Dose optimization via index-dose gradient minimization

Commissioning of a 3D image-based treatment planning system for high-dose-rate brachytherapy of cervical cancer

The objective of this work is to present commissioning procedures to clinically implement a three-dimensional (3D), image-based, treatment-planning system (TPS) for high-dose-rate (HDR) brachytherapy (BT) for gynecological (GYN) cancer. The physical dimensions of the GYN applicators and their values in the virtual applicator library were varied by 0.4 mm of their nominal values. Reconstruction uncertainties of the titanium tandem and ovoids (T&O) were less than 0.4 mm on CT phantom studies and on average between 0.8-1.0 mm on MRI when compared with X-rays. In-house software, HDRCalculator, was developed to check HDR plan parameters such as independently verifying active tandem or cylinder probe length and ovoid or cylinder size, source calibration and treatment date, and differences between average Point A dose and prescription dose. Dose-volume histograms were validated using another independent TPS. Comprehensive procedures to commission volume optimization algorithms and process in 3D image-based planning were presented. For the difference between line and volume optimizations, the average absolute differences as a percentage were 1.4% for total reference air KERMA (TRAK) and 1.1% for Point A dose. Volume optimization consistency tests between versions resulted in average absolute differences in 0.2% for TRAK and 0.9 s (0.2%) for total treatment time. The data revealed that the optimizer should run for at least 1 min in order to avoid more than 0.6% dwell time changes. For clinical GYN T&O cases, three different volume optimization techniques (graphical optimization, pure inverse planning, and hybrid inverse optimization) were investigated by comparing them against a conventional Point A technique. End-to-end testing was performed using a T&O phantom to ensure no errors or inconsistencies occurred from imaging through to planning and delivery. The proposed commissioning procedures provide a clinically safe implementation technique for 3D image-based TPS for HDR BT for GYN cancer.

Direct aperture optimization using an inverse form of back-projection

Direct aperture optimization (DAO) has been used to produce high dosimetric quality intensity-modulated radiotherapy (IMRT) treatment plans with fast treatment delivery by directly modeling the multileaf collimator segment shapes and weights. To improve plan quality and reduce treatment time for our in-house treatment planning system, we implemented a new DAO approach without using a global objective function (GFO). An index concept is introduced as an inverse form of back-projection used in the CT multiplicative algebraic reconstruction technique (MART). The index, introduced for IMRT optimization in this work, is analogous to the multiplicand in MART. The index is defined as the ratio of the optima over the current. It is assigned to each voxel and beamlet to optimize the fluence map. The indices for beamlets and segments are used to optimize multileaf collimator (MLC) segment shapes and segment weights, respectively. Preliminary data show that without sacrificing dosimetric quality, the implementation of the DAO reduced average IMRT treatment time from 13 min to 8 min for the prostate, and from 15 min to 9 min for the head and neck using our in-house treatment planning system PlanUNC. The DAO approach has also shown promise in optimizing rotational IMRT with burst mode in a head and neck test case.

Dosimetric evaluation of an ipsilateral intensity modulated radiotherapy beam arrangement for parotid malignancies

BACKGROUND

We conducted a dosimetric comparison of an ipsilateral beam arrangement for intensity modulated radiotherapy (IMRT) with off-axis beams.

PATIENTS AND METHODS

Six patients who received post-operative radiotherapy (RT) for parotid malignancies were used in this dosimetric study. Four treatment plans were created for each CT data set (24 plans): 1) ipsilateral 4-field off-axis IMRT (4fld-OA), 2) conventional wedge pair (WP), 3) 7 field co-planar IMRT (7fld), and 4) ipsilateral co-planar 4-field quartet IMRT (4fld-CP). Dose, volume statistics for the planning target volumes (PTVs) and planning risk volumes (PRVs) were compared for the four treatment techniques.

RESULTS

Wedge pair plans inadequately covered the deep aspect of the PTV. The 7-field IMRT plans delivered the largest low dose volumes to normal tissues. Mean dose to the contralateral parotid was highest for 7 field IMRT. Mean dose to the contralateral submandibular gland was highest for 7 field IMRT and WP. 7 field IMRT plans had the highest dose to the oral cavity. The mean doses to the brainstem, spinal cord, ipsilateral temporal lobe, cerrebellum and ipsilateral cochlea were similar among the four techniques.

CONCLUSIONS

For postoperative treatment of the parotid bed, 4-field ipsilateral IMRT techniques provided excellent coverage while maximally sparing the contralateral parotid gland and submandibular gland.

