Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

Dosimetric comparison of helical tomotherapy and VMAT for anal cancer: A single institutional experience

To compare the dosimetric results of helical tomotherapy (HT) and volumetric arc therapy (VMAT) in the treatment of anal cancer. Plans were created for 20 (n = 20) patients treated for anal cancer using HT and 2 arc VMAT. Dosimetric comparison was assessed for doses to targets and organs at risk (small bowel, bladder, external genitalia, and femoral heads). Delivery time and dosimetric verification results were also compared. HT showed a higher V95% for both primary and nodal targets (V95% increase by 0.5% to 1.3%; p = ≤0.05). No differences were seen in V105%, V107%, or V110 % between techniques. HT provided better sparing of the small bowel for dose levels V30, V35, and V40 (p = 0.005, 0.001, and 0.030), but was similar at higher doses. Similarly HT provided better bladder dose at V35 only (p = 0.020). Doses to femoral heads and genitalia were similar. Delivery time was higher for the HT plans (4.58 ± 1.1 min) than VMAT (3.13 ± 0.2 minutes) (p = 0.011). Dose verification results were 99.5 ± 0.9% and 100 ± 0% (HT, n = 6) vs 95.0 ± 3.1% and 99.2 ± 0.8% (VMAT, n = 20) for global gamma criteria 3%/3 mm and 4%/4 mm, respectively. Both HT and VMAT produced high quality plans that frequently met most of the dose objectives apart from genitalia V20, V40, bladder V35, and V50. Although absolute dose differences were small, the PTV V95%, small bowel V30, V35, and V40 and bladder V35 were statistically better in the HT plans. VMAT provided a shorter delivery time by 1.45 minutes; however, our HT plans were more likely to pass tighter plan dose verification criteria than VMAT.

Advanced Treatment Planning

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.

Automation in intensity modulated radiotherapy treatment planning-a review of recent innovations

Radiotherapy treatment planning of complex radiotherapy techniques, such as intensity modulated radiotherapy and volumetric modulated arc therapy, is a resource-intensive process requiring a high level of treatment planner intervention to ensure high plan quality. This can lead to variability in the quality of treatment plans and the efficiency in which plans are produced, depending on the skills and experience of the operator and available planning time. Within the last few years, there has been significant progress in the research and development of intensity modulated radiotherapy treatment planning approaches with automation support, with most commercial manufacturers now offering some form of solution. There is a rapidly growing number of research articles published in the scientific literature on the topic. This paper critically reviews the body of publications up to April 2018. The review describes the different types of automation algorithms, including the advantages and current limitations. Also included is a discussion on the potential issues with routine clinical implementation of such software, and highlights areas for future research.

Investigating multi-objective fluence and beam orientation IMRT optimization

Radiation Oncology treatment planning requires compromises to be made between clinical objectives that are invariably in conflict. It would be beneficial to have a 'bird's-eye-view' perspective of the full spectrum of treatment plans that represent the possible trade-offs between delivering the intended dose to the planning target volume (PTV) while optimally sparing the organs-at-risk (OARs). In this work, the authors demonstrate Pareto-aware radiotherapy evolutionary treatment optimization (PARETO), a multi-objective tool featuring such bird's-eye-view functionality, which optimizes fluence patterns and beam angles for intensity-modulated radiation therapy (IMRT) treatment planning. The problem of IMRT treatment plan optimization is managed as a combined monolithic problem, where all beam fluence and angle parameters are treated equally during the optimization. To achieve this, PARETO is built around a powerful multi-objective evolutionary algorithm, called Ferret, which simultaneously optimizes multiple fitness functions that encode the attributes of the desired dose distribution for the PTV and OARs. The graphical interfaces within PARETO provide useful information such as: the convergence behavior during optimization, trade-off plots between the competing objectives, and a graphical representation of the optimal solution database allowing for the rapid exploration of treatment plan quality through the evaluation of dose-volume histograms and isodose distributions. PARETO was evaluated for two relatively complex clinical cases, a paranasal sinus and a pancreas case. The end result of each PARETO run was a database of optimal (non-dominated) treatment plans that demonstrated trade-offs between the OAR and PTV fitness functions, which were all equally good in the Pareto-optimal sense (where no one objective can be improved without worsening at least one other). Ferret was able to produce high quality solutions even though a large number of parameters, such as beam fluence and beam angles, were included in the optimization.

