a generalized inverse planning tool for volumetric-modulated arc therapy

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A generalized inverse planning tool for volumetric-modulated arc therapy This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2009 Phys. Med. Biol. 54 6725 (http://iopscience.iop.org/0031-9155/54/21/018) Download details: IP Address: 128.210.126.199 The article was downloaded on 15/09/2013 at 10:13 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience

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Page 1: A generalized inverse planning tool for volumetric-modulated arc therapy

A generalized inverse planning tool for volumetric-modulated arc therapy

This article has been downloaded from IOPscience. Please scroll down to see the full text article.

2009 Phys. Med. Biol. 54 6725

(http://iopscience.iop.org/0031-9155/54/21/018)

Download details:

IP Address: 128.210.126.199

The article was downloaded on 15/09/2013 at 10:13

Please note that terms and conditions apply.

View the table of contents for this issue, or go to the journal homepage for more

Home Search Collections Journals About Contact us My IOPscience

Page 2: A generalized inverse planning tool for volumetric-modulated arc therapy

IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY

Phys. Med. Biol. 54 (2009) 6725–6738 doi:10.1088/0031-9155/54/21/018

A generalized inverse planning tool forvolumetric-modulated arc therapy

Daliang Cao, Muhammad K N Afghan, Jinsong Ye, Fan Chen andDavid M Shepard

Swedish Cancer Institute, Seattle, WA 98104, USA

E-mail: [email protected]

Received 17 March 2009, in final form 28 September 2009Published 20 October 2009Online at stacks.iop.org/PMB/54/6725

AbstractThe recent development in linear accelerator control systems, namedvolumetric-modulated arc therapy (VMAT), has generated significant interest inarc-based intensity-modulated radiation therapy (IMRT). The VMAT deliverytechnique features simultaneous changes in dose rate, gantry angle and gantryrotation speed as well as multi-leaf collimator (MLC) leaf positions whileradiation is on. In this paper, we describe a generalized VMAT planningtool that is designed to take full advantage of the capabilities of the newlinac control systems. The algorithm incorporates all of the MLC deliveryconstraints such as restrictions on MLC leaf interdigitation and the MLC leafvelocity constraints. A key feature of the algorithm is that it is able to plan forboth single- and multiple-arc deliveries. Compared to conventional step-and-shoot IMRT plans, our VMAT plans created using this tool can achieve similaror better plan quality with less MU and better delivery efficiency. The accuracyof the obtained VMAT plans is also demonstrated through plan verificationsperformed on an Elekta Synergy linear accelerator equipped with a conventionalMLC of 1 cm leaf width using a PreciseBeam R© VMAT linac control system.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

The concept of rotational intensity-modulated radiation therapy (IMRT) was first described byRock Mackie in his 1993 manuscript entitled ‘Tomotherapy: a new concept for the deliveryof dynamic conformal radiotherapy’ (Mackie et al 1993). In 1995, Cedric Yu introducedan alternative approach to the delivery of rotational IMRT in a paper entitled ‘Intensity-modulated arc therapy with dynamic multileaf collimation: an alternative to tomotherapy’ (Yu1995). Intensity-modulated arc therapy (IMAT) delivers rotational IMRT using a cone-beam

0031-9155/09/216725+14$30.00 © 2009 Institute of Physics and Engineering in Medicine Printed in the UK 6725

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of radiation. IMAT differs from tomotherapy in that it can be delivered using a conventionallinear accelerator and a conventional (non-binary) multileaf collimator (MLC).

More recently, volumetric-modulated arc therapy (VMAT) and arc-modulated radiationtherapy (AMRT) were proposed by different research groups as the single-arc approachto deliver rotational IMRT on a conventional linear accelerator (Otto 2008, Wang et al2008). During single-arc VMAT/AMRT delivery, each individual beam angle only sees asingle aperture shape without any modulated intensity pattern, and a highly conformal dosedistribution can still be achieved through the large number of segments within each arc and thevariable dose rate during the gantry rotation. Recent studies also suggested that a single-arcVMAT technique could provide dosimetric benefit over IMRT for certain cases, if one acceptsthe low dose spread over a larger volume of tissue (Bortfeld and Webb 2009).