Comparison of User-Directed and Automatic Mapping of the Planned Isocenter to Treatment Space for Prostate IGRT

Image-guided radiotherapy (IGRT), adaptive radiotherapy (ART), and online reoptimization rely on accurate mapping of the radiation beam isocenter(s) from planning to treatment space. This mapping involves rigid and/or nonrigid registration of planning (pCT) and intratreatment (tCT) CT images. The purpose of this study was to retrospectively compare a fully automatic approach, including a non-rigid step, against a user-directed rigid method implemented in a clinical IGRT protocol for prostate cancer. Isocenters resulting from automatic and clinical mappings were compared to reference isocenters carefully determined in each tCT. Comparison was based on displacements from the reference isocenters and prostate dose-volume histograms (DVHs). Ten patients with a total of 243 tCTs were investigated. Fully automatic registration was found to be as accurate as the clinical protocol but more precise for all patients. The average of the unsigned x, y, and z offsets and the standard deviations (σ) of the signed offsets computed over all images were (avg. ±  σ (mm)): 1.1 ± 1.4, 1.8 ± 2.3, 2.5 ± 3.5 for the clinical protocol and 0.6 ± 0.8, 1.1 ± 1.5 and 1.1 ± 1.4 for the automatic method. No failures or outliers from automatic mapping were observed, while 8 outliers occurred for the clinical protocol.

Optimization of beam angles for intensity modulated radiation therapy treatment planning using genetic algorithm on a distributed computing platform

Planning intensity modulated radiation therapy (IMRT) treatment involves selection of several angle parameters as well as specification of structures and constraints employed in the optimization process. Including these parameters in the combinatorial search space vastly increases the computational burden, and therefore the parameter selection is normally performed manually by a clinician, based on clinical experience. We have investigated the use of a genetic algorithm (GA) and distributed-computing platform to optimize the gantry angle parameters and provide insight into additional structures, which may be necessary, in the dose optimization process to produce optimal IMRT treatment plans. For an IMRT prostate patient, we produced the first generation of 40 samples, each of five gantry angles, by selecting from a uniform random distribution, subject to certain adjacency and opposition constraints. Dose optimization was performed by distributing the 40-plan workload over several machines running a commercial treatment planning system. A score was assigned to each resulting plan, based on how well it satisfied clinically-relevant constraints. The second generation of 40 samples was produced by combining the highest-scoring samples using techniques of crossover and mutation. The process was repeated until the sixth generation, and the results compared with a clinical (equally-spaced) gantry angle configuration. In the sixth generation, 34 of the 40 GA samples achieved better scores than the clinical plan, with the best plan showing an improvement of 84%. Moreover, the resulting configuration of beam angles tended to cluster toward the patient's sides, indicating where the inclusion of additional structures in the dose optimization process may avoid dose hot spots. Additional parameter selection in IMRT leads to a large-scale computational problem. We have demonstrated that the GA combined with a distributed-computing platform can be applied to optimize gantry angle selection within a reasonable amount of time.

A carbon nanotube field emission multipixel x-ray array source for microradiotherapy application

The authors report a carbon nanotube (CNT) field emission multipixel x-ray array source for microradiotherapy for cancer research. The developed multipixel x-ray array source has 50 individually controllable pixels and it has several distinct advantages over other irradiation source including high-temporal resolution (millisecond level), the ability to electronically shape the form, and intensity distribution of the radiation fields. The x-ray array was generated by a CNT cathode array (5×10) chip with electron field emission. A dose rate on the order of >1.2 Gy∕min per x-ray pixel beam is achieved at the center of the irradiated volume. The measured dose rate is in good agreement with the Monte Carlo simulation result.

A two-stage sequential linear programming approach to IMRT dose optimization

The conventional IMRT planning process involves two stages in which the first stage consists of fast but approximate idealized pencil beam dose calculations and dose optimization and the second stage consists of discretization of the intensity maps followed by intensity map segmentation and a more accurate final dose calculation corresponding to physical beam apertures. Consequently, there can be differences between the presumed dose distribution corresponding to pencil beam calculations and optimization and a more accurately computed dose distribution corresponding to beam segments that takes into account collimator-specific effects. IMRT optimization is computationally expensive and has therefore led to the use of heuristic (e.g., simulated annealing and genetic algorithms) approaches that do not encompass a global view of the solution space. We modify the traditional two-stage IMRT optimization process by augmenting the second stage via an accurate Monte Carlo-based kernel-superposition dose calculations corresponding to beam apertures combined with an exact mathematical programming-based sequential optimization approach that uses linear programming (SLP). Our approach was tested on three challenging clinical test cases with multileaf collimator constraints corresponding to two vendors. We compared our approach to the conventional IMRT planning approach, a direct-aperture approach and a segment weight optimization approach. Our results in all three cases indicate that the SLP approach outperformed the other approaches, achieving superior critical structure sparing. Convergence of our approach is also demonstrated. Finally, our approach has also been integrated with a commercial treatment planning system and may be utilized clinically.

