclinical goals of highest priority fullfilled? Yes Are clinical goals of the next priority level fulfilled? No Add objec ve func ons Op mize Are the clinical goals and higher priority level goals fullfilled? Goal: Automa cally generated plan No Yes No No more clinical goals? Plan cannot be improved? Modify objec ve func on(s) Modify objec ve func on(s) FIG. 3. Workflow of automatic plan generation based on lexicographic principles.

7 e1017 Wedenberg et al.: Advanced treatment planning e1017 priority level. Objective functions that correspond to the clinical goals for the ROIs considered at the current priority level are automatically created by the algorithm, and their priority weights and dose levels are modified iteratively until the optimized plan fulfills the clinical goals stated for them. For each group of goals, objective functions are automatically added and modified with the aim of fulfilling the clinical goals without violating the levels achieved for the previous (higher prioritized) goals. If a clinical goal cannot be reached within a certain number of iterations, the objective function giving the closest match is chosen and the goal takes on the best value obtained in the optimization. An illustration of the process is shown in Fig. 3. With this method, the planner needs to state the clinical goals in a well thought out way since these drive the optimization. The clinical goals need to cover every aspect required in a treatment plan. Highly prioritized goals that are very hard to satisfy may hinder achievement of all other goals of lower priority. Instead, several goals for an ROI may be set with decreasing priorities for goals achieved with increasing difficulty. There is also active research in obtaining a priori estimations of achievable results that can provide better input to the optimization so that neither too unambitious results nor impossible ones are requested 27 (see also Section 3.D.). This automatic process can be performed for different beam configurations, other treatment machines, treatment techniques and modalities, depending on what resources the clinic has. With effective methods to filter and browse among candidates, even a large number of plans can be efficiently searched through to find a desirable plan for the patient. 3.D. Knowledge-based planning The idea of knowledge-based planning is to learn from experience of previous patients. Clinical trials are of great importance, but a lot can also be learnt from everyday practice. From the large amount of patient data in clinics, patterns can be discovered that can be utilized in the treatment of new patients. The term knowledge-based planning is usually used in radiation treatment planning for methods that predict, e.g., plan quality metrics, treatment plan parameters, or voxel-byvoxel dose distributions, based on prior treatment plans and explanatory variables that quantify the geometry of the new patient of interest. Instead of using templates of population based objectives, the geometric information of the individual patient is taken into account and matched with previous patients with similar spatial configuration between the OARs and target in order to utilize these patients treatment plans to automate the creation of a new treatment plan. There are different knowledge-based planning approaches that seek to predict different metrics. 28 Many approaches try to find dose volume objectives to be used in plan optimization. In DVH point prediction, specific points on an OAR s DVH are predicted in order to estimate a new patient s achievable DVH objectives In the approach of Wu 29 a search was made in a patient data reference library for a group of patients with similar anatomic features based on the overlap volume histogram (OVH). OVH is a compact representation of the spatial relation between an OAR and a target 29 that describes the fractional volume of an OAR that is within a specified distance of the target boundary. In a database, the DVH and OVH curves for each patient were stored. A query in the database can then be made to find the lowest dose used in historical patients who have OVH values as low or lower than those of the new patient. In some studies, the aim was to predict the complete DVH curves of OARs. In the works by Zhu et al. 35 and Yuan et al. 39 the anatomical information was described by OAR and target volumes together with the OAR distance-to-target (DTH) histograms. To identify the most dominant components of the DTHs and DVHs of the OARs in the database, principal component analysis (PCA) was used. The first two or three components of the principle component scores of the DTHs together with organ volumes were then used as variables in the mapping function that aims to find the correlation between the patient s anatomical information (volume and DTH) and the resulting DVHs. Different machine learning algorithms were used to model this correlation. Another approach is to predict objective function priority weights. 41,42 In the studies by Boutilier 42 and Lee, 41 the patient s anatomy quantified by OVHs, were utilized for determining priority weight values for treatment planning. An inverse optimization model 43 takes the dose distribution of optimized historical treatment plans as input and determines objective function weights that recreates each of those plans as output. The inversely determined priority weights together with OVH features for each patient were used to train the priority weight prediction models. The prediction models estimate the objective function weight of an OAR for a new patient given anatomical features. Recently, there have been efforts to predict the spatial dose distribution, i.e., the dose per voxel 26,44,45 rather than predicting dose volume objectives. In a study by McIntosh and Purdie, 44 a dataset composed of patient images and their corresponding clinical dose distributions were used for training. CT image features were extracted, and optionally also target and organ geometries. Atlas regression forests was used to decide what planning CT image features for each voxel of previous plans are important for dose prediction, and the atlases most similar the new patient according to these image features were automatically selected. The selected atlases were then used to predict the spatial dose distribution. The dose-per-voxel distribution could be combined with dose volume objectives. The dose from the selected atlases was mapped onto the new patient. The output was a spatial dose objective. Shiraishi and Moore 45 developed an artificial neural network approach for voxel-based dose prediction, which uses one trained model for all patients instead of an atlasselection approach. 3.E. Future The first steps toward automation involve a process where the treatment plan is generated interactively with

