直肠癌术前同步推量RapidPlan模型用于术后单一处方计划优化的改造测试

目的:测试直肠癌术前同步推量RapidPlan模型用于术后单一处方计划优化的可行性,探索改造和拓展已有模型的应用方法。方法:（1）对现有直肠癌术前同步推量41.8 Gy（PTV）/50.6 Gy（PGTV）RapidPlan模型进行改造;（2）复制直肠癌术后单一PTV处方临床计划18例（45 Gy的7例,50 Gy的11例）,保持布野条件、能量、加速器配置及原有剂量算法等不变,将PTV分别匹配模型中的PGTV和PTV,预测可实现的DVH区间并重新优化;（3）将自动计划靶区剂量归一至与临床计划相似后比较各剂量学参数。结果:单一处方靶区匹配模型中的PTV会导致严重的剂量热区,匹配PGTV的RapidPlan计划质量和临床计划相似或略好,但其危及器官剂量学参数的标准差均小于临床计划。结论:直肠癌术前同步推量RapidPlan模型可用于术后单一处方放疗计划的自动优化并且其质量一致性更好,但需将单一靶区匹配给模型中最高处方剂量对应的靶区结构。     

不同多叶准直器对RapidPlan模型应用的剂量学影响

目的:探讨RapidPlan模型在不同多叶准直器（MLC）系统间的建模和拓展应用情况。方法:选取北京大学肿瘤医院2014年5月至2015年6月接受放疗的直肠癌患者的历史计划（配置为MMLC加速器）共81例和2017年11月至2019年5月接受立体定向放疗（SBRT）的肺癌患者的历史计划（配置为HDMLC的加速器）共35...     

剂量体积优化算法与光子优化算法在儿童全中枢调强放射治疗计划的剂量学比较

目的:分析剂量体积优化（DVO）算法与光子优化（PO）算法在儿童全中枢调强放射治疗（IMRT）中的剂量学比较。方法:选择2018年7月~2020年1月于广东三九脑科医院行全中枢IMRT计划的15例儿童肿瘤患者作为研究对象,分别采用DVO算法和PO算法设计计划,比较两组计划的剂量学参数、优化效率及机器跳数。结果:与PO算法相比,DVO算法计划的靶区[D50%]和适形度指数更佳,差异有统计学意义（P<0.05）,且颈段计划靶区（PTV）低于95%处方剂量的体积更低（P<0.05）,但在靶区[D2%、D98%]、均匀性指数和梯度跌落指数差异无统计学意义（P>0.05）。与PO算法相比,DVO算法计划在双肺、右肾和心脏的受照剂量偏低,差异有统计学意义（P<0.05）,而在其它危及器官剂量学参数差异无统计学意义（P>0.05）。与PO算法相比,DVO算法计划增加了较少的机器跳数（约63 MU）,但算法优化时间翻倍,约224 s。结论:儿童全中枢IMRT计划采用DVO算法可提高靶区适形性,降低颈段PTV低于处方剂量的体积,有可能减少颈段靶区肿瘤复发率,因此建议在儿童全中枢IMRT计划中采用DVO算法优化。     

基于蒙特卡罗模拟的直肠癌术前容积调强放射治疗计划剂量验证

目的: 通过蒙特卡罗模拟评价基于各向异性解析算法（AAA）直肠癌术前容积调强放射治疗计划（VMAT）的剂量计算精度。方法: 选取20例基于AAA算法和RapidPlan模型优化的直肠癌术前VMAT计划,通过对比蒙卡模拟与治疗计划计算结果的平均DVH、靶区适形度（CI）、靶区均匀性（HI）和Gamma 3D通过率等参数,评估基于AAA算法的VMAT治疗计划剂量计算精度。结果: 两种Gamma 3D评估策略通过率的均值与标准差分别为97.58±0.47%（Max Dose）、92.46±1.76%（Local Dose）,且差异具有统计学意义（P<0.05）;对PTV和PGTV的CI、DMin、膀胱的D50%、DMean等不符合正态分布的参数做相关样本非参数检验,除PGTV的CI和Dmin外,差异均具有统计学意义（P < 0.05）;其他服从正态分布的参数做配对样本T检验,差异均具有统计学意义（P < 0.05）。结论: Rapidplan模型计划在低剂量区通过率较低,说明AAA算法射野边缘低剂量区计算偏差较大;靶区Dmin与算法的精度较为相关,CI和HI参数相对于蒙卡模拟结果有一定差异;AAA算法在股骨头和膀胱的D50%、DMean相对蒙卡模型有不同程度的低估。     

