Multiobjective decision theory for computational optimization in radiation therapy

Comparison of volumetric modulated arc therapy and helical tomotherapy for prostate cancer using Pareto fronts

BACKGROUND

Studies comparing different radiotherapy treatment techniques-such as volumetric modulated arc therapy (VMAT) and helical tomotherapy (HT)-typically compare one treatment plan per technique. Often, some dose metrics favor one plan and others favor the other, so the final plan decision involves subjective preferences. Pareto front comparisons provide a more objective framework for comparing different treatment techniques. A Pareto front is the set of all treatment plans where improvement in one criterion is possible only by worsening another criterion. However, different Pareto fronts can be obtained depending on the chosen machine settings.

PURPOSE

To compare VMAT and HT using Pareto fronts and blind expert evaluation, to explain the observed differences, and to illustrate limitations of using Pareto fronts.

METHODS

We generated Pareto fronts for twenty-four prostate cancer patients treated at our clinic for VMAT and HT techniques using an in-house script that controlled a commercial treatment planning system. We varied the PTV under-coverage (100% - V95%) and the rectum mean dose, and fixed the mean doses to the bladder and femoral heads. In order to ensure a fair comparison, those fixed mean doses were the same for the two treatment techniques and the sets of objective functions were chosen so that the conformity indexes of the two treatment techniques were also the same. We used the same machine settings as are used in our clinic. Then, we compared the VMAT and HT Pareto fronts using a specific metric (clinical distance measure) and validated the comparison using a blinded expert evaluation of treatment plans on these fronts for all patients in the cohort. Furthermore, we investigated the observed differences between VMAT and HT and pointed out limitations of using Pareto fronts.

RESULTS

Both clinical distance and blind treatment plan comparison showed that VMAT Pareto fronts were better than HT fronts. VMAT fronts for 10 and 6 MV beam energy were almost identical. HT fronts improved with different machine settings, but were still inferior to VMAT fronts.

CONCLUSIONS

That VMAT Pareto fronts are better than HT fronts may be explained by the fact that the linear accelerator can rapidly vary the dose rate. This is an advantage in simple geometries that might vanish in more complex geometries. Furthermore, one should be cautious when speaking about Pareto optimal plans as the best possible plans, as their calculation depends on many parameters.

Influence of optimisation parameters on directly deliverable Pareto fronts explored for prostate cancer

PURPOSE

In inverse radiotherapy treatment planning, the Pareto front is the set of optimal solutions to the multi-criteria problem of adequately irradiating the planning target volume (PTV) while reducing dose to organs at risk (OAR). The Pareto front depends on the chosen optimisation parameters whose influence (clinically relevant versus not clinically relevant) is investigated in this paper.

METHODS

Thirty-one prostate cancer patients treated at our clinic were randomly selected. We developed an in-house Python script that controlled the commercial treatment planning system RayStation to calculate directly deliverable Pareto fronts. We calculated reference Pareto fronts for a given set of objective functions, varying the PTV coverage and the mean dose of the primary OAR (rectum) and fixing the mean doses of the secondary OARs (bladder and femoral heads). We calculated the fronts for different sets of objective functions and different mean doses to secondary OARs. We compared all fronts using a specific metric (clinical distance measure).

RESULTS

The in-house script was validated for directly deliverable Pareto front calculations in two and three dimensions. The Pareto fronts depended on the choice of objective functions and fixed mean doses to secondary OARs, whereas the parameters most influencing the front and leading to clinically relevant differences were the dose gradient around the PTV, the weight of the PTV objective function, and the bladder mean dose.

CONCLUSIONS

Our study suggests that for multi-criteria optimisation of prostate treatments using external therapy, dose gradient around the PTV and bladder mean dose are the most influencial parameters.

A small number of objective function weight vectors is sufficient for automated treatment planning in prostate cancer

Current practice for treatment planning optimization can be both inefficient and time consuming. In this paper, we propose an automated planning methodology that aims to combine both explorative and prescriptive approaches for improving the efficiency and the quality of the treatment planning process. Given a treatment plan, our explorative approach explores trade-offs between different objectives and finds an acceptable region for objective function weights via inverse optimization. Intuitively, the shape and size of these regions describe how 'sensitive' a patient is to perturbations in objective function weights. We then develop an integer programming-based prescriptive approach that exploits the information encoded by these regions to find a set of five representative objective function weight vectors such that for each patient there exists at least one representative weight vector that can produce a high quality treatment plan. Using 315 patients from Princess Margaret Cancer Centre, we show that the produced treatment plans are comparable and, for [Formula: see text] of cases, improve upon the inversely optimized plans that are generated from the historical clinical treatment plans.

Models for predicting objective function weights in prostate cancer IMRT

PURPOSE

To develop and evaluate the clinical applicability of advanced machine learning models that simultaneously predict multiple optimization objective function weights from patient geometry for intensity-modulated radiation therapy of prostate cancer.

