Monte Carlo and TLD dosimetry of an 192 Ir high dose-rate brachytherapy sourceP. Karaiskos, A. Angelopoulos, L. Sakelliou, P. Sandilos, C. Antypas, L. Vlachos, and E. Koutsouveli

Citation: Medical Physics 25, 1975 (1998); doi: 10.1118/1.598371 View online: http://dx.doi.org/10.1118/1.598371 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/25/10?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Dosimetry comparison of 192 Ir Sources Med. Phys. 29, 2239 (2002); 10.1118/1.1508378 Technical note: Monte-Carlo dosimetry of the HDR 12i and Plus 192 Ir sources Med. Phys. 28, 2586 (2001); 10.1118/1.1420398 Erratum: “Fitted dosimetric parameters of high dose-rate 192 Ir sources according to the AAPM TG43 formalism”[Med. Phys. 28(4), 654–660 (2001)] Med. Phys. 28, 1964 (2001); 10.1118/1.1398562 Dosimetry close to an 192 Ir HDR source using N-vinylpyrrolidone based polymer gels and magnetic resonanceimaging Med. Phys. 28, 1416 (2001); 10.1118/1.1382603 Fitted dosimetric parameters of high dose-rate 192 Ir sources according to the AAPM TG43 formalism Med. Phys. 28, 654 (2001); 10.1118/1.1359438

Monte Carlo and TLD dosimetry of an 192Ir high dose-ratebrachytherapy source

P. Karaiskos,a) A. Angelopoulos,b) and L. SakelliouNuclear and Particle Physics Section, Physics Department, University of Athens, Panepistimioupolis, Ilisia,157 71 Athens, Greece

P. Sandilos, C. Antypas, and L. VlachosDepartment of Radiology, Medical School, University of Athens, Areteion Hospital, 76 Vas. Sofias Avenue,115 28 Athens, Greece

E. KoutsouveliMedical Physics Department, Hygeia Hospital, Kiffisias Ave. 24 Erythroy Stavrou, Marousi,151 23 Athens, Greece

~Received 12 December 1997; accepted for publication 17 July 1998!

An analytical Monte Carlo simulation code has been used to perform dosimetry calculations aroundan 192Ir high dose-rate brachytherapy source utilized in the widely used microSelectron afterloadedsystem. Radial dose functions, dose rate constant and anisotropy functions, utilized in the AAPMTask Group 43 dose estimation formalism, have been calculated. In addition, measurements ofanisotropy functions using LiF TLD-100 rods have been performed in a polystyrene phantom tosupport our Monte Carlo calculations. The energy dependence of LiF TLD response was investi-gated over the whole range of measurement distances and angles. TLD measurements and MonteCarlo calculations are in agreement to each other and agree with published data. The influence ofphantom dimensions on calculations was also investigated. Radial dose functions were found todepend significantly on phantom dimensions at radial distances near phantom edges. Deviations ofup to 25% are observed at these distances due to the lack of full scattering conditions, indicatingthat body dimensions should be taken into account in treatment planning when the absorbed dose iscalculated near body edges. On the other hand, anisotropy functions do not demonstrate a strongdependence on phantom dimensions. However, these functions depend on radial distance at anglesclose to the longitudinal axis of the source, where deviations of up to 20% are observed. ©1998American Association of Physicists in Medicine.@S0094-2405~98!00310-1#

Key words: 192Ir, high dose rate brachytherapy, anisotropy, Monte Carlo, TLD

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I. INTRODUCTION

The use of192Ir sources in high dose-rate~HDR! remotelyafterloaded brachytherapy treatments has greatly increasrecent years and a variety of such sources are commercavailable.1 In these treatments a single high-strength~1–10Ci! cylindrical 192Ir source, welded to the end of a transfcable, is utilized. The subject of this work is an192Ir HDRsource~Mallinckrodt Diagnostica, The Netherlands! utilizedin the widely used Nucletron microSelectron HDR remoafterloader.