Model Analytics辅助的智能放疗计划建模

目的:利用瓦里安公司开发的Model Analytics(MA)工具减少人工处理RapidPlan模型离群值的繁琐和主观因素导致模型构成的不确定性,评估MA工具在效率、改善统计学参数及模型优化效果等方面的表现。方法:(1)选取81例优质计划导入RapidPlan系统并建立初始模型;(2)将初始模型上传MA进行自动分析统计,根据报告提示对离群值进行批量统计学确认,比较模型验证前后统计学指标的变化;(3)利用20例测试病例评估统计学确认前后Rapid Plan模型的剂量学表现,并与原临床计划比较。结果:MA只需几分钟便可得到构成模型计划的几何学、剂量学等特征统计,5轮分析共找出8个股骨头剂量学离群值,分别高于各自预测范围上限的11.11%、5.88%、5.56%、5.56%、5.00%、5.26%、5.56%和5.88%,R~2由0.32提高至0.45;仅用一轮分析便找出所有3个膀胱几何和剂量学离群值,其中几何离群值分别高于均值62.22%或低于均值55.35%,剂量学离群值高于预测范围上限3.33%,处理完离群值后,R~2由0.35升至0.37。测试计划表明,Rapid Plan计划质量显著优于人工计划(P0.05),使用验证前后的模型可分别降低股骨头剂量23.15%和27.55%,降低膀胱剂量8.14%和6.79%。结论:使用MA工具可快速获取模型构成计划的整体描述,并准确查找出模型中的离群值,从而提高智能放疗计划建模的效率,但统计学确认对模型的剂量学表现影响不大。     

两套商用治疗计划系统中VMAT计划质量及其验证的对比研究

目的:探讨两套商用治疗计划系统（TPS）用于喉癌与直肠癌患者容积旋转调强放疗（VMAT）的剂量学特性与验证结果差异,为其临床应用提供一定的依据。 方法:选取喉癌患者10例、直肠癌患者12例,分别利用Eclipse和Pinnacle商用TPS进行VMAT及其验证计划设计,利用ArcCheck实施剂量数据的采集,分析标准为3%/3 mm和2%/2 mm条件下Gamma通过率。从计划质量、实施效率、验证结果等方面评价两套系统执行VMAT技术的差异性。 结果:计划质量方面:喉癌VMAT计划中,Eclipse在危及器官保护以及计划靶区（PTV）的适形度指数（CI）、均匀性指数（HI）上与 Pinnacle相近（P>0.05）,Eclipse的MU要少于Pinnacle,但无统计学差异（P>0.05）;直肠癌VMAT计划中,Eclipse在MU、PTV的CI和HI以及对膀胱、小肠的保护上与Pinnacle相近,在左右股骨头的V40上,Eclipse略优于Pinnacle,但无统计学差异（P>0.05）。剂量验证方面:无论是喉癌还是直肠癌VMAT计划,在分析评价标准3%/3 mm和2%/2 mm条件下,Eclipse的Gamma通过率均高于Pinnacle,且均具有统计学差异（P<0.05）。 结论:尽管两套TPS的喉癌和直肠癌VMAT计划质量相近,且剂量验证均能满足临床治疗的要求,但两套计划系统在MU以及剂量验证通过率上存在一定的差异性,仍需选择更多的病例进一步探讨以确定其差异的原因。     

