Quantifying the e�ect of seed orientation in postplanning dosimetryof low-dose-rate prostate brachytherapy

Charles-Antoine Collins Fekete and Mathieu Plamondon

Département de Physique, de Génie Physique et D’optique et Centre de Recherche Sur le Cancer,Université Laval, Québec G1K 7P4, Canada and Département de Radio-oncologie et CRCHU de Québec,CHU de Québec, Québec G1R 2J6, Canada

André-Guy Martin and Éric Vigneault

Département de Radio-oncologie et CRCHU de Québec, CHU de Québec, Québec G1R 2J6, Canada

Frank Verhaegen

Department of Radiation Oncology (MAASTRO), GROW—School for Oncology and Developmental Biology,Maastricht University Medical Center, Maastricht 6201 BN, The Netherlands and Medical Physics Unit,McGill University Health Centre and Department of Oncology, McGill University, Montréal,Québec H3G 1A4, Canada

Luc Beaulieu

a)

Département de Physique, de Génie Physique et D’optique et Centre de Recherche Sur le Cancer,Université Laval, Québec G1K 7P4, Canada and Département de Radio-oncologie et CRCHU de Québec,CHU de Québec, Québec G1R 2J6, Canada

(Received 14 January 2014; revised 16 August 2014; accepted for publication 24 August 2014;published 23 September 2014)

Purpose: Radioactive seed orientations are usually ignored in clinical brachytherapy dosimetry forprostate implants. Associated with the anisotropic dose distribution of seeds, these orientations couldcause dose di↵erences between the planning configurations and the clinical postplanning dosimetry.This study will quantify the impact of seed orientation on the dosimetry.Methods: 3D seed positions and ✓ and ' polar angles were obtained using five independent fluoro-scopic images for 287 patients. Five dose calculation methods are compared: TG43-1D (1), TG43-2Dparallel to implant axis (2) and with orientations (3), Monte Carlo (MC) simulations parallel (4), andMC simulations with orientations (5). geant4 v4.9.6 MC simulations were made in 1 mm3 voxelizedgeometries based on the DICOM-RT information. Materials were assigned using thresholds basedon the HU number, as recommended in TG186 reports. Seed voxels are overridden with prostaticmaterials and the layered mass geometry [Enger et al., Phys. Med. Biol. 57(19), 6269–6277 (2012)]allows subsequent placement of the source geometry. 500 million histories were used per patient. 3Ddose and DVHs for each structure were calculated.Results: The various seed orientations do not result in statistically significant di↵erences on thedose metrics for the clinical target volume (CTV) or the urethra, based on the Student t-test p-value.Di↵erence as low as �0.238% and 0.059% has been seen on the CTV D90, respectively, for the MCand the TG43. The di↵erence between parallel and oriented calculations for the organs at risk (OARs)can di↵er by 2% on average.Conclusions: Based on the results from this study, seed orientations have no significant impact ofCTV and urethra dose metrics but can a↵ect OARs that are external to the CTV. C 2014 AmericanAssociation of Physicists in Medicine. [http://dx.doi.org/10.1118/1.4895012]

Key words: prostate brachytherapy, TG43, TG186, Monte Carlo, LDR, seeds orientation

1. INTRODUCTION

Permanent prostate brachytherapy (PPB) is a popular treat-ment option for localized prostate cancer. In this technique,low-dose-rate (LDR) radioactive sources (seeds) are im-planted through needles into the prostate. The AmericanAssociation of Physicists in Medicine (AAPM), the Ameri-can Brachytherapy Society (ABS), and the European Soci-ety for Radiotherapy and Oncology (ESTRO)2–4 recommendthat postimplant dosimetry, related to the treatment quality,should be performed on every patient undergoing PPB. Pre-vious studies5–7 have shown that the actual implant technique

may lead to di↵erences in the position and orientation of theseeds between the treatment plan and the post-treatment do-simetry, potentially influencing the treatment quality. Theseed misplacement problem has been investigated and cat-egorized,8–10 but the seed orientation problem has yet tobe precisely studied. Wan et al.11 have demonstrated thedivergence between the idealized line source configurationand the clinical seeds orientation caused by needle deflection.

The need to have a consistent method to detect seedorientation has been studied by various authors. Chng et al.7

have developed a reconstructed strand trajectories method toestimate seeds orientation in prostate brachytherapy based on

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postplanning CT. Tubic et al.12,13 have used five fluoroscopicimages at di↵erent angles to reconstruct the seed orientationand position and match them to the postplanning CT.

