Evaluation of the interfractional biological effective dose (BED) variation in MammoSite high dose rate brachytherapy

The objective of this work is to evaluate the interfractional biological effective dose (BED) variation in MammoSite high dose rate (HDR) brachytherapy. Dose distributions of 19 patients who received 34 Gy in 10 fractions were evaluated. A method was employed to account for nonuniform dose distribution in the BED calculation. Furthermore, a range of α/β values was utilized for specific clinical end points: fibrosis, telangiectasia, erythema, desquamation and breast carcinoma. Two scenarios were simulated to calculate the BED value using: i) the same dose distribution of fraction 1 over fractions 2–10 (constant case, CC), and ii) the actual delivered dose distribution for each fraction 1–10 (interfraction dose variation case, IVC). Although the average BED difference (IVC – CC) was <0.7 Gy for all clinical endpoints, the range of difference for fibrosis and telangiectasia reached −11% to +3% and −9% to +9% for one of the patients, respectively. By disregarding high inhomogeneity in HDR brachytherapy, the conventional BED calculation tends to overestimate the BED for fibrosis by 16% on average, while it underestimates the BED for erythema (7.6%) and desquamation (10.2%). In conclusion, the BED calculation accounting for the nonuniform dose distribution provides a more clinically relevant description of the clinical delivered dose. Though the average BED difference was clinically insignificant, the maximum difference of BED for late effects can differ by a single fractional dose (10%) for a specific patient due to the interfraction dose variation in MammoSite treatment. PACS number: 87.53.Jw


Received 1 December, 2009; accepted 3 May, 2010
The objective of this work is to evaluate the interfractional biological effective dose (BED) variation in MammoSite high dose rate (HDR) brachytherapy. Dose distributions of 19 patients who received 34 Gy in 10 fractions were evaluated. A method was employed to account for nonuniform dose distribution in the BED calculation. Furthermore, a range of α/β values was utilized for specific clinical end points: fibrosis, telangiectasia, erythema, desquamation and breast carcinoma. Two scenarios were simulated to calculate the BED value using: i) the same dose distribution of fraction 1 over fractions 2-10 (constant case, CC), and ii) the actual delivered dose distribution for each fraction 1-10 (interfraction dose variation case, IVC). Although the average BED difference (IVC-CC)was<0.7Gyforallclinicalendpoints,therangeofdifferencefor fibrosisandtelangiectasiareached-11%to+3%and-9%to+9%foroneofthe patients, respectively. By disregarding high inhomogeneity in HDR brachytherapy, theconventionalBEDcalculationtendstooverestimatetheBEDforfibrosisby16% onaverage,whileitunderestimatestheBEDforerythema(7.6%)anddesquamation (10.2%).Inconclusion,theBEDcalculationaccountingforthenonuniformdose distribution provides a more clinically relevant description of the clinical delivered dose.ThoughtheaverageBEDdifferencewasclinicallyinsignificant,themaximum differenceofBEDforlateeffectscandifferbyasinglefractionaldose(10%)fora specificpatientduetotheinterfractiondosevariationin MammoSitetreatment.

I. IntroDuctIon
MammoSite high dose rate (HDR) brachytherapy has been widely used for early stage breast cancer patients. (1) A spherically shaped dose distribution around the MammoSite balloon applicator (Hologic Corporation, Marlborough, Massachusetts, USA) can be easily reproduced. An intended dose can be delivered with high accuracy by a remotely controlled afterloader using a single plan for multifractional delivery.
In a previous multifractional HDR brachytherapy study, (2) the deformity of the MammoSite balloon applicator from a sphere and the movement of a balloon toward the ipsilateral lung or skin during the course of HDR brachytherapy were measured. Additionally, the interfraction physical dose variations resulting from interfraction changes (shape and location) of the balloon applicator and trapped air gap volume were evaluated. In general, the interfraction physical dose variationswerefoundtobeclinicallyinsignificantoverthecourseoftreatment.However,for certain fractions in some patients, clinically unacceptable dose variations may occur, such as lessthan90%oftargetvolumecoverageandhighdosestoskinandipsilaterallung.Adjustment of the MammoSite balloon applicator and replanning were suggested for those cases.
Measuring the interfraction dose variation with a biological metric can provide a better understanding of the overall biologic effect for the average interfraction dose variation as well as the potential high dose variation for certain treatment fractions in MammoSite delivery. In this work, the concept of biological effective dose (BED) was used to evaluate the interfraction dose variations resulting from the interfraction changes of the balloon applicator for 188 treatment fractions of 19 MammoSite HDR patients (patient 1 to 19). No computed tomography (CT) image data were available for two treatment fractions. This study was approved by the institutional review board.