Although the concept of IMAT was first proposed more than 10 years ago, this techniquewas not widely adopted in the clinics despite its promising nature. One major reason thatheld back the IMAT implementation was a lack of proper linac control systems that couldchange the MLC leaf positions and vary the dose rate and gantry speed during gantry rotation.Recently, the new linac control system with IMAT/VMAT capability made the delivery offully inverse planned IMAT/VMAT plans possible. As VMAT is referred by the vendors asthe general terminology for arc-based IMRT delivery using conventional linear acceleratorsregardless of the number of arcs used for the treatment, we will then use the same term in thispaper.

A second technical hurdle to the routine clinical adoption of VMAT has been the lackof robust inverse planning tools for VMAT. The inverse planning problem for VMAT issignificantly more complicated than the inverse planning problem for fixed-field IMRT. Thisis due to the interconnectedness of the beam shapes within a given VMAT arc. From oneangle to the next, the inverse planning algorithm must constrain the magnitude of the MLCleaf motion to ensure that the resulting plans can be delivered efficiently and accurately.

A number of researchers have explored planning solutions and clinical applications forIMAT (Cotrutz et al 2000, Earl et al 2003, Shepard et al 2007, Luan et al 2008, Otto 2008, Maet al 2001, Wang et al 2008, Wong et al 2002, 2005, Yu et al 2002, Duthoy et al 2004, Gladwishet al 2007). One approach is to determine the aperture shapes based on the patient’s anatomy(Wong et al 2005, 2002, Duthoy et al 2004, Yu et al 2002, Ma et al 2001). After the apertureshapes are determined, a beam-weight or segment-weight optimization is typically used toimprove the plan quality. Although such forward (or semi-forward) planning techniques canprovide excellent dose conformity for certain treatment sites such as prostate, they may failto produce adequate plan quality for more complicated cases, such as head-and-neck cancerwith multiple targets prescribed to different doses. In other words, the predetermined apertureshapes limit this planning technique from fully utilizing the potential of the VMAT technology.

A direct aperture optimization (DAO)-based inverse planning tool was introduced by Earlet al in 2003 for multiple-arc VMAT delivery (Earl et al 2003). Due to the large amount of3D volumetric dose data involved in the optimization process, it was very time consuming forthe optimizer to reach a reasonable solution. Another DAO-based VMAT optimization forsingle-arc planning proposed by Otto (2008) uses progressive sampling during optimization,which can create VMAT plans more efficiently with better plan quality. This algorithm,however, was designed specifically for single-arc delivery with Varian MLC design. Luan etal recently proposed a graph algorithm approach to VMAT inverse planning for both single-arcand multiple-arc deliveries (Luan et al 2008, Wang et al 2008), which works exclusively withMLC designs that allow leaf inter-digitations.

In previous work, we have described an arc-sequencing approach to VMAT inverseplanning (Shepard et al 2007). With arc sequencing, IMRT optimization is performed and the

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sequencer translates the optimized intensity maps into deliverable VMAT plans. Numerouscase studies were presented and treatment planning comparisons were made with helicaltomotherapy (Cao et al 2007). Our initial work with the arc sequencer focused on multiple-arcVMAT planning using Varian MLC design.

More recently, we have made further development in the arc sequencer and expanded itstesting. Key milestones have included the following: (1) the algorithm has been improved toallow for both single- and multiple-arc planning; (2) comparisons with multiple cases weremade on plan quality and delivery efficiency between step-and-shoot IMRT and the sequencedVMAT plans, and (3) numerous plans have been verified on an Elekta Synergy and an ElektaPrecise linac with VMAT delivery capabilities.