Evaluation of the optimal combinations of modulation factor and pitch for Helical TomoTherapy plans made with TomoEdge using Pareto optimal fronts

Background

Modulation factor (MF) and pitch have an impact on Helical TomoTherapy (HT) plan quality and HT users mostly use vendor-recommended settings. This study analyses the effect of these two parameters on both plan quality and treatment time for plans made with TomoEdge planning software by using the concept of Pareto optimal fronts.

Methods

More than 450 plans with different combinations of pitch [0.10–0.50] and MF [1.2–3.0] were produced. These HT plans, with a field width (FW) of 5 cm, were created for five head and neck patients and homogeneity index, conformity index, dose-near-maximum (D2), and dose-near-minimum (D98) were analysed for the planning target volumes, as well as the mean dose and D2 for most critical organs at risk. For every dose metric the median value will be plotted against treatment time. A Pareto-like method is used in the analysis which will show how pitch and MF influence both treatment time and plan quality.

Results

For small pitches (≤0.20), MF does not influence treatment time. The contrary is true for larger pitches (≥0.25) as lowering MF will both decrease treatment time and plan quality until maximum gantry speed is reached. At this moment, treatment time is saturated and only plan quality will further decrease.

Conclusion

The Pareto front analysis showed optimal combinations of pitch [0.23–0.45] and MF > 2.0 for a FW of 5 cm. Outside this range, plans will become less optimal. As the vendor-recommended settings fall within this range, the use of these settings is validated.

Toward optimal organ at risk sparing in complex volumetric modulated arc therapy: an exponential trade-off with target volume dose homogeneity

PURPOSE

Conventional radiotherapy typically aims for homogenous dose in the planning target volume (PTV) while sparing organs at risk (OAR). The authors quantified and characterized the trade-off between PTV dose inhomogeneity (IH) and OAR sparing in complex head and neck volumetric modulated arc therapy plans.

METHODS

Thirteen simultaneous integrated boost plans were created per patient, for ten patients. PTV boost(B)/elective(E) optimization priorities were systematically increased. IHB and IHE, defined as (100% - V95%) + V107%, were evaluated against the average of the mean dose to the combined composite swallowing and combined salivary organs (D-OAR(comp)). To investigate the influence of OAR size and position with respect to PTVB/E, OAR dose was evaluated against a modified Euclidean distance (DMB/DME) between OAR and PTV.

RESULTS

Although the achievable D-OAR(comp) for a given level of PTV IH differed between patients, excellent logarithmic fits described the D-OAR(comp)/IHB and IHE relationship in all patients (mean R(2) of 0.98 and 0.97, respectively). Allowing an increase in average IHB and IHE over a clinically acceptable range, e.g., from 0.4% ± 0.5% to 2.0% ± 2.0% and 6.9% ± 2.8% to 14.8% ± 2.7%, respectively, corresponded to a decrease in average dose to the composite salivary and swallowing structures from 30.3 ± 6.5 to 23.6 ± 4.7 Gy and 32.5 ± 8.3 to 26.8 ± 9.3 Gy. The increase in PTVE IH was mainly accounted for by an increase in V107, by on average 5.9%, rather than a reduction in V95, which was on average only 2%. A linear correlation was found between the OAR dose to composite swallowing structures and contralateral parotid and submandibular gland, with DME (R(2) = 0.83, 0.88, 0.95). Only mean ipsilateral parotid dose correlated with DMB (R(2) = 0.87).

CONCLUSIONS

OAR sparing is highly dependent on the permitted PTVB/E IH. PTVE IH substantially influences OAR doses. These results are relevant for clinical practice and for future automated treatment-planning strategies.