METHODS

A previously developed inverse optimization method was applied retrospectively to determine optimal objective function weights for 315 treated patients. The authors used an overlap volume ratio (OV) of bladder and rectum for different PTV expansions and overlap volume histogram slopes (OVSR and OVSB for the rectum and bladder, respectively) as explanatory variables that quantify patient geometry. Using the optimal weights as ground truth, the authors trained and applied three prediction models: logistic regression (LR), multinomial logistic regression (MLR), and weighted K-nearest neighbor (KNN). The population average of the optimal objective function weights was also calculated.

RESULTS

The OV at 0.4 cm and OVSR at 0.1 cm features were found to be the most predictive of the weights. The authors observed comparable performance (i.e., no statistically significant difference) between LR, MLR, and KNN methodologies, with LR appearing to perform the best. All three machine learning models outperformed the population average by a statistically significant amount over a range of clinical metrics including bladder/rectum V53Gy, bladder/rectum V70Gy, and dose to the bladder, rectum, CTV, and PTV. When comparing the weights directly, the LR model predicted bladder and rectum weights that had, on average, a 73% and 74% relative improvement over the population average weights, respectively. The treatment plans resulting from the LR weights had, on average, a rectum V70Gy that was 35% closer to the clinical plan and a bladder V70Gy that was 29% closer, compared to the population average weights. Similar results were observed for all other clinical metrics.

CONCLUSIONS

The authors demonstrated that the KNN and MLR weight prediction methodologies perform comparably to the LR model and can produce clinical quality treatment plans by simultaneously predicting multiple weights that capture trade-offs associated with sparing multiple OARs.

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.

Role of step size and max dwell time in anatomy based inverse optimization for prostate implants

In high dose rate (HDR) brachytherapy, the source dwell times and dwell positions are vital parameters in achieving a desirable implant dose distribution. Inverse treatment planning requires an optimal choice of these parameters to achieve the desired target coverage with the lowest achievable dose to the organs at risk (OAR). This study was designed to evaluate the optimum source step size and maximum source dwell time for prostate brachytherapy implants using an Ir-192 source. In total, one hundred inverse treatment plans were generated for the four patients included in this study. Twenty-five treatment plans were created for each patient by varying the step size and maximum source dwell time during anatomy-based, inverse-planned optimization. Other relevant treatment planning parameters were kept constant, including the dose constraints and source dwell positions. Each plan was evaluated for target coverage, urethral and rectal dose sparing, treatment time, relative target dose homogeneity, and nonuniformity ratio. The plans with 0.5 cm step size were seen to have clinically acceptable tumor coverage, minimal normal structure doses, and minimum treatment time as compared with the other step sizes. The target coverage for this step size is 87% of the prescription dose, while the urethral and maximum rectal doses were 107.3 and 68.7%, respectively. No appreciable difference in plan quality was observed with variation in maximum source dwell time. The step size plays a significant role in plan optimization for prostate implants. Our study supports use of a 0.5 cm step size for prostate implants.

Tomotherapy-like versus VMAT-like treatments: a multicriteria comparison for a prostate geometry

PURPOSE

To perform a methodological comparison of volumetric modulated arc therapy (VMAT)-like and tomotherapy-like techniques for a prostate geometry, exploring the dependence on machine, delivery, and optimization parameters of cost function values optimized for each technique.

METHODS

A gradient-descent algorithm is used to optimize tomotherapy-like treatments, while VMAT-like optimization is carried out using a direct-aperture simulated annealing algorithm with 180 control points equispaced at 2° angles. Dose distributions are linked to fluences via a three-dimensional double-gaussian pencil beam model. Plans are optimized for a prostate geometry, outlined according to the CHHiP protocol. The cost function used for optimization contains ten simple functions, each of which describes a single planning objective. These functions are split into three structure groups according to whether they are used to control PTV, rectal or bladder dose levels. Different optimizations have been performed by varying the relative weights of each of these structure groups, exploring in this way a three-dimensional Pareto front. Plan quality is studied according to the value of the optimized cost function and the relative Euclidean distance between the components of the cost function and those of the nearest plan lying on a reference Pareto front obtained for tomotherapy-like plans generated using a 1 cm fan-beam width and 1/3 pitch.

RESULTS

The quality of tomotherapy-like optimization depends on the fan-beam width, s, and rotation pitch, p, used to deliver the treatment. These values together define the effective longitudinal resolution with which fluence can be modulated, and lower cost function values are obtained for treatments optimized with tighter pitches and narrower fan-beam widths (higher modulation resolution). On the other hand, the cost function values of VMAT-like optimizations depends on the optimization running time, leaf displacement constraints, and number of arcs employed, as well as on the size of the beamlets used in the optimization (a change in leaf width from 5 to 10 mm clearly worsens the value of the objective function, but only a marginal improvement is observed when the leaf movement discretization step is reduced from 5 to 5/3 mm). However, for no combination of these parameter values did VMAT-like optimizations match the cost function values of optimized tomo-like plans obtained for s = 1 cm and p = 1∕3 (or 1/2). This is the case all across the Pareto front. On the other hand, cost function values of VMAT-like plans are generally lower than those of optimized tomotherapy-like plans obtained for s = 2.5 cm.