In this paper, we presented detailed information on how we create single-arc or multiple-arc VMAT plans. We also demonstrated the capability of the new arc sequencer by comparingplan qualities and delivery efficiencies of VMAT and IMRT plans. The VMAT plan QAresults for a prostate case and a head-and-neck case were shown to verify that the VMAT planscreated using this arc sequencer can be accurately delivered.

2. Materials and methods

A two-step process was used to generate VMAT plans. First, a step-and-shoot IMRT planwith multiple equal-spaced coplanar beams was created using the direct machine parameteroptimization (DMPO) IMRT planning module in Pinnacle3. We have tested beam angleseparations of 10◦, 20◦ and 30◦. Generally, a finer beam angle separation is needed for morecomplex targets (Cao et al 2009). For multiple-arc planning, the typical number of beams usedin the initial step-and-shoot IMRT plan is 35 with a 10◦ beam angle separation independentof the plan complexity. For single-arc planning, 12 beams with 30◦ separation can be usedfor simple prostate cases while 35 beams with a 10◦ beam angle separation are needed formore complicated head-and-neck cases. The beam angle of 180◦ (where the gantry cannotrotate through) was not used in our VMAT planning as it will create undeliverable arc thatrotate through 180◦ due to the way the sequencer creates single-arc plans (see later part of thissection for detailed description).

After the optimization, a ‘deliverable fluence map’ was reconstructed based on theshapes and weights of the resulting apertures for each beam. As compared with the fluencemaps obtained from conventional beamlet-based optimization, the intensity modulation in thereconstructed maps obtained using DMPO was significantly reduced as a result of using only alimited number of apertures per beam angle (typically between 2 and 6). Figure 1(a) illustrateshow the ‘deliverable fluence map’ is reconstructed based on the available aperture shapes andweights. Figure 1(b) plots two sample fluence maps: the first fluence map was created usingPinnacles’ conventional beamlet-based optimization (before leaf sequencing) and the secondfluence map was reconstructed using the DMPO-optimized aperture shapes and weights. Thetwo maps were extracted from the same patient at the same beam angle.

The reconstructed DMPO map is significantly less modulated as compared to the fluencemap from the beamlet-based optimization. Due to the large number of available beam angles,the much simpler fluence maps do not lead to a significant degradation of the plan quality.Figure 2 shows a plan comparison between a 35-field DMPO plan with 99 total controlpoints and a 35-field beamlet-optimized plan with ideal fluence maps (pre-leaf sequencing)calculated using the convolution/superposition dose engine. In the DMPO plan optimization,the maximum number of apertures was set to be 100; the minimum MU per segment was 1;and the minimum segment area was 4 cm2. Both plans were created within Pinnacle3 usingthe same set of optimization objectives. As shown in figure 2, only slight plan degradation

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(a)

(b)

Figure 1. (a) Demonstration of the ‘deliverable fluence map’ reconstruction process from a setof aperture shapes and weights. The aperture shapes are represented by the non-zero units andthe non-zero value is the corresponding aperture weight. (b) Sample fluence maps obtained frombeamlet inverse planning and DMPO. Both maps were extracted from the same gantry angle in a35-field head-and-neck case.

Figure 2. DVH comparison of 35-field plans optimized using beamlet inverse planning andDMPO for a head-and-neck case. For the plan with beamlet inverse planning, no leaf sequencingwas performed, and the plan was calculated using convolution/superposition dose engine toaccount for the phantom scatter. However, no head scatter can be corrected as no apertureshapes exist in this plan. For the 35-field DMPO plan, the final dose calculation was done usingconvolution/superposition dose engine with both phantom scatter and head scatter considered.

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Figure 3. Picture showing how single-arc and multiple-arc VMAT plans are generated using thearc sequencer. The arrows between all sequenced apertures indicate how the aperture shapes areconnected within the VMAT arc(s).

was observed for the 35-field DMPO plan. Since this reduction in the fluence map complexityleads to a reduction in the number of apertures required after sequencing without significantlysacrificing the plan quality, the reconstructed ‘deliverable fluence map’ is clearly a betterchoice for VMAT planning purposes.