Advantages and limitations of navigation-based multicriteria optimization (MCO) for localized prostate cancer IMRT planning

Efficacy of inverse planning is becoming increasingly important for advanced radiotherapy techniques. This study's aims were to validate multicriteria optimization (MCO) in RayStation (v2.4, RaySearch Laboratories, Sweden) against standard intensity-modulated radiation therapy (IMRT) optimization in Oncentra (v4.1, Nucletron BV, the Netherlands) and characterize dose differences due to conversion of navigated MCO plans into deliverable multileaf collimator apertures. Step-and-shoot IMRT plans were created for 10 patients with localized prostate cancer using both standard optimization and MCO. Acceptable standard IMRT plans with minimal average rectal dose were chosen for comparison with deliverable MCO plans. The trade-off was, for the MCO plans, managed through a user interface that permits continuous navigation between fluence-based plans. Navigated MCO plans were made deliverable at incremental steps along a trajectory between maximal target homogeneity and maximal rectal sparing. Dosimetric differences between navigated and deliverable MCO plans were also quantified. MCO plans, chosen as acceptable under navigated and deliverable conditions resulted in similar rectal sparing compared with standard optimization (33.7 ± 1.8 Gy vs 35.5 ± 4.2 Gy, p = 0.117). The dose differences between navigated and deliverable MCO plans increased as higher priority was placed on rectal avoidance. If the best possible deliverable MCO was chosen, a significant reduction in rectal dose was observed in comparison with standard optimization (30.6 ± 1.4 Gy vs 35.5 ± 4.2 Gy, p = 0.047). Improvements were, however, to some extent, at the expense of less conformal dose distributions, which resulted in significantly higher doses to the bladder for 2 of the 3 tolerance levels. In conclusion, similar IMRT plans can be created for patients with prostate cancer using MCO compared with standard optimization. Limitations exist within MCO regarding conversion of navigated plans to deliverable apertures, particularly for plans that emphasize avoidance of critical structures. Minimizing these differences would result in better quality treatments for patients with prostate cancer who were treated with radiotherapy using MCO plans.

Quality assessment for VMAT prostate radiotherapy planning based on data envelopment analysis

The majority of commercial radiotherapy treatment planning systems requires planners to iteratively adjust the plan parameters in order to find a satisfactory plan. This iterative trial-and-error nature of radiotherapy treatment planning results in an inefficient planning process and in order to reduce such inefficiency, plans can be accepted without achieving the best attainable quality. We propose a quality assessment method based on data envelopment analysis (DEA) to address this inefficiency. This method compares a plan of interest to a set of past delivered plans and searches for evidence of potential further improvement. With the assistance of DEA, planners will be able to make informed decisions on whether further planning is required and ensure that a plan is only accepted when the plan quality is close to the best attainable one. We apply the DEA method to 37 prostate plans using two assessment parameters: rectal generalized equivalent uniform dose (gEUD) as the input and D95 (the minimum dose that is received by 95% volume of a structure) of the planning target volume (PTV) as the output. The percentage volume of rectum overlapping PTV is used to account for anatomical variations between patients and is included in the model as a non-discretionary output variable. Five plans that are considered of lesser quality by DEA are re-optimized with the goal to further improve rectal sparing. After re-optimization, all five plans improve in rectal gEUD without clinically considerable deterioration of the PTV D95 value. For the five re-optimized plans, the rectal gEUD is reduced by an average of 1.84 Gray (Gy) with only an average reduction of 0.07 Gy in PTV D95. The results demonstrate that DEA can correctly identify plans with potential improvements in terms of the chosen input and outputs.

Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning

We consider multicriteria radiation therapy treatment planning by navigation over the Pareto surface, implemented by interpolation between discrete treatment plans. Current state of the art for calculation of a discrete representation of the Pareto surface is to sandwich this set between inner and outer approximations that are updated one point at a time. In this paper, we generalize this sequential method to an algorithm that permits parallelization. The principle of the generalization is to apply the sequential method to an approximation of an inexpensive model of the Pareto surface. The information gathered from the model is sub-sequently used for the calculation of points from the exact Pareto surface, which are processed in parallel. The model is constructed according to the current inner and outer approximations, and given a shape that is difficult to approximate, in order to avoid that parts of the Pareto surface are incorrectly disregarded. Approximations of comparable quality to those generated by the sequential method are demonstrated when the degree of parallelization is up to twice the number of dimensions of the objective space. For practical applications, the number of dimensions is typically at least five, so that a speed-up of one order of magnitude is obtained.

Multicriteria optimization for volumetric-modulated arc therapy by decomposition into a fluence-based relaxation and a segment weight-based restriction

PURPOSE

To develop a method for inverse volumetric-modulated arc therapy (VMAT) planning that combines multicriteria optimization (MCO) with direct machine parameter optimization. The ultimate goal is to provide an efficient and intuitive method for generating high quality VMAT plans.