CONCLUSIONS

Tomotherapy-like plans created for the prostate geometry using a 1 cm fan-beam width and pitches of 1/3 or 1/2 have lower cost function values than VMAT-like plans, although the associated dosimetric improvements are quite small, both techniques generating very good dose distributions. When a 2.5 cm wide fan-beam is used for tomotherapy-like treatments the pattern is reversed, the tomotherapy-like plans having higher cost functions than the VMAT-like ones.

Automated IMRT planning with regional optimization using planning scripts

Intensity‐modulated radiation therapy (IMRT) has become a standard technique in radiation therapy for treating different types of cancers. Various class solutions have been developed for simple cases (e.g., localized prostate, whole breast) to generate IMRT plans efficiently. However, for more complex cases (e.g., head and neck, pelvic nodes), it can be time‐consuming for a planner to generate optimized IMRT plans. To generate optimal plans in these more complex cases which generally have multiple target volumes and organs at risk, it is often required to have additional IMRT optimization structures such as dose limiting ring structures, adjust beam geometry, select inverse planning objectives and associated weights, and additional IMRT objectives to reduce cold and hot spots in the dose distribution. These parameters are generally manually adjusted with a repeated trial and error approach during the optimization process. To improve IMRT planning efficiency in these more complex cases, an iterative method that incorporates some of these adjustment processes automatically in a planning script is designed, implemented, and validated. In particular, regional optimization has been implemented in an iterative way to reduce various hot or cold spots during the optimization process that begins with defining and automatic segmentation of hot and cold spots, introducing new objectives and their relative weights into inverse planning, and turn this into an iterative process with termination criteria. The method has been applied to three clinical sites: prostate with pelvic nodes, head and neck, and anal canal cancers, and has shown to reduce IMRT planning time significantly for clinical applications with improved plan quality. The IMRT planning scripts have been used for more than 500 clinical cases.

PACS numbers: 87.55.D, 87.55.de

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.

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%.

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.

Modeling plan-related clinical complications using machine learning tools in a multiplan IMRT framework

PURPOSE

To predict organ-at-risk (OAR) complications as a function of dose-volume (DV) constraint settings without explicit plan computation in a multiplan intensity-modulated radiotherapy (IMRT) framework.

METHODS AND MATERIALS

Several plans were generated by varying the DV constraints (input features) on the OARs (multiplan framework), and the DV levels achieved by the OARs in the plans (plan properties) were modeled as a function of the imposed DV constraint settings. OAR complications were then predicted for each of the plans by using the imposed DV constraints alone (features) or in combination with modeled DV levels (plan properties) as input to machine learning (ML) algorithms. These ML approaches were used to model two OAR complications after head-and-neck and prostate IMRT: xerostomia, and Grade 2 rectal bleeding. Two-fold cross-validation was used for model verification and mean errors are reported.

RESULTS

Errors for modeling the achieved DV values as a function of constraint settings were 0-6%. In the head-and-neck case, the mean absolute prediction error of the saliva flow rate normalized to the pretreatment saliva flow rate was 0.42% with a 95% confidence interval of (0.41-0.43%). In the prostate case, an average prediction accuracy of 97.04% with a 95% confidence interval of (96.67-97.41%) was achieved for Grade 2 rectal bleeding complications.

CONCLUSIONS

ML can be used for predicting OAR complications during treatment planning allowing for alternative DV constraint settings to be assessed within the planning framework.

Analyzing the main trade-offs in multiobjective radiation therapy treatment planning databases

Multiobjective radiotherapy planning aims to capture all clinically relevant trade-offs between the various planning goals. This is accomplished by calculating a representative set of Pareto optimal solutions and storing them in a database. The structure of these representative Pareto sets is still not fully investigated. We propose two methods for a systematic analysis of multiobjective databases: principal component analysis and the isomap method. Both methods are able to extract the key trade-offs from a database and provide information which can lead to a better understanding of the clinical case and intensity-modulated radiation therapy planning in general.

Balancing control and simplicity: A variable aggregation method in intensity modulated radiation therapy planning

It is commonly believed that not all degrees of freedom are needed to produce good solutions for the treatment planning problem in intensity modulated radiation therapy (IMRT). However, typical methods to exploit this fact either increase the complexity of the optimization problem or are heuristic in nature. In this work we introduce a technique based on adaptively refining variable clusters to successively attain better treatment plans. The approach creates approximate solutions based on smaller models that may come arbitrarily close to the optimal solution. Although the method is illustrated using a specific treatment planning model, the components constituting the variable clustering and the adaptive refinement are independent of the particular optimization problem.

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 multiplan treatment-planning framework: a paradigm shift for intensity-modulated radiotherapy

PURPOSE

To describe a multiplan intensity-modulated radiotherapy (IMRT) planning framework, and to describe a decision support system (DSS) for ranking multiple plans and modeling the planning surface.

METHODS AND MATERIALS

One hundred twenty-five plans were generated sequentially for a head-and-neck case and a pelvic case by varying the dose-volume constraints on each of the organs at risk (OARs). A DSS was used to rank plans according to dose-volume histogram (DVH) values, as well as equivalent uniform dose (EUD) values. Two methods for ranking treatment plans were evaluated: composite criteria and pre-emptive selection. The planning surface determined by the results was modeled using quadratic functions.