Comparison of three concomitant boost techniques for early-stage breast cancer

PURPOSE

Whole breast radiotherapy (RT) followed by a tumor bed boost typically spans 5-6 weeks of treatment. Interest is growing in RT regimens, such as concomitant boost, that decrease overall treatment time, lessening the time/cost burden to patients and facilities.

METHODS AND MATERIALS

Computed tomography (CT) scans from 20 cases were selected for this retrospective, dosimetric study to compare three different techniques of concomitant boost delivery: (1) standard tangents plus an electron boost, (2) intensity-modulated RT (IMRT) tangents using custom compensators plus an electron boost, and (3) IMRT tangents plus a conformal photon boost. The equivalent uniform dose model was used to compare the plans.

RESULTS

The average breast equivalent uniform dose value for the three techniques (standard, IMRT plus electrons, and IMRT plus photons) was 48.6, 47.9, and 48.3, respectively. The plans using IMRT more closely approximated the prescribed dose of 46 Gy to the whole breast. The breast volume receiving >110% of the dose was less with the IMRT tangents than with standard RT (p = 0.037), but no significant difference in the maximal dose or other evaluated parameters was noted.

CONCLUSION

Although the IMRT techniques delivered the prescribed dose with better dose uniformity, the small improvement seen did not support a goal of improved resource use.

Predicting radiotherapy-induced cardiac perfusion defects

The purpose of this work is to compare the efficacy of mathematical models in predicting the occurrence of radiotherapy-induced left ventricular perfusion defects assessed using single-photon emission computed tomography (SPECT). The basis of this study is data from 73 left-sided breast/ chestwall patients treated with tangential photon fields. The mathematical models compared were three commonly used parametric models [Lyman normal tissue complication probability (LNTCP), relative serialty (RS), generalized equivalent uniform dose (gEUD)] and a nonparametric model (Linear discriminant analysis--LDA). Data used by the models were the left ventricular dose--volume histograms, or SPECT-based dose-function histograms, and the presence/absence of SPECT perfusion defects 6 months postradiation therapy (21 patients developed defects). For the parametric models, maximum likelihood estimation and F-tests were used to fit the model parameters. The nonparametric LDA model step-wise selected features (volumes/function above dose levels) using a method based on receiver operating characteristics (ROC) analysis to best separate the groups with and without defects. Optimistic (upper bound) and pessimistic (lower bound) estimates of each model's predictive capability were generated using ROC curves. A higher area under the ROC curve indicates a more accurate model (a model that is always accurate has area = 1). The areas under these curves for different models were used to statistically test for differences between them. Pessimistic estimates of areas under the ROC curve using dose-volume histogram/ dose-function histogram inputs, in order of increasing prediction accuracy, were LNTCP (0.79/0.75), RS (0.80/0.77), gEUD (0.81/0.78), and LDA (0.84/0.86). Only the LDA model benefited from SPECT-based regional functional information. In general, the LDA model was statistically superior to the parametric models. The LDA model selected as features the left ventricular volumes above approximately 23 Gy (V23), essentially volume in field, and 33 Gy (V33), as best separating the groups with and without defects. In conclusion, the nonparametric LDA model appears to be a more accurate predictor of radiotherapy-induced left ventricular perfusion defects than commonly used parametric models.