The di↵erence between line source and point sourceformalism has been the subject of many studies. Leclercet al.14 and Fox et al.15 have compared a line source and apoint source formalism to study anisotropy e↵ects and havefound no significant di↵erences between the two approxima-tions. In a similar way, Chibani et al.16 have compared thee↵ects of a point source formalism, an idealized line sourceformalism, and an idealized Monte Carlo (MC) simulationwith material fully defined and have found similar di↵erencesbetween the Monte Carlo and either line source or pointsource formalism. Lindsay et al.17 have studied the e↵ectof seed anisotropy on brachytherapy dose distribution withthe two main brachytherapy isotopes, i.e., 125I and 103Pd.They found no di↵erence on the DVH but found that seedsanisotropy can have a significant e↵ect on the dosimetricquality of prostate brachytherapy implant.

The impact brought by needle divergence on a prostatedosimetry has been briefly looked. Nath et al.18 have studiedneedle divergence of varying degrees on spherical target vol-umes and actual patient implants and found that they degradethe dosimetric quality of an implant between pretreatmentand implantation dosimetry as well as the tumor biologicale↵ective dose when compared to the reference implant. Cor-bett et al.19 have investigated the problem by first creating aprobability distribution of seeds orientation as identified frompostimplant radiography of ten patients. They subsequentlyassigned the seeds orientation for five prostates seed implantcase by sampling orientations from this probability distribu-tion. They found no significant di↵erences on the DVH be-tween the anisotropic seeds distributions with those sampledorientations and the isotropic point source formalism on theclinical target volume (CTV) for all five cases.

At this time, the AAPM (Refs. 3 and 5) and the ABS (Refs. 2and 20) recommend the use of the TG43-1D isotropic algo-rithm. While actual clinical techniques can evaluate the seedposition accurately,21 di�culties encountered in determiningseed orientation in the CT scans make the TG43-2D anisotropyformalism imprecise. Additionally, the fact that there is noconsensus in the scientific community on the method to detectseed orientation and that no software is widely available toreconstruct seed orientations enforce the choice of a 1D for-malism.

The goal of this paper is to characterize and quantify theimpact of seed orientation in low-dose-rate prostate brachy-therapy from a large clinical postimplant data set.

2. METHODS AND MATERIALSA cohort of 287 prostate cancer patients who underwent

brachytherapy treatment for which postimplant seed orienta-tions and positions were extracted was selected. Each casehas five fluoroscopic projections of the pelvic area (gantryangles = �40�, �35�, 0�, 35�, 40� where 0� corresponds to anAP image) as well as postplanning CT (Somatom Emotion;

Siemens, Munich, Germany) acquired 30 days postimplant.Voxel sizes are [0.289,0.289,2.5] mm3. Contours of the rec-tum, the urethra, the prostate, and the bladder drawn by thephysician on the CT images are taken from the DICOM-RSfiles.

For each patient, five hypothetical dose deposition scenar-ios are studied. Dose is calculated from the TG43-1D algo-rithm (1), from the TG43-2D algorithm with seeds parallelto the DICOM Z-axis (2: D kTG43) and with seeds oriented (3:D✓

TG43), and finally from the Monte Carlo simulation withseeds parallel to the DICOM Z-axis (4: D kMC) and with seedsoriented (5: D✓

MC).

2.A. Patient geometry2.A.1. Electron density assignation based

on CT calibration curve

Day 30 postimplant CT images are used. Their Hounsfieldunit (HU) numbers are acquired and converted to electrondensities to scale the cross-sections for increased simulationaccuracy. For this purpose, the clinical calibration curve forour Siemens CT scanner, obtained using a CIRS phantom(model 062M; Norfolk), was used.

2.A.2. Composition of human tissues protocol

based on TG186

Task Group 186 (Ref. 22) (TG186) prescribes the formal-ism to allocate the material for each voxel within the geome-try studied. Thresholds were applied within each organ of in-terest to separate materials composition. Thresholds (Table I)are chosen as the midpoint in density (HU) between twomaterial densities. ICRP Report 23,23 TG186 (Ref. 22), andICRU Report 46 (Ref. 24) prescribe elemental compositionand mass density of the materials. Air (40% humidity) com-position is based on the TG43 (Ref. 25) recommendation.