RESULTS

The DSS provided an easy-to-use interface for the comparison of multiple plan features. Plan ranking resulted in the identification of one to three "optimal" plans. The planning surface models had good predictive capability with respect to both DVH values and EUD values and generally, errors of <6%. Models generated by minimizing the maximum relative error had significantly lower relative errors than models obtained by minimizing the sum of squared errors. Using the quadratic model, plan properties for one OAR were determined as a function of the other OAR constraint settings. The modeled plan surface can then be used to understand the interdependence of competing planning objectives.

CONCLUSION

The DSS can be used to aid the planner in the selection of the most desirable plan. The collection of quadratic models constructed from the plan data to predict DVH and EUD values generally showed excellent agreement with the actual plan values.

Reduced-order parameter optimization for simplifying prostate IMRT planning

Intensity-modulated radiotherapy (IMRT) has become an effective tool for cancer treatment with radiation. However, even expert radiation planners still need to spend a substantial amount of time manually adjusting IMRT optimization parameters such as dose limits and costlet weights in order to obtain a clinically acceptable plan. In this paper, we describe two main advances that simplify the parameter adjustment process for five-field prostate IMRT planning. First, we report the results of a sensitivity analysis that quantifies the effect of each hand-tunable parameter of the IMRT cost function on each clinical objective and the overall quality of the resulting plan. Second, we show that a recursive random search over the six most sensitive parameters as an outer loop in IMRT planning can quickly and automatically determine parameters for the cost function that lead to a plan meeting the clinical requirements. Our experiments on a ten-patient dataset show that for 70% of the cases, we can automatically determine a plan in 10 min (on the average) that is either clinically acceptable or requires only minor adjustment by the planner. The outer-loop optimization can be easily integrated into a traditional IMRT planning system.

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.

Learning the relationship between patient geometry and beam intensity in breast intensity-modulated radiotherapy

Intensity modulated radiotherapy (IMRT) has become an effective tool for cancer treatment with radiation. However, even expert radiation planners still need to spend a substantial amount of time adjusting IMRT optimization parameters in order to get a clinically acceptable plan. We demonstrate that the relationship between patient geometry and radiation intensity distributions can be automatically inferred using a variety of machine learning techniques in the case of two-field breast IMRT. Our experiments show that given a small number of human-expert-generated clinically acceptable plans, the machine learning predictions produce equally acceptable plans in a matter of seconds. The machine learning approach has the potential for greater benefits in sites where the IMRT planning process is more challenging or tedious.

Exploration of tradeoffs in intensity-modulated radiotherapy

The purpose of this study is to calculate Pareto surfaces in multi-criteria radiation treatment planning and to analyse the dependency of the Pareto surfaces on the objective functions used for the volumes of interest. We develop a linear approach that allows us to calculate truly Pareto optimal treatment plans, and we apply it to explore the tradeoff between tumour dose homogeneity and critical structure sparing. We show that for two phantom and two clinical cases, a smooth (as opposed to kinked) Pareto tradeoff curve exists. We find that in the paraspinal cases the Pareto surface is invariant to the response function used on the spinal cord: whether the mean cord dose or the maximum cord dose is used, the Pareto plan database is similar. This is not true for the lung studies, where the choice of objective function on the healthy lung tissue influences the resulting Pareto surface greatly. We conclude that in the special case when the tumour wraps around the organ at risk, e.g. prostate cases and paraspinal cases, the Pareto surface will be largely invariant to the objective function used to model the organ at risk.

IMRT planning on adaptive volume structures—a decisive reduction in computational complexity

The objective of radiotherapy planning is to find a compromise between the contradictive goals of delivering a sufficiently high dose to the target volume while widely sparing critical structures. The search for such a compromise requires the computation of several plans, which mathematically means solving several optimization problems. In the case of intensity modulated radiotherapy (IMRT) these problems are large-scale, hence the accumulated computational expense is very high. The adaptive clustering method presented in this paper overcomes this difficulty. The main idea is to use a preprocessed hierarchy of aggregated dose-volume information as a basis for individually adapted approximations of the original optimization problems. This leads to a decisively reduced computational expense: numerical experiments on several sets of real clinical data typically show computation times decreased by a factor of about 10. In contrast to earlier work in this field, this reduction in computational complexity will not lead to a loss in accuracy: the adaptive clustering method produces the optimum of the original optimization problem.

Target volume uncertainty and a method to visualize its effect on the target dose prescription

PURPOSE

To consider the uncertainty in the construction of target boundaries for optimization, and to demonstrate how the principles of mathematical programming can be applied to determine and display the effect on the tumor dose of making small changes to the target boundary.

METHODS

The effect on the achievable target dose of making successive small shifts to the target boundary within its range of uncertainty was found by constructing a mixed-integer linear program that automated the placement of the beam angles using the initial target volume.