光子优化算法在宫颈癌术后调强计划中的剂量学分析

目的:探讨宫颈癌术后调强放射治疗（IMRT）计划中采用光子优化（PO）算法与常规的剂量体积优化（DVO）算法的 剂量学差异。方法:选取20例接受宫颈癌术后IMRT的患者。勾画靶区和危及器官后,分别设计基于PO算法和DVO算 法的两种IMRT计划,比较两种计划的剂量学特性、剂量验证通过率和治疗计划的效率。结果:两种计划中计划靶区 （PTV）的D98%、靶区覆盖率和均匀性指数无明显差异,但是PO计划在PTV的D2%、Dmean均低于DVO计划（P=0.019, 0.016）, 同时PTV的适形度指数优于DVO计划（P=0.005）。在危及器官保护上,PO计划的膀胱V30和左股骨头V20低于DVO计划 （P=0.000, 0009）,但是小肠V15、直肠V30和左右侧股骨头V30高于DVO计划（P=0.000, 0.001, 0.000, 0.000）。PO计划在正 常组织V30的受量上低于DVO计划（P=0.005）,但在V5和V10的受量上高于DVO计划（P=0.000, 0.000）。两种计划的剂量 验证通过率均能满足治疗的要求,其中PO计划通过率为（98.06±0.81）%,优于DVO计划通过率（96.05±1.09）%。PO计划 相比DVO计划,机器跳数平均减少10.7%,治疗时间平均减少10.5%,优化耗时平均缩短35.4%。结论:PO计划和DVO计 划都能满足临床要求。PO算法应用于宫颈癌术后IMRT在靶区剂量分布上略有优势,能够提高靶区适形度,减少机器跳 数,缩短计划设计时间和治疗时间,同时剂量投照更准确。     

自动IMRT计划在宫颈癌术后放疗中的可行性

目的:通过比较自动IMRT计划与人工IMRT计划的剂量学差异,探讨自动计划在宫颈癌术后IMRT计划设计中的可行性。 方法:使用飞利浦Pinnacle3 9.10计划系统的自动IMRT和人工IMRT方法分别对25例宫颈癌术后患者进行计划设计,比较2种计划得到的靶区和危及器官的剂量学参数、机器跳数、调试次数及计划设计时间。结果:自动和人工IMRT计划靶区的Dmean、D95、CI及HI等参数均无明显差异（P>0.05）;自动IMRT计划得到的危及器官剂量学参数均优于人工IMRT计划,其中膀胱V40减少2.5%（P<0.05）,直肠V40减少0.9%（P<0.05）,骨V35减少2.8%（P<0.05）,小肠V30减少4.2%（P<0.05）,左侧股骨头V30减少5.2%（P<0.05）以及右侧股骨头V30减少5.5%（P<0.05）;并且自动计划明显减少了计划调试次数,将人工IMRT计划的平均调试次数由3次减少到平均2次,计划设计时间由人工IMRT的69.5 min减少到42.7 min;但自动计划的平均跳数（1 042 MU）高于人工计划（931 MU）。结论:基于Pinnacle3的自动IMRT计划质量可以达到人工IMRT计划水平的同时,明显提高了计划设计效率,在宫颈癌术后的IMRT计划设计中具有可行性。     

食管癌调强放疗计划中AAA算法与PBC算法的对比研究

目的：比较Varian治疗计划系统Eclipse中AAA算法和PBC算法在食管癌调强放疗中的剂量学差异。方法：选择22例中段食管癌患者,分别采用AAA算法与PBC算法设计两种调强计划,比较靶区的剂量分布,肺、脊髓和心脏等危及器官受照剂量的差异。结果：PGTV最大剂量、PTV平均剂量和左肺的平均剂量两种算法无显著性差异（P〉0．05）,PGTV和PTV最小剂量、PTV最大剂量、参考剂量所包靶区的体积（V95）和其他危及器官的受量,两种算法均有显著性差异（P〈0．05）。结论：与PBC算法相比,AAA算法对不均匀组织的修正更加精确,对于食管癌这种与肺相关的剂量计算采用AAA算法更准确一些。     

算法差异在Compass调强计划验证中的作用

目的:用IBA Compass系统对Varian Eclipse计划系统各向异性解析算法(AAA)计算的肺癌和直肠癌计划进行验证,研究差异原因并进行分类分析。方法:分别选取肺癌和直肠癌术前放疗患者各10例,用Compass系统在加速器实测验证,将Eclipse AAA计算的TPS Dose、Compass卷积/超分割算法(CCC)再计算的Compute Dose以及Compass通过实测并基于CCC算法重建的Reconstructed Dose进行两两对比(AAA/CR、CC/CR、AAA/CC),比较分析计划最大点剂量的10%生成的区域的Gamma结果和剂量体积直方图(DVH)结果。结果:在3 mm/3%/Global标准下,直肠癌术前计划:AAA/CRγ通过率为(97.37±2.41)%,CC/CRγ通过率为(97.88±2.21)%,AAA/CCγ通过率为(99.69±0.15)%,AAA/CRγ通过率与CC/CRγ通过率的差异无统计学意义(P=0.598)。肺癌计划:AAA/CRγ通过率为(92.09±2.79)%,CC/CRγ通过率为(96.17±2.78)%,AAA/CCγ通过率为(98.96±1.06)%,AAA/CRγ通过率与CC/CRγ通过率的差异具有显著统计学意义(P=0.005)。结论:用Compass验证AAA算法计划,在肺癌病例中AAA与CCC算法的差异是影响计划通过率的主要原因,在直肠癌计划中AAA与CCC算法的差异影响相对较低,通过率更多受到MLC到位精度、机架旋转精度、剂量准确度等执行不确定性影响。     

