Multiobjective inverse planning for intensity modulated radiotherapy with constraint-free gradient-based optimization algorithms

Clinical commissioning and introduction of an in-house artificial intelligence (AI) platform for automated head and neck intensity modulated radiation therapy (IMRT) treatment planning

BACKGROUND AND PURPOSE

To describe the clinical commissioning of an in-house artificial intelligence (AI) treatment planning platform for head-and-neck (HN) Intensity Modulated Radiation Therapy (IMRT).

MATERIALS AND METHODS

The AI planning platform has three components: (1) a graphical user interface (GUI) is built within the framework of a commercial treatment planning system (TPS). The GUI allows AI models to run remotely on a designated workstation configured with GPU acceleration. (2) A template plan is automatically prepared involving both clinical and AI considerations, which include contour evaluation, isocenter placement, and beam/collimator jaw placement. (3) A well-orchestrated suite of AI models predicts optimal fluence maps, which are imported into TPS for dose calculation followed by an optional automatic fine-tuning. Six AI models provide flexible tradeoffs in parotid sparing and Planning Target Volume (PTV)-organ-at-risk (OAR) preferences. Planners could examine the plan dose distribution and make further modifications as clinically needed. The performance of the AI plans was compared to the corresponding clinical plans.

RESULTS

The average plan generation time including manual operations was 10-15  min per case, with each AI model prediction taking ∼1 s. The six AI plans form a wide range of tradeoff choices between left and right parotids and between PTV and OARs compared with corresponding clinical plans, which correctly reflected their tradeoff designs.

CONCLUSION

The in-house AI IMRT treatment planning platform was developed and is available for clinical use at our institution. The process demonstrates outstanding performance and robustness of the AI platform and provides sufficient validation.

Input feature design and its impact on the performance of deep learning models for predicting fluence maps in intensity-modulated radiation therapy

Objective. Deep learning (DL) models for fluence map prediction (FMP) have great potential to reduce treatment planning time in intensity-modulated radiation therapy (IMRT) by avoiding the lengthy inverse optimization process. This study aims to improve the rigor of input feature design in a DL-FMP model by examining how different designs of input features influence model prediction performance.Approach. This study included 231 head-and-neck intensity-modulated radiation therapy patients. Three input feature designs were investigated. The first design (D1) assumed that information of all critical structures from all beam angles should be combined to predict fluence maps. The second design (D2) assumed that local anatomical information was sufficient for predicting radiation intensity of a beamlet at a respective beam angle. The third design (D3) assumed the need for both local anatomical information and inter-beam modulation to predict radiation intensity values of the beamlets that intersect at a voxel. For each input design, we tailored the DL model accordingly. All models were trained using the same set of ground truth plans (GT plans). The plans generated by DL models (DL plans) were analyzed using key dose-volume metrics. One-way ANOVA with multiple comparisons correction (Bonferroni method) was performed (significance level = 0.05).Main results. For PTV-related metrics, all DL plans had significantly higher maximum dose (p < 0.001), conformity index (p < 0.001), and heterogeneity index (p < 0.001) compared to GT plans, with D2 being the worst performer. Meanwhile, except for cord+5 mm (p < 0.001), DL plans of all designs resulted in OAR dose metrics that are comparable to those of GT plans.Significance. Local anatomical information contains most of the information that DL models need to predict fluence maps for clinically acceptable OAR sparing. Input features from beam angles are needed to achieve the best PTV coverage. These results provide valuable insights for further improvement of DL-FMP models and DL models in general.

Insights of an AI agent via analysis of prediction errors: a case study of fluence map prediction for radiation therapy planning

Purpose.We have previously reported an artificial intelligence (AI) agent that automatically generates intensity-modulated radiation therapy (IMRT) plans via fluence map prediction, by-passing inverse planning. This AI agent achieved clinically comparable quality for prostate cases, but its performance on head-and-neck patients leaves room for improvement. This study aims to collect insights of the deep-learning-based (DL-based) fluence map prediction model by systematically analyzing its prediction errors.Methods.From the modeling perspective, the DL model's output is the fluence maps of IMRT plans. However, from the clinical planning perspective, the plan quality evaluation should be based on the clinical dosimetric criteria such as dose-volume histograms. To account for the complex and non-intuitive relationships between fluence map prediction errors and the corresponding dose distribution changes, we propose a novel error analysis approach that systematically examines plan dosimetric changes that are induced by varying amounts of fluence prediction errors. We investigated four decomposition modes of model prediction errors. The two spatial domain decompositions are based on fluence intensity and fluence gradient. The two frequency domain decompositions are based on Fourier-space banded frequency rings and Fourier-space truncated low-frequency disks. The decomposed error was analyzed for its impact on the resulting plans' dosimetric metrics. The analysis was conducted on 15 test cases spared from the 200 training and 16 validation cases used to train the model.Results.Most planning target volume metrics were significantly correlated with most error decompositions. The Fourier space disk radii had the largest Spearman's coefficients. The low-frequency region within a disk of ∼20% Fourier space contained most of errors that impact overall plan quality.Conclusions.This study demonstrates the feasibility of using fluence map prediction error analysis to understand the AI agent's performance. Such insights will help fine-tune the DL models in architecture design and loss function selection.

An artificial intelligence-driven agent for real-time head-and-neck IMRT plan generation using conditional generative adversarial network (cGAN)

PURPOSE

To develop an artificial intelligence (AI) agent for fully automated rapid head-and-neck intensity-modulated radiation therapy (IMRT) plan generation without time-consuming dose-volume-based inverse planning.

METHODS

This AI agent was trained via implementing a conditional generative adversarial network (cGAN) architecture. The generator, PyraNet, is a novel deep learning network that implements 28 classic ResNet blocks in pyramid-like concatenations. The discriminator is a customized four-layer DenseNet. The AI agent first generates multiple customized two-dimensional projections at nine template beam angles from a patient's three-dimensional computed tomography (CT) volume and structures. These projections are then stacked as four-dimensional inputs of PyraNet, from which nine radiation fluence maps of the corresponding template beam angles are generated simultaneously. Finally, the predicted fluence maps are automatically postprocessed by Gaussian deconvolution operations and imported into a commercial treatment planning system (TPS) for plan integrity check and visualization. The AI agent was built and tested upon 231 oropharyngeal IMRT plans from a TPS plan library. 200/16/15 plans were assigned for training/validation/testing, respectively. Only the primary plans in the sequential boost regime were studied. All plans were normalized to 44 Gy prescription (2 Gy/fx). A customized Harr wavelet loss was adopted for fluence map comparison during the training of the PyraNet. For test cases, isodose distributions in AI plans and TPS plans were qualitatively evaluated for overall dose distributions. Key dosimetric metrics were compared by Wilcoxon signed-rank tests with a significance level of 0.05.