RESULTS

The method was demonstrated using contours taken from a nasopharynx case, with dose limits placed on surrounding structures. In the illustrated case, enlarging the target anteriorly to provide greater assurance of disease coverage did not force a sacrifice in the minimum or mean tumor doses. However, enlarging the margin posteriorly, near a critical structure, dramatically changed the minimum, mean, and maximum tumor doses.

CONCLUSION

Tradeoffs between the position of the target boundary and the minimum target dose can be developed using mixed-integer programming, and the results projected as a guide to contouring and plan selection.

Feasibility study of beam orientation class-solutions for prostate IMRT

IMRT is being increasingly used for treatment of prostate cancer. In practice, however, the beam orientations used for the treatments are still selected empirically, without any guideline. The purpose of this work was to investigate interpatient variation of the optimal beam configuration and to facilitate intensity modulated radiation therapy (IMRT) prostate treatment planning by proposing a set of beam orientation class-solutions for a range of numbers of incident beams. We used fifteen prostate cases to generate the beam orientation class-solutions. For each patient and a given number of incident beams, a multiobjective optimization engine was employed to provide optimal beam directions. For the fifteen cases considered, the gantry angle of any of the optimized plans were all distributed within a certain range The angular distributions of the optimal beams were analyzed and the most selected directions are identified as optimal directions. The optimal directions for all patients are averaged to obtain the class-solution. The class-solution gantry angles for prostate IMRT were found to be: three beams (0 degrees, 120 degrees, 240 degrees), five beams (35 degrees, 110 degrees, 180 degrees, 250 degrees, 325 degrees), six beams (0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees), seven beams (25 degrees, 75 degrees, 130 degrees, 180 degrees, 230 degrees, 285 degrees, 335 degrees), eight beams (20 degrees, 70 degrees, 110 degrees, 150 degrees, 200 degrees, 250 degrees, 290 degrees, 340 degrees), and nine beams (20 degrees, 60 degrees, 100 degrees, 140 degrees, 180 degrees, 220 degrees, 260 degrees, 300 degrees, 340 degrees). The level of validity of the class-solutions was tested using an additional clinical prostate case by comparing with the individually optimized beam configurations. The difference between the plans obtained with class-solutions and patient-specific optimizations was found to be clinically insignificant.

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

We consider the behaviour of the limited memory L-BFGS algorithm as a representative constraint-free gradient-based algorithm which is used for multiobjective (MO) dose optimization for intensity modulated radiotherapy (IMRT). Using a parameter transformation, the positivity constraint problem of negative beam fluences is entirely eliminated: a feature which to date has not been fully understood by all investigators. We analyse the global convergence properties of L-BFGS by searching for the existence and the influence of possible local minima. With a fast simulated annealing (FSA) algorithm we examine whether the L-BFGS solutions are globally Pareto optimal. The three examples used in our analysis are a brain tumour, a prostate tumour and a test case with a C-shaped PTV. In 1% of the optimizations global convergence is violated. A simple mechanism practically eliminates the influence of this failure and the obtained solutions are globally optimal. A single-objective dose optimization requires less than 4 s for 5400 parameters and 40000 sampling points. The elimination of the problem of negative beam fluences and the high computational speed permit constraint-free gradient-based optimization algorithms to be used for MO dose optimization. In this situation, a representative spectrum of possible solutions is obtained which contains information such as the trade-off between the objectives and range of dose values. Using simple decision making tools the best of all the possible solutions can be chosen. We perform an MO dose optimization for the three examples and compare the spectra of solutions, firstly using recommended critical dose values for the organs at risk and secondly, setting these dose values to zero.

Application of influence diagrams to prostate intensity-modulated radiation therapy plan selection

The purpose is to incorporate clinically relevant factors such as patient-specific and dosimetric information as well as data from clinical trials in the decision-making process for the selection of prostate intensity-modulated radiation therapy (IMRT) plans. The approach is to incorporate the decision theoretic concept of an influence diagram into the solution of the multiobjective optimization inverse planning problem. A set of candidate IMRT plans was obtained by varying the importance factors for the planning target volume (PTV) and the organ-at-risk (OAR) in combination with simulated annealing to explore a large part of the solution space. The Pareto set for the PTV and OAR was analysed to demonstrate how the selection of the weighting factors influenced which part of the solution space was explored. An influence diagram based on a Bayesian network with 18 nodes was designed to model the decision process for plan selection. The model possessed nodes for clinical laboratory results, tumour grading, staging information, patient-specific information, dosimetric information, complications and survival statistics from clinical studies. A utility node was utilized for the decision-making process. The influence diagram successfully ranked the plans based on the available information. Sensitivity analyses were used to judge the reasonableness of the diagram and the results. In conclusion, influence diagrams lend themselves well to modelling the decision processes for IMRT plan selection. They provide an excellent means to incorporate the probabilistic nature of data and beliefs into one model. They also provide a means for introducing evidence-based medicine, in the form of results of clinical trials, into the decision-making process.

The need for evolution in healthcare decision modeling

STATEMENT OF PROBLEM

Many healthcare decisions are difficult because they are complex and have important consequences such as the impact on survival or quality-of-life of individuals and on allocation of limited resources. The present state-of-the-art in healthcare decision modeling is often inadequate to properly assess these decisions.