After the deliverable fluence maps were extracted, a home-grown arc sequencer was thenapplied to convert these maps into deliverable VMAT plans. As described in our originalpaper, this sequencer is a simulated annealing-based optimization algorithm that is designedto minimize the difference between the ideal and the sequenced fluence maps (Cao et al 2006).

In addition to the capability of producing multiple-arc VMAT plans, this sequencer wasfurther improved to generate single-arc VMAT plans. Similar to the procedure of creatinga multiple-arc plan, the original fluence map from each beam angle was first sequenced intomultiple aperture shapes for single-arc planning. Instead of placing the sequenced aperturesat the original beam angle to form multiple arcs, each sequenced aperture was placed adjacentto the original beam angle to form a single VMAT arc (Crooks et al 2003, Wang et al 2008).

The major challenge in VMAT inverse planning is the delivery constraint to limit themaximum leaf motion per degree of gantry rotation in order to ensure the VMAT plandeliverability and the delivery accuracy. In multiple-arc planning, only the aperture shapeswithin the same arc need to be connected (the motion of each MLC leaf does not exceed apreset limit from one control point to the next). However, this delivery constraint becomesmore stringent in single-arc VMAT planning where all aperture shapes from every beam angleneed to be connected. A cartoon is plotted in figure 3 to illustrate the differences between oursingle-arc and multiple-arc VMAT planning techniques.

The user can select either single- or multiple-arc delivery based on the plan complexityand the balance one is seeking between plan quality and delivery efficiency. After thearc sequencer was applied, each VMAT plan was loaded back into Pinnacle3 for a finalconvolution/superposition dose calculation and for plan evaluation. In some cases, a segment-weight optimization was performed to help recover any loss in plan quality that resulted fromthe arc sequencing.

In general, the first step of creating the step-and-shoot IMRT plan takes between 8 and15 min depending on the plan complexity and the number of initial beam angles used duringthe optimization. The second step of arc sequencing generally takes about 9 min for simple

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Figure 4. Plot showing the arc sequencer objective function value as a function of the number oftotal successful iterations. The objective function value is normalized to the one obtained at 30 000iterations. Both prostate case (represented by the diamonds) and head-and-neck case (representedby the squares) are shown in this figure.

prostate cases. The time increases to about 15 min for more complicated head-and-neck cases.During the simulated annealing optimization, the objective function improves at a slower andslower rate as the optimization progresses. Therefore, one needs to balance the quality andefficiency of the arc-sequencing process.

In practice, the typical number of iterations needed to obtain a reasonable sequencedplan is 200 000 for simple prostate cases and 300 000 for head-and-neck cases. As shown infigure 4, the final objective value only decreases slightly as the number of iterations increasesbeyond these values. The final segment-weight optimization performed in Pinnacle3 takesbetween 8 and 20 min depending on the number of total control points in the VMAT plan.Therefore, the total planning time for each VMAT plan ranges from 25 to 50 min.

All VMAT and IMRT plans presented in this paper were planned using an Elektaconventional MLC with 1 cm leaf width projected at the isocenter. Unlike with the VarianMillennium 120-leaf MLC, no MLC leaf interdigitation is allowed for this type of MLCdesign. In addition, the minimum gap between the opposed leaves and the opposed adjacentleaves was set to be 0.5 cm as suggested by the vendor. To demonstrate the deliverability ofthe VMAT plan produced using the above procedure, each plan was delivered on an ElektaSynergy linear accelerator using a PreciseBeam R© VMAT linac control system. Plan QA wasperformed using a MatriXXTM 2D ion chamber array inserted in a MULTICubeTM phantomwith Omnipro I′MRT R© software.