RESULTS

All 15 AI plans were successfully generated. Isodose gradients outside of PTV in AI plans were comparable to those of the TPS plans. After PTV coverage normalization, D_mean of left parotid (D_AI  = 23.1 ± 2.4 Gy; D_TPS  = 23.1 ± 2.0 Gy), right parotid (D_AI  = 23.8 ± 3.0 Gy; D_TPS  = 23.9 ± 2.3 Gy), and oral cavity (D_AI  = 24.7 ± 6.0 Gy; D_TPS  = 23.9 ± 4.3 Gy) in the AI plans and the TPS plans were comparable without statistical significance. AI plans achieved comparable results for maximum dose at 0.01cc of brainstem (D_AI  = 15.0 ± 2.1 Gy; D_TPS  = 15.5 ± 2.7 Gy) and cord + 5mm (D_AI  = 27.5 ± 2.3 Gy; D_TPS  = 25.8 ± 1.9 Gy) without clinically relevant differences, but body D_max results (D_AI  = 121.1 ± 3.9 Gy; D_TPS  = 109.0 ± 0.9 Gy) were higher than the TPS plan results. The AI agent needed ~3 s for predicting fluence maps of an IMRT plan.

CONCLUSIONS

With rapid and fully automated execution, the developed AI agent can generate complex head-and-neck IMRT plans with acceptable dosimetry quality. This approach holds great potential for clinical applications in preplanning decision-making and real-time planning.

Comparison of two inverse planning algorithms for cervical cancer brachytherapy

PURPOSE

To compare two inverse planning algorithms, the hybrid inverse planning optimization (HIPO) algorithm and the inverse planning simulated annealing (IPSA) algorithm, for cervical cancer brachytherapy and provide suggestions for their usage.

MATERIAL AND METHODS

This study consisted of 24 cervical cancer patients treated with CT image-based high-dose-rate brachytherapy using various combinations of tandem/ovoid applicator and interstitial needles. For fixed catheter configurations, plans were retrospectively optimized with two methods: IPSA and HIPO. The dosimetric parameters with respect to target coverage, localization of high dose volume (LHDV), conformal index (COIN), and sparing of organs at risk (OARs) were evaluated. A plan assessment method which combines a graphical analysis and a scoring index was used to compare the quality of two plans for each case. The characteristics of dwell time distributions of the two plans were also analyzed in detail.

RESULTS

Both IPSA and HIPO can produce clinically acceptable treatment plans. The rectum D_2cc was slightly lower for HIPO as compared to IPSA (P = 0.002). All other dosimetric parameters for targets and OARs were not significantly different between the two algorithms. The generated radar plots and scores intuitively presented the plan properties and enabled to reflect the clinical priorities for the treatment plans. Significant different characteristics were observed between the dwell time distributions generated by IPSA and HIPO.

CONCLUSIONS

Both algorithms could generate high-quality treatment plans, but their performances were slightly different in terms of each specific patient. The clinical decision on the optimal plan for each patient can be made quickly and consistently with the help of the plan assessment method. Besides, the characteristics of dwell time distribution were suggested to be taken into account during plan selection. Compared to IPSA, the dwell time distributions generated by HIPO may be closer to clinical preference.

Intensity-Modulated Radiation Therapy Optimization for Acceptable and Remaining-One Unacceptable Dose-Volume and Mean-Dose Constraint Planning

We give a novel approach for obtaining an intensity-modulated radiation therapy (IMRT) optimization solution based on the idea of continuous dynamical methods. The proposed method, which is an iterative algorithm derived from the discretization of a continuous-time dynamical system, can handle not only dose-volume but also mean-dose constraints directly in IMRT treatment planning. A theoretical proof for the convergence to an equilibrium corresponding to the desired IMRT planning is given by using the Lyapunov stability theorem. By introducing the concept of "acceptable," which means the existence of a nonempty set of beam weights satisfying the given dose-volume and mean-dose constraints, and by using the proposed method for an acceptable IMRT planning, one can resolve the issue that the objective and evaluation are different in the conventional planning process. Moreover, in the case where the target planning is totally unacceptable and partly acceptable except for one group of dose constraints, we give a procedure that enables us to obtain a nearly optimal solution close to the desired solution for unacceptable planning. The performance of the proposed approach for an acceptable or unacceptable planning is confirmed through numerical experiments simulating a clinical setup.

Artificial Intelligence in Radiotherapy Treatment Planning: Present and Future

Treatment planning is an essential step of the radiotherapy workflow. It has become more sophisticated over the past couple of decades with the help of computer science, enabling planners to design highly complex radiotherapy plans to minimize the normal tissue damage while persevering sufficient tumor control. As a result, treatment planning has become more labor intensive, requiring hours or even days of planner effort to optimize an individual patient case in a trial-and-error fashion. More recently, artificial intelligence has been utilized to automate and improve various aspects of medical science. For radiotherapy treatment planning, many algorithms have been developed to better support planners. These algorithms focus on automating the planning process and/or optimizing dosimetric trade-offs, and they have already made great impact on improving treatment planning efficiency and plan quality consistency. In this review, the smart planning tools in current clinical use are summarized in 3 main categories: automated rule implementation and reasoning, modeling of prior knowledge in clinical practice, and multicriteria optimization. Novel artificial intelligence-based treatment planning applications, such as deep learning-based algorithms and emerging research directions, are also reviewed. Finally, the challenges of artificial intelligence-based treatment planning are discussed for future works.

RapidPlan knowledge based planning: iterative learning process and model ability to steer planning strategies

Purpose

To determine if the performance of a knowledge based RapidPlan (RP) planning model could be improved with an iterative learning process, i.e. if plans generated by an RP model could be used as new input to re-train the model and achieve better performance.