Subsequently, for each voxel, materials definitions arescaled to include the CT electron density value while keepingintact elemental composition. This increases the accuracy of

Table I. Material assignments for Monte Carlo geant4 simulations. Detailedcomposition provided in TG186 (Ref. 22), TG43 (Ref. 25), and ICRU 46(Ref. 24).

OrganThreshold

(HU)Material/base density

(g/cm3)

Background [�1000, �477] Air/0.001205[�477, 832] Mean male soft tissue/1.0[832, 2000] Cortical bone/1.85

Bladder [�1000, �477] Air/0.001205[�477, 2000] Mean male soft tissue/0.75

Rectum [�1000, �477] Air/0.001205[�477, 2000] Rectum/0.75

CTV [�1000, 2000] Prostatic tissue/1.045Urethra [�1000, �477] Air/0.001205

[�477, 2000] Mean male soft tissue/1.0

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the simulation by allowing multiple materials with the sameelemental composition and variable density within the simu-lation.

2.A.3. Simple threshold region artifact removal

algorithm

The high density of the brachytherapy seeds causes sig-nificant imaging artifacts in the surrounding tissues5 reducingthe image quality by increasing the noise in the surroundingareas and decreasing the soft-tissue contrast.9 Not taking intoaccount those artifacts will allocate high-density and e↵ec-tive atomic number (Ze↵) material to the area surroundingthe seed and may cause significant dose di↵erences in theMonte Carlo calculation. Therefore, a spherical region is de-fined (r = 2 mm) around each seed position and overriddenwith TG186 (Ref. 22) prostate density and material. The pre-cise material and geometric definitions of the seeds are thenadded back to the simulation in a geant4 parallel world1 to takeinto account the e↵ect of the interseeds attenuation on the dosedistribution.

2.B. Semiautomated seed detection algorithm

3D seed projections from di↵erent angles during fluo-roscopy are needed to reconstruct the implants in a 3D grid.For this study, a semiautomated seed detection algorithm,developed in our lab, is used to retrieve the seed positionsand orientations.12,13 First, the algorithm retrieves as manyseed positions and orientations as the resolution allows, thena human operator performs a revision to ensure no seedsare missed and corrects for wrong angles (on each 2Dplane). The process and the human revision retrieve 100%of the seeds implanted (nseed= 32–94 per patient for LDRbrachytherapy).

2.C. TG43 formalism

The TG43 formalism and its update TG43-U1 (Ref. 25)have been a standard for nearly 20 yr of brachytherapytreatment planning. It superposes the dose kernel of one seed,calculated in a spherical medium of water of 15 cm, onto allseed positions. Both 2D (cylindrically symmetric line source)and 1D (point source) formalisms are provided by TG43 tocalculate the dose distribution.

The dose calculation geometry varies significantly be-tween patients due to di↵erences in the contours positions,the seeds placements, and the seeds orientations. Thesefactors make the direct comparison of dose metrics betweenpatients impossible. Thus for every patient, the four lastsimulation scenarios were normalized by the TG43-1D dose.This choice was also motivated by the fact that TG43-1D wasused by the clinical planning system.

2.D. Monte Carlo simulation code and analysis tool

The Monte Carlo geant4 simulation code (v 4.9.6.p01)was chosen because of its new parallel world functionality,

the layered mass geometry (LMG),1 improving the simula-tion accuracy. This parallel world enables placing a param-eterized seed26–28 in any position or orientation according tothe initial world geometry construction.

All simulations in our study use the linear track-lengthestimator (LTE)29 in conjunction with the material photonattenuation coe�cients extracted from the NIST (Ref. 30)database to score the kerma. All doses are transported andscored to medium, as recommended by TG186.22 Chargedparticle equilibrium is assumed and no electrons are simu-lated. The Monte Carlo brachytherapy algorithm ALBEGRA(Ref. 31) was used in this work. Voxel dimensions wererescaled to obtain 1 mm3 bins to increase the simulationspeed and decrease the standard error per simulation.

2.D.1. Brachytherapy seed model

The mean 125I photon energy is approximately 28 keV.This study is performed using three di↵erent 125I brachyther-apy seeds distributed over 287 cases. A phase space file isgenerated for each seed type by recording isotope decaysproduced inside the inner core for which the decay prod-ucts reach the outer capsule. Energy, position, and directioninformation are recorded for each event. Precise geometricdefinition and composition are used for each seed [NucletronSelectSeed,26,32,33 Amersham OncoSeed 6711 (Refs. 25 and27), and Mills Bio. Pharm. ProstaSeed 125SL].25,28,33 Onebillion decays (average 1.4 photons per decay3) were sim-ulated for each seed phase space and 500 million historieswere simulated for each patient.