192Ir emits a wide spectrum of relatively low energiemostly in the range of 201–884 keV with an average val2

of 360 keV, and has a relatively high atomic numberZ577). The dose distribution around this source dependsboth source dimensions and encapsulation and tends thighly anisotropic mainly due to the absorption of the phtons within the high density source material (r522.42 g cm23) and second due to the absorption in tsource capsule. Anisotropy is further distorted due topresence of the steel cable needed to drive the sourcethough its clinical use requires an extensive base of dositry data, mainly in terms of anisotropy functions, relativefew data are available for the given192Ir source design.1,3–7

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The experimental determination of such data at clinicainteresting short distances is difficult and may involve laruncertainties due to the large dose rate gradients in thecinity of the source combined with the finite size of dosimeters, the energy dependence of dosimeters response anneed of accurate determination of measurement distanThe Monte Carlo~MC! simulation of the treatment can significantly reduce these experimental uncertainties andprovide the required accurate calculations.5,8,9

In this work, an MC simulation code incorporating,detail, the construction and dimensions of the192Ir microSe-lectron HDR source has been used for the determinationall necessary dosimetry data. In addition, an experimeverification of anisotropy function calculations has been pformed in a limited range of radial distances using LiF TLD100 rods.

II. MATERIALS AND METHODS

A. Radioactive source

The internal construction and dimensions of the souinvestigated are presented in Fig. 1. The active source csists of a 0.60 mm in diameter by 3.5 mm long cylinder

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pure iridium metal within which the radioactive materialuniformly distributed. It is encapsulated in stainless steelwelded to a steel cable. The capsule is 5 mm long andmm in overall diameter and its distal end is a steel cap wa 0.55 mm radius.

B. Dose calculation formalism

The dose calculation formalism proposed by AAPM TaGroup 43 has been followed.10 Dose rate,D(r ,u), in me-dium at point (r ,u), wherer is the distance in cm from theactive source center andu is the polar angle relative to thlongitudinal axis of the source, is expressed as:

D~r ,u!5SkLG~r ,u!

G~r 0 ,u0!F~r ,u!g~r !, ~1!

where Sk is the source air kerma strength in units of(1 U51 mGy m2 h2151 cGy cm2 h21).

L is the dose-rate constant defined as the dose rate inmedium per unit source strength at radial distancer 0

51 cm along the transverse axis,u05p/2,

L5D~r 0 ,u0!/Sk . ~2!

G(r ,u) is the geometry function in units of cm22, whichaccounts for the variation of relative dose due only tospatial distribution of activity within the source ignorinphoton absorption and scattering in the source structuredistances greater than approximately 2–3 times the acsource dimension~i.e., for the given source greater than aproximately 1 cm! the geometry function is well approximated~within 1%! by the inverse square law used in poisource approximation.11

g(r ) is the dimensionless radial dose function, which acounts for photon attenuation and scattering in the medand encapsulation along the transverse axis (u05p/2) and isby definition unity atr 051 cm, i.e.,g(1)51,

g~r !5D~r ,u0!G~r 0 ,u0!

D~r 0 ,u0!G~r ,u0!. ~3!

F(r ,u) is the dimensionless dose anisotropy functiowhich accounts for photon attenuation and scattering atpolar angleu, relative to that foru05p/2, and is by defini-tion unity atu05p/2, i.e.,F(r ,p/2)51,

FIG. 1. Internal construction and dimensions of192Ir microSelectron HDRsource. The figure is not to scale.

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F~r ,u!5D~r ,u!G~r ,u0!

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An equivalent dose calculation formalism in terms of ttissue attenuation factor,T(r ), is also used in manycomputer-assisted brachytherapy treatment plannsystems:10

D~r ,u!5Skf1

r 2 T~r !F~r ,u!. ~5!

In this expression the productLg(r ) of Eq. ~1! has beenreplaced by the productf T(r ). The factorf is the air kermain air to water kerma in air conversion factor which is equto the ratio of mean mass energy absorption coefficientswater and air. This ratio is almost constant and has a valu1.11 for energies between 150 keV and 4 MeV.12 Thus, f isalso equal to 1.11 for the192Ir primary energy range. ThefactorT(r ) is well approximated by the ratio of water kermin water to water kerma in air and accounts for the combinattenuation and scattering in water.10,13It is noted that for thegiven source the formalism of Eq.~5! is valid at radial dis-tances greater than approximately 1 cm where, as mentioabove, the geometry factorG(r ,u) is well approximated bythe inverse square law.