Methods

Clinical VMAT plans from 83 patients presenting with head and neck cancer were selected to train an RP model, CL-1. With this model, new plans on the same patients were generated, and subsequently used as input to train a novel model, CL-2. Both models were validated on a cohort of 20 patients and dosimetric results compared. Another set of 83 plans was realised on the same patients with different planning criteria, by using a simple template with no attempt to manually improve the plan quality. Those plans were employed to train another model, TP-1. The differences between the plans generated by CL-1 and TP-1 for the validation cohort of patients were compared with respect to the differences between the original plans used to build the two models.

Results

The CL-2 model presented an improvement relative to CL-1, with higher R² values and better regression plots. The mean doses to parallel organs decreased with CL-2, while D_1% to serial organs increased (but not significantly). The different models CL-1 and TP-1 were able to yield plans according to each original strategy.

Conclusion

A refined RP model allowed the generation of plans with improved quality, mostly for parallel organs at risk and, possibly, also the intrinsic model quality.

Intelligent inverse treatment planning via deep reinforcement learning, a proof-of-principle study in high dose-rate brachytherapy for cervical cancer

Inverse treatment planning in radiation therapy is formulated as solving optimization problems. The objective function and constraints consist of multiple terms designed for different clinical and practical considerations. Weighting factors of these terms are needed to define the optimization problem. While a treatment planning optimization engine can solve the optimization problem with given weights, adjusting the weights to yield a high-quality plan is typically performed by a human planner. Yet the weight-tuning task is labor intensive, time consuming, and it critically affects the final plan quality. An automatic weight-tuning approach is strongly desired. The procedure of weight adjustment to improve the plan quality is essentially a decision-making problem. Motivated by the tremendous success in deep learning for decision making with human-level intelligence, we propose a novel framework to adjust the weights in a human-like manner. This study used inverse treatment planning in high-dose-rate brachytherapy (HDRBT) for cervical cancer as an example. We developed a weight-tuning policy network (WTPN) that observes dose volume histograms of a plan and outputs an action to adjust organ weighting factors, similar to the behaviors of a human planner. We trained the WTPN via end-to-end deep reinforcement learning. Experience replay was performed with the epsilon greedy algorithm. After training was completed, we applied the trained WTPN to guide treatment planning of five testing patient cases. It was found that the trained WTPN successfully learnt the treatment planning goals and was able to guide the weight tuning process. On average, the quality score of plans generated under the WTPN's guidance was improved by ~8.5% compared to the initial plan with arbitrarily set weights, and by 10.7% compared to the plans generated by human planners. To our knowledge, this was the first time that a tool was developed to adjust organ weights for the treatment planning optimization problem in a human-like fashion based on intelligence learnt from a training process, which was different from existing strategies based on pre-defined rules. The study demonstrated potential feasibility to develop intelligent treatment planning approaches via deep reinforcement learning.

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.

A new strategy for volumetric-modulated arc therapy planning using AutoPlanning based multicriteria optimization for nasopharyngeal carcinoma

BACKGROUND

A new strategy for making the appropriate choice of the representative optimization parameters in planning processes and accurate selection criteria during Pareto surface navigation for general multicriteria optimization (MCO) was recommended in the study. The purpose was to combine both benefits of AutoPlanning optimization and MCO (APMCO) for achieving an individual volumetric-modulated arc therapy (VMAT) plan according to the clinically achieved patient-specific tradeoff among conflicting priorities. The preclinical investigation of this optimization approach for nasopharyngeal carcinoma (NPC) radiotherapy was performed and compared to general MCO VMAT.

METHODS

A total of 60 NPC patients with various stages were enrolled in this study. General MCO and APMCO plans were generated for each patient on the treatment planning system. The differences between two planning schemes were evaluated and compared.

RESULTS

All plans were capable of achieving the prescription requirement. The planning target volume coverage and conformation number were remarkably similar between general MCO and APMCO plans. There were no significant differences in most of organs at risk (OARs) sparing. However, in APMCO plans, relatively remarkable decreases were observed in the mean dose (D_mean) to the glottic larynx and pharyngeal constrictor muscles. The reductions of average D_mean to the two OARs were 10.5% (p < 0.0001) and 8.4% (p < 0.0001), respectively. APMCO technique was found to increase the planning time for an average of approximately 5 h and did not lead to a significant increase of monitor units compared to general MCO.

CONCLUSIONS

The potential of the APMCO strategy is best realized with a clinical implementation that exploits individual generation of Pareto surface representations without manual interaction. It also assists physicians to ensure navigation in a more efficient and straightforward manner.

Multicriteria plan optimization in the hands of physicians: a pilot study in prostate cancer and brain tumors

BACKGROUND

The purpose of this study was to demonstrate the feasibility of physician driven planning in intensity modulated radiotherapy (IMRT) with a multicriteria optimization (MCO) treatment planning system and template based plan optimization. Exploiting the full planning potential of MCO navigation, this alternative planning approach intends to improve planning efficiency and individual plan quality.

METHODS

Planning was retrospectively performed on 12 brain tumor and 10 post-prostatectomy prostate patients previously treated with MCO-IMRT. For each patient, physicians were provided with a template-based generated Pareto surface of optimal plans to navigate, using the beam angles from the original clinical plans. We compared physician generated plans to clinically delivered plans (created by dosimetrists) in terms of dosimetric differences, physician preferences and planning times.

RESULTS

Plan qualities were similar, however physician generated and clinical plans differed in the prioritization of clinical goals. Physician derived prostate plans showed significantly better sparing of the high dose rectum and bladder regions (p(D1) < 0.05; D1: dose received by 1% of the corresponding structure). Physicians' brain tumor plans indicated higher doses for targets and brainstem (p(D1) < 0.05). Within blinded plan comparisons physicians preferred the clinical plans more often (brain: 6:3 out of 12, prostate: 2:6 out of 10) (not statistically significant). While times of physician involvement were comparable for prostate planning, the new workflow reduced the average involved time for brain cases by 30%. Planner times were reduced for all cases. Subjective benefits, such as a better understanding of planning situations, were observed by clinicians through the insight into plan optimization and experiencing dosimetric trade-offs.