2.D.2. Physical processes

For the processes of photoelectric absorption, incoherentand coherent scattering, and Compton scattering, probabilis-tic data based on a set of total, partial, and di↵erential cross-sections from the geant4 cross-section database for low-energy electromagnetic process are used, extracted from theLivermore data libraries.34

2.E. Clinical organs of interest and related dosemetrics

The selection of clinical organ of interest follows boththe AAPM Task Group 137 (TG137) and the ESTRO/EAU/EORTC recommendations on tumor and target volumes forprostatic cancer.5,35 These include the CTV as the maintarget. The urethra, the rectum, and the bladder are definedas organs at risk (OARs). For the CTV, the prescription is145 Gy for 125I implants, based on ESTRO/EAU/EORTC rec-ommendations.4 Additional constraints are imposed at plan-ning to obtain V100 > 99% and D90 of about 170–180 Gy.However, since our database covers a period of four years,during which the implant procedure has evolved, somecontours are omitted from a certain number of patients;e.g., the Foley catheter for postplanning dosimetry urethraidentification was used only for 187 cases. Therefore, there isnpatients-CTV= 287, npatients-rectum= 255, npatients-bladder= 256, and

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npatients-urethra= 187. The choice of dose metrics follows ES-TRO/EAU/EORTC (Ref. 35) recommendations: CTV D90,V100(%) and V150(%); urethra D10 and D30; rectum (andbladder) D2cc, D0.1cc, and V100(%). Finally, urethra V125 isinvestigated as it has been correlated with toxicity in the re-cent Radiation Oncology Therapy Group-0321 (Refs. 36–38)results.

3. RESULTS3.A. Seeds orientation and dose distributions

The polar angle is defined as the angle between thesuperior–inferior (SUP–INF) patient axis and the seed ori-entation vector, referenced on the CT grid. The azimuthalangle is defined as the orthogonal projection on the transverseplane (CT slice) of the seeds orientation vector with referencein the antero-posterior (ANT–POST) direction. The seed XYplane of symmetry allowed us to reduce the polar angle toa range between 0� and 90� and the X Z plane of symmetryallowed us to reduce the azimuthal angle between �90� and90�. Of the 287 cases, 110 used the Amersham OncoSeed6711 seeds, 10 used SelectSeed 125I seeds, and 176 used

ProstaSeed SL-125 seeds. The seed angle distributions of all17 016 seeds from the 287 cases are plotted in Fig. 1.

3.A.1. Polar and azimuthal angle

Figures 1(a) and 1(b) shows that there might be some im-portant angular di↵erences between the clinical orientationand the parallel planning configurations. For the polar angle,the average seed orientation is of 37.4�. The average az-imuthal angle is �1.8�, clearly close to the insertion direction.

The fluoroscopic image illustrates [Fig. 1(d)] a patientwith large seed polar angles. An obvious large systematicorientation discrepancy in the implant geometry is a↵ectingmost of the seeds in this particular implant.

3.B. E�ect on clinical dose metrics3.B.1. CTV

For each simulation, dose di↵erences to organs are calcu-lated and shown with the standard error in Table II. It shouldbe noted that the large standard deviation observed for MCcalculations (Fig. 2) is expected from di↵erences in anatomyand composition between the patients as well as the variationin the number of seeds in the treatment, a↵ecting the interseed

Seed Vector

Polar θ

Azimuthal ϕYX

Z

(A) Azimuthal angle distribution (B) Polar angle distribution

(D) 90 degree fluoroscopic images of a post-implantpatient

(C) Polar and azimuthal angle on the CT reference axis

Fig. 1. Azimuthal (a) and polar (b) angle distribution for nseed = 17 016. The azimuthal reference angle is parallel to the Y -DICOM axis, and the polar referenceangle is parallel to the Z -DICOM axis (c). A 90� projection of a fluoroscopic image is shown as an example (d).

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Table II. Summary of dose metrics for each organ included in the 30-day postimplant dosimetry for both orientedand parallel configurations.