C. Monte Carlo simulation code

An analytical MC simulation code9,14 was used to calcu-late the dose-rate distribution in water around the microlectron HDR192Ir source.

An analytical tracking is performed for every primarphoton initiated in a random position and emitted in a radom direction within the source. Primary and secondary pduced photons are sampled individually in direct analogythe main processes, namely photoabsorption, coherentincoherent scattering. The tracking and interactions of ptons are based on up-to-date and self-consistent total, paand differential cross sections,12,15–19and the procedure outlined by Chan and Doi20 for the sampling of coherent anincoherent scattering. The electron binding energy ofscattering atom is taken into account in the incoherent stering process. For electrons, the continuous slowing doapproximation~CSDA! is followed.21–24 For the necessarycontinuous interpolations Newton’s divided difference fomula ~DIVDIF, CERN Computer Program Library! with anaccuracy of the order of 1% is used.

The code incorporates the detailed construction andmensions of the source including source encapsulationtransfer cable. All stainless steel components~capsule andcable! were approximated by the composition1 of AISI 304~by weight, 2% Mn, 1% Si, 19% Cr, 10% Ni and 68% Fe!,which has a density of 8.02 g cm23. To speed up calculations, the source was positioned at the center of a sphephantom although the code can handle a variety of phangeometries. The diameter of the phantom was chosen t30 cm so that our results can be compared directly to Wiamson and Li1 calculations. However, calculations for pha

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toms with other diameters were also performed to investigthe influence of phantom dimensions on calculations. Evprimary and secondary photon is tracked through the sphcal phantom which is divided into discrete concentric sphcal shells of 1 mm thickness, each split into angular intervof up to 2°. In this way the phantom is finally divided inlarge number of very small volumes~voxels!. In these vox-els, quantities such as the number and kind of interactiothe energy transferred to electrons by primary and/or secoary interactions, photon spectra, as well as the primary, stered and total energy deposition are scored. Using thquantities, absorbed dose, air kerma, water kerma, doseisotropy function and radial dose function can be calculafor all voxels in a single run. Due to the small dimensionsvoxels, the above quantities are considered to refer topoints located at their centers. Thus, doseD(r ,u) at a point(r ,u) in the phantom is calculated by dividing the enerdeposition within the voxel centered at this point by tvoxel mass.

The calculation of energy deposition was performedther directly from the electron energy deposition within tvoxel volume,9,14 or from the photon energy fluence usinthe equation:

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Ei~men /r!Eil i , ~6!

whereE is the energy deposition,Ei is the energy of thei thphoton, (men /r)Ei is the mass energy absorption coefficieof the absorbing medium at energyEi andl i the track lengthof the photon within the voxel.25,26 For the energies considered in this work both of the above mentioned methods gresults within statistical errors, with the first method, hoever, being time consuming. In order to speed up calctions all the presented results were generated using theond method based on the photon energy fluence calculatand for at least 108 primary photons yielding statistical error,1%.

D. TLD measurements

To support our MC calculations, anisotropy measuments were performed in a polystyrene phantom usingTLD-100 rods27,28 ~1 mm in diam and 6 mm long! calibratedin a 6 MV x-ray linear accelerator. The thermal treatmeconsisted of a pre-irradiation annealing of 400 °C for 1 h and100 °C for 2 h aswell as a post-irradiation annealing o100 °C for 10 min, prior to their read out. The reading wperformed using a Harshaw 2000 B-C TLD System.

TLDs were placed in small cylindrical TLD polystyrenreceptors~3 mm in diam and 6 mm long! having a cylindri-cal hole of 1 mm in diameter in their centers to accommodthe dosimeters. A 3033031.1 cm3 slab of polystyrene, prepared in a milling machine with an accuracy of 0.1 mm, wconstructed to accommodate TLD receptors and a placatheter~2 mm in outer diameter! inside which the source isdriven. This slab was sandwiched between other identpolystyrene slabs to build a 30330330 cm3 phantom whichapproximates the water spherical phantom of 30 cm in dia

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eter used in MC calculations. To accommodate TLD rectors, holes were prepared along polar anglesu50° – 165° atradial distancesr 51.5, 3.0, 5.0 and 7.0 cm from the origiof the coordinate system which was set at the center ofmachined slab. The centers of the holes, along with thathe source, were placed on the same plane containinglong axis of the source, with the long axes of the holes ppendicular to the plane and the long source axis. To avinterTLD attenuation effects, polar TLD measurements wperformed separately for each radial distance; TLDs wplaced within their receptors along the polar angles atdistance of measurement while the holes of TLD receptorthe rest of the radial distance had been filled with solid postyrene cylinders having the same outer dimensions wTLD receptors~Fig. 2!.