CONCLUSIONS

We introduce physician driven planning with MCO for brain and prostate tumors as a feasible planning workflow. The proposed approach standardizes the planning process by utilizing site specific templates and integrates physicians more tightly into treatment planning. Physicians' navigated plan qualities were comparable to the clinical plans. Given the reduction of planning time of the planner and the equal or lower planning time of physicians, this approach has the potential to improve departmental efficiencies.

Personalized treatment planning with a model of radiation therapy outcomes for use in multiobjective optimization of IMRT plans for prostate cancer

PURPOSE

To build a new treatment planning approach that extends beyond radiation transport and IMRT optimization by modeling the radiation therapy process and prognostic indicators for more outcome-focused decision making.

METHODS

An in-house treatment planning system was modified to include multiobjective inverse planning, a probabilistic outcome model, and a multi-attribute decision aid. A genetic algorithm generated a set of plans embodying trade-offs between the separate objectives. An influence diagram network modeled the radiation therapy process of prostate cancer using expert opinion, results of clinical trials, and published research. A Markov model calculated a quality adjusted life expectancy (QALE), which was the endpoint for ranking plans.

RESULTS

The Multiobjective Evolutionary Algorithm (MOEA) was designed to produce an approximation of the Pareto Front representing optimal tradeoffs for IMRT plans. Prognostic information from the dosimetrics of the plans, and from patient-specific clinical variables were combined by the influence diagram. QALEs were calculated for each plan for each set of patient characteristics. Sensitivity analyses were conducted to explore changes in outcomes for variations in patient characteristics and dosimetric variables. The model calculated life expectancies that were in agreement with an independent clinical study.

CONCLUSIONS

The radiation therapy model proposed has integrated a number of different physical, biological and clinical models into a more comprehensive model. It illustrates a number of the critical aspects of treatment planning that can be improved and represents a more detailed description of the therapy process. A Markov model was implemented to provide a stronger connection between dosimetric variables and clinical outcomes and could provide a practical, quantitative method for making difficult clinical decisions.

A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization

PURPOSE

To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters.

METHODS

In the treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for a set of the objective functions associated to the organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems.

RESULTS

The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the impact of using different objective functions on plan qualities and Pareto surfaces. The main discoveries are threefold: (1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives.

CONCLUSIONS

The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

Multicriteria optimization of the spatial dose distribution

PURPOSE

Treatment planning for radiation therapy involves trade-offs with respect to different clinical goals. Typically, the dose distribution is evaluated based on few statistics and dose-volume histograms. Particularly for stereotactic treatments, the spatial dose distribution represents further criteria, e.g., when considering the gradient between subregions of volumes of interest. The authors have studied how to consider the spatial dose distribution using a multicriteria optimization approach.

METHODS

The authors have extended a stepwise multicriteria optimization approach to include criteria with respect to the local dose distribution. Based on a three-dimensional visualization of the dose the authors use a software tool allowing interaction with the dose distribution to map objectives with respect to its shape to a constrained optimization problem. Similarly, conflicting criteria are highlighted and the planner decides if and where to relax the shape of the dose distribution.

RESULTS

To demonstrate the potential of spatial multicriteria optimization, the tool was applied to a prostate and meningioma case. For the prostate case, local sparing of the rectal wall and shaping of a boost volume are achieved through local relaxations and while maintaining the remaining dose distribution. For the meningioma, target coverage is improved by compromising low dose conformality toward noncritical structures. A comparison of dose-volume histograms illustrates the importance of spatial information for achieving the trade-offs.

CONCLUSIONS

The results show that it is possible to consider the location of conflicting criteria during treatment planning. Particularly, it is possible to conserve already achieved goals with respect to the dose distribution, to visualize potential trade-offs, and to relax constraints locally. Hence, the proposed approach facilitates a systematic exploration of the optimal shape of the dose distribution.

Maximizing dosimetric benefits of IMRT in the treatment of localized prostate cancer through multicriteria optimization planning

We examine the quality of plans created using multicriteria optimization (MCO) treatment planning in intensity-modulated radiation therapy (IMRT) in treatment of localized prostate cancer. Nine random cases of patients receiving IMRT to the prostate were selected. Each case was associated with a clinically approved plan created using Corvus. The cases were replanned using MCO-based planning in RayStation. Dose-volume histogram data from both planning systems were presented to 2 radiation oncologists in a blinded evaluation, and were compared at a number of dose-volume points. Both physicians rated all 9 MCO plans as superior to the clinically approved plans (p<10(-5)). Target coverage was equivalent (p = 0.81). Maximum doses to the prostate and bladder and the V50 and V70 to the anterior rectum were reduced in all MCO plans (p<0.05). Treatment planning time with MCO took approximately 60 minutes per case. MCO-based planning for prostate IMRT is efficient and produces high-quality plans with good target homogeneity and sparing of the anterior rectum, bladder, and femoral heads, without sacrificing target coverage.

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.

The use of a multiobjective evolutionary algorithm to increase flexibility in the search for better IMRT plans

PURPOSE

To evaluate how a more flexible and thorough multiobjective search of feasible IMRT plans affects performance in IMRT optimization.

METHODS

A multiobjective evolutionary algorithm (MOEA) was used as a tool to investigate how expanding the search space to include a wider range of penalty functions affects the quality of the set of IMRT plans produced. The MOEA uses a population of IMRT plans to generate new IMRT plans through deterministic minimization of recombined penalty functions that are weighted sums of multiple, tissue-specific objective functions. The quality of the generated plans are judged by an independent set of nonconvex, clinically relevant decision criteria, and all dominated plans are eliminated. As this process repeats itself, better plans are produced so that the population of IMRT plans will approach the Pareto front. Three different approaches were used to explore the effects of expanding the search space. First, the evolutionary algorithm used genetic optimization principles to search by simultaneously optimizing both the weights and tissue-specific dose parameters in penalty functions. Second, penalty function parameters were individually optimized for each voxel in all organs at risk (OARs) in the MOEA. Finally, a heuristic voxel-specific improvement (VSI) algorithm that can be used on any IMRT plan was developed that incrementally improves voxel-specific penalty function parameters for all structures (OARs and targets). Different approaches were compared using the concept of domination comparison applied to the sets of plans obtained by multiobjective optimization.