OrganMC k

[DkMC/DTG43-1D]MC ✓

[D✓MC/DTG43-1D]

TG43-2D k[DkTG43/DTG43-1D]

TG43-2D ✓

[D✓TG43/DTG43-1D]

CTV

D10 0.988 ± 0.051 0.992 ± 0.048 0.963 ± 0.014 0.966 ± 0.009D90 0.908 ± 0.071 0.909 ± 0.062 0.994 ± 0.025 0.995 ± 0.013V100 0.987 ± 0.021 0.988 ± 0.020 0.997 ± 0.026 0.999 ± 0.012V150 0.967 ± 0.036 0.968 ± 0.034 0.999 ± 0.006 0.999 ± 0.004V200 0.946 ± 0.060 0.944 ± 0.058 1.001 ± 0.011 0.998 ± 0.009Bladder

D10 0.815 ± 0.072 0.839 ± 0.068 0.961 ± 0.031 0.985 ± 0.033D2cc 0.849 ± 0.066 0.868 ± 0.063 0.965 ± 0.031 0.984 ± 0.031V100 0.662 ± 0.141 0.708 ± 0.135 0.911 ± 0.074 0.966 ± 0.090Rectum

D10 0.896 ± 0.063 0.883 ± 0.063 1.019 ± 0.017 1.004 ± 0.023D2cc 0.915 ± 0.059 0.903 ± 0.060 1.019 ± 0.016 1.005 ± 0.026V100 0.817 ± 0.130 0.788 ± 0.127 1.063 ± 0.065 1.021 ± 0.062Urethra

D5 1.040 ± 0.098 1.031 ± 0.090 1.004 ± 0.033 0.992 ± 0.026D10 1.023 ± 0.086 1.013 ± 0.079 1.012 ± 0.029 1.000 ± 0.021D90 0.932 ± 0.084 0.933 ± 0.069 1.001 ± 0.036 1.002 ± 0.021V125 0.986 ± 0.071 0.985 ± 0.069 0.995 ± 0.041 0.996 ± 0.054

attenuation. Figure 2 shows that no major di↵erences betweenD kMC and D✓

MC and between D kTG43 and D✓TG43 are observed for

the CTV, while larger di↵erences are seen between TG43 andMC calculation methods. The average di↵erence is about 7%for D90, in line with a previous study.

3.B.2. Bladder

For several patients, a significant section of the bladderis located in the implant-axis direction. Hence, the low-doseplanning region of the seed will be facing it. Therefore,any orientation configuration will increase the dose to thebladder. To compare both sets of orientations (k and ✓) apaired Student t-test is done (Table III). A statistically signif-icant increase is seen for D2cc [Fig. 3(a)] for the oriented con-figuration, when compared with the parallel configuration.

3.B.3. Rectum

The rectum is located posteriorly to the prostate along theimplant axis. Planning configurations exhibit the high doseregion toward the rectum. Hence, any deviation from thataxis moves the seed anisotropic low-dose region toward therectum and produces an e↵ect that is opposite to that seenfor the bladder. This is illustrated by Fig. 3(b), which showslower doses for oriented configurations. A similar statisticaltest is used for the rectum as was used for the bladder toensure the validity of the results.

3.C. Summary

Finally, Table III provides the relative di↵erence betweeneach configuration (k and ✓) for the two simulation methods,MC and TG43 using the equation �X = (D kXX�D✓

XX)/D kXX.

For the CTV and urethra, no statistical di↵erences (paired Stu-dent t-test) between oriented and parallel configurations areobserved, except for the D10 and D5 metrics, which accountfor the small volume high-dose regions. As seen before, therectum D2cc parameter is higher in the parallel case, on average1.3% ± 2.4% (described as the mean di↵erence ± the standarddeviation on the di↵erence) in the MC study and on average1.5% ± 2.4% when using TG43. For the bladder, the dose inthe parallel clinical configuration is decreased by up to 2.1%±3.4% and 1.8% ± 3.6% for the MC and TG43 D2cc parameters.

To get a better understanding of the worst-case scenario,the number of patients for whom the di↵erence is of clinicalsignificance has been quantified. To do so, the number ofpatients for whom the di↵erence between the oriented andparallel configuration is greater than 5% has been extractedfor both the TG43 and MC configurations for the rectum andthe bladder D2cc. For the bladder, 14% (17%) of the patientshave a di↵erence of clinical significance when comparing theTG43 (MC) method between oriented and parallel configu-rations. For the rectum, a single patient in both cases hasdemonstrated clinical significance.