METHODS

Multicriteria radiation therapy treatment planning amounts to approximating the relevant treatment options by a discrete set of plans, and selecting the combination thereof that strikes the best possible balance between conflicting objectives. This approach is applied to two decompositions of the inverse VMAT planning problem: a fluence-based relaxation considered at a coarsened gantry angle spacing and under a regularizing penalty on fluence modulation, and a segment weight-based restriction in a neighborhood of the solution to the relaxed problem. The two considered variable domains are interconnected by direct machine parameter optimization toward reproducing the dose-volume histogram of the fluence-based solution.

RESULTS

The dose distribution quality of plans generated by the proposed MCO method was assessed by direct comparison with benchmark plans generated by a conventional VMAT planning method. The results for four patient cases (prostate, pancreas, lung, and head and neck) are highly comparable between the MCO plans and the benchmark plans: Discrepancies between studied dose-volume statistics for organs at risk were-with the exception of the kidneys of the pancreas case-within 1 Gy or 1 percentage point. Target coverage of the MCO plans was comparable with that of the benchmark plans, but with a small tendency toward a shift from conformity to homogeneity.

CONCLUSIONS

MCO allows tradeoffs between conflicting objectives encountered in VMAT planning to be explored in an interactive manner through search over a continuous representation of the relevant treatment options. Treatment plans selected from such a representation are of comparable dose distribution quality to conventionally optimized VMAT plans.

Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning

PURPOSE

To introduce a method to efficiently identify and calculate meaningful tradeoffs between criteria in an interactive IMRT treatment planning procedure. The method provides a systematic approach to developing high-quality radiation therapy treatment plans.

METHODS

Treatment planners consider numerous dosimetric criteria of varying importance that, when optimized simultaneously through multicriteria optimization, yield a Pareto frontier which represents the set of Pareto-optimal treatment plans. However, generating and navigating this frontier is a time-consuming, nontrivial process. A lexicographic ordering (LO) approach to IMRT uses a physician's criteria preferences to partition the treatment planning decisions into a multistage treatment planning model. Because the relative importance of criteria optimized in the different stages may not necessarily constitute a strict prioritization, the authors introduce an interactive process, sensitivity analysis in lexicographic ordering (SALO), to allow the treatment planner control over the relative sequential-stage tradeoffs. By allowing this flexibility within a structured process, SALO implicitly restricts attention to and allows exploration of a subset of the Pareto efficient frontier that the physicians have deemed most important.

RESULTS

Improvements to treatment plans over a LO approach were found by implementing the SALO procedure on a brain case and a prostate case. In each stage, a physician assessed the tradeoff between previous stage and current stage criteria. The SALO method provided critical tradeoff information through curves approximating the relationship between criteria, which allowed the physician to determine the most desirable treatment plan.

CONCLUSIONS

The SALO procedure provides treatment planners with a directed, systematic process to treatment plan selection. By following a physician's prioritization, the treatment planner can avoid wasting effort considering clinically inferior treatment plans. The planner is guided by criteria importance, but given the information necessary to accurately adjust the relative importance at each stage. Through these attributes, the SALO procedure delivers an approach well balanced between efficiency and flexibility.

Pareto fronts in clinical practice for pinnacle

PURPOSE

Our aim was to develop a framework to objectively perform treatment planning studies using Pareto fronts. The Pareto front represents all optimal possible tradeoffs among several conflicting criteria and is an ideal tool with which to study the possibilities of a given treatment technique. The framework should require minimal user interaction and should resemble and be applicable to daily clinical practice.

METHODS AND MATERIALS

To generate the Pareto fronts, we used the native scripting language of Pinnacle(3) (Philips Healthcare, Andover, MA). The framework generates thousands of plans automatically from which the Pareto front is generated. As an example, the framework is applied to compare intensity modulated radiation therapy (IMRT) with volumetric modulated arc therapy (VMAT) for prostate cancer patients. For each patient and each technique, 3000 plans are generated, resulting in a total of 60,000 plans. The comparison is based on 5-dimensional Pareto fronts.

RESULTS

Generating 3000 plans for 10 patients in parallel requires on average 96 h for IMRT and 483 hours for VMAT. Using VMAT, compared to IMRT, the maximum dose of the boost PTV was reduced by 0.4 Gy (P=.074), the mean dose in the anal sphincter by 1.6 Gy (P=.055), the conformity index of the 95% isodose (CI(95%)) by 0.02 (P=.005), and the rectal wall V(65 Gy) by 1.1% (P=.008).