RESULTS

MOEA optimizations that simultaneously searched both importance weights and dose parameters generated sets of IMRT plans that were superior to sets of plans produced when either type of parameter was fixed for four example prostate plans. The amount of improvement increased with greater overlap between OARs and targets. Allowing the MOEA to search for voxel-specific penalty functions improved results for simple cases with three structures but did not improve results for a more complex case with seven structures. For this modification, the amount of improvement increased with less overlap between OARs and targets. The voxel-specific improvement algorithm improved results for all cases, and its clinical relevance was demonstrated in a complex prostate and a very complex head and neck case.

CONCLUSIONS

Using an evolutionary algorithm as a tool, it was found that allowing more flexibility in the search space enhanced performance. The two strategies of (a) varying the weights and reference doses in the objective function and (b) removing the constraint of equal penalties for all voxels in a structure both generated sets of plans that dominated sets of plans considered to be "Pareto optimal" within the conventional, more limited search space. When considering voxel-specific objectives, the very large search space can lead to convergence problems in the MOEA for complex cases, but this is not an issue for the VSI algorithm.

A comparison of three commercial IMRT treatment planning systems for selected paediatric cases

This work aimed at evaluating the performance of three different intensity‐modulated radiotherapy (IMRT) treatment planning systems (TPSs) — KonRad, XiO and Prowess — for selected pediatric cases. For this study, 11 pediatric patients with different types of brain, orbit, head and neck cancer were selected. Clinical step‐and‐shoot IMRT treatment plans were designed for delivery on a Siemens ONCOR accelerator with 82‐leaf multileaf collimators (MLCs). Plans were optimized to achieve the same clinical objectives by applying the same beam energy and the same number and direction of beams. The analysis of performance was based on isodose distributions, dose‐volume histograms (DVHs) for planning target volume (PTV), the relevant organs at risk (OARs), as well as mean dose (Dmean), maximum dose (Dmax), 95% dose (D95), volume of patient receiving 2 and 5 Gy, total number of segments, monitor units per segment (MU/Segment), and the number of MU/cGy. Treatment delivery time and conformation number were two other evaluation parameters that were considered in this study. Collectively, the Prowess and KonRad plans showed a significant reduction in the number of MUs that varied between 1.8% and 61.5% (p−value=0.001) for the different cases, compared to XiO. This was reflected in shorter treatment delivery times. The percentage volumes of each patient receiving 2 Gy and 5 Gy were compared for the three TPSs. The general trend was that KonRad had the highest percentage volume, Prowess showed the lowest (p−value=0.0001). The KonRad achieved better conformality than both of XiO and Prowess. Based on the present results, the three treatment planning systems were efficient in IMRT, yet XiO showed the lowest performance. The three TPSs achieved the treatment goals according to the internationally approved standards.

Comparative analysis of Pareto surfaces in multi-criteria IMRT planning

In the multi-criteria optimization approach to IMRT planning, a given dose distribution is evaluated by a number of convex objective functions that measure tumor coverage and sparing of the different organs at risk. Within this context optimizing the intensity profiles for any fixed set of beams yields a convex Pareto set in the objective space. However, if the number of beam directions and irradiation angles are included as free parameters in the formulation of the optimization problem, the resulting Pareto set becomes more intricate. In this work, a method is presented that allows for the comparison of two convex Pareto sets emerging from two distinct beam configuration choices. For the two competing beam settings, the non-dominated and the dominated points of the corresponding Pareto sets are identified and the distance between the two sets in the objective space is calculated and subsequently plotted. The obtained information enables the planner to decide if, for a given compromise, the current beam setup is optimal. He may then re-adjust his choice accordingly during navigation. The method is applied to an artificial case and two clinical head neck cases. In all cases no configuration is dominating its competitor over the whole Pareto set. For example, in one of the head neck cases a seven-beam configuration turns out to be superior to a nine-beam configuration if the highest priority is the sparing of the spinal cord. The presented method of comparing Pareto sets is not restricted to comparing different beam angle configurations, but will allow for more comprehensive comparisons of competing treatment techniques (e.g., photons versus protons) than with the classical method of comparing single treatment plans.

Investigation of effective decision criteria for multiobjective optimization in IMRT

PURPOSE

To investigate how using different sets of decision criteria impacts the quality of intensity modulated radiation therapy (IMRT) plans obtained by multiobjective optimization.

METHODS

A multiobjective optimization evolutionary algorithm (MOEA) was used to produce sets of IMRT plans. The MOEA consisted of two interacting algorithms: (i) a deterministic inverse planning optimization of beamlet intensities that minimizes a weighted sum of quadratic penalty objectives to generate IMRT plans and (ii) an evolutionary algorithm that selects the superior IMRT plans using decision criteria and uses those plans to determine the new weights and penalty objectives of each new plan. Plans resulting from the deterministic algorithm were evaluated by the evolutionary algorithm using a set of decision criteria for both targets and organs at risk (OARs). Decision criteria used included variation in the target dose distribution, mean dose, maximum dose, generalized equivalent uniform dose (gEUD), an equivalent uniform dose (EUD(alpha,beta) formula derived from the linear-quadratic survival model, and points on dose volume histograms (DVHs). In order to quantatively compare results from trials using different decision criteria, a neutral set of comparison metrics was used. For each set of decision criteria investigated, IMRT plans were calculated for four different cases: two simple prostate cases, one complex prostate Case, and one complex head and neck Case.

RESULTS

When smaller numbers of decision criteria, more descriptive decision criteria, or less anti-correlated decision criteria were used to characterize plan quality during multiobjective optimization, dose to OARs and target dose variation were reduced in the final population of plans. Mean OAR dose and gEUD (a = 4) decision criteria were comparable. Using maximum dose decision criteria for OARs near targets resulted in inferior populations that focused solely on low target variance at the expense of high OAR dose. Target dose range, (D(max) - D(min)), decision criteria were found to be most effective for keeping targets uniform. Using target gEUD decision criteria resulted in much lower OAR doses but much higher target dose variation. EUD(alpha,beta) based decision criteria focused on a region of plan space that was a compromise between target and OAR objectives. None of these target decision criteria dominated plans using other criteria, but only focused on approaching a different area of the Pareto front.