The source dwell position was chosen so that the souwas centered at the origin of the coordinate system. Tposition was found radiographically in a way similar withat described by Muller-Runkel and Cho.4 A Kodac X-OMAT V film was placed in close contact with the cathetand the empty holes prepared to accommodate TLD rectors, and was exposed to the source in its actual dwell ption. The source was removed and a second exposureobtained with x-rays from a mobile machine. The developfilms show the source position and the empty holes, frwhich the origin of the coordinate system was found. Tabove method was used for various dwell positions space1 mm to each other and the position which places the souclosest to the origin was found. In this way, the source cenis determined with an accuracy of less than 1 mm.

III. RESULTS AND DISCUSSION

As noted in Sec. I, relatively few publications presenticlinically useful dosimetry data for192Ir microSelectronHDR source are available.1,3–7 Measurements of Thomasoand Higgins,29 Meli et al.,30 Cerra and Rogers,31 Thomasonet al.,32 Nath et al.33 and Wang and Sloboda34 refer to other192Ir source designs. Baltaset al.3 and Mishraet al.7 pub-lished anisotropy functions in water for the given sourceing a miniature ionization chamber. Despite the relativelarge detector volume compared to TLD dimensions, the figroup measured anisotropy functions at polar anglesu

FIG. 2. Experimental arrangement. The figure is not to scale.

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50°–170° and radial distancesr 53, 5 and 7 cm, while thesecond group measured the same quantities at polar au510° – 170° relative to the long axis of the source at rada distancer 55 cm. Muller-Runkel and Cho4 performed an-isotropy measurements in polystyrene and air using TLDradial distancesr 51 – 10 cm at polar angles restricted, however, to645° with respect to the long axis of the sourcWilliamson and Li1 and Kirovet al.5 published an extensivebase of dosimetry data based on MC calculations and Tand diode measurements, including dose-rate constant

FIG. 3. Radial dose functions,g(r ), as a function of radial distance,r , alongthe perpendicular bisector of the source. Our Monte Carlo calculationscalculations of Williamson and Li~Ref. 1!, both performed with192Ir mi-croSelectron HDR source centered at a spherical water phantomd530 cm in diameter, are shown.

TABLE I. Radial dose functions,g(r ), and the combined attenuation anscattering factor,T(r ), calculated with the192Ir microSelectron HDR sourcecentered at a spherical water phantom ofd530 cm in diameter.

Radial distance~cm! g(r ) T(r )

0.1 0.990 0.9950.2 0.993 0.9980.3 0.994 0.9990.5 0.996 1.0010.8 0.998 1.0031.0 1.000 1.0051.5 1.003 1.0082.0 1.004 1.0093.0 1.005 1.0103.5 1.003 1.0084.0 1.000 1.0054.5 0.996 1.0015.0 0.991 0.9966.0 0.979 0.9848.0 0.940 0.94510.0 0.880 0.88512.0 0.800 0.80414.0 0.692 0.69615.0 0.608 0.611

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isotropy functions at distancesr 50.25– 5 cm and polaranglesu50° – 180° relative to the source cable, and raddose functions at distances from 0.25 to 14 cm, in a 30diameter liquid–water sphere with the source positionedits center. Russel and Ahnesjo6 performed MC calculationsbased on EGS4 code, of the same quantities in a water ptom with infinite dimensions at distancesr 51 – 20 cm, with-out, however, taking into account the electron binding eergy of the scattering atom in the incoherent scatterprocess.

A. Monte Carlo calculations

The quantities needed for the calculation of dose distrition according to AAPM TG 43@Eq. ~1!#, such as dose-rateconstant, radial dose functions and anisotropy functionswell as the values of the factorT(r ) of the widely usedformalism of Eq.~5!, have been calculated according to tprocedure outlined in Sec. II C. The192Ir HDR source wascentered in a variety of spherical water phantoms in ordeinvestigate the influence of phantom dimensions on calctions.

