gamma histograms for radiotherapy plan evaluation

Radiotherapy and Oncology 79 (2006) 224–230www.thegreenjournal.com

Gamma histograms

Gamma histograms for radiotherapy plan evaluation

Emiliano Spezi*, D. Geraint Lewis

Department of Medical Physics, Velindre Hospital, Cardiff, UK

Abstract

Background and purpose: The technique known as the ‘g evaluation method’ incorporates pass–fail criteria for bothdistance-to-agreement and dose difference analysis of 3D dose distributions and provides a numerical index (g) as ameasure of the agreement between two datasets. As the g evaluation index is being adopted in more centres as part oftreatment plan verification procedures for 2D and 3D dose maps, the development of methods capable of encapsulatingthe information provided by this technique is recommended.

Patients and methods: In this work the concept of g index was extended to create gamma histograms (GH) in order toprovide a measure of the agreement between two datasets in two or three dimensions. Gamma area histogram (GAH) andgamma volume histogram (GVH) graphs were produced using one or more 2D g maps generated for each slice of theirradiated volume. GHs were calculated for IMRT plans, evaluating the 3D dose distribution from a commercial treatmentplanning system (TPS) compared to a Monte Carlo (MC) calculation used as reference dataset.

Results: The extent of local anatomical inhomogenities in the plans under consideration was strongly correlated withthe level of difference between reference and evaluated calculations. GHs provided an immediate visual representationof the proportion of the treated volume that fulfilled the g criterion and offered a concise method for comparativenumerical evaluation of dose distributions.

Conclusions: We have introduced the concept of GHs and investigated its applications to the evaluation andverification of IMRT plans. The gamma histogram concept set out in this paper can provide a valuable technique forquantitative comparison of dose distributions and could be applied as a tool for the quality assurance of treatmentplanning systems.q 2006 Elsevier Ireland Ltd. All rights reserved. Radiotherapy and Oncology 79 (2006) 224–230.

Keywords: Radiation therapy; Verification; Evaluation; Gamma index

As conformal radiotherapy and especially IMRT arecomplex techniques, which demand careful verification,the development and use of methods capable of assessingthe quality of competing treatment plans and verifying theirdosimetric accuracy has been strongly recommended [6,2].The quantitative evaluation of dose distributions through acomposite analysis of distance-to-agreement (DTA) and dosedifference was presented by Low et al. [8]. This technique,known as the ‘g evaluation method’, incorporates pass–failcriteria for both DTA and dose difference analysis of 3D dosedistributions and provides a numerical index (g) as a measureof the agreement between two datasets. A clinicalassessment of the g method has been reported by Depuydtet al. [3], who investigated the use of the g algorithm as aroutine verification quality control tool for IMRT dosedistributions. Predicted portal images were compared toacquired images through a refined gamma filter developedby the authors. In this approach, adopted in most centres

0167-8140/$ - see front matter q 2006 Elsevier Ireland Ltd. All rights rese

implementing IMRT, reference and evaluated dataset arevisually examined for each treatment beam. In clinicalpractice it is realistic to expect regions where the g criterionis not satisfied. The validation or rejection of the IMRT fieldis left to subjective observer interpretation of the obtainedg image. This is the limitation of this procedure. The visualexamination is both time consuming and subject to theobserver interpretation of the overall goodness of theagreement between evaluated and reference datasets. Atool capable of expressing quantitatively the confidence thatcan be associated with a certain dose calculation is thusneeded.

In this work, the concept of g index was extended tocreate gamma histograms (GH) in order to provide a measureof the agreement between two datasets in three dimensions.By analogy with dose volume histograms, DVHs [4], Gammaarea histograms (GAHs) and Gamma Volume Histograms(GVHs) were produced on a basis of individual 2D g maps

rved. doi:10.1016/j.radonc.2006.03.020

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E. Spezi, D.G. Lewis / Radiotherapy and Oncology 79 (2006) 224–230 225

generated for each slice of the irradiated volume. GHs werecalculated for two IMRT plans, evaluating the 3D dosedistribution from a commercial treatment planning system(TPS) compared to a Monte Carlo (MC) calculation used asreference dataset.