CONCLUSIONS

The choice of decision criteria implemented in the MOEA had a significant impact on the region explored and the rate of convergence toward the Pareto front. When more decision criteria, anticorrelated decision criteria, or decision criteria with insufficient information were implemented, inferior populations are resulted. When more informative decision criteria were used, such as gEUD, EUD(alpha,beta), target dose range, and mean dose, MOEA optimizations focused on approaching different regions of the Pareto front, but did not dominate each other. Using simple OAR decision criteria and target EUD(alpha,beta) decision criteria demonstrated the potential to generate IMRT plans that significantly reduce dose to OARs while achieving the same or better tumor control when clinical requirements on target dose variance can be met or relaxed.

A detailed dosimetric comparison between manual and inverse plans in HDR intracavitary/interstitial cervical cancer brachytherapy

PURPOSE

The purpose of this study was to compare two inverse planning algorithms for cervical cancer brachytherapy and a conventional manual treatment planning according to the MUW (Medical University of Vienna) protocol.

MATERIAL AND METHODS

For 20 patients, manually optimized, and, inversely optimized treatment plans with Hybrid Inverse treatment Planning and Optimization (HIPO) and with Inverse Planning Simulated Annealing (IPSA) were created. Dosimetric parameters, absolute volumes of normal tissue receiving reference doses, absolute loading times of tandem, ring and interstitial needles, Paddick and COIN conformity indices were evaluated.

RESULTS

HIPO was able to achieve a similar dose distribution to manual planning with the restriction of high dose regions. It reduced the loading time of needles and the overall treatment time. The values of both conformity indices were the lowest. IPSA was able to achieve acceptable dosimetric results. However, it overloaded the needles. This resulted in high dose regions located in the normal tissue. The Paddick index for the volume of two times prescribed dose was outstandingly low.

CONCLUSIONS

HIPO can produce clinically acceptable treatment plans with the elimination of high dose regions in normal tissue. Compared to IPSA, it is an inverse optimization method which takes into account current clinical experience gained from manual treatment planning.

A hierarchical evolutionary algorithm for multiobjective optimization in IMRT

PURPOSE

The current inverse planning methods for intensity modulated radiation therapy (IMRT) are limited because they are not designed to explore the trade-offs between the competing objectives of tumor and normal tissues. The goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans.

METHODS

A hierarchical evolutionary multiobjective algorithm designed to quickly generate a small diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the optimal trade-offs in any radiation therapy plan was developed. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. The population size is not fixed, but a specialized niche effect, domination advantage, is used to control the population and plan diversity. The number of fitness objectives is kept to a minimum for greater selective pressure, but the number of genes is expanded for flexibility that allows a better approximation of the Pareto front.

RESULTS

The MOEA improvements were evaluated for two example prostate cases with one target and two organs at risk (OARs). The population of plans generated by the modified MOEA was closer to the Pareto front than populations of plans generated using a standard genetic algorithm package. Statistical significance of the method was established by compiling the results of 25 multiobjective optimizations using each method. From these sets of 12-15 plans, any random plan selected from a MOEA population had a 11.3% +/- 0.7% chance of dominating any random plan selected by a standard genetic package with 0.04% +/- 0.02% chance of domination in reverse. By implementing domination advantage and protocol objectives, small and diverse populations of clinically acceptable plans that approximated the Pareto front could be generated in a fraction of 1 h. Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for multiobjective optimizations.

CONCLUSIONS

The MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. The final goal is to improve practical aspects of the algorithm and integrate it with a decision analysis tool or human interface for selection of the IMRT plan with the best possible balance of successful treatment of the target with low OAR dose and low risk of complication for any specific patient situation.

New inverse planning technology for image-guided cervical cancer brachytherapy: description and evaluation within a clinical frame

PURPOSE

To test the feasibility of a new inverse planning technology based on the Hybrid Inverse treatment Planning and Optimisation (HIPO) algorithm for image-guided cervical cancer brachytherapy in comparison to conventional manual optimisation as applied in recent clinical practice based on long-term intracavitary cervical cancer brachytherapy experience.

MATERIALS AND METHODS

The clinically applied treatment plans of 10 tandem/ring (T/R) and 10 cases with additional needles (T/R+N) planned with PLATO v14.3 were included. Standard loading patterns were manually optimised to reach an optimal coverage with 7 Gy per fraction to the High Risk CTV and to fulfil dose constraints for organs at risk. For each of these patients an inverse plan was retrospectively created with Oncentra GYN v0.9.14. Anatomy based automatic source activation was based on the topography of target and organs. The HIPO algorithm included individual gradient and modification restrictions for the T/R and needle dwell times to preserve the spatial high-dose distribution as known from the long-term clinical experience in the standard cervical cancer brachytherapy and with manual planning.

RESULTS

HIPO could achieve a better target coverage (V100) for all T/R and 7 T/R+N patients. Changes in the shape of the overdose volume (V200/400) were limited. The D(2 cc) per fraction for bladder, rectum and sigmoid colon was on average lower by 0.2 Gy, 0.4 Gy, 0.2 Gy, respectively, for T/R patients and 0.6 Gy, 0.3 Gy, 0.3 Gy for T/R+N patients (a decrease from 4.5 to 4 Gy per fraction means a total dose reduction of 5 Gy EQD2 for a 4-fraction schedule). In general the dwell times in the additional needles were lower compared to manual planning. The sparing factors were always better for HIPO plans. Additionally, in 7 T/R and 7 T/R+N patients all three D(0.1 cc), D(1 cc) and D(2 cc) for vagina wall were lower and a smaller area of vagina was covered by the reference dose in HIPO plans. Overall loading times in the tandem, the ring and the needles, as well as dose distribution, were largely preserved with adaptations performed due to specific topographical variations, in particular in lateral and caudal directions.

CONCLUSIONS

Inverse planning based on the HIPO algorithm can produce treatment plans for cervical cancer brachytherapy which are comparable to plans based on manual optimisation as applied in clinical practice. It is essential to take into account the spatial dose distribution in addition to the DVH-based constraints. The proposed inverse planning concept is feasible for improving the therapeutic ratio and limiting substantial high-dose regions around needles.

Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning

One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.