CONCLUSIONS

We showed the feasibility of automatically generating Pareto fronts with Pinnacle(3). Pareto fronts provide a valuable tool for performing objective comparative treatment planning studies. We compared VMAT with IMRT in prostate patients and found VMAT had a dosimetric advantage over IMRT.

Quantitative metrics for assessing plan quality

Despite many studies over the last 3 decades that have attempted to explicitly quantify the decision-making process for radiotherapy treatment plan evaluation, judgments of an individual plan's degree of quality are still largely subjective and can show inter- and intra-practitioner variability even if the clinical treatment goals are the same. Several factors conspire to confound the full quantification of treatment plan quality, including uncertainties in dose response of cancerous and normal tissue, the rapid pace of new technology adoption, and the human component of treatment planning. However, new developments in clinical informatics and automation are lowering the bar for developing and implementing quantitative metrics into the treatment planning process. This review discusses general strategies for using quantitative metrics in the treatment planning process and presents a case study in intensity-modulated radiation therapy planning whereby control was established on a variable system via such techniques.

PARETO: A novel evolutionary optimization approach to multiobjective IMRT planning

PURPOSE

In radiation therapy treatment planning, the clinical objectives of uniform high dose to the planning target volume (PTV) and low dose to the organs-at-risk (OARs) are invariably in conflict, often requiring compromises to be made between them when selecting the best treatment plan for a particular patient. In this work, the authors introduce Pareto-Aware Radiotherapy Evolutionary Treatment Optimization (pareto), a multiobjective optimization tool to solve for beam angles and fluence patterns in intensity-modulated radiation therapy (IMRT) treatment planning.

METHODS

pareto is built around a powerful multiobjective genetic algorithm (GA), which allows us to treat the problem of IMRT treatment plan optimization as a combined monolithic problem, where all beam fluence and angle parameters are treated equally during the optimization. We have employed a simple parameterized beam fluence representation with a realistic dose calculation approach, incorporating patient scatter effects, to demonstrate feasibility of the proposed approach on two phantoms. The first phantom is a simple cylindrical phantom containing a target surrounded by three OARs, while the second phantom is more complex and represents a paraspinal patient.

RESULTS

pareto results in a large database of Pareto nondominated solutions that represent the necessary trade-offs between objectives. The solution quality was examined for several PTV and OAR fitness functions. The combination of a conformity-based PTV fitness function and a dose-volume histogram (DVH) or equivalent uniform dose (EUD) -based fitness function for the OAR produced relatively uniform and conformal PTV doses, with well-spaced beams. A penalty function added to the fitness functions eliminates hotspots. Comparison of resulting DVHs to those from treatment plans developed with a single-objective fluence optimizer (from a commercial treatment planning system) showed good correlation. Results also indicated that pareto shows promise in optimizing the number of beams.

CONCLUSIONS

This initial evaluation of the evolutionary optimization software tool pareto for IMRT treatment planning demonstrates feasibility and provides motivation for continued development. Advantages of this approach over current commercial methods for treatment planning are many, including: (1) fully automated optimization that avoids human controlled iterative optimization and potentially improves overall process efficiency, (2) formulation of the problem as a true multiobjective one, which provides an optimized set of Pareto nondominated solutions refined over hundreds of generations and compiled from thousands of parameter sets explored during the run, and (3) rapid exploration of the final nondominated set accomplished by a graphical interface used to select the best treatment option for the patient.

Improved planning time and plan quality through multicriteria optimization for intensity-modulated radiotherapy

PURPOSE

To test whether multicriteria optimization (MCO) can reduce treatment planning time and improve plan quality in intensity-modulated radiotherapy (IMRT).

METHODS AND MATERIALS

Ten IMRT patients (5 with glioblastoma and 5 with locally advanced pancreatic cancers) were logged during the standard treatment planning procedure currently in use at Massachusetts General Hospital (MGH). Planning durations and other relevant planning information were recorded. In parallel, the patients were planned using an MCO planning system, and similar planning time data were collected. The patients were treated with the standard plan, but each MCO plan was also approved by the physicians. Plans were then blindly reviewed 3 weeks after planning by the treating physician.