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FIG. 4. Radial dose functions,g(r ), as a function of radial distance,r ,calculated by our code with the192Ir microSelectron HDR source centereda spherical water phantom of different diameters (d510– 50 cm). Experi-mental data of Meisbergeret al. ~Ref. 13! performed using a different192Irsource design centered at a 25325330 cm3 water phantom and MonteCarlo calculations of Russel and Ahnesjo~Ref. 6! performed using the192IrmicroSelectron HDR source centered at an unbounded water phantomalso been plotted for comparison.

TABLE II. Dose-rate constants,L, for the 192Ir microSelectron HDR source

Author L (cGy h21 U21)

Williamson and Li~Ref. 1! 1.115 (60.5%)Kirov et al. ~Ref. 5! 1.143 (65%)Russel and Anhesjo~Ref. 6! 1.131 (61%)This study 1.116 (60.5%)

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1. Radial dose functions and dose-rate constant

Our calculations of radial dose functions,g(r ), at radialdistances,r 50.1– 15 cm, for a spherical phantom ofd530 cm in diameter, are presented in Table I and Fig. 3.it can been seen from Fig. 3, our results are in excelagreement with MC calculations of Williamson and Li,1 per-formed for the same source design and for the same sphewater phantom. In Table I, we also present the results ofcombined attenuation and scattering factorT(r ) of Eq. ~5!.As expected, the only difference between these valuesthe values ofg(r ), is the normalization of the latter at 1 cmsince10 g(r )5T(r )/T( l ).

The dose-rate constant,L, was calculated to be (1.1160.006) cGy h21 U21. This value is presented in Tablealong with the corresponding ones available in the literatfor the given source design. Again excellent agreemenobserved.

In Fig. 4, radial dose functions calculated for spheriwater phantoms of different diameters (d510– 50 cm) arepresented. The MC calculations of Russel and Ahnesjo6 ofthe same192Ir source design performed in infinite phantodimensions, as well as the widely used data of Meisberet al.13 for a different source design and phantom dimesions, are also shown for comparison@the data of Meisbergeet al. refer to the values of the factorT(r ) and have beennormalized at 1 cm in order to be comparable with the valof the radial dose functions,g(r )#. The figure demonstratethat phantom dimensions affect significantly the radial d

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functions at radial distances near phantom edges, whereviations of up to 25% are observed. This effect is due toreduction of scatter contribution to overall dose at the edof the phantom and should be taken into account in the cof estimating the dose near body edges. The above obsetion is in agreement with measurements of Vanselaaret al.35

performed for the same source design and with MC calcutions of Williamson and Li1 applied for the pulse dose-rat~PDR! 192Ir microSelectron source. The use of 3D dose planing techniques which can accurately determine sourcesition and body contour, in combination with the use of tappropriate phantom for the calculation of the radial dofunctions, can significantly improve dose determination nbody edges.

The present calculations for both radial dose functioand dose-rate constant, are in good agreement~within 2%!with previous calculations performed by our group9,14 as-suming an192Ir point source. They also agree~within 3%!with recent calculations concerning different192Ir sourcedesigns,29,32–34,36as well as with the old data of Meisbergeet al.13 considering similar phantom dimensions. This obsvation suggests that source dimensions and encapsulationot significantly affect the values of the dose-rate constand the radial dose functions.

2. Anisotropy functions

Our calculations of the anisotropy functions,F(r ,u), atradial distances r 50.1– 15 cm, at polar anglesu

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TABLE III. Anisotropy functions,F(r ,u), calculated for the192Ir microSelectron HDR source.