3. Results and discussions

3.1. VMAT plan quality and delivery efficiency

The first test case is a prostate patient with the planning target volume (PTV) covering bothprostate and seminal vesicle. The prescribed dose is 75.6 Gy for a total of 42 fractions. Forthis case, a 12-field DMPO plan was created with beam spacing of 30◦. A single-arc VMAT

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(a) (b)

Figure 5. 2D isodose distribution of a single-arc VMAT plan for a prostate case. Panel (a) showsan axial slice, while panel (b) shows a sagittal slice.

Figure 6. DVH comparison between a single-arc VMAT plan and a 35-field DMPO plan for aprostate case. The dashed lines represent the single-arc VMAT plan with a total of 60 controlpoints. The solid lines represent the 35-DMPO plan with a total of 199 control points.

plan with 60 total control points (each original beam was sequenced into five apertures) wasthen produced by the arc-sequencing algorithm. The 2D isodose distributions on axial andsagittal planes are plotted in figure 5 for this plan. The PTV is covered in a conformal mannerby the 96% isodose line.

For this prostate case, we also created a DMPO plan with 35 equal-spaced beams inPinnacle3 and compared the dose–volume histogram (DVH) between this plan and the single-arc VMAT plan as shown in figure 6. The 35-field DMPO plan used the same set of optimizationobjectives as used in the VMAT plan with the maximum number of control points set to 200.With the large number of control points and large number of available beam angles, the 35-fieldDMPO plan can be considered as a gold standard in terms of IMRT plan quality. As indicatedin figure 6, the single-arc VMAT plan managed to achieve a very similar plan quality. Infact the V95, which is defined as the target volume receiving at least 95% of the prescribed

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Figure 7. DVH comparison for VMAT plans using one arc (dashed lines) and three arcs (solidlines) for a head-and-neck case.

dose, was reduced from 99.7% in the DMPO plan to 98.9% in the VMAT plan. The targetdose uniformity, represented by the standard deviation of the PTV dose per fraction (σ PTV), is2.3 cGy for the 35-field DMPO plan, while this value increases to 4.4 cGy in the VMAT plan.In terms of critical structure sparing, the mean dose to rectum increased from 3169 cGy to3294 cGy for the VMAT plan. Overall, the single-arc VMAT plan provides very high planquality which is comparable to that of the 35-field DMPO plan. Using the same optimizationobjectives for both VMAT and 35-field DMPO plans makes this comparison fair in terms ofbenchmarking the capabilities of our arc sequencer.

For more complicated head-and-neck cases, the arc-sequencing algorithm can alsoproduce high quality VMAT plans using either single arc or multiple arcs. Figure 7 illustratesthe DVH differences in single- and three-arc VMAT plans for a head-and-neck case. Threetarget volumes in this case were planned to receive prescription doses of 60, 54 and 51 Gy,respectively. The main critical structures in this case were left and right parotids, brainstemas well as spinal cord. Both plans were created using an Elekta 80-leaf conventional MLC.The single-arc plan has a total of 175 control points each separated by 2◦, while the three-arcplan has a total of 105 control points (35 control points for each arc). As shown in the figure,the two plans result in very similar DVHs and both provide highly uniform target dose withexcellent spring to the nearby critical organs. The average V95 (average over all three targets)are 97.7% and 98.9% for the single-arc plan and the three-arc plan, respectively. The meandoses to the left and right parotids are 1585 and 1396 cGy, respectively, for the single-arcplan, and these values are 1553 and 1430 cGy, respectively, for the three-arc plan. The single-arc plan provides slightly better sparing to the spinal cord with a maximum cord dose of3394 cGy.

It has been shown that the IMRT plan quality improves as the number of fields increases,while the total integral dose is almost independent of the number of fields (Shepard et al 1999).The VMAT delivery technique therefore provides greater flexibility to shaping radiation dosedistributions than is possible with a limited number of fixed fields. A comparison of a single-arc VMAT plan and a seven-field IMRT plan for a prostate case is shown in figure 8(a).