RESULTS

In all cases, the treatment planning time was vastly shorter for the MCO planning (average MCO treatment planning time was 12 min; average standard planning time was 135 min). The physician involvement time in the planning process increased from an average of 4.8 min for the standard process to 8.6 min for the MCO process. In all cases, the MCO plan was blindly identified as the superior plan.

CONCLUSIONS

This provides the first concrete evidence that MCO-based planning is superior in terms of both planning efficiency and dose distribution quality compared with the current trial and error-based IMRT planning approach.

A practical approach to assess clinical planning tradeoffs in the design of individualized IMRT treatment plans

BACKGROUND AND PURPOSE

To investigate the tradeoffs between organ at risk sparing and tumour coverage for IMRT treatment of lung tumours, and to develop a tool for clinical use to graphically represent these tradeoffs.

MATERIAL AND METHODS

For 5 patients with inoperable non-small cell lung cancer (NSCLC) different IMRT plans were generated using a standard TPS. The plans were automatically generated for a range of IMRT settings (weights and dose levels of the objective functions) and were systematically evaluated, focusing on the tradeoffs between organ at risk (OAR) dose and target coverage. A method to analyze and visualize planning tradeoffs was developed and evaluated.

RESULTS

Lung and oesophagus were identified as the critical organs at risk for NSCLC, the sparing of which strongly influences PTV coverage. Systematically analyzing the tradeoffs between these organs revealed that the sparing of these organs was approximately linearly related to PTV coverage parameters. Using this property, a tool was developed to graphically present the tradeoffs between the sparing of these organs at risk and the PTV coverage. The tool is an effective method to visualize the tradeoffs.

CONCLUSIONS

A tool was developed to assist IMRT plan design and selection. The clear presentation of the tradeoffs between OAR dose and coverage facilitates the optimization process and offers additional information to the clinician for a patient specific choice of the optimal IMRT plan.

An approach to multiobjective optimization of rotational therapy. II. Pareto optimal surfaces and linear combinations of modulated blocked arcs for a prostate geometry

PURPOSE

The purpose of this work is twofold: To further develop an approach to multiobjective optimization of rotational therapy treatments recently introduced by the authors [J. Pardo-Montero and J. D. Fenwick, "An approach to multiobjective optimization of rotational therapy," Med. Phys. 36, 3292-3303 (2009)], especially regarding its application to realistic geometries, and to study the quality (Pareto optimality) of plans obtained using such an approach by comparing them with Pareto optimal plans obtained through inverse planning.

METHODS

In the previous work of the authors, a methodology is proposed for constructing a large number of plans, with different compromises between the objectives involved, from a small number of geometrically based arcs, each arc prioritizing different objectives. Here, this method has been further developed and studied. Two different techniques for constructing these arcs are investigated, one based on image-reconstruction algorithms and the other based on more common gradient-descent algorithms. The difficulty of dealing with organs abutting the target, briefly reported in previous work of the authors, has been investigated using partial OAR unblocking. Optimality of the solutions has been investigated by comparison with a Pareto front obtained from inverse planning. A relative Euclidean distance has been used to measure the distance of these plans to the Pareto front, and dose volume histogram comparisons have been used to gauge the clinical impact of these distances. A prostate geometry has been used for the study.

RESULTS

For geometries where a blocked OAR abuts the target, moderate OAR unblocking can substantially improve target dose distribution and minimize hot spots while not overly compromising dose sparing of the organ. Image-reconstruction type and gradient-descent blocked-arc computations generate similar results. The Pareto front for the prostate geometry, reconstructed using a large number of inverse plans, presents a hockey-stick shape comprising two regions: One where the dose to the target is close to prescription and trade-offs can be made between doses to the organs at risk and (small) changes in target dose, and one where very substantial rectal sparing is achieved at the cost of large target underdosage. Plans computed following the approach using a conformal arc and four blocked arcs generally lie close to the Pareto front, although distances of some plans from high gradient regions of the Pareto front can be greater. Only around 12% of plans lie a relative Euclidean distance of 0.15 or greater from the Pareto front. Using the alternative distance measure of Craft ["Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization," Phys. Medica (to be published)], around 2/5 of plans lie more than 0.05 from the front. Computation of blocked arcs is quite fast, the algorithms requiring 35%-80% of the running time per iteration needed for conventional inverse plan computation.