A closer look at RapidArc® radiosurgery plans using very small fields

RapidArc? has become the treatment of choice for an increasing number of treatment sites in many clinics. The extensive use of multiple subfields in RapidArc? treatments presents unique challenges, especially for small targets treated in few fractions. In this work, very small static fields and subsequently RapidArc? and conventional plans for two targets (0.4 and 9.9 cm(3)) were investigated. Doses from static fields 1-4 MLC leaves (0.25-1.00 cm) wide, and larger fields with 1-4 MLC leaves closed in their centres, were measured using the portal dosimeter-based QA system EPIQA (v?1.3) and gafchromic film. RapidArc and conventional plans for two tumours were then measured using EPIQA, gafchromic EBT2 film and the phantom-based QA system Delta4. Eclipse 8.6 and 8.9, grid spacings of 1.25 and 2.50 mm and a Varian HD linac were used. For static fields one MLC leaf wide, the dose was underestimated by Eclipse by as much as 53% (v?8.6, 2.5 mm grid). Eclipse underestimated the dose downstream from a few MLC leaves closed in the centre of a large MLC field by as much as 30%. Eclipse consistently overestimated the width of the penumbra by about 100%. For the conventional plans, there was good agreement between the calculated and measured dose for the 9.9 cm(3) PTV, but a 10% underdose was observed for the 0.4 cm(3) PTV. For the RapidArc? plans, the measured dose for the 9.9 cm(3) PTV was in good agreement with the calculated one. However, for the 0.4 cm(3) PTV about 10% overdosing was detected (Eclipse v 8.6, 2.5 mm grid spacing). EPIQA data indicated that the measured dose profiles were overmodulated compared to the calculated one. The use of small subfields, typically a few MLC leaves wide, or larger fields with one or a few MLC leaves closed in its centre can result in significant errors in the dose calculation. The detector systems used vary in their ability to detect the discrepancies. Using a smaller grid size and newer version of Eclipse reduces the discrepancies observed in this work but does not eliminate them.     

The dosimetric impact of leaf interdigitation and leaf width on VMAT treatment planning in Pinnacle: comparing Pareto fronts

To evaluate in an objective way the effect of leaf interdigitation and leaf width on volumetric modulated arc therapy plans in Pinnacle. Three multileaf collimators (MLCs) were modeled: two 10?mm leaf width MLCs, with and without interdigitating leafs, and a 5?mm leaf width MLC with interdigitating leafs. Three rectum patients and three prostate patients were used for the planning study. In order to compare treatment techniques in an objective way, a Pareto front comparison was carried out. 200 plans were generated in an automated way, per patient per MLC model, resulting in a total of 3600 plans. From these plans, Pareto-optimal plans were selected which were evaluated for various dosimetric variables. The capability of leaf interdigitation showed little dosimetric impact on the treatment plans, when comparing the 10?mm leaf width MLC with and without leaf interdigitation. When comparing the 10?mm leaf width MLC with the 5?mm leaf width MLC, both with interdigitating leafs, improvement in plan quality was observed. For both patient groups, the integral dose was reduced by 0.6 J for the thin MLC. For the prostate patients, the mean dose to the anal sphincter was reduced by 1.8 Gy and the conformity of the V(95%)?was reduced by 0.02 using the thin MLC. The V(65%)?of the rectum was reduced by 0.1% and the dose homogeneity with 1.5%. For rectum patients, the mean dose to the bowel was reduced by 1.4 Gy and the mean dose to the bladder with 0.8 Gy for the thin MLC. The conformity of the V(95%)?was equivalent for the 10 and 5?mm leaf width MLCs for the rectum patients. We have objectively compared three types of MLCs in a planning study for prostate and rectum patients by analyzing Pareto-optimal plans which were generated in an automated way. Interdigitation of MLC leafs does not generate better plans using the SmartArc algorithm in Pinnacle. Changing the MLC leaf width from 10 to 5?mm generates better treatment plans although the clinical relevance remains to be proven.     