3.D. Extreme case3.D.1. Extreme implant angles

Thirty eight cases are identified for whom the average polarangles were greater than 55�. The objective was to quantifyif these extreme implant angles could cause any major dif-ferences in the dose distribution between k and ✓ configura-tions. The same four dose calculations were performed on thissubsample. The results did not di↵er significantly from thosemeasured on the whole cohort of patients (Table IV).

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(a)

(b)

(c)

Fig. 2. (a) V100, (b) V150, and (c) D90 dose metrics for the CTV and thefour simulation methods normalized to the TG43-1D. DYY

XX represents theorientation configuration (YY ) and the simulation algorithms (XX ).

3.D.2. Worst-case scenario

Two new TG43-2D configurations have been simulated toinvestigate the worst-case scenario for the seed orientations.First, all seeds were oriented at 90� on the ANT–POSTdirection. Then all seeds were oriented along the left–right(LEFT–RIG) direction. Both the rectum and the bladderD2cc dose metrics were quantified in each configuration andcompared to the idealized line source configuration, on theSUP–INF direction.

For the bladder, when all seeds are oriented along theLEFT–RIG axis, D2cc metric is increased by 7.3%. On theother hand, if all seeds are oriented along the ANT–POSTaxis, the D2cc metric is increased by 4.5%. This is due to the

Table III. Di↵erence of dose metrics extracted for oriented and parallelconfigurations for the cohort of patients (n = 287). p-values for the pairedStudent t-test are given in brackets. Negative values indicate a smaller dosefor the parallel configuration compared to the oriented configuration, and apositive value indicates a higher dose.

Organ�MC

[%] (p-value)� TG43

[%] (p-value)

CTV

D10 �0.471 ± 0.091 (0.002) �0.243 ± 0.083 (0.023)D90 �0.238 ± 0.143 (0.116) �0.059 ± 0.135 (0.567)V100 �0.025 ± 0.173 (0.279) �0.112 ± 0.139 (0.355)V150 �0.110 ± 0.077 (0.234) 0.310 ± 0.014 (0.045)V200 0.198 ± 0.053 (0.550) 0.305 ± 0.053 (0.155)Bladder

D10 �2.774 ± 0.223 (<0.001) �2.419 ± 0.214 (<0.001)D2cc �2.174 ± 0.221 (<0.001) �1.863 ± 0.212 (<0.001)V100 �7.886 ± 0.987 (<0.001) �6.390 ± 0.926 (<0.001)Rectum

D10 1.421 ± 0.155 (<0.001) 1.553 ± 0.152 (<0.001)D2cc 1.326 ± 0.144 (<0.001) 1.536 ± 0.141 (<0.001)V100 8.571 ± 3.695 (<0.001) 12.012 ± 4.909 (<0.001)Urethra

D5 �0.206 ± 0.212 (0.023) �0.043 ± 0.194 (0.003)D10 0.959 ± 0.139 (0.118) 1.193 ± 0.126 (0.254)D90 0.864 ± 0.090 (0.082) 1.165 ± 0.042 (0.361)V125 �0.240 ± 1.676 (0.085) �0.027 ± 1.549 (0.075)

(a)

(b)

Fig. 3. D2cc dose metrics for the bladder (a) and the rectum (b) for thefour calculation methods normalized to the TG43-1D. DYY

XX represents theorientation configuration (YY ) and the simulation algorithms (XX ).

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Table IV. Summary of dosimetric indices for each organ included in the treatment contoured by the physician foreach of 38 patients with a defined systematic implant polar angle greater than 55�.

OrganMC k

[DkMC/DTG43-1D]MC ✓

[D✓MC/DTG43-1D]

TG-43 2D k[DkTG43/DTG43-1D]

TG-43 2D ✓

[D✓TG43/DTG43-1D]

CTV

D10 0.984 ± 0.055 0.987 ± 0.054 0.962 ± 0.006 0.963 ± 0.006D90 0.921 ± 0.060 0.921 ± 0.056 0.998 ± 0.018 0.996 ± 0.016V100 0.982 ± 0.024 0.983 ± 0.023 0.999 ± 0.004 1.000 ± 0.003V150 0.962 ± 0.056 0.962 ± 0.052 1.000 ± 0.006 0.999 ± 0.005V200 0.935 ± 0.096 0.931 ± 0.093 1.002 ± 0.016 0.997 ± 0.015Bladder