We believe GHs are a useful tool for the graphicalrepresentation of area or volumetric gamma maps. A GH canalso provide a method to extract an index characterizing theoverall degree of acceptability of a 3D dose distribution withrespect to a reference dataset. Our initial exposition of theuse of gamma maps in histogram format was set out inprevious work [14,15]. Recently, Stock et al. [16] proposedevaluation filters for IMRT hybrid plan verification based onthe g method and utilizing a similar concept to the one setout in this paper. This confirms the interest of the scientificcommunity in decision guidelines for the practicalimplementation of gamma based tools for the verificationof IMRT plans.

Materials and methodsEvaluated and reference dataset

This investigation involves two retrospective IMRTtreatment plans for tumours of the head and neck region,produced by our clinical TPS: Helax-TMS (Nucletron, TheNetherlands). The pencil beam (PB) algorithm [1] was usedfor both beam fluence optimization and for the calculationof the final delivered dose with Helax-TMS. The beam setupfor both treatment plans is shown in Fig. 1. Results have beenevaluated and compared with calculations provided by theMC method. The BEAM MC code system [11] was used. Acareful verification of the MC module definition for ourradiotherapy linac (Varian Clinac 2100 CD incorporating aMillennium MLC-80 and operating at 6MV) has beenpresented elsewhere [12]. The CT dataset, TPS plan data(such as plan settings, etc.) and 3D dose distribution wereexported in DICOM format [9] and processed within theMatlab environment (The MathWorks Inc., Natick USA) usinga DICOM-RT Toolbox developed specifically for the evalu-ation and the verification of radiotherapy treatment plans[13]. MC calculations were performed in identical conditions

Fig. 1. Beam configuration for two IMRT plans, (a) p1 and (b) p2. Beam s(norm). The PTV outline is also shown (dashed line).

on the basis of the optimized TPS dose plan and used as thereference dataset.

Gamma histogramsWhen evaluating the acceptability of a calculated dose

distribution Dc with respect to a reference dataset Dm, foreach reference point ðrm the composite dose/distance valueGððrm;ðrcÞ is determined, with respect to each calculationpoint ðrc, as given by the following equation

GZ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir2ððrm;ðrcÞ

Dd2M

Cd2ððrm;ðrcÞ

DD2M

s(1)

where

rððrm;ðrcÞZ jðrcKðrmj (2)

and

dððrm;ðrcÞZDcððrcÞKDmððrmÞ (3)

is the dose difference between calculated and referencedose distribution. These parameters are normally scaled toobtain dimensionless quantities and in this work they wereset at 3% and 3 mm, respectively, based on the valuesselected by Low et al. [8] and Harms et al. [5]. For eachreference point ðrm there can then be defined a g index ateach point in the evaluation plane ðrcKðrm so thatgððrmÞZminfGððrc;ðrmÞg; c fðrcg. The evaluation point passesthe composite pass–fail criterion with respect to thereference dataset when gððrmÞ%1.

When evaluating a 3D dose distribution versus a referencedataset the g calculation algorithm can be executed slice-by-slice, obtaining a 3D g volume as a stack of 2D maps. Thisrepresents in most situations a very large amount of data,which needs to be classified.

In this investigation, we present in fuller form theconcept and possible applications of gamma histograms. AGamma histogram represents the relation between a certaing value and the area or volume characterized by such avalue. This is analogous to the definition of DVHs [4].

A frequency GAH (fGAH) or a cumulative GAH (cGAH)characterizes the information provided by a 2D g maprepresenting the number of pixels or the percentage ofthe area covered by a specific g value. A frequency GVH

ettings are displayed on the transverse plane through the isocentre

Fig. 2. Gamma histograms: the information provided by individual 2D g maps generated for each slice of a treatment volume (a) is representedas stacked cumulative GAHs (b) or in frequency or cumulative GVHs (c and d). For clarity only a subset of gamma maps is shown in (a).

Gamma histograms for rtp evaluation226

(fGVH) or a cumulative GVH (cGVH) summarizes volumetricg data in one plot providing the number of voxels or thepercentage volume covered by a specific g value. GHs can bealso calculated for each volume of interest (VOI) defined inthe segmentation process.