An integrated Monte Carlo dosimetric verification system for radiotherapy treatment planning

An integrated Monte Carlo (MC) dose calculation system, MCRTV (Monte Carlo for radiotherapy treatment plan verification), has been developed for clinical treatment plan verification, especially for routine quality assurance (QA) of intensity-modulated radiotherapy (IMRT) plans. The MCRTV system consists of the EGS4/PRESTA MC codes originally written for particle transport through the accelerator, the multileaf collimator (MLC), and the patient/phantom, which run on a 28-CPU Linux cluster, and the associated software developed for the clinical implementation. MCRTV has an interface with a commercial treatment planning system (TPS) (Eclipse, Varian Medical Systems, Palo Alto, CA, USA) and reads the information needed for MC computation transferred in DICOM-RT format. The key features of MCRTV have been presented in detail in this paper. The phase-space data of our 15 MV photon beam from a Varian Clinac 2300C/D have been developed and several benchmarks have been performed under homogeneous and several inhomogeneous conditions (including water, aluminium, lung and bone media). The MC results agreed with the ionization chamber measurements to within 1% and 2% for homogeneous and inhomogeneous conditions, respectively. The MC calculation for a clinical prostate IMRT treatment plan validated the implementation of the beams and the patient/phantom configuration in MCRTV.     

Incorporating multi-leaf collimator leaf sequencing into iterative IMRT optimization

Intensity modulated radiation therapy (IMRT) treatment planning typically considers beam optimization and beam delivery as separate tasks. Following optimization, a multi-leaf collimator (MLC) or other beam delivery device is used to generate fluence patterns for patient treatment delivery. Due to limitations and characteristics of the MLC, the deliverable intensity distributions often differ from those produced by the optimizer, leading to differences between the delivered and the optimized doses. Objective function parameters are then adjusted empirically, and the plan is reoptimized to achieve a desired deliverable dose distribution. The resulting plan, though usually acceptable, may not be the best achievable. A method has been developed to incorporate the MLC restrictions into the optimization process. Our in-house IMRT system has been modified to include the calculation of the deliverable intensity into the optimizer. In this process, prior to dose calculation, the MLC leaf sequencer is used to convert intensities to dynamic MLC sequences, from which the deliverable intensities are then determined. All other optimization steps remain the same. To evaluate the effectiveness of deliverable-based optimization, 17 patient cases have been studied. Compared with standard optimization plus conversion to deliverable beams, deliverable-based optimization results show improved isodose coverage and a reduced dose to critical structures. Deliverable-based optimization results are close to the original nondeliverable optimization results, suggesting that IMRT can overcome the MLC limitations by adjusting individual beamlets. The use of deliverable-based optimization may reduce the need for empirical adjustment of objective function parameters and reoptimization of a plan to achieve desired results.     

Monte Carlo simulation of RapidArc radiotherapy delivery

RapidArc radiotherapy technology from Varian Medical Systems is one of the most complex delivery systems currently available, and achieves an entire intensity-modulated radiation therapy (IMRT) treatment in a single gantry rotation about the patient. Three dynamic parameters can be continuously varied to create IMRT dose distributions-the speed of rotation, beam shaping aperture and delivery dose rate. Modeling of RapidArc technology was incorporated within the existing Vancouver Island Monte Carlo (VIMC) system (Zavgorodni et al 2007 Radiother. Oncol. 84 S49, 2008 Proc. 16th Int. Conf. on Medical Physics). This process was named VIMC-Arc and has become an efficient framework for the verification of RapidArc treatment plans. VIMC-Arc is a fully automated system that constructs the Monte Carlo (MC) beam and patient models from a standard RapidArc DICOM dataset, simulates radiation transport, collects the resulting dose and converts the dose into DICOM format for import back into the treatment planning system (TPS). VIMC-Arc accommodates multiple arc IMRT deliveries and models gantry rotation as a series of segments with dynamic MLC motion within each segment. Several verification RapidArc plans were generated by the Eclipse TPS on a water-equivalent cylindrical phantom and re-calculated using VIMC-Arc. This includes one 'typical' RapidArc plan, one plan for dual arc treatment and one plan with 'avoidance' sectors. One RapidArc plan was also calculated on a DICOM patient CT dataset. Statistical uncertainty of MC simulations was kept within 1%. VIMC-Arc produced dose distributions that matched very closely to those calculated by the anisotropic analytical algorithm (AAA) that is used in Eclipse. All plans also demonstrated better than 1% agreement of the dose at the isocenter. This demonstrates the capabilities of our new MC system to model all dosimetric features required for RapidArc dose calculations.     