D10 0.835 ± 0.053 0.845 ± 0.059 0.968 ± 0.030 0.977 ± 0.034D2cc 0.860 ± 0.087 0.875 ± 0.079 0.974 ± 0.066 0.982 ± 0.065V100 0.627 ± 0.193 0.648 ± 0.187 0.879 ± 0.115 0.903 ± 0.106Rectum

D10 0.895 ± 0.082 0.884 ± 0.068 1.030 ± 0.015 1.015 ± 0.010D2cc 0.909 ± 0.298 0.901 ± 0.079 1.021 ± 0.015 1.013 ± 0.013V100 0.768 ± 0.190 0.734 ± 0.199 1.115 ± 0.107 1.054 ± 0.057Urethra

D5 1.047 ± 0.059 1.034 ± 0.058 1.005 ± 0.030 0.995 ± 0.035D10 1.053 ± 0.032 1.042 ± 0.031 1.018 ± 0.021 1.012 ± 0.021D90 0.972 ± 0.039 0.970 ± 0.028 1.016 ± 0.014 1.009 ± 0.015V125 0.985 ± 0.101 0.984 ± 0.059 1.004 ± 0.021 0.999 ± 0.084

fact that, for this patient, a small part of the bladder is in theANT–POST direction and therefore when all seeds face thisaxis, the low-dose region will be facing it. For the rectum, theD2cc metric is increased by 1.5% when all seeds are in theLEFT–RIG axis and decreased by �6.1% when all seeds arein the ANT–POST axis.

3.E. E�ects of the scoring medium on the orientations

TG186 (Ref. 22) recommends scoring dose to medium inmedium (Dm,m) as it is the natural quantity to score with dosecalculation algorithms such as Monte Carlo codes, insteadof dose to water in medium (Dw,m). On the other hand,the di↵erences between Dm,m and Dw,m have been shownto be significant at low energy (<50 keV).39–41 The LDR125I isotope emits photons at a mean energy of 28 keV, inthe low-energy region. For low energy brachytherapy seeds,di↵erences can be as high as 70% in soft tissue.40

This study used a patient-based geometry with 1 mm3

voxels. In comparison with these radiation target volumes,125I secondary electron ranges (20 µm) can be consideredsmall, and large cavity theory applies. According to thistheory, the ratio of Dw,m to Dm,m is related by the ratio of themass–energy absorption coe�cients (µen/⇢)wm.40–42 Thus, toconvert Dm,m into Dw,m, it is only needed to scale each voxelby (µen/⇢)wm and no e↵ects on the photon transportation areseen.

The di↵erences of the Monte Carlo calculations and theclinical point source algorithm (TG43-1D) will be greatlyinfluenced by the scoring medium. But this study calculatesthe orientation e↵ects as a relative di↵erence between theseeds configurations (k and ✓) on a unique cohort of patient.

Therefore, converting both D kMC and D✓MC to Dw,m will not

a↵ect the relative dose di↵erence between them as they arescaled by the same factor.

Finally, it has been proven that the MC relative orientatione↵ects shown here can be e↵ectively isolated from the scor-ing medium e↵ects and only depend on the transportationmedium. This modification in the transportation mediumexplains the di↵erence seen between the MC and TG43results when comparing oriented and idealized formalism.

3.F. Anisotropy e�ects

287 patients have been investigated and the TG43-2Didealized line source formalism has been calculated for eachof them. The TG43-2D formalism accurately represents theanisotropy in the seed introduced by the internal constructionof the seed. However, comparing TG43-2D and TG43-1DCTV dose metrics with a paired Student t-test shows thatthe two distributions are not significantly di↵erent (p < 0.05),even when the seed orientations are taken into account. Theseresults are in agreement with previous studies.14–16

4. DISCUSSIONSeeds orientation e↵ects on the dose distribution have

been investigated using day 30 postimplant configurations inLDR brachytherapy. 287 patients for whom seed orientationswere known from multiple angle fluoroscopic projectionswith high resolution have been used. The seed orientation canarise from three di↵erent origins. First, the seeds themselvesmight have a random orientation due to the implant techniqueand edema-related e↵ects. Then they can have a potentialsystematic orientation caused by the di↵erence between the

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real needle implantation angle and the planned angle alongthe patient Z-axis, a↵ecting all seeds within the needle.Finally, the di↵erence between the implantation Z-axis (onthe surgical table) and the CT patient Z-axis (on the CTscan bed), due to a pelvis rotation, can introduce anothersystematic angle. The last two e↵ects can clearly be seenfrom Fig. 1(d) and will produce systematically larger seedangles (seen in about 10% of our patients).