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(a) (b)

Figure 8. (a) DVH comparison between a single-arc VMAT plan (solid lines) and a seven-fieldstep-and-shoot IMRT plan (dashed lines) for a prostate case. (b) DVH comparison between athree-arc VMAT plan (solid lines) and a nine-field IMRT plan (dashed lines). Note that the targetdose coverage is very similar for this head-and-neck case. However, the VMAT plan providesbetter sparing to the critical structures in this case.

The VMAT plan has a total of 60 control points with the gantry rotating from 177◦ to 186◦

(counterclockwise), while the beam angles for the IMRT plan were set to be 150◦, 100◦, 50◦,0◦, 310◦, 260◦, 210◦. The seven-field IMRT plan was created in Pinnacle3 using the DMPOinverse planning module with 69 total control points. The same optimization objectives wereused to create both plans.

As shown in figure 8(a), both plans are very similar in terms of both target dose coverageand critical structure sparing. Although we do observe slightly better target dose uniformityfor the VMAT plan, the difference does not appear to be clinically significant. The mostsignificant difference between the two plans is with respect to the delivery efficiency. Thedelivery time for the single-arc VMAT plan was only 2.5 min as compared to 7.4 min for theseven-field IMRT.

A similar comparison was also carried out for a more complicated head-and-neck case.For this case, a DMPO plan with nine equal-spaced beams along with a three-arc VMAT planwas created. The total number of control points in the nine-field DMPO plan is 90, whileeach arc of the VMAT plan has 35 control points (105 total). The DVH comparison is shownin figure 8(b). Again, no significant difference in the plan quality was observed between thetwo plans. The average V95 for all three targets are 99.1% and 99.0% for the IMRT plan andthe VMAT plan, respectively. The VMAT plan, however, provides slightly better sparing tonearby critical organs. For example, the mean doses to the left and right parotids are 1553 and1431 cGy, respectively, in the VMAT plan, while these values increase to 1684 and 1632 cGy,respectively, in the IMRT plan. The maximum cord dose also drops from 3790 cGy in theDMPO plan to 3647 cGy in the VMAT plan. In terms of delivery efficiency, the delivery timesfor the fixed-field IMRT plan and the VMAT plan were 12.8 and 4.5 min, respectively (a 65%reduction).

Table 1 provides a more detailed comparison for five cases covering various treatment sites.The two prostate cases represent simple IMRT cases and serve to benchmark the capabilitiesof the arc sequencer. The three head-and-neck cases provide more complex and challengingIMRT planning problems. It is clear that the VMAT technique consistently provides improveddelivery efficiency while keeping similar or better plan quality as compared with conventionalstep-and-shoot IMRT. On average, the VMAT delivery reduces the treatment time by 65%.The results also indicate that VMAT plans are more MU-efficient. The average reduction inMU per fraction for the VMAT plans is 22% compared to the DMPO plans.

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Cao

etal

Table 1. Detailed information on the comparison of plan quality and plan efficiency between VMAT plans and step-and-shoot IMRT plans for different treatment sites. Target dosecoverage is specified using V95. Critical structure sparing is specified using either mean or max dose. Mean dose is used for rectum, bladder, left and right parotids, while max dose isused for cord dose evaluation.

No ofarcs/segments

Target coverage:average V95 (%)

Critical structure sparingmean/max dose (cGy) MU per fraction

Delivery time(min)

Treatment site VMAT IMRT VMAT IMRT OAR VMAT IMRT VMAT IMRT VMAT IMRT

Rectum 2950 3027Prostate #1 1 69 99.1 97.6 554 626 2.5 7.4

Bladder 4408 4294

Rectum 2861 3733Prostate # 2 1 49 96.5 97.1 490 620 2.2 6.5

Bladder 4217 4272

Lt Parotid 1448 1543Head and neck #1 3 86 94.1 94.3 Rt Parotid 2299 2534 488 573 4.1 11.9

Cord 3362 3562

Lt Parotid 1040 1347Head and neck #2 3 96 98.4 98.0 Rt Parotid 1257 1397 602 671 4.5 12.4

Cord 2119 2109

Lt Parotid 1553 1684Head and neck #3 3 90 99.0 99.1 Rt Parotid 1431 1632 479 875 4.6 12.8

Cord 3647 3790

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(a) (b)

Figure 9. (a) The planned 2D dose distribution on a coronal slice from a single-arc VMAT planfor a prostate case. (b) The measured 2D dose distribution on the same slice.