Inverse planning for intensity-modulated arc therapy using direct aperture optimization

Intensity-modulated arc therapy (IMAT) is a radiation therapy delivery technique that combines gantry rotation with dynamic multi-leaf collimation (MLC). With IMAT, the benefits of rotational IMRT can be realized using a conventional linear accelerator and a conventional MLC. Thus far, the advantages of IMAT have gone largely unrealized due to the lack of robust automated planning tools capable of producing efficient IMAT treatment plans. This work describes an inverse treatment planning algorithm, called 'direct aperture optimization' (DAO) that can be used to generate inverse treatment plans for IMAT. In contrast to traditional inverse planning techniques where the relative weights of a series of pencil beams are optimized, DAO optimizes the leaf positions and weights of the apertures in the plan. This technique allows any delivery constraints to be enforced during the optimization, eliminating the need for a leaf-sequencing step. It is this feature that enables DAO to easily create inverse plans for IMAT. To illustrate the feasibility of DAO applied to IMAT, several cases are presented, including a cylindrical phantom, a head and neck patient and a prostate patient.     

两种准直器宽度对鼻咽癌放疗中的剂量学差异影响

目的:研究两种规格（等中心处投影0.5和1.0 cm）多叶准直器（MLC）在鼻咽癌调强放射治疗（IMRT）计划中的区别,从剂量学方面探究MLC的宽度对患者靶区和危及器官的影响。方法:随机选取已完成治疗的31例鼻咽癌患者计划,在放疗处方和物理优化参数不变的情况下分别使用两种规格MLC的加速器射野模型进行重新优化计算,统计靶区及主要危及器官的体积剂量、平均剂量（Dmean）、适形度指数（CI）、均匀性指数（HI）等参数,分析其差异性。结果:全样本分析显示,所有靶区HI和部分靶区（PGTVnx、PCTV2）CI差异有统计学意义（P<0.05）,0.5 cm MLC优于1.0 cm MLC;危及器官中,右侧视神经和视交叉最大剂量（Dmax）、左侧颞叶和右侧颞颌关节Dmean、左右腮腺V30、气管和脊髓Dmean差异有统计学意义（P<0.05）,0.5 cm MLC优于1.0 cm MLC,其他危及器官无统计学差异（P>0.05）;在Pinnacle3和Monaco计划系统中得到了相似结果,两种MLC在靶区适形度和均匀性方面及部分危及器官受量差异有统计学意义（P<0.05）。结论:0.5 cm MLC在鼻咽癌调强计划中能有效提高靶区适形度和均匀性,也能有效降低部分危及器官受量,可以更好地保护与靶区邻近或有重叠的一些危及器官,推荐有条件的医院使用。     

A difference-matrix metaheuristic for intensity map segmentation in step-and-shoot IMRT delivery

At an intermediate stage of radiation treatment planning for IMRT, most commercial treatment planning systems for IMRT generate intensity maps that describe the grid of beamlet intensities for each beam angle. Intensity map segmentation of the matrix of individual beamlet intensities into a set of MLC apertures and corresponding intensities is then required in order to produce an actual radiation delivery plan for clinical use. Mathematically, this is a very difficult combinatorial optimization problem, especially when mechanical limitations of the MLC lead to many constraints on aperture shape, and setup times for apertures make the number of apertures an important factor in overall treatment time. We have developed, implemented and tested on clinical cases a metaheuristic (that is, a method that provides a framework to guide the repeated application of another heuristic) that efficiently generates very high-quality (low aperture number) segmentations. Our computational results demonstrate that the number of beam apertures and monitor units in the treatment plans resulting from our approach is significantly smaller than the corresponding values for treatment plans generated by the heuristics embedded in a widely use commercial system. We also contrast the excellent results of our fast and robust metaheuristic with results from an 'exact' method, branch-and-cut, which attempts to construct optimal solutions, but, within clinically acceptable time limits, generally fails to produce good solutions, especially for intensity maps with more than five intensity levels. Finally, we show that in no instance is there a clinically significant change of quality associated with our more efficient plans.