A dose-volume-based tool for evaluating and ranking IMRT treatment plans

External beam radiotherapy is commonly used for patients with cancer. While tumor shrinkage and palliation are frequently achieved, local control and cure remain elusive for many cancers. With regard to local control, the fundamental problem is that radiotherapy‐induced normal tissue injury limits the dose that can be delivered to the tumor. While intensity‐modulated radiation therapy (IMRT) allows for the delivery of higher tumor doses and the sparing of proximal critical structures, multiple competing plans can be generated based on dosimetric and/or biological constraints that need to be considered/compared. In this work, an IMRT treatment plan evaluation and ranking tool, based on dosimetric criteria, is presented. The treatment plan with the highest uncomplicated target conformity index (TCI+) is ranked at the top. The TCI+ is a dose‐volume‐based index that considers both a target conformity index (TCI) and a normal tissue‐sparing index (NTSI). TCI+ is designed to assist in the process of judging the merit of a clinical treatment plan. To demonstrate the utility of this tool, several competing lung and prostate IMRT treatment plans are compared. Results show that the plan with the highest TCI+ values accomplished the competing goals of tumor coverage and critical structures sparing best, among rival treatment plans for both treatment sites. The study demonstrates, first, that dose‐volume‐based indices, which summarize complex dose distributions through a single index, can be used to automatically select the optimal plan among competing plans, and second, that this dose‐volume‐based index may be appropriate for ranking IMRT dose distributions.

PACS numbers: 87.53.‐j, 87.53.Tf

Penalized likelihood fluence optimization with evolutionary components for intensity modulated radiation therapy treatment planning

A novel iterative penalized likelihood algorithm with evolutionary components for the optimization of beamlet fluences for intensity modulated radiation therapy (IMRT) is presented. This algorithm is designed to be flexible in terms of the objective function and automatically escalates dose, as long as the objective function increases and all constraints are met. For this study, the objective function employed was the product of target equivalent uniform dose (EUD) and fraction of target tissue within set homogeneity constraints. The likelihood component of the algorithm iteratively attempts to minimize the mean squared error between a homogeneous dose prescription and the actual target dose distribution. The updated beamlet fluences are then adjusted via a quadratic penalty function that is based on the dose-volume histogram (DVH) constraints of the organs at risk. The evolutionary components were included to prevent the algorithm from converging to a local maximum. The algorithm was applied to a prostate cancer dataset, with especially difficult DVH constraints on bladder, rectum, and femoral heads. Dose distributions were generated for manually selected sets of three-, four-, five-, and seven-field treatment plans. Additionally, a global search was performed to find the optimal orientations for an axial three-beam plan. The results from this optimal orientation set were compared to results for manually selected orientation (gantry angle) sets of 3- (0 degrees, 90 degrees, 270 degrees), 4- (0 degrees, 90 degrees, 180 degrees, 270 degrees), 5- (0 degrees, 50 degrees, 130 degrees, 230 degrees, 310 degrees), and 7- (0 degrees, 40 degrees, 90 degrees, 140 degrees, 230 degrees, 270 degrees, 320 degrees) field axial treatment plans. For all the plans generated, all DVH constraints were met and average optimization computation time was approximately 30 seconds. For the manually selected orientations, the algorithm was successful in providing a relatively homogeneous target dose distribution, while simultaneously satisfying dose-volume limits by diverting dose away from proximal critical structures. The global search for an optimal three-beam orientation set yielded gantry angles of 70 degrees, 170 degrees, and 320 degrees. The EUD for this orientation set was 58 Gy, with 96% of the target within the set upper and lower limits. In comparison, optimized EUDs for the manually selected orientation sets of three, four, five and seven beams were 52.3, 52.6, 56.9, and 61.3 Gy, respectively. The orientation optimized three-beam plan yielded higher EUDs than the manually selected three-, four-, and five-beam plans, but lower EUDs than the seven-beam plan. In conclusion, a novel penalized likelihood algorithm with evolutionary components has successfully been implemented to optimize beamlet fluences for IMRT. Initial results are promising for dose conformity and uniformity of dose to target. When combined with optimal beam orientation selection for prostate cancer treatment planning, the results indicate that plans with a small number of optimized beam orientations achieve results comparable to those with a larger number of conventionally oriented beams.

Treatment planning considerations of reshapeable automatic intensity modulator for intensity modulated radiation therapy