3.2. Delivery accuracy of VMAT plans

To verify the delivery accuracy of the VMAT plans produced by the arc-sequencing algorithm,plan-specific QA was performed using a MatriXXTM 2D ion chamber array inserted in aMULTICubeTM water equivalent phantom. With the MatriXXTM detector array aligned eitherparallel or perpendicular to the couch top, cumulative 2D dose distributions can be measuredin a coronal or a sagittal plane. The attenuation caused by the Elekta couch top was accountedfor in the QA plan calculation.

Figure 9 shows the planned and measured 2D dose distributions on a coronal plane for asingle-arc prostate case with 60 total control points. The two dose maps showed very similardose distribution. This is further confirmed by the 2D isodose overlay plotted in figure 10(a),where excellent agreement of all four isodose lines can be observed with both maps normalizedto 191 cGy. A gamma analysis calculated a pass rate of 99.7% with 3% and 3 mm criteria,and the detailed results are shown in figure 10(b).

Another QA was performed for a head-and-neck VMAT plan, which consisted of threearcs with a total of 105 control points (35 control points for each arc). The cumulative dosedistribution on a coronal plane from all three arcs was measured for this case. As shown infigure 11, the planned and measured 2D dose distributions on this coronal slice match eachother very well. The 2D isodose overlay plotted in figure 12 showed the excellent agreementbetween the plan and the measurement for this head-and-neck case. The result of gammaanalysis was 98.6% passing rate using 3% and 3 mm criteria.

4. Summary

An arc-sequencing algorithm has been developed to serve as a generalized inverse planningtool for VMAT. The algorithm is robust and can produce VMAT plans for targets covering arange of sizes and levels of complexity. A key feature of this algorithm is the ability to produceboth single-arc and multiple-arc VMAT plans. As compared with conventional step-and-shoot

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(a) (b)

Figure 10. Panel (a): isodose overlay for the planned and measured 2D dose distribution for asingle-arc prostate case. The four isodose levels are 90%, 70%, 50% and 30%, respectively. Bothsets of data were normalized at 191 cGy as 100%. Panel (b): 2D gamma analysis result for thissingle-arc prostate VMAT plan QA. Light color represents the gamma value close to zero, whiledark color represents the gamma value close or above 1.0. The gamma analysis passing criteriawas set to be 3.0 mm and 3%.

(a) (b)

Figure 11. Panel (a): the planned 2D dose distribution on a coronal slice for a head-and-neckcase. Panel (b): the measured 2D dose distribution on the same slice.

IMRT, the resulting VMAT plans provide comparable or better plan quality in terms of bothtarget dose coverage and critical structure sparing. The VMAT plans are also MU efficientwith improved delivery efficiency. The average reductions in MU per fraction and deliverytime are 22% and 65%, respectively. The VMAT plan QAs using 2D ion-chamber array

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Figure 12. 2D isodose overlay for planned and measured data on a coronal plane for a three-archead-and-neck VMAT plan.

suggest that both single-arc and multiple-arc VMAT plans created using this arc-sequencingalgorithm can be delivered accurately using a PreciseBeam R© VMAT linac control system.