CONCLUSIONS

The geometry-based arc approach to multicriteria optimization of rotational therapy allows solutions to be obtained that lie close to the Pareto front. Both the image-reconstruction type and gradient-descent algorithms produce similar modulated arcs, the latter one perhaps being preferred because it is more easily implementable in standard treatment planning systems. Moderate unblocking provides a good way of dealing with OARs which abut the PTV. Optimization of geometry-based arcs is faster than usual inverse optimization of treatment plans, making this approach more rapid than an inverse-based Pareto front reconstruction.

The minimum knowledge base for predicting organ-at-risk dose-volume levels and plan-related complications in IMRT planning

IMRT treatment planning requires consideration of two competing objectives: achieving the required amount of radiation for the planning target volume and minimizing the amount of radiation delivered to all other tissues. It is important for planners to understand the tradeoff between competing factors so that the time-consuming human interaction loop (plan-evaluate-modify) can be eliminated. Treatment-plan-surface models have been proposed as a decision support tool to aid treatment planners and clinicians in choosing between rival treatment plans in a multi-plan environment. In this paper, an empirical approach is introduced to determine the minimum number of treatment plans (minimum knowledge base) required to build accurate representations of the IMRT plan surface in order to predict organ-at-risk (OAR) dose-volume (DV) levels and complications as a function of input DV constraint settings corresponding to all involved OARs in the plan. We have tested our approach on five head and neck patients and five whole pelvis/prostate patients. Our results suggest that approximately 30 plans were sufficient to predict DV levels with less than 3% relative error in both head and neck and whole pelvis/prostate cases. In addition, approximately 30-60 plans were sufficient to predict saliva flow rate with less than 2% relative error and to classify rectal bleeding with an accuracy of 90%.

Comparing planning time, delivery time and plan quality for IMRT, RapidArc and Tomotherapy

The purpose of this study is to examine plan quality, treatment planning time, and estimated treatment delivery time for 5- and 9-field sliding window IMRT, single and dual arc RapidArc, and tomotherapy. For four phantoms, 5- and 9-field IMRT, single and dual arc RapidArc and tomotherapy plans were created. Plans were evaluated based on the ability to meet dose-volume constraints, dose homogeneity index, radiation conformity index, planning time, estimated delivery time, integral dose, and volume receiving more than 2 and 5 Gy. For all of the phantoms, tomotherapy was able to meet the most optimization criteria during planning (50% for P1, 67% for P2, 0% for P3, and 50% for P4). RapidArc met less of the optimization criteria (25% for P1, 17% for P2, 0% for P3, and 0% for P4), while IMRT was never able to meet any of the constraints. In addition, tomotherapy plans were able to produce the most homogeneous dose. Tomotherapy plans had longer planning time, longer estimated treatment times, lower conformity index, and higher integral dose. Tomotherapy plans can produce plans of higher quality and have the capability to conform dose distributions better than IMRT or RapidArc in the axial plane, but exhibit increased dose superior and inferior to the target volume. RapidArc, however, is capable of producing better plans than IMRT for the test cases examined in this study.

An approach to multiobjective optimization of rotational therapy

Multiobjective optimization is used in radiotherapy, especially IMRT, to generate treatment plans which meet different objectives to varying extents. Trade-off surfaces can be constructed representing the gains and losses of different objectives when switching from one plan to another, and the planner can interactively explore different treatment possibilities without the need for reoptimization. In this work a method for the multiobjective optimization of rotational therapy is introduced. The proposed method is applied slice per slice and uses the geometry of the slice directly to construct several arcs, each conformally irradiating the tumor and blocking a number (0,1,2,...) of different organs at risk present in the treatment. The blocked arc dose distributions so obtained are quite inhomogeneous in the target. An algorithm, based on the iterative reconstruction of images from projections, has been developed to compensate for this inhomogeneity, leading to compensated blocked arcs which deliver more uniform target doses but still block critical structures. Different treatments can be obtained as linear combinations of these arcs, each involving different trade-offs among the objectives involved. The compensatory algorithm substantially improves the target dose uniformity of blocked arcs at the cost of slightly increasing the dose to the rest of the body, allowing delivery of good uniform dose distributions to the target without significantly irradiating the blocked organ(s). Trade-off surfaces are presented for slices containing a target and one or two critical structures. The method is directly implementable using axial or helical tomotherapy. Implementation for conventional linear accelerators will be more difficult because the number of arcs needed to deliver such treatments can be large, an issue to be explored in future work.