A. BED calculation
The cell survival (S) fraction from the total dose of "D" delivered in the number of fractions of "n"withfractionaldoseof"d"isknownasfollowingequationbasedonthelinear-quadratic (LQ)model: (3,4) (1) The "αnd" and "βnd 2 "arethelinearandquadraticcomponentsofcellkillingandα (in units of Gy -1 ) and β (in units of Gy -2 )aretheradiosensitivitycoefficientsforeachcomponent.Ifthe cellrepopulationistakenintoaccountasthesecondterm,theEq.(1)becomesthefollowing equation: (2) T eff is the effective cell doubling time over the treatment time T. Allowance for a delay time (T delay )isnotincludedintheequation,sothedoublingtimetobeusedistheaverageoverthe given treatment duration. Note that the second term is not needed for late-responding tissue since cell repopulation does not usually occur in these tissues during the course of irradiation. Traditionally, the BED method has been used to assess the biological effectiveness (E) of a dose "D" to the irradiated cells by the relationship of BED = E/α = -(ln S)/α. Therefore, the conventional BED formulism (BED C :Conventionalmethod)canbewritteninEq.(3): The biological effectiveness for a certain fractionation scheme is represented by the value of"1+d/(α/β)", depending upon the fractional dose "d" and "α/β" (the dose at which the linearandquadraticcomponentsofradiationdamageareequal).Theα/β ratio depends on the characteristics of the tissue of interest and is measured in units of Gy.
The underlying hypothesis of the conventional BED calculation (BED C ) is that all cells of interest receive the same dose as the prescribed dose throughout the treatment and the cell repopulationtermisonlyaffectedbythetreatmenttimeTforaspecifictissue.However,the prescribed dose cannot be shaped ideally to cover the entire target volume in a clinical treatmentplanandalltargetcellscannotreceiveexactlythesamedoseastheprescribeddose. Moreover,thedelivereddosedistributionforaspecifictreatmentfractioncannotbethesame astheplanneddosedistribution.Forexample,thegroupaverage (5,6) differential dose volume histogram (dDVH) calculated using a dose bin size of 0.1 Gy for the 19 MammoSite HDR patients( Fig.1)showsthattheprescribeddoseof34Gy(33.9Gy<Dose≤34.1GyinTable1) wasonlydeliveredto0.49%ofthetargetvolumewhilethemajorityoftargetvolumereceived muchhigherdose.Themostprobable(modal)andmeandosetothetargetwere37.7Gyand 48.0 Gy for the 19 patients, on average. In dDVH, the sum of the fractional target volume for all doserangesis100%andthefractionaltargetvolumereceivingacertaindosevaries de pending upon the size of dose bin. In order to account for the nonuniform dose distribution (heterogeneity) within the target volume, we utilized a more clinically relevant approach for the BED calculation (BED H :Heterogeneitymethod).Specifically,theBEDvaluewascalculatedforacertainsubvolumewithin the target volume where dose distribution was uniform although it was heterogeneous for the entiretargetvolume.TheBEDvalueforthespecificsubvolumeof"i"canbecomputedusing the cell survival fraction of subvolume i by BED C , i = -(ln s i )/α. Hence, the overall BED H value is computed by summing the volume weighted survival fraction over the entire target volume asfollowsinEq.(4): (7)(8)(9) (4) where v i is fraction of the subvolume in the target and the sum of all fractional subvolumes isunity.Nisthetotalnumberofdosebins.However,itisdifficulttospecifythesubvolume within the target whose dose distribution is uniform. Instead, the dDVH was employed in thisstudy.Allfixedsizedosebinsareselectedfirstandtheircorrespondingsubvolume(s)are determinedaccordingly.Ifaspecificnonuniformdosedistributionwithinthetargetvolume remainsunchanged(CC:constantcase)throughoutthefullcourseofradiationdelivery,the total value for the dose of "D" delivered in the total number of fraction "n" can be computed as follows.
(5) α α α/β αT T where d i and v i are the dose in each bin and its fractional volume. However, in a clinical practice, the nonuniform dose distribution varies according to the change of patient anatomy as wellasapplicatorgeometryforeachfraction.Consequently,afractional value for acertainfraction"f"whichhasaspecificnonuniformdosedistributioncanbecomputedby thefollowingequation: Because the cell repopulation term is not related to the dose distribution for each fraction, the effect of cell repopulation term was considered to be constant for each fraction. More clinically relevant value for the dose of "D" delivered in "n" treatment fractions can be calculated by the summation of the fractional valueforeachfractionwithitsspecific nonuniformdosedistribution(IVC:interfractionvariationcase).
If a nonuniform dose distribution is the same throughout the full course of treatment, the valuefromEq. (7) (10) ThePTVwasdefinedasasphericalshellwith1cmthickness. Balloonsurfacewasexpandedwith1cminthree-dimensions(3D)andthePTVwasobtained byextractingtheballoonvolumefromthe1cmexpansion.Theaveragediameteroftheballoon for19patientswas4.6cmrangingfrom4.0cmto5.5cm.Therefore,thenumberofavailable dwell positions was different for each patient depending upon the diameter of the balloon and rangedfrom7to10.ThePTV_EVALvolumewasconstructedthesameasthePTVexceptfor excludingthevolumesofskin+5mmandlung/pectoralismuscle.Toreducetheuncertainty in localizing the catheter lumen inside the MammoSite balloon, the CT images were rotated in3D,andtheircontrastandbrightnessweremodifiedtobestvisualizethelumeninsidethe balloon. The desired fractional dose of 3.4 Gy was prescribed to dose grid points located on the surfaceofthe1cmexpansionoftheballoonin3D.Tominimizethehighdependencyofdose distribution on the location of a single dwell position at the center of balloon, a multiple dwell position approach was used for all patients. Figure 2 shows the dwell positions for patient 19.
Inthisexample,eightdwellpositionswereavailabletooptimizethedwelltimedistribution.In addition,thesurfaceoptimizationtechniqueinthecommercialTPSwasutilizedforoptimizing the dwell time distribution to achieve better target dose coverage. (11)(12)(13) The optimal dwell time distribution was different depending upon the geometry of the balloon for each patient. The resultantdosedistributionwasshapedtocover1cmexpansionfromtheballoon(asshownin Fig.2).Therewasacoldspotalongtheaxisoftheballooncatheterduetothecharacteristic of line source.