8 e1018 Wedenberg et al.: Advanced treatment planning e1018 the planner where some steps are fully automated, and in other parts the treatment planning system warns for inferior plans, proposes improvements, gives alternative solutions, and helps in decision-making. Ultimately the goal is to learn from earlier patient outcomes. Predicting and generating DVH curves and dose distributions are just surrogates for the clinical outcome. With an advanced oncology information system, patterns between outcome in terms of tumor status, side effects, and quality of life, and patient-specific information such as medical history, genetic information, tumor specifics, and anatomical information together with treatment specifics such as dose distributions, fractionation schedules, and treatment techniques, as well as other treatment strategies including surgery, chemotherapy, and immunotherapy can be discovered. Highly advanced methods applied to data of high quantity and quality may find also intricate covariates. In the end, a vision of automated planning would be an automated process from start to end that creates a fully personalized treatment that includes also patient preferences. 4. ROBUST OPTIMIZATION Proton therapy relies on the localized proton dose deposition, i.e., Bragg Peak, to deliver conformal dose to the target while minimizing the dose to surrounding organs at risk However, small uncertainties can have a notable consequence on the dose distribution for proton therapy. 23,53,54 These uncertainties include variation in patient setup, proton stopping power modeling, dose calculation limitations, and changes to the patients anatomy, both internal and external. The impact of uncertainties on IMPT can be particularly large. The nonuniform field dose distributions of IMPT in the patient can be moved along individual beam directions by uncertainties. These dose modifications can result in hot and cold spots in the combined plan dose distribution. Due to these factors, a simple margin expansion for a planning target volume, like what is done in photon treatments, is not appropriate A. State of the art There have been efforts to develop robust proton therapy treatment plans that are less sensitive to uncertainties. Many of them can be classified into three broad categories: the worst-case robust optimization, 23,55 63 the probabilistic robust optimization, 64 and the all-scenario robust optimization. 65 The details of each of these methods can be found in the referenced publications, but a general description follows. During the setup of the treatment plan, the planner decides on beam angles (generally 2 4 beams), defines the scanning target volume, and determines the uncertainties that will be used during the optimization. The scanning target volume is a per-field structure that defines where the Bragg peak of proton spots are allowed to be placed. In general, a dose influence map is generated for the nominal scenario, plus each of the uncertainty scenarios and all of their combinations. For example, a range of dose influence maps may be generated if the treatment planner lists uncertainty in the x, y, z (position), and R (range) for the image set. At each iteration of the optimization process, the cost function will be evaluated including the uncertainty scenarios. The different robust optimization methods generally differ in how they formulate the cost function. For example, a voxel-based worst-case scenario will create an entirely new dose influence map for each constraint by evaluating each scenario at every voxel for that constraint and keeping the worst one. There are different implementation methods of the voxel-based worst case, but in general they create a new dose influence map at every iteration. Another version of worst case, the DVH based version, evaluates only the scenario that has the largest contribution to the cost function per constraint. The all-scenario method keeps all the constraints for all the scenarios in the cost function for every iteration. Regardless of which method is used, the purpose of robust optimization is to explicitly include certain uncertainties into the optimization process. As mentioned above, uncertainties often included are positional/setup errors and range uncertainties, with typical values around 3 4 mm and 3% 4%, respectively. Another uncertainty scenario that is generally used and supported by most commercial treatment planning systems is interfield uncertainties. For example, on a threefield plan, one may list a positional uncertainty of field 2 relative to 1 and 3. This aids in reducing very sharp gradients and simplifies match lines for cranial spinal fields. Recently, robustness to organ motion has started to be commercially available. These uncertainties can be estimated from dose calculation on several images (real or simulated) where each image is handled as a scenario. 66,67 The choice of realistic and reasonable uncertainty amplitudes for the scenarios is as essential for robust optimization as is the choice of the uncertainty margin to create the PTV. Over- and underestimation of uncertainties create the same detrimental effects in robust optimization as over- and underestimation of safety margins, i.e., excess OAR dose and potential loss of target coverage, respectively. Changes to the patients anatomy, such as tumor shrinkage, changes in skin folds in the beam path, large weight loss or gain, etc. are not accounted for in robust optimization. The current best guard against this is weekly or biweekly CT verification scans. The other uncertainty that is not currently explicitly accounted for is the limitation in the analytical dose calculation engines. However, fast Monte Carlo dose calculations that can be used for robust optimization are now clinically available. 65,68 4.B. Future The ability to use beam angle optimization that includes robust parameters is on the forefront. Currently the beam angles are chosen a priori with the intent that those angles will give a robust and high-quality plan. But including the beam angles in the optimization may lead to improvements in plan quality. Also on the horizon for robust optimization is