This study demonstrates that the CTV and urethra dosedistributions for the di↵erent seed orientations (k and ✓) arenot statistically di↵erent, based on the two-sided Studentt-test p-value. The multi-institutional cooperative RadiationTherapy Oncology Group-0321 (Ref. 43) has demonstrateda clear correlation on the urethra V125 and the toxicity.However, this study also demonstrates no significant impactof the seed orientation on this dose metric.

However, seed orientations a↵ect the organs external tothe CTV, namely, bladder and the rectum. It has beenproved15–17 that the isodose distribution for a NucletronSelectSeed 125I seed demonstrates an anisotropic butterflyshaped dose distribution, which shows low-dose region at thetips of the seeds due to the additional titanium material inthe welded end. Relative to this low-dose region is a high-dose region on the polar XY plane. The di↵erences in thedose distribution have a significant impact when consideringthe OAR position. The location of the bladder, superior tothe prostate on the SUP–INF axis, is within the plannedseed low-dose region. The location of the rectum, on theANT–POST axis, is exposed to the seeds high dose regionat planning. Therefore, any seed orientation that deviatesfrom the implant axis will result in a decreasing dose to therectum and an increased dose [Figs. 3(a) and 3(b)] to thebladder. This is in agreement with the presented calculations(Table II). The e↵ect of the orientation alone for these twoorgans is between 2% and 10% when comparing eitherD kMC to D✓

MC or D kTG43 to D✓TG43 and are all statistically

significant (Table III). However, the average di↵erence forthe bladder D2cc (�2.17%) is not clinically significant. It hasbeen found that 14% (17%) of the patients have a TG43-2D(MC) clinically significant di↵erence, i.e., greater than 5%di↵erence, in the dose to the bladder between the orientedand the parallel configurations. Similar studies for the rectumhave shown that a single patient exhibits such di↵erences.

One can expect the penile bulb to be a↵ected in a similarfashion as the bladder. However, it is important to considerthat this organ is generally further away from the prostate.At such distance, the anisotropy e↵ect caused by the seedgeometry will be negligible and the di↵erence will be muchsmaller.

On the other hand, the e↵ects of tissue heterogeneities,scoring dose medium and interseed attenuation (e.g., compar-ing D kMC to D kTG43) are much more pronounced, ranging be-tween 10% and 30% depending on the clinical dose metricsconsidered for these two OARs. The results of those threecombined e↵ects are similar to what is found from the lit-erature.16,33 Based on these results, seed orientation can beconsidered a second-order e↵ect when compared with tissuedefinition and interseed attenuation.

It is important to point out that two of the e↵ects relatedto the seed orientation, the pelvis rotation (OR vs 30 daysCT scan) and the true needle insertion angle (relative toplanned parallel configuration), will apply to the stranded-seed implants as well. Thus the conclusions of this studyshould apply equally to this type of implant. The presenceof calcifications within the prostate region was seen in someof the patients of this cohort but has not been considered.This will be the subject of a separate study.

Finally, from the results presented, it appears that useof the TG43-2D algorithm without some knowledge of theseeds orientations will have little impact on the CTV dosemetrics but can lead to errors in the dose to the OARs andthus might not be appropriate.

5. CONCLUSIONIt has been shown that the seed angle distributions in

low-dose-rate permanent prostate brachytherapy a↵ect OARdose distributions by 2.1% on average, for dose metricssuch as D2cc. However, seed orientations do not a↵ect in astatistically significant way (based on the p-value) the CTVor urethra main clinical dosimetric quantities of interest. Wehave further demonstrated that seed orientation is a second-order e↵ect relative to tissue heterogeneities and interseedattenuation.

ACKNOWLEDGMENTSThis work was supported by Grant No. 2011-700810 from

the Canadian Cancer Society Research Institute (CCSRI).Charles-Antoine Collins-Fekete was supported by an Alexan-der Graham Bell scholarship from the Natural Sciences andEngineering Research Council of Canada. The authors wouldlike to acknowledge Compute Canada and CLUMEQ foraccess to high performance computing clusters and technicalsupport.

a)Author to whom correspondence should be addressed. Electronic mail:beaulieu@phy.ulaval.ca

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