c. BED calculation for interfraction dose variation
Clinically,thetreatmentplanoffraction1isusedforthetreatmentoffractions2-10without anymodificationunlessasignificantchangeoftheMammoSiteapplicatorisobservedsuch asaruptureoftheballoon,alargechange(i.e.>10%)intheairgapvolumerelativetothe PTV_EVAL, or noticeable movement of the balloon between fractions when comparing the prefractional treatment CT images with the planning CT images. To mimic this clinical practice, we assumed in this work that the shape and location of MammoSite balloon applicator are reproducibleforeachfraction1-10andtheinterfractiondosevariationcanbeignored.The samenonuniformdosedistributionoffraction1isemployedforallfractions1-10,andinthis constant case (CC) the valueiscomputedusingEq. (5). To account for the interfraction dose variation, the actual delivered dose distribution for each fraction should be employed in the fractional calculation(Eq. (6)).Tosimulate this interfraction variation case (IVC), a plan was retrospectively generated for each fraction 2-10.ThePTV_EVALandcriticalstructuresweredelineatedandtheballooncatheterwas alsoidentifiedontheCTimagestakenpriortoeachfraction2-10.Thedwelltimedistribution ofthefraction1planwasmanuallytransferredtotheplansforfractions2-10tomimicthe clinicalsituationwherethefraction1planisemployedforfraction2-10withoutmodification. Toeliminateerrorsduringthemanualtransferprocess,theplanreportoffractions2-10was validatedincomparisonwiththatoffraction1.Consequently,thedosedistributionoffraction 1wasimplementedonthetargetandcriticalstructuresoffractions2-10.Ifthereisnointerfraction variation of the MammoSite balloon applicator, the dose distribution of the target and criticalstructureswouldbethesameforfractions1-10.However,inreality,astheshapeor location of MammoSite balloon applicator changes, the dose received by the target and critical structures varies and is different for each fraction. The change in delivered dose to the target and critical structures depends on the magnitude of the change in the shape and/or location of the MammoSiteapplicator.Atotalof188plans(19plansforfraction1and169plansforfraction 2-10)weregeneratedfor19patients.ACTscanwasunavailableforfraction10ofpatient4 andfraction6ofpatient6.The value in this IVC was computed by the summation of the different fractional valuesoverfractions1-10(Eq. (7))usingthedifferentdose distribution for each fraction.

E. comparison of BED calculation methods
As shown in Fig. 1, MammoSite plans have a marked nonuniform dose distribution in the target volume which may potentially vary throughout the treatment. While the heterogeneity is accounted for in the BED calculation in this work using either or (H-method), it is disregarded in the conventional BED calculation (C-method). Therefore, assessing the discrepancy of BED values between H-method and C-method can demonstrate the characteristics of both BED calculation methods for various α/β ratios. The BED value ( ) using H-method(Eq.(5))wascomparedwithBED C,t valueusingC-method(Eq.(3))for19Mam-moSitepatients.Equation(3)assumesthattheentiretargetvolumereceivedtheprescribed dose,whileEq.(5)accountsfortheheterogeneityoftargetdosedistributionforeachpatient.
For a consistent comparison between H-method and C-method, the heterogeneity of target dose distribution was assumed to be unchanged over the fractions in the H-method.