Polar angle~degrees! 0.25 cm 0.5 cm

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179.0 0.573 0.630 0.693 0.715 0.732 0.73175.9 0.533 0.620 0.675 0.742 0.786 0.761 0.7173.0 0.654 0.675 0.695 0.731 0.770 0.802 0.799 0.8170.9 0.683 0.689 0.706 0.726 0.756 0.791 0.824 0.815 0.169.3 0.721 0.727 0.741 0.758 0.787 0.810 0.843 0.835 0.164.3 0.813 0.811 0.813 0.824 0.835 0.852 0.866 0.886 0.882 0159.6 0.866 0.864 0.865 0.869 0.874 0.887 0.898 0.913 0.908 0149.6 0.928 0.927 0.927 0.929 0.930 0.936 0.941 0.953 0.944 0139.7 0.959 0.958 0.959 0.958 0.960 0.963 0.966 0.972 0.966 0129.6 0.978 0.978 0.977 0.978 0.977 0.980 0.982 0.985 0.981 0119.2 0.990 0.990 0.989 0.989 0.989 0.990 0.989 0.992 0.992 0109.7 0.996 0.995 0.996 0.995 0.996 0.998 0.997 0.996 0.996 099.4 0.999 0.998 0.999 0.998 0.998 0.998 1.001 1.001 1.000 0.89.3 1.001 1.002 1.001 1.001 1.001 1.000 1.000 1.002 1.000 1.79.2 1.000 1.000 1.000 0.999 0.998 0.999 0.998 1.000 1.000 0.70.3 0.995 0.994 0.995 0.995 0.994 0.995 0.994 0.996 0.997 0.59.2 0.988 0.988 0.987 0.988 0.987 0.989 0.987 0.989 0.992 0.50.4 0.976 0.976 0.975 0.976 0.976 0.978 0.979 0.979 0.980 0.40.3 0.957 0.956 0.956 0.958 0.959 0.964 0.965 0.966 0.967 0.30.4 0.927 0.925 0.921 0.928 0.932 0.938 0.943 0.945 0.947 0.19.5 0.848 0.842 0.844 0.863 0.861 0.875 0.888 0.889 0.901 0.14.6 0.787 0.785 0.791 0.798 0.810 0.830 0.855 0.855 0.866 0.12.2 0.760 0.751 0.760 0.771 0.788 0.812 0.839 0.841 0.851 0.9.1 0.735 0.733 0.734 0.749 0.773 0.795 0.828 0.836 0.845 0.7.0 0.724 0.720 0.725 0.740 0.762 0.787 0.820 0.829 0.839 0.4.1 0.715 0.711 0.715 0.731 0.751 0.778 0.811 0.821 0.830 0.0.0 0.711 0.708 0.711 0.727 0.748 0.775 0.788 0.817 0.826 0.

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50°–179° relative to the long axis of the source, for a phtom of d530 cm in diameter, are presented in Table III.Fig. 5~a! our results for three selected radial distancesr50.5, 5 and 15 cm, are plotted as a function of polar anu, relative to the long axis of the source. These data revthat anisotropy is nearly independent of radial distancepolar angles 30°,u,150°. However, at polar angles closto the longitudinal axis of the source, a significant depdence on both the radial distance,r , and the polar angle,u,due to the oblique filtration of the source, is observed. Dviations in anisotropy functions of up to 20% are observfor the same polar angle, at different radial distances of u5 cm. As the radial distance from the source increasesanisotropy function increases due to the increasing contrtion of scattered radiation in water which compensatesthe attenuation of primary radiation in the source andencapsulation. This result is clearly demonstrated in Fig. 5~b!where the ratio of the scatter dose~i.e., the dose only due toscattered radiation! to the total dose~i.e., the dose due to

FIG. 5. ~a! Anisotropy functions,F(r ,u), as a function of polar angle,u,relative to the long axis of the source, derived from our code at radistancesr 50.5, 5 and 15 cm from the192Ir microSelectron HDR sourcecentered at a spherical water phantom ofd530 cm in diameter.~b!Dscat/D tot , i.e., the ratio of scatter to total~primary and scatter! dose, as afunction of radial distance,r , at polar anglesu590° and 0°.

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both primary and scattered radiation!, Dscat/D tot , is plottedas a function of radial distance,r , at polar angles 90° and 0relative to the long axis of the source.