References

Bortfeld T and Webb S 2009 Single-arc IMRT? Phys. Med. Biol. 54 N9–20Cao D, Earl M A, Luan S and Shepard D M 2006 Continuous intensity map optimization (CIMO): a novel approach

to leaf sequencing in step and shoot IMRT Med. Phys. 33 859–67Cao D, Holmes T W, Afghan M K and Shepard D M 2007 Comparison of plan quality provided by intensity-modulated

arc therapy and helical tomotherapy Int. J. Radiat. Oncol. Biol. Phys. 69 240–50Cao D, Rao M, Chen F, Afghan M K N, Ye J and Shepard D M 2009 Comparison of single-arc and multiple-arc

VMAT plans (in preparation)Cotrutz C, Kappas C and Webb S 2000 Intensity modulated arc therapy (IMAT) with centrally blocked rotational

fields Phys. Med. Biol. 45 2185–206Crooks S M, Wu X, Takita C, Watzich M and Xing L 2003 Aperture modulated arc therapy Phys. Med. Biol.

48 1333–44Duthoy W, De Gersem W, Vergote K, Boterberg T, Derie C, Smeets P, De Wagter C and De Neve W 2004

Clinical implementation of intensity-modulated arc therapy (IMAT) for rectal cancer Int. J. Radiat. Oncol. Biol.Phys. 60 794–806

Page 15: A generalized inverse planning tool for volumetric-modulated arc therapy

6738 D Cao et al

Earl M A, Shepard D M, Naqvi S, Li X A and Yu C X 2003 Inverse planning for intensity-modulated arc therapyusing direct aperture optimization Phys. Med. Biol. 48 1075–89

Gladwish A, Oliver M, Craig J, Chen J, Bauman G, Fisher B and Wong E 2007 Segmentation and leaf sequencingfor intensity modulated arc therapy Med. Phys. 34 1779–88

Luan S, Wang C, Cao D, Chen D Z, Shepard D M and Yu C X 2008 Leaf-sequencing for intensity-modulated arctherapy using graph algorithms Med. Phys. 35 61–9

Ma L, Yu C X, Earl M, Holmes T, Sarfaraz M, Li X A, Shepard D, Amin P, DiBiase S, Suntharalingam M andMansfield C 2001 Optimized intensity-modulated arc therapy for prostate cancer treatment Int. J. Cancer96 379–84

Mackie T R, Holmes T, Swerdloff S, Reckwerdt P, Deasy J O, Yang J, Paliwal B and Kinsella T 1993 Tomotherapy:a new concept for the delivery of dynamic conformal radiotherapy Med. Phys. 20 1709–19

Otto K 2008 Volumetric modulated arc therapy: IMRT in a single gantry arc Med. Phys. 35 310–7Shepard D M, Cao D, Afghan M K and Earl M A 2007 An arc-sequencing algorithm for intensity modulated arc

therapy Med. Phys. 34 464–70Shepard D M, Olivera G, Angelos L, Sauer O, Reckwerdt P and Mackie T R 1999 A simple model for examining

issues in radiotherapy optimization Med. Phys. 26 1212–21Wang C, Luan S, Tang G, Chen D Z, Earl M A and Yu C X 2008 Arc-modulated radiation therapy (AMRT): a

single-arc form of intensity-modulated arc therapy Phys. Med. Biol. 53 6291–303Wong E, Chen J Z and Greenland J 2002 Intensity-modulated arc therapy simplified Int. J. Radiat. Oncol. Biol. Phys.

53 222–35Wong E, D’Souza D P, Chen J Z, Lock M, Rodrigues G, Coad T, Trenka K, Mulligan M and Bauman G S 2005

Intensity-modulated arc therapy for treatment of high-risk endometrial malignancies Int. J. Radiat. Oncol. Biol.Phys. 61 830–41

Yu C X 1995 Intensity-modulated arc therapy with dynamic multileaf collimation: an alternative to tomotherapyPhys. Med. Biol. 40 1435–49

Yu C X, Li X A, Ma L, Chen D, Naqvi S, Shepard D, Sarfaraz M, Holmes T W, Suntharalingam M and Mansfield C M2002 Clinical implementation of intensity-modulated arc therapy Int. J. Radiat. Oncol. Biol. Phys. 53 453–63