IV. DIScuSSIon
Aspecificclinicalendpointresultsfromtheradiationdosetoaspecifictissue.Forinstance, consider when the same radiation dose is delivered to two different types of tissues. One tissue develops a certain clinical endpoint while the other tissue responds with a different clinical endpoint depending upon the characteristics of each tissue. Skin tissue of the breast may respond witheithererythemaordesquamation.Someconnectivetissuesinthebreastformadevelopmentoffibrosisandsomebloodvesselscandeveloptelangiectasiaafterirradiation.Also,the radiation dose kills breast cancer cells. In the clinical planning, the volume of PTV_EVAL mayconsistofthemixtureofmanytypesoftissuesforaparticularpatient,asreportedby Rosenstein et al. (21) Inanidealsituationwhereeachtypeoftissuecanbeexclusivelyidentified inthebreastanddelineatedontheplanningCTimages,tissue-specificDVHcanbegenerated for each volume of tissue type. However, with current MammoSite planning systems it is impossibletoextractthosetissue-specificDVHdata.Inthisstudy,thevolumeofPTV_EVAL wasconsideredasauniquevolumecontainingalltypeoftissuescorrespondingtoallclinical endpoints.Consequently,thesamedDVHforPTV_EVALwasusedintheBEDcalculation for all type of clinical endpoints. Even though the average BED difference stemming from interfraction dose variation was < 0.7Gyfor19patients,somepatient-specificdeviationwassignificant.Themaximumdeviationwasfrom-11%to+13%forlaterespondingeffects(α/βratioof2Gy)andfrom-9%to +6%forearlyrespondingeffects(α/β ratio of 8 or 11 Gy). Therefore, interfractional physical dosevariationforaspecificpatientcanmakethetotalBEDdifferby10%foracertainclinical endpoint which corresponds to the single fractional dose out of 10 total fractions.
By disregarding high inhomogeneity in HDR brachytherapy, the conventional simple calcu-lationtendstooverestimatetheBEDvalueforfibrosiswhileunderestimatingtheBEDvalue forerythemaanddesquamation.Hence,inordertoevaluatetheclinicalendpoints,ourdata suggest it is more clinically relevant to utilize the BED calculation accounting for the dose heterogeneity in target volume. However, one must stress that the BED and the underlying LQ model were derived from cell survival curves generated from uniform irradiation, and therefore we must be cautious when using the BED concept.
The high heterogeneity of target dose can be anticipated in MammoSite plans because an Ir-192 source mostly located at the center of the balloon yields a spherically shaped dose distribution with a gradual dose fall-off. (28) Ingeneral,theaveragedoseismorethan200%ofthe prescribed dose at the surface of the balloon and it is gradually reduced to the prescribed dose at the1cmexpansionofballoonsurface.Hence,themaximumdoseinthetargetisalwaysmore than200%oftheprescribeddoseforMammoSiteplanning.Astheα/β ratio is increased from 2 Gy to 11 Gy, the standard deviation of BED value (from the H-method) between patients was reducedfrom7%to2%(Table4).Thiscanbeinterpretedtomeanthattargetdoseheterogeneity in MammoSite plans is less patient-dependent for early effects than late effects.
Although the inhomogeneity of the target volume was accounted for in the BED calculation,onecannotexplaintheradiationdoseresponseandpredicttheclinicaloutcomesexactly basedonthecomputedBEDvalue.Thissimplifiedmathematicalmodelcannotdescribeall tissue responses to a given radiation dose. In addition, the biologic parameters such as α/β ratio, α value and value of T eff used in the BED calculation have intrinsic uncertainty even though the values used in this work were based on clinical data in the literature. Despite these limitations,theBEDmodelisthebestavailabletoolwehaveatpresent.Anextensiveclinical follow-up study, such as the NSABP B-39 / RTOG 0413 protocol, will afford a greater opportunity to assess the computed BED values and correlate these with clinical outcomes. However, the computed BED values from the protocol will be based on the uniform dose distributionbecauseitisverydifficulttoaccountfortheheterogeneousdosedistributionforthe multi-institutional protocol patients.

V. concLuSIonS
The BED calculation accounting for nonuniform dose distribution is more clinically relevant compared to the conventional simple method, assuming uniform dose distribution across the target volume. By disregarding high inhomogeneity in HDR brachytherapy, the conventional calculationtendstooverestimatetheBEDforfibrosiswhileitunderestimatestheBEDfor erythemaanddesquamation.BasedontheBEDanalysisforgivenα/β values, the interfraction physical dose variations due to the changes of balloon shape and location in MammoSite HDR brachytherapycanproduceBEDdifferenceby10%(asinglefractionoutoftotal10fractions) foraspecificpatienteventhoughtheaveragedifferencefor19patientswaslessthan0.7Gy.