METHODS

Based on a literature search and the experience of the authors, typical methodologies used in healthcare decision analysis modeling are explored and compared with methods used in other practices. An example of hormonal therapy decisions is used.

RESULTS

Useful methods that have been developed in other fields are presented. These include methods targeted toward appropriate assessment and representation of the complexity of decisions, assessment of uncertainty, use of nonexpected value decision analysis, and use of multi-attribute decision criteria.

CONCLUSION

The state-of-the-art in healthcare decision modeling can be improved through learning from other practices.

Treatment plan modification using voxel-based weighting factors/dose prescription

Under various clinical situations, it is desirable to modify the original treatment plan to better suit the clinical goals. In this work, a method to help physicians modify treatment plans based on their clinical preferences is proposed. The method uses a weighted quadratic dose objective function. The commonly used organ-/ROI-based weighting factors are expanded to a set of voxel-based weighting factors in order to obtain greater flexibility in treatment plan modification. Two different but equivalent modification schemes based on Rustem's quadratic programming algorithms--modification of a weighting matrix and modification of prescribed doses--are presented. Case studies demonstrated the effectiveness of the two methods with regard to their capability to fine-tune treatment plans.

[IMCO(++)--a Monte Carlo based IMRT system]

The application of intensity modulated radiotherapy (IMRT) to dose escalation in the target volume sets particular demands in terms of accuracy of dose calculation. Dose calculation errors due to approximations are compensated by the optimization algorithm, a procedure that ultimately leads to incorrect fluence modulation. Such inaccuracies affect particularly the dose distribution in areas with secondary electron disequilibrium. In case tissues heterogeneity predominates, conventional dose calculation methods (such as Pencil Beam) can produce relative errors up to more than 10%. The accuracy can be significantly improved by the application of a Monte-Carlo (MC) algorithm. This paper describes a MC-based inverse treatment planning algorithm (IMCO++), based on a non-iterative approach with a feedback-controlling process. The convergence behavior of IMCO++ was investigated and the used MC dose-calculation codes MMms and XVMC were compared by means of a heterogeneous phantom. IMCO++ plans were optimized in various phantoms. All plans showed conformity in terms of dose distribution of the target volume and dose reduction in risk organs (according to the requirements of the target parameter), as well as a very fast convergence of the algorithm (in less than 10 optimization steps).

A multiobjective gradient-based dose optimization algorithm for external beam conformal radiotherapy

A multiobjective gradient-based algorithm has been developed for the purpose of dose distribution optimization in external beam conformal radiotherapy. This algorithm is based on the concept of gathering the values of all objectives into a single value. The weighting factors of the composite objective values are varied in different steps, allowing the reconstruction of the trade-off surfaces (three or more objectives) or curves (two objectives) which define the boundary between the feasible and non-feasible domain regions. The analysis of these curves allows the decision-maker to select the solution that best fits the clinical goals. In contrast to all the other algorithms, our method provides not a single solution but a sample of solutions representing all possible clinical importance factors (weights) for the objectives used. The application of this algorithm to two test cases shows that a correct selection for the importance factors to multiply the individual objectives in the global objective value is not trivial and that the location and shape of the boundary region between the feasible and non-feasible solution regions are case dependent. Provided that the individual objective functions are analytically differentiable and that the number of objectives is the range of two to three, the computation times are acceptable for clinical use. Furthermore, the optimization for a unique combination of importance factors within the aggregate objective function is performed in less than 1 min.

An optimization method for importance factors and beam weights based on genetic algorithms for radiotherapy treatment planning

We propose a new method for selecting importance factors (for regions of interest like organs at risk) used to plan conformal radiotherapy. Importance factors, also known as weighting factors or penalty factors, are essential in determining the relative importance of multiple objectives or the penalty ratios of constraints incorporated into cost functions, especially in dealing with dose optimization in radiotherapy treatment planning. Researchers usually choose importance factors on the basis of a trial-and-error process to reach a balance between all the objectives. In this study, we used a genetic algorithm and adopted a real-number encoding method to represent both beam weights and importance factors in each chromosome. The algorithm starts by optimizing the beam weights for a fixed number of iterations then modifying the importance factors for another fixed number of iterations. During the first phase, the genetic operators, such as crossover and mutation, are carried out only on beam weights, and importance factors for each chromosome are not changed or 'frozen'. In the second phase, the situation is reversed: the beam weights are 'frozen' and the importance factors are changed after crossover and mutation. Through alternation of these two phases, both beam weights and importance factors are adjusted according to a fitness function that describes the conformity of dose distribution in planning target volume and dose-tolerance constraints in organs at risk. Those chromosomes with better fitness are passed into the next generation, showing that they have a better combination of beam weights and importance factors. Although the ranges of the importance factors should be set in advance by using this algorithm, it is much more convenient than selecting specific numbers for importance factors. Three clinical examples are presented and compared with manual plans to verify this method. Three-dimensional standard displays and dose-volume histograms are shown to demonstrate that this method is feasible, automatic and convenient.