In this work, 20 g maps were calculated for each slice ofthe 3D TPS dose datasets when compared with the reference3D MC dose. A 3D g map was then generated, as shown inFig. 2a. GAHs were then calculated for each slice of the 3Dvolume. GAHs can be shown slice by slice or as a stackedhistogram plot as depicted in Fig. 2b. Frequency GVHs andcGVHs are shown in Fig. 2c and d. In the treatment instancesconsidered in this study GHs, similarly to DVHs, werecalculated on the basis of the dose calculation grid set bythe TPS, i.e. (0.4!0.4!0.5) cm3. Since the evaluation of gcan be a computationally intensive task, for large 3Dmatrices a ‘search range’ SR was implemented in our g

algorithm. If DTA or dose difference criteria are not satisfiedwithin SR, the value g(r) is set to a specific character1.Therefore during the production of GHs, values of g, whichare set to this specific character are set to the highest g

number encountered.

1 Correspond to the IEEE arithmetic representation for Not-a-Number (NaN).

ResultsIMRT plan 1 (P1)

Fig. 3 shows the cGAH calculated for the PTV of P1. It canbe noted that the percentage (A) of each PTV section, whichsatisfies the acceptance criterion g(r)R1 becomes graduallyreduced towards the extremities of the tumour volume. Thisis also shown in Table 1 where A is reported for all thesections of the PTV. In particular from Table 1 one canobserve that the agreement between TPS and MC is maximalon the central slices of the PTV (CT slice no. 6�8), with thelowest values of A scored in the inferior part of the targetvolume. This anatomical area, corresponding to the oralcavity (CT slice no. 1) and the patient’s left mandible, ishighly inhomogeneous and therefore more likely to showthe limitations of the PB algorithm. This is shown in Fig. 4where isodose contours are depicted for both TPS and MCcalculations. This case shows the capabilities of GAHs inidentifying regions of disagreement between reference andevaluated dose distributions.

IMRT plan 2 (P2)The percentage area of each PTV section where the

Helax-TMS dose distribution fulfils the acceptance criterioncompared to MC is listed in Table 2. The inferior part of thePTV (towards CT slice no. 1) is characterised by a high levelof agreement between TPS and MC. This is because in theregion being considered the PTV section does not encompassany anatomical inhomogeneity. However, more superiorly

Fig. 3. Cumulative gamma area histograms for P1 target volume. cGAH is shown for CT slice no. 1 (a), no. 4 (b), no. 8 (c) and no. 12 (d) (cf.Table 1). A values are lowest for the inferior part of the CT volume (a), where inhomogeneities are most prevalent. The area where the g

criterion is satisfied is also shown.

Table 1Percentage are A for each PTV section of P1, which satisfies the acceptance criterion g%1

CT sliceno.

1 2 3 4 5 6 7 8 9 10 11 12

Z (cm) K5.64 K5.34 K5.04 K4.74 K4.44 K4.14 K3.84 K3.54 K3.24 K2.94 K2.64 K2.34

A 83.7 83.6 87.1 88.1 88.4 88.9 89.1 89.0 88.2 87.6 87.2 86.7

Fig. 4. P1 isodose distribution in the transverse plane through the inferior target slice for TPS (a) and MC (b) generated data. PTV, cord andpatient outlines are shown in white.


Tab

le2

Perc

enta

gear

eA

for

eac

hPTV

sect

ion

of

P2,

whic

hsa

tisfi

es

the

acce

pta

nce

crit

eri

ong%

1

CT

slic

eno.

12

34

56

78

910

1112

1314

1516

1718

1920

2122

23

Z(c

m)

K8.

32K

8.02

K7.

72K

7.42

K7.

12K

6.82

K6.

52K

6.22

K5.

92K

5.62

K5.

32K

5.02

K4.

72K

4.42

K4.

12K

3.8

2K

3.5

2K

3.2

2K

2.9

2K

2.6

2K

2.3

2K

2.0

2K

1.7

2

A10

0.0

100.