Pareto navigation: algorithmic foundation of interactive multi-criteria IMRT planning

Inherently, IMRT treatment planning involves compromising between different planning goals. Multi-criteria IMRT planning directly addresses this compromising and thus makes it more systematic. Usually, several plans are computed from which the planner selects the most promising following a certain procedure. Applying Pareto navigation for this selection step simultaneously increases the variety of planning options and eases the identification of the most promising plan. Pareto navigation is an interactive multi-criteria optimization method that consists of the two navigation mechanisms 'selection' and 'restriction'. The former allows the formulation of wishes whereas the latter allows the exclusion of unwanted plans. They are realized as optimization problems on the so-called plan bundle -- a set constructed from pre-computed plans. They can be approximately reformulated so that their solution time is a small fraction of a second. Thus, the user can be provided with immediate feedback regarding his or her decisions. Pareto navigation was implemented in the MIRA navigator software and allows real-time manipulation of the current plan and the set of considered plans. The changes are triggered by simple mouse operations on the so-called navigation star and lead to real-time updates of the navigation star and the dose visualizations. Since any Pareto-optimal plan in the plan bundle can be found with just a few navigation operations the MIRA navigator allows a fast and directed plan determination. Besides, the concept allows for a refinement of the plan bundle, thus offering a middle course between single plan computation and multi-criteria optimization. Pareto navigation offers so far unmatched real-time interactions, ease of use and plan variety, setting it apart from the multi-criteria IMRT planning methods proposed so far.

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.

Lexicographic ordering: intuitive multicriteria optimization for IMRT

Optimization problems in IMRT inverse planning are inherently multicriterial since they involve multiple planning goals for targets and their neighbouring critical tissue structures. Clinical decisions are generally required, based on tradeoffs among these goals. Since the tradeoffs cannot be quantitatively determined prior to optimization, the decision-making process is usually indirect and iterative, requiring many repetitive optimizations. This situation becomes even more challenging for cases with a large number of planning goals. To address this challenge, a multicriteria optimization strategy called lexicographic ordering (LO) has been implemented and evaluated for IMRT planning. The LO approach is a hierarchical method in which the planning goals are categorized into different priority levels and a sequence of sub-optimization problems is solved in order of priority. This prioritization concept is demonstrated using two clinical cases (a simple prostate case and a relatively complex head and neck case). In addition, a unique feature of LO in a decision support role is discussed. We demonstrate that a comprehensive list of planning goals (e.g., approximately 23 for the head and neck case) can be optimized using only a few priority levels. Tradeoffs between different levels have been successfully prohibited using the LO method, making the large size problem representations simpler and more manageable. Optimization time needed for each level was practical, ranging from approximately 26 s to approximately 217 s. Using prioritization, the LO approach mimics the mental process often used by physicians as they make decisions handling the various conflicting planning goals. This method produces encouraging results for difficult IMRT planning cases in a highly intuitive manner.

Multiobjective optimization with a modified simulated annealing algorithm for external beam radiotherapy treatment planning

Inverse planning in external beam radiotherapy often requires a scalar objective function that incorporates importance factors to mimic the planner's preferences between conflicting objectives. Defining those importance factors is not straightforward, and frequently leads to an iterative process in which the importance factors become variables of the optimization problem. In order to avoid this drawback of inverse planning, optimization using algorithms more suited to multiobjective optimization, such as evolutionary algorithms, has been suggested. However, much inverse planning software, including one based on simulated annealing developed at our institution, does not include multiobjective-oriented algorithms. This work investigates the performance of a modified simulated annealing algorithm used to drive aperture-based intensity-modulated radiotherapy inverse planning software in a multiobjective optimization framework. For a few test cases involving gastric cancer patients, the use of this new algorithm leads to an increase in optimization speed of a little more than a factor of 2 over a conventional simulated annealing algorithm, while giving a close approximation of the solutions produced by a standard simulated annealing. A simple graphical user interface designed to facilitate the decision-making process that follows an optimization is also presented.

A sensitivity-guided algorithm for automated determination of IMRT objective function parameters

Optimizing intensity-modulated radiotherapy (IMRT) plans involves tradeoffs that balance normal-tissue objectives against each other and against tumor objectives. Adjusting the parameters that determine the appropriate contributions of individual anatomic structures to the objective functions through trial and error is time consuming and may not produce the best achievable plans. We have developed a sensitivity-guided parameter optimization (SGPO) method to assist in the automatic determination of parameters to drive the IMRT optimization to better achieve, or even exceed, specified planning goals. The method is based on the trade-off relationships among multiple objectives: In a globally optimal plan (or within a convex subspace of the plan objectives), any attempt to improve the achievement of goals for a structure will result in sacrificing the goals for at least one other structure. However, different objectives may have different sensitivities to the overall goal of an IMRT plan. For instance, changes in dose distribution, hence the subscore corresponding to an objective for a given normal structure, may minimally impact the target dose distribution. Stated differently, the target coverage is insensitive to the changes in dose distribution of the specific normal structure. A lung cancer treatment plan designed with the SGPO method was used to demonstrate that IMRT plans could be designed to favor a structure with the highest target sensitivity and spare the structures with the least target sensitivity without compromising the target coverage. Using one case each of prostate and paranasal sinus cancers, we also demonstrated that several alternative optimal solutions could be designed with the SGPO algorithm favoring different structures. Finally, we applied the method to eight oropharyngeal cancer cases to obtain objective function parameters that satisfied the Radiation Therapy Oncology Group RTOG-H-0022 protocol. The eight plans optimized using the computer-generated objective function parameters met the protocol's scoring criteria with no or only minor protocol violations. Our preliminary study indicates that the SGPO method may be an effective and practical way to improve IMRT planning.

Beam angle optimization and reduction for intensity-modulated radiation therapy of non–small-cell lung cancers

PURPOSE

To optimize beam angles and reduce the number of beams used for intensity-modulated radiation therapy (IMRT) of non-small-cell lung cancer (NSCLC).

METHODS AND MATERIALS

An exhaustive search scheme was used to perform beam angle optimization (BAO) for IMRT of NSCLC. This approach involved intercomparison of all possible beam angle combinations and selection of the best angles based on the scores or costs of the objective functions used in the treatment plan optimization. Ten Stage III NSCLC cases were selected to evaluate the BAO algorithm and dosimetry benefits of IMRT-BAO. IMRT plans using five or seven coplanar beams were optimized and compared with those using nine equal-spaced beams. Results of BAO were also compared between plans using different numbers of beams with or without fluence modulation.