A method to dynamically balance intensity modulated radiotherapy dose between organs-at-risk

The IMRT treatment planning process typically follows a path that is based on the manner in which the planner interactively adjusts the target and organ-at-risk (OAR) constraints and priorities. The time-intensive nature of this process restricts the planner from fully understanding the dose tradeoff between structures, making it unlikely that the resulting plan fully exploits the extent to which dose can be redistributed between anatomical structures. Multiobjective Pareto optimization has been used in the past to enable the planner to more thoroughly explore alternatives in dose trade-off by combining pre-generated Pareto optimal solutions in real time, thereby potentially tailoring a plan more exactly to requirements. However, generating the Pareto optimal solutions can be nonintuitive and computationally time intensive. The author presents an intuitive and fast non-Pareto approach for generating optimization sequences (prior to planning), which can then be rapidly combined by the planner in real time to yield a satisfactory plan. Each optimization sequence incrementally reduces dose to one OAR at a time, starting from the optimization solution where dose to all OARs are reduced with equal priority, until user-specified target coverage limits are violated. The sequences are computationally efficient to generate, since the optimization at each position along a sequence is initiated from the end result of the previous position in the sequence. The pre-generated optimization sequences require no user interaction. In real time, a planner can more or less instantaneously visualize a treatment plan by combining the dose distributions corresponding to user-selected positions along each of the optimization sequences (target coverage is intrinsically maintained in the combination). Interactively varying the selected positions along each of the sequences enables the planner to rapidly understand the nature of dose trade-off between structures and, thereby, arrive at a suitable plan in a short time. This methodology is demonstrated on a prostate cancer case and olfactory neuroblastoma case.

A novel approach to multi-criteria inverse planning for IMRT

Treatment plan optimization is a multi-criteria process. Optimizing solely on one objective or on a sum of a priori weighted objectives may result in inferior treatment plans. Manually adjusting weights or constraints in a trial and error procedure is time consuming. In this paper we introduce a novel multi-criteria optimization approach to automatically optimize treatment constraints (dose-volume and maximum-dose). The algorithm tries to meet these constraints as well as possible, but in the case of conflicts it relaxes lower priority constraints so that higher priority constraints can be met. Afterwards, all constraints are tightened, starting with the highest priority constraints. Applied constraint priority lists can be used as class solutions for patients with similar tumour types. The presented algorithm does iteratively apply an underlying algorithm for beam profile optimization, based on a quadratic objective function with voxel-dependent importance factors. These voxel-dependent importance factors are automatically adjusted to reduce dose-volume and maximum-dose constraint violations.

A new concept for interactive radiotherapy planning with multicriteria optimization: first clinical evaluation

BACKGROUND AND PURPOSE

Currently, inverse planning for intensity-modulated radiotherapy (IMRT) can be a time-consuming trial and error process. This is because many planning objectives are inherently contradictory and cannot reach their individual optimum all at the same time. Therefore in clinical practice the potential of IMRT cannot be fully exploited for all patients. Multicriteria (multiobjective) optimization combined with interactive plan navigation is a promising approach to overcome these problems.

PATIENTS AND METHODS

We developed a new inverse planning system called "Multicriteria Interactive Radiotherapy Assistant (MIRA)". The optimization result is a database of patient specific, Pareto-optimal plan proposals. The database is explored with an intuitive user interface that utilizes both a new interactive element for plan navigation and familiar dose visualizations in form of DVH and isodose projections. Two clinical test cases, one paraspinal meningioma case and one prostate case, were optimized using MIRA and compared with the clinically approved planning program KonRad.

RESULTS

Generating the databases required no user interaction and took approx. 2-3h per case. The interactive exploration required only a few minutes until the best plan was identified, resulting in a significant reduction of human planning time. The achievable plan quality was comparable to KonRad with the additional benefit of having plan alternatives at hand to perform a sensitivity analysis or to decide for a different clinical compromise.

CONCLUSIONS

The MIRA system provides a complete database and interactive exploration of the solution space in real time. Hence, it is ideally suited for the inherently multicriterial problem of inverse IMRT treatment planning.