Application of a genetic algorithm to optimizing radiation therapy treatment plans for pancreatic carcinoma

The performance of an automated treatment planning algorithm was tested using cases of patients with pancreatic carcinoma; the system implements optimization tools that suggest high-quality plans for consideration by the planner and physician, making best use of the capabilities of a conventional linear accelerator: isocentric setup, shaped fields, and wedges. Ten consecutive patients presenting with pancreatic cancer were first planned using a conventional 3-field protocol to provide a basis for comparison. Each was then planned using an automated optimization technique using a genetic algorithm and a dose-based score function subject to volume-dose constraints. Two sets of optimized plans were created, 1 using only axial beams and the other permitting non-axial beams. The improvement afforded by the optimization was assessed by comparing the score function results and by computing the combined normal tissue complication probability (NTCP) for a constant isocenter dose. In all 10 cases, optimization improved the dose-based score function. In 9 cases, the non-axial plan scored higher than the axial plan. Optimization driven by the dose-based score function improved or equaled the predicted NTCP in 8 axial and 9 nonaxial plans. This study demonstrates progress toward the goal of developing an automated planning tool that can robustly suggest high-quality plans.

A mixed-encoding genetic algorithm with beam constraint for conformal radiotherapy treatment planning

In this paper we propose a new hierarchical evolutionary algorithm that combines binary encoding and floating-point encoding to automatically select the beam directions and determine the weights of the selected beams. With traditional optimization methods the beam directions are fixed a priori by the operator in recognition of the fact that computer selection of beam directions is a difficult problem. In this investigation, we used a hybrid-encoding scheme. The binary encoding part of each chromosome was used to select the beam directions, and its corresponding floating-point encoding part of the same chromosome was used to determine the weights of those selected beams. Before beginning the optimization process, we set a constraint on the number of the beam directions we wanted in the final solution. We present three examples to verify this method. These examples differ with each other in tumor sites, problem sizes, and optimization parameters. Three-dimensional optimization results and statistical data showed that this method is feasible. We think this method can be easily extended to solve more complex target problems (such as nonconvex target problems).

Generation of uniformly distributed dose points for anatomy-based three-dimensional dose optimization methods in brachytherapy

We have studied the accuracy of statistical parameters of dose distributions in brachytherapy using actual clinical implants. These include the mean, minimum and maximum dose values and the variance of the dose distribution inside the PTV (planning target volume), and on the surface of the PTV. These properties have been studied as a function of the number of uniformly distributed sampling points. These parameters, or the variants of these parameters, are used directly or indirectly in optimization procedures or for a description of the dose distribution. The accurate determination of these parameters depends on the sampling point distribution from which they have been obtained. Some optimization methods ignore catheters and critical structures surrounded by the PTV or alternatively consider as surface dose points only those on the contour lines of the PTV. D(min) and D(max) are extreme dose values which are either on the PTV surface or within the PTV. They must be avoided for specification and optimization purposes in brachytherapy. Using D(mean) and the variance of D which we have shown to be stable parameters, achieves a more reliable description of the dose distribution on the PTV surface and within the PTV volume than does D(min) and D(max). Generation of dose points on the real surface of the PTV is obligatory and the consideration of catheter volumes results in a realistic description of anatomical dose distributions.

Multi-objective optimization in radiotherapy: applications to stereotactic radiosurgery and prostate brachytherapy

Treatment planning for radiation therapy is a multi-objective optimization process. Here we present a machine intelligent scheme for treatment planning based on multi-objective decision analysis (MODA) and genetic algorithm (GA) optimization. Multi-objective ranking strategies are represented in the L(p) metric under the displaced ideal model. Goal setting, protocol satisficing and fuzzy ranking of objective importance can be incorporated into the decision scheme to assimilate clinical decision making. For distance measures in the L(p) metric, a dynamic gauge function is defined based on the state energy of the decision system, which is assumed to undergo thermodynamic cooling with iteration time. The MODA scheme interacts with a robust GA engine, which adaptively evolves in the multi-modal landscape that defines the treatment plan quality. A conventionally challenging case of stereotactic radiosurgery of a brain lesion was selected for GA optimization. The resulting dose distributions are compared to human-developed plans, which are commonly regarded as clinically relevant and empirically optimal. The GA-optimized plans achieve substantially better sparing of critical normal neuroanatomy surrounding the brain lesion while respecting the preset constraints on tumor dose uniformity. In addition, machine optimization tends to produce novel treatment strategies which complements expert knowledge. The run time for producing an optimal plan is considerably shorter than the typical planning time for human experts, thus GA can also be used to aid the human treatment planning process. In prostate brachytherapy, MODA-GA was specifically applied to non-ideal conditions in which typical surgical uncertainties in seed implant positioning occur, where noisy objectives were introduced into the optimization scheme. The noisy system is found to be manageable by MODA-GA at uncertainty levels corresponding to reasonably proficient surgery teams. In contrast, noisy objectives would be very difficult to explore by human expert planners. Potential use of noisy optimization with time series analysis is being explored for error-corrective computer guidance in the operating room for prostate seed implantation. In conclusion, the combination of MODA and GA optimization offers both a solution to practical treatment planning tasks and the potential for real time applications in radiotherapy.