RESULTS

Each anatomic structure, e.g., tumor or lung, had its own preferred beam angles. Thus, BAO required appropriate balance of competing objective functions. Plans using fewer angles (five or seven beams) could achieve plan quality similar to those using nine equal-spaced beams, however with reduced monitor units and field segments. The number of beams used for the treatment (five vs. seven) and the fluence modulation (open or IMRT beams) did not have a significant impact on the results of the BAO.

CONCLUSIONS

Use of fewer beams (e.g., five) for lung IMRT could result in acceptable plan quality but improved treatment efficiency. A multiresolution search scheme could be developed for BAO using fewer and nonmodulated beams to reduce the computation cost of BAO.

Dose–volume based ranking of incident beam direction and its utility in facilitating IMRT beam placement

PURPOSE

Beam orientation optimization in intensity-modulated radiation therapy (IMRT) is computationally intensive, and various single beam ranking techniques have been proposed to reduce the search space. Up to this point, none of the existing ranking techniques considers the clinically important dose-volume effects of the involved structures, which may lead to clinically irrelevant angular ranking. The purpose of this work is to develop a clinically sensible angular ranking model with incorporation of dose-volume effects and to show its utility for IMRT beam placement.

METHODS AND MATERIALS

The general consideration in constructing this angular ranking function is that a beamlet/beam is preferable if it can deliver a higher dose to the target without exceeding the tolerance of the sensitive structures located on the path of the beamlet/beam. In the previously proposed dose-based approach, the beamlets are treated independently and, to compute the maximally deliverable dose to the target volume, the intensity of each beamlet is pushed to its maximum intensity without considering the values of other beamlets. When volumetric structures are involved, the complication arises from the fact that there are numerous dose distributions corresponding to the same dose-volume tolerance. In this situation, the beamlets are not independent and an optimization algorithm is required to find the intensity profile that delivers the maximum target dose while satisfying the volumetric constraints. In this study, the behavior of a volumetric organ was modeled by using the equivalent uniform dose (EUD). A constrained sequential quadratic programming algorithm (CFSQP) was used to find the beam profile that delivers the maximum dose to the target volume without violating the EUD constraint or constraints. To assess the utility of the proposed technique, we planned a head-and-neck and abdominal case with and without the guidance of the angular ranking information. The qualities of the two types of IMRT plans were compared quantitatively.

RESULTS

An effective angular ranking model with consideration of volumetric effect has been developed. It is shown that the previously reported dose-based angular ranking represents a special case of the general formalism proposed here. Application of the technique to a abdominal and a head-and-neck IMRT case indicated that the proposed technique is capable of producing clinically sensible angular ranking. In both cases, we found that the IMRT plans obtained under the guidance of EUD-based angular ranking were improved in comparison with that obtained using the conventional uniformly spaced beams.

CONCLUSIONS

The EUD-based function is a general approach for angular ranking and allows us to identify the potentially good and bad angles for clinically complicated cases. The ranking can be used either as a guidance to facilitate the manual beam placement or as prior information to speed up the computer search for the optimal beam configuration. Thus the proposed technique should have positive clinical impact in facilitating the IMRT planning process.

Clinical knowledge-based inverse treatment planning

Clinical IMRT treatment plans are currently made using dose-based optimization algorithms, which do not consider the nonlinear dose-volume effects for tumours and normal structures. The choice of structure specific importance factors represents an additional degree of freedom of the system and makes rigorous optimization intractable. The purpose of this work is to circumvent the two problems by developing a biologically more sensible yet clinically practical inverse planning framework. To implement this, the dose-volume status of a structure was characterized by using the effective volume in the voxel domain. A new objective function was constructed with the incorporation of the volumetric information of the system so that the figure of merit of a given IMRT plan depends not only on the dose deviation from the desired distribution but also the dose-volume status of the involved organs. The conventional importance factor of an organ was written into a product of two components: (i) a generic importance that parametrizes the relative importance of the organs in the ideal situation when the goals for all the organs are met; (ii) a dose-dependent factor that quantifies our level of clinical/dosimetric satisfaction for a given plan. The generic importance can be determined a priori, and in most circumstances, does not need adjustment, whereas the second one, which is responsible for the intractable behaviour of the trade-off seen in conventional inverse planning, was determined automatically. An inverse planning module based on the proposed formalism was implemented and applied to a prostate case and a head-neck case. A comparison with the conventional inverse planning technique indicated that, for the same target dose coverage, the critical structure sparing was substantially improved for both cases. The incorporation of clinical knowledge allows us to obtain better IMRT plans and makes it possible to auto-select the importance factors, greatly facilitating the inverse planning process. The new formalism proposed also reveals the relationship between different inverse planning schemes and gives important insight into the problem of therapeutic plan optimization. In particular, we show that the EUD-based optimization is a special case of the general inverse planning formalism described in this paper.

A unifying framework for multi-criteria fluence map optimization models

Models for finding treatment plans for intensity modulated radiation therapy are usually based on a number of structure-based treatment plan evaluation criteria, which are often conflicting. Rather than formulating a model that a priori quantifies the trade-offs between these criteria, we consider a multi-criteria optimization approach that aims at finding the so-called undominated treatment plans. We present a unifying framework for studying multi-criteria optimization problems for treatment planning that establishes conditions under which treatment plan evaluation criteria can be transformed into convex criteria while preserving the set of undominated treatment plans. Such transformations are identified for many of the criteria that have been proposed to date, establishing equivalences between these criteria. In addition, it is shown that the use of a nonconvex criterion can often be avoided by transformation to an equivalent convex criterion. In particular, we show that models employing criteria such as tumour control probability, normal tissue complication probability, probability of uncomplicated tumour control, as well as sigmoidal transformations of (generalized) equivalent uniform dose are equivalent to models formulated in terms of separable voxel-based criteria that penalize dose in individual voxels.

Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy

We propose a hybrid multiobjective (MO) evolutionary optimization algorithm (MOEA) for intensity-modulated radiotherapy inverse planning and apply it to optimize the number of incident beams, their orientations and intensity profiles. The algorithm produces a set of efficient solutions, which represent different clinical trade-offs and contains information such as variety of dose distributions and dose-volume histograms. No importance factors are required and solutions can be obtained in regions not accessible by conventional weighted sum approaches. The application of the algorithm using a test case, a prostate and a head and neck tumour case is shown. The results are compared with MO inverse planning using a gradient-based optimization algorithm.