096

.998

.099

.097

.095

.595

.193

.592

.490

.590

.590

.590

.290

.190.1

89.8

89.3

88.7

87.9

86.8

86.5

86.6


(towards slice no. 23), the agreement between TPS and MCcalculations becomes gradually poorer due to the presenceof inhomogeneities such as air cavities and bony structuresinvolved in the PTV. This is shown in Fig. 5 where the gammamap for PTV sections no. 2, and no. 20 (Ref. Table 2) aredisplayed with the corresponding CT slice and PTV outline atthat coordinate and the calculated cGAH. It can be notedthat the value of g rises in correspondence with anatomicalinhomogeneities, which increase in number and in extent asone moves superiorly through the volume. Fig. 5a shows avery good agreement between TPS and MC. This is confirmedby the cGAH in Fig. 5b where all the evaluation points satisfythe pass–fail criterion. However, Fig. 5c and d indicate howthe g criterion is not satisfied in slice no. 20 for z12% of thecalculation points. The disagreements correspond to air gapsand bony structures encompassed by the PTV, as shown inthe transverse section of Fig. 5c. Overall the percentage ofPTV, which satisfies the acceptance criterion (g%1) for P2 is86.6%. This is similar to what was found for the P1 case.However, the spectrum of values in 3D can be very different.In Fig. 6, the cGVHs for both evaluation instances arecompared. Although, the overall level of acceptance issimilar, there is a higher percentage of volume satisfyinglower g for P1 than P2. In the P1 case 70% of the volumesatisfies g%0.5 compared to 60% of P2. This differenceincreases for lower values of g. Although, P1 and P2 are twodifferent radiotherapy cases, this comparative analysis ofcGVHs gives greater confidence in the P1 evaluation case, asthe level of agreement between the TPS and MC distributionsis better than in the P2 evaluation case.

Discussion and conclusionsWe believe the gamma histogram concept set out in this

paper provides a valuable method for quantitative com-parison of dose distributions. DVHs and GHs providecomplementary functions. While DVHs describe how thecalculated dose is delivered to anatomical structures suchas target and organs at risk, GHs describe how good theperformed calculation is with respect to a referencedataset, which can be measured or MC-generated. Inparticular GAHs yield an immediate visual representationof the proportion of the treated area that fulfils theagreement criteria. Moreover, a stack of GAH plots (cf.Fig. 2b) can be very useful in locating regions whereunacceptable discrepancies between evaluated and refer-ence dose distributions occur. The GVH provides arepresentative index of the agreement over a given volume.GH analysis results can be easily included in local guidelinesas a criterion to accept or reject radiotherapy treatmentplans. Mijnheer et al. [10] have recently suggested thatGAHs could be used as a tool for the quality assurance oftreatment planning systems. The possibility of defininglevels of acceptance criteria of dose plans when comparedto reference datasets using the proposed GH concept couldbe explored using this approach.

As with DVHs, GHs represent a surrogate dataset wherespatial information about the g map is lost. However, spatialinformation is already difficult to interpret in intensitymodulated beams, which are characterized by very complex

Fig. 5. Gamma maps for PTV sections no. 2 and no. 20 in P2 (ref. Table 2). Respectively, the corresponding CT slices and PTV outline are alsoshown (a, c), together with the calculated cGAHs (b, d). The shaded area where the g criterion is satisfied is also shown.

Fig. 6. Comparison of cumulative gamma volume histogram (cGVH)for P1 and P2. The shaded area where the g criterion is satisfied isalso shown.


and non intuitive fluence maps. Moreover, the clinicalinfluence of the spatial information in currentIMRT verification techniques, where radiation beams aredelivered to a uniform water phantom still needs to beaddressed.

In this paper, we set out a methodology and describe atool that can be used in a simple and effective way torepresent the degree of acceptability of radiotherapyplans. The extraction of indices characterizing the overalldegree of acceptability of a single plan (or in other wordsthe definition of GH-based criteria to be used forvalidating or rejecting a treatment plan) is a subsequentstep, which undoubtedly needs to be addressed. Theapproach followed by Stock et al. [16] in defining gammabased filters for IMRT hybrid plan verification representsan example of how such tools could be used. However,the definition of such recommendations for reporting dosevalidation in radiotherapy treatment planning, similarly topublished ICRU guidelines, is work, which would alsoinvolve extended and multi-centred practical clinicalexperience.