Evolutionary computation in medicine: an overview

The term evolutionary computation encompasses a host of methodologies inspired by natural evolution that are used to solve hard problems. This paper provides an overview of evolutionary computation as applied to problems in the medical domains. We begin by outlining the basic workings of six types of evolutionary algorithms: genetic algorithms, genetic programming, evolution strategies, evolutionary programming, classifier systems, and hybrid systems. We then describe how evolutionary algorithms are applied to solve medical problems, including diagnosis, prognosis, imaging, signal processing, planning, and scheduling. Finally, we provide an extensive bibliography, classified both according to the medical task addressed and according to the evolutionary technique used.

Permanent prostate seed implant brachytherapy: report of the American Association of Physicists in Medicine Task Group No. 64

There is now considerable evidence to suggest that technical innovations, 3D image-based planning, template guidance, computerized dosimetry analysis and improved quality assurance practice have converged in synergy in modern prostate brachytherapy, which promise to lead to increased tumor control and decreased toxicity. A substantial part of the medical physicist's contribution to this multi-disciplinary modality has a direct impact on the factors that may singly or jointly determine the treatment outcome. It is therefore of paramount importance for the medical physics community to establish a uniform standard of practice for prostate brachytherapy physics, so that the therapeutic potential of the modality can be maximally and consistently realized in the wider healthcare community. A recent survey in the U.S. for prostate brachytherapy revealed alarming variance in the pattern of practice in physics and dosimetry, particularly in regard to dose calculation, seed assay and time/method of postimplant imaging. Because of the large number of start-up programs at this time, it is essential that the roles and responsibilities of the medical physicist be clearly defined, consistent with the pivotal nature of the clinical physics component in assuring the ultimate success of prostate brachytherapy. It was against this background that the Radiation Therapy Committee of the American Association of Physicists in Medicine formed Task Group No. 64, which was charged (1) to review the current techniques in prostate seed implant brachytherapy, (2) to summarize the present knowledge in treatment planning, dose specification and reporting, (3) to recommend practical guidelines for the clinical medical physicist, and (4) to identify issues for future investigation.

Brachytherapy optimal planning with application to intravascular radiation therapy

We have been studying brachytherapy planning with the objective of minimizing the maximum deviation of the delivered dose from prescribed dose bounds for treatment volumes. A general framework for optimal treatment planning is presented and the minmax optimization is formulated as a linear program. Dose rate calculations are based on the dosimetry formulation of the American Association of Physicists in Medicine, Task Group 43. We apply the technique to optimal planning for intravascular brachytherapy of intimal hyperplasia using ultrasound data and 192Ir seeds. The planning includes determination of an optimal dwell-time sequence for a train of seeds that deliver radiation while stepping through the vessel lesion. The results illustrate the advantage of this strategy over the common approach of delivering radiation by positioning a single train of seeds along the whole lesion.

Monte Carlo-based inverse treatment planning

A Monte Carlo based inverse treatment planning system (MCI) has been developed which combines arguably the most accurate dose calculation method (Monte Carlo particle transport) with a 'guaranteed' optimization method (simulated annealing). A distribution of photons is specified in the tumour volume; they are transported using an adjoint calculation method to outside the patient surface to build up an intensity distribution. This intensity distribution is used as the initial input into an optimization algorithm. The dose distribution from each beam element from a number of fields is pre-calculated using Monte Carlo transport. Simulated annealing optimization is then used to find the weighting of each beam element, to yield the optimal dose distribution for the given criteria and constraints. MCI plans have been generated in various theoretical phantoms and patient geometries. These plans show conformation of the dose to the target volume and avoidance of critical structures. To verify the code, an experiment was performed on an anthropomorphic phantom.

Intraoperative optimized inverse planning for prostate brachytherapy: early experience

PURPOSE

To demonstrate the feasibility of an intraoperative inverse planning technique with advanced optimization for prostate seed implantation.

METHODS AND MATERIALS

We have implemented a method for optimized inverse planning of prostate seed implantation in the operating room (OR), based on the genetic algorithm (GA) driven Prostate Implant Planning Engine for Radiotherapy (PIPER). An integrated treatment planning system was deployed, which includes real-time ultrasound image acquisition, treatment volume segmentation, GA optimization, real-time decision making and sensitivity analysis, isodose and DVH evaluation, and virtual reality navigation and surgical guidance. Ten consecutive patients previously scheduled for implantation were included in the series.

RESULTS

The feasibility of the technique was established by careful monitoring of each step in the OR and comparison with conventional preplanned implants. The median elapsed time for complete image capture, segmentation, GA optimization, and plan evaluation was 4, 10, 2.2, and 2 min, respectively. The dosimetric quality of the OR-based plan was shown to be equivalent to the corresponding preplan.

CONCLUSION

An intraoperative optimized inverse planning technique was developed for prostate brachytherapy. The feasibility of the method was demonstrated through an early clinical experience.