As compared with multi-leaf collimator based intensity modulated radiation therapy (IMRT) techniques, physical modulators have the major advantage of temporally invariant intensity map delivery which makes it more flexible with monitor unit rate, simpler resolution of interrupted treatment and easier implementation and use with respiratory gating. However, traditional physical modulator techniques require long fabrication time and operator intervention during treatments. It has been previously proposed [Xu et al., Med. Phys. 29, 2222-2229 (2002)] that a reshapeable automatic intensity modulator (RAIM) can automatically produce physical modulators by molding a deformable high x-ray attenuation material using a matrix of computer-controlled pistons. RAIM can potentially eliminate the limitations of traditional physical modulators. The present study addresses the treatment planning considerations of RAIM for IMRT. In this study, a 3D treatment-planning system (PLUNC) was modified to include the capability of providing treatment planning using RAIM. Two clinically representative cases were studied: nasopharyngeal and prostate tumors. First, the RAIM system with two different spatial resolutions at isocenter, 1 x 1 cm2 and 0.5 x 0.5 cm2, were evaluated. The treatment planning results of RAIM were then compared with other IMRT techniques such as smooth modulator with ideal (100%-2%) and limited (100%-13%) intensity modulation ranges, segmental multi-leaf collimator (SMLC) with ten intensity levels, 1 cm leaf width and 0.5 cm step size and serial tomotherapy using the Peacock system. Bringing the spatial resolution of RAIM down to 0.5 x 0.5 cm2 did not show improvement due to the effect of penumbra. The RAIM system with 1 x 1 cm2 proved slightly inferior as compared to the ideal smooth physical modulator but better than the SMLC technique and the smooth modulator with limited modulation range. When compared to serial tomotherapy, RAIM is only inferior in brain stem sparing for the nasopharynx case. Furthermore, the RAIM system with 1 x 1 cm2 resolution required significantly lower monitor units as compared to the other IMRT techniques for the two cases studied.

Compensators: an alternative IMRT delivery technique

Seven years of experience in compensator intensity-modulated radiotherapy (IMRT) clinical implementation are presented. An inverse planning dose optimization algorithm was used to generate intensity modulation maps, which were delivered via either the compensator or segmental multileaf collimator (MLC) IMRT techniques. The in-house developed compensator-IMRT technique is presented with the focus on several design issues. The dosimetry of the delivery techniques was analyzed for several clinical cases. The treatment time for both delivery techniques on Siemens accelerators was retrospectively analyzed based on the electronic treatment record in LANTIS for 95 patients. We found that the compensator technique consistently took noticeably less time for treatment of equal numbers of fields compared to the segmental technique. The typical time needed to fabricate a compensator was 13 min, 3 min of which was manual processing. More than 80% of the approximately 700 compensators evaluated had a maximum deviation of less than 5% from the calculation in intensity profile. Seventy-two percent of the patient treatment dosimetry measurements for 340 patients have an error of no more than 5%. The pros and cons of different IMRT compensator materials are also discussed. Our experience shows that the compensator-IMRT technique offers robustness, excellent intensity modulation resolution, high treatment delivery efficiency, simple fabrication and quality assurance (QA) procedures, and the flexibility to be used in any teletherapy unit.

The PLUNC 3D treatment planning system: a dynamic alternative to commercially available systems

Three-dimensional (3D) treatment planning is an integral step in the treatment of various cancers when radiation is prescribed as either the primary or adjunctive modality, especially when the gross tumor volume lies in a difficult to reach area or is proximal to critical bodily structures. Today, 3D systems have made it possible to more precisely localize tumors in order to treat a higher ratio of cancer cells to normal tissue. Over the past 15 years, these systems have evolved into complex tools that utilize powerful computational algorithms that offer diverse functional capabilities, while simultaneously attempting to maintain a user-friendly quality. A major disadvantage of commercial systems is that users do not have access to the programming source code, resulting in significantly limited clinical and technological flexibility. As an alternative, in-house systems such as Plan-UNC (PLUNC) offer optimal flexibility that is vital to research institutions and important to treatment facilities. Despite this weakness, commercially available systems have become the norm because their commissioning time is significantly less and because many facilities do not have computer experts on-site.

Feasibility of optimizing the dose distribution in lung tumors using fluorine-18-fluorodeoxyglucose positron emission tomography and single photon emission computed tomography guided dose prescriptions