9 e1019 Wedenberg et al.: Advanced treatment planning e1019 the inclusion of biological effects 69 of proton therapy. Finally, work is ongoing in combining all the above aspects with MCO, thereby allowing a clinician to visualize the various trade-offs that must be made between robustness, normal tissue sparing (including potential biological hot spots), and target coverage. 5. BIOLOGICAL-BASED PLANNING The biological effect of physical dose is a variable of many factors. The practice of photon radiotherapy that equates dose with effect is an artifact of the neglect of fraction size dependence and the tacit convention of a standard 2 Gy fractionation to the target. Thus, expressing radiation effect in terms of photon dose is somewhat of an oversimplification, but justified by long-standing practice. The link between particle dose and photon dose (as a measure of effect) is made by RBE, which is a factor that converts physical particle dose into its photon equivalent at the same fractionation. Treatment planning and optimization deals in RBE-weighted dose, in other words: photon dose, for practicality and conventional reasons. The customary use of RBE = 1.1 for protons allows us to translate the methods and procedures of photon to proton radiotherapy, but has to be seen as a coarse approximation. Though the variation of LET d for clinical proton spot beams is small compared to heavier ions, models of proton RBE have been derived that predict variations of RBE between 1.0 and These models usually require a computation of the local LET d and an estimate of the tissue or tumor-specific (a/b) x ratio for photon treatments. The effect of these models can be studied by re-computing treatment plans optimized with constant RBE, or via including the models into the optimization Typically, the variations are largest at the distal end of the beams, where little averaging of the LET d over multiple spots and beam directions occurs. This may have implications for the choice of beam angles. 76,77 RBE variations can also perturb the dose inside the target volume if the treatment is delivered in the presence of intrafractional motion. 77 In these cases, the mean RBE-weighted target dose would always be slightly less in delivery than in planning. Treatment planning systems may eventually provide both, LET d computation and libraries of (a/b) x for various tissues/ tumors, whereby it has to be noted that the uncertainty about these parameters is still large. The magnitude of RBE corrections is obviously much greater for heavier ions, with the consequence that RBE with all its dependencies on dose, LET d, particle type, fraction size, and tissue-specific parameters inevitably has to be included in the dose optimization. On a computational level, optimization algorithms benefit from two characteristics of the problem formulation: convexity and linearity of the effective dose in the individual spot doses. The former is a property of the overall cost function that rules out the presence of local minima. However, its absence does not mean that local minima need to be taken into account. Conventional dose volume constraints are nonconvex, but no commercial treatment planning system takes special measures to ensure global convergence. Some RBE models may also be nonconvex, but due to the overall small variation of RBE in a given point for a given treatment plan, local minima due to this can safely be ruled out. Much more severe on many levels is the loss of linearity of local effective dose. While the physical dose obviously is linear, the RBE and therefore the effective dose depend on LET d, which normally changes when two dose distributions are added. (In general, the RBE of the added dose distributions is lower than the maximum of the individual doses.) As a consequence, not only does this require more computational effort in multifield dose optimization but it also raises issues for single-field optimization (the effective doses of each beam are no longer as homogeneous after adding them together) and certain multicriteria navigation/optimization algorithms that depend on dose interpolation. The largest challenges would be met for certain robust optimization approaches that either rely on some kind of dose averaging, or point-wise dose robustness criteria. Well-chosen approximations and (local) linearization of equations may be beneficial, as well as perturbation-theory-like approaches whereby RBE is updated only intermittently during iterative processes. In practice, treatment planning systems may offer tools to display and avoid sharp RBE gradients in the proximity of organs at risk. 6. LIGHT IONS Since the first clinical applications of ion beams to radiation therapy half a century ago at Lawrence Berkeley Laboratory (LBL 78,79 ), the interest in particle therapy has grown considerably. Currently, the hadron therapy centers in operation use either carbon ions or protons. Other ion beam modalities have been investigated clinically in the past at LBL (neon, silicon and argon ions) and more have been suggested (oxygen and lithium ion beams) for future clinical practice. At the National Institute of Radiological Sciences (NIRS 80 ) in Japan, the HIMAC (Heavy Ion Medial Accelerator) can accelerate various ions (H, He, C, O, Ne, Ar, Fe, Kr, and Xe) in the therapeutic energy range. However, patients are treated only with carbon ion beams. In Germany, at the Heidelberg Ion Therapy center (HIT 81 ), in addition to the clinically used protons and carbon ions beams, two other ion beam species are available for physical and biological research: 4 He and 16 O ions. Interest in using these particles for clinical purposes has increased over the last years, but meets with a lack of published data. Most studies available in literature are based either on Monte Carlo simulations or analytical models, providing comparisons of the physical dosimetric characteristics or biological effects when coupled with biological models. Helium ions, used for patient treatment in the Berkeley trial, 82 show physical and biological properties in between proton and carbon ions (see Fig. 4). Compared to protons, they offer improved dose conformation to the target due to reduced lateral scattering and they exhibit in general a higher RBE. 83 In comparison to carbon ions, they allow better sparing of the healthy tissue located behind the tumor due to the reduced fragmentation tail.