Finally, we are currently investigating the benefits ofimplementing a full 3D algorithm for the calculation ofvolumetric g maps, rather than volumes built up as asummation of 2D slices, as is commonly the case. Theinclusion of the third dimension is expected to improve the g

based evaluation of treatment plans, as non-transverse dosegradients will be taken into account in the analysis. The GH

method could also be used successfully to compare thevarious classes of treatment planning algorithms, e.g. pencilbeam v. ‘collapsed cone’ convolution. The increasedavailability of reference 3D dose distributions independentlygenerated using MC technology or polymer gel dosimetry [7]is expected to make this application very useful in clinicalpractice.


Acknowledgements

ES is grateful for financial support from Cancer Research Walesand Yr Ysgol Uwchradd Tregaron.

* Corresponding author. E. Spezi, Present address: Servizio diFisica Sanitaria, Policlinico S. Orsola-Mapighi, via Massarenti 9,40138 Bologna (Italy). E-mail address: [email protected]

Received 16 June 2005; received in revised form 12 January 2006;accepted 21 March 2006; Available online 11 May 2006

References[1] Ahnesjo A, Saxner M, Trepp A. A pencil beam model for photon

dose calculation. Med Phys 1992;19:263–73.[2] Deasy JO, Niemierko A, Herbert D, et al. Methodological issues

in radiation dose-volume outcome analysis: summary of a jointAAPM/NIH workshop. Med Phys 2002;29:2109–27.

[3] Depuydt T, van Esch A, Huyskens DP. A quantitativeevaluation of IMRT dose distributions: refinement andclinical assessment of the gamma evaluation. Radiat Oncol2002;62:309–19.

[4] Drzymala RE, Mohan R, Brewster L, et al. Dose�volumehistograms. Int J Radiat Oncol Biol Phys 1991;21:71–8.

[5] Harms W, Low DA, Wong JW, Purdy JA. A software tool for thequantitative evaluation of 3D dose calculation algorithms. MedPhys 1998;25:1830–6.

[6] IMRTCWG Intensity-modulated radiation therapy: currentstatus and issues of interest. Int J Radiat Oncol Biol Phys2005;51(4):880–914.

[7] Love PA, Lewis DG, Smith GW, et al. A three-way comparison ofradiotherapy dose distributions using polymer gel dosimetry,Monte Carlo simulation and treatment planning system. MedPhys 1999;26:1085.

[8] Low DA, Harms WB, Mutic S, Purdy JA. A technique for thequantitative evaluation of dose distributions. Med Phys 1998;25:656–61.

[9] NEMA Digital Imaging and Communications in Medicine(DICOM). Rosslyn: National Electrical Manufacturers Associ-ation; 2001.

[10] Mijnheer B, Olszewska A, Fiorino C, et al. Quality assurance oftreatment planning systems: practical examples for non-IMRTphoton beams. Brussels: ESTRO Booklet; 2004.

[11] Rogers DWO, Faddegon BA, Ding GX, Ma CM, Wei J, Mackie TR.BEAM: a Monte Carlo code to simulate radiotherapy treatmentunits. Med Phys 1995;22:503–24.

[12] Spezi E, Lewis DG. Full forward Monte Carlo calculation ofportal dose from MLC collimated treatment beams. Phys MedBiol 2002;47:377–90.

[13] Spezi E, Lewis DG, Smith CW. DICOM-RT-based toolbox for theevaluation and verification of radiotherapy plans. Phys Med Biol2002;47:4223–32.

[14] Spezi E. A Monte Carlo investigation of the accuracy of intensitymodulated radiotherapy. PhD dissertation, University of Wales(UK); 2003.

[15] Spezi E, Lewis DG, Millin AE, Cuffin R. MC based QA of IMRT.Radiat Oncol 2003;68:S46.

[16] Stock M, Kroupa B, Georg D. Interpretation and evaluation ofthe g index and the g index angle for the verification of IMRThybrid plans. Phys Med Biol 2005;50:399–411.

gamma histograms for radiotherapy plan evaluation

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