The information provided by functional images may be used to guide radiotherapy planning by identifying regions that require higher radiation dose. In this work we investigate the dosimetric feasibility of delivering dose to lung tumors in proportion to the fluorine-18-fluorodeoxyglucose activity distribution from positron emission tomography (FDG-PET). The rationale for delivering dose in proportion to the tumor FDG-PET activity distribution is based on studies showing that FDG uptake is correlated to tumor cell proliferation rate, which is shown to imply that this dose delivery strategy is theoretically capable of providing the same duration of local control at all voxels in tumor. Target dose delivery was constrained by single photon emission computed tomography (SPECT) maps of normal lung perfusion, which restricted irradiation of highly perfused lung and imposed dose-function constraints. Dose-volume constraints were imposed on all other critical structures. All dose-volume/function constraints were considered to be soft, i.e., critical structure doses corresponding to volume/function constraint levels were minimized while satisfying the target prescription, thus permitting critical structure doses to minimally exceed dose constraint levels. An intensity modulation optimization methodology was developed to deliver this radiation, and applied to two lung cancer patients. Dosimetric feasibility was assessed by comparing spatially normalized dose-volume histograms from the nonuniform dose prescription (FDG-PET proportional) to those from a uniform dose prescription with equivalent tumor integral dose. In both patients, the optimization was capable of delivering the nonuniform target prescription with the same ease as the uniform target prescription, despite SPECT restrictions that effectively diverted dose from high to low perfused normal lung. In one patient, both prescriptions incurred similar critical structure dosages, below dose-volume/function limits. However, in the other patient, critical structure dosage from the nonuniform dose prescription exceeded dose-volume/function limits, and greatly exceeded that from the uniform dose prescription. Strict compliance to dose-volume/ function limits would entail reducing dose proportionality to the FDG-PET activity distribution, thereby theoretically reducing the duration of local control. Thus, even though it appears feasible to tailor lung tumor dose to the FDG-PET activity distribution, despite SPECT restrictions, strict adherence to dose-volume/function limits could compromise the effectiveness of functional image guided radiotherapy.

Incorporation of functional imaging data in the evaluation of dose distributions using the generalized concept of equivalent uniform dose

Advances in the fields of IMRT and functional imaging have greatly increased the prospect of escalating the dose to highly active or hypoxic tumour sub-volumes and steering the dose away from highly functional critical structure regions. However, current clinical treatment planning and evaluation tools assume homogeneous activity/function status in the tumour/critical structures. A method was developed to incorporate tumour/critical structure heterogeneous functionality in the generalized concept of equivalent uniform dose (EUD). The tumour and critical structures functional EUD (FEUD) values were calculated from the dose-function histogram (DFH), which relates dose to the fraction of total function value at that dose. The DFH incorporates flouro-deoxyglucose positron emission tomography (FDG-PET) functional data for tumour, which describes the distribution of metabolically active tumour clonogens, and single photon emission computed tomography (SPECT) perfusion data for critical structures. To demonstrate the utility of the method, the lung dose distributions of two non-small cell lung cancer patients, who received 3D conformal external beam radiotherapy treatment with curative intent, were evaluated. Differences between the calculated lungs EUD and FEUD values of up to 50% were observed in the 3D conformal plans. In addition, a non-small cell lung cancer patient was inversely planned with a target dose prescription of 76 Gy. Two IMRT plans (plan-A and plan-B) were generated for the patient based on the CT, FDG-PET and SPECT treatment planning images using dose-volume objective functions. The IMRT plans were generated with the goal of achieving more critical structures sparing in plan-B than plan-A. Results show the target volume EUD in plan-B is lower than plan-A by 5% with a value of 73.31 Gy, and the FEUD in plan-B is lower than plan-A by 2.6% with a value of 75.77 Gy. The FEUD plan-B values for heart and lungs were lower than plan-A by 22% and 18%, respectively. While EUD values show plan-A is marginally better than plan-B in terms of target volumetric coverage, the FEUD plan-B values show adequate target function coverage with significant critical structure function sparing. In conclusion, incorporating functional data in the calculation of EUD is important in evaluating the biological merit of treatment plans.

Conversion of dose–volume constraints to dose limits

The purpose of this study is to introduce two techniques for converting dose-volume constraints to dose limits for treatment planning optimization, and to evaluate their performance. The first technique, called dose-sorting, is based on the assumption that higher dose limits should be assigned to the constraint points receiving higher doses, and vice versa. The second technique, the hybrid technique, is a hybrid of the dose-sorting technique and the mixed integer linear programming (MILP) technique. Among all constraint points in an organ at risk, the dose limits for the points far from a dose-volume constraint are determined by dose-sorting, while the dose limits for the points close to a dose-volume constraint are determined by MILP. We evaluated the performance of the two new techniques for one treatment geometry by comparing them with the MILP technique. The dose-sorting technique had a high probability of finding the global optimum when no more than three organs at risk have dose-volume constraints. It was much faster than the MILP technique. The hybrid technique always found the global optimum when the MILP percentage (the percentage of constraint points for which the dose limits are determined by the MILP technique) was large enough, but its computation time increased dramatically with the MILP percentage. In conclusion, the dose-sorting technique and the hybrid technique with a low MILP percentage are clinically feasible.