Figures 6~a!, 6~b! and 6~c! present our anisotropy data aradial distancesr 51, 5 and 9 cm, respectively, along witdata available in literature,1,3,4,6,7for comparison. An overallgood agreement between the different data sets is obseOur results agree within 3%, with MC calculations of Wiliamson and Li,1 at polar anglesu510° – 180°, while devia-tions of 10%–20% are observed at angles near 0°. Howeour calculations for these angles are closer to the experimtal data of Baltaset al.,3 Mishra et al.7 and Muller-Runkeland Cho4 and MC calculations of Russel and Ahnesjo.6

It must be mentioned that anisotropy data must be uwith caution concerning the specification of polar angleu.Williamson and Li1 and Kirov et al.5 specify angleu as theangle relative to source cable with the angle 180° on the sof the distal end of the source and the angle 0° on the sidthe source cable. In all the other available studies,3,4,6,7angleu has been specified as the angle relative to the long axithe source with the angle 0° on the side of the distal endthe source and the angle 180° on the side of the source cIn this work, the second specification is followed~Fig. 2!. Inthe presented figures the data of Williamson and Li1 havebeen properly modified concerning the angleu.

The influence of phantom dimensions on anisotropy futions is presented in Fig. 7. The data refer to calculationa radial distancer 510 cm for spherical phantoms of different diameters~20, 30 and 40 cm!. Our results show thaanisotropy functions do not demonstrate a strong dependon phantom dimensions and to our knowledge, no previstudy concerning this influence has been reported in theerature.

B. TLD measurements

Measurement data are the average of three measuremperformed in each radial distance. Taking into accountstandard deviations of the calculated mean values (<3%)and the uncertainties in TLD positions (,1 mm), an overallerror of the order of 3% was estimated.

The radial and directional~angular! variation of the re-sponse of LiF TLD per unit dose to water, over the whorange of measurement distances and angles, were invgated using the photon and generated electron spectra clated by our MC code. According to Burlin cavity theory,37

LiF TLD response is given by the equation:

DLiF TLD

Dwater5dS S

r Dwater

LiF

1~12d!S men

r Dwater

LiF

, ~7!

where(men /r)waterLiF is the mean mass energy absorption c

efficient ratio for LiF and water, (S/r)waterLiF is the mean mass

collisional stopping power ratio for LiF and water,d is aweighting factor which gives the contribution to the dosethe TLD cavity from electrons generated in water and2d) is the contribution to the dose in the TLD cavity from

l

rses

D,

nethe

ro-ofbeent

ityted

nc

ncecal

1981 Karaiskos et al. : Monte Carlo and TLD dosimetry 1981

FIG. 6. Anisotropy functions,F(r ,u), as a function of polar angle,u, rela-tive to the long axis of the source, calculated by our code at radial dista~a! r 51 cm, ~b! r 55 cm and~c! r 59 cm from the192Ir microSelectronHDR. Monte Carlo calculations of Williamson and Li~Ref. 1! and Russeland Ahnesjo~Ref. 6!, as well as experimental data of Baltaset al. ~Ref. 3!Mishra et al. ~Ref. 7!, and Muller-Runkel and Cho~Ref. 4! have also beenplotted, where available.

Medical Physics, Vol. 25, No. 10, October 1998

electrons generated by photon interactions in it. The factodgradually changes from 1 to 0 as the cavity size increaand it is given by the equation:

d512ebL

bL, ~8!

where L is the pathlength of electrons entering the TLconsidered as four times the TLD volume (V) divided by itssurface density (S), (L54V/S), while the quantityb can beevaluated using the empirical formula:38

exp~2bR!50.04, ~9!

where R is the maximum depth of electron penetratiowhich, for the low-Z TLD material, can be taken as thCSDA electron range for the average starting energy ofelectrons generated in the TLD material.

Using our MC code and the CSDA electron ranges pposed by ICRU39 Report 37, the average starting energythe electrons generated in the TLD material was found toless than 100 keV over the whole range of measuremdistances and angles, and the correspondingR less than0.006 cm, thus giving the value of factord less than 0.02. Asa result of this, the TLD material behaves like a large cavin 192Ir g-rays and the LiF TLD response can be calculausing the simplified equation:

DLiF TLD

Dwater5S men

r Dwater

LiF

5(i

Ei S men

r DEi ,LiF

Y (i

Ei S men

r DEi ,water

,

~10!

es

FIG. 7. Anisotropy functions,F(r ,u), as a function of polar angle,u, rela-tive to the long axis of the source, derived from our code at radial distar 510 cm with the192Ir microSelectron HDR source centered at a spheriwater phantom of different diameters (d510, 15 and 20 cm).

.

1982 Karaiskos et al. : Monte Carlo and TLD dosimetry 1982

FIG. 8. Photon spectra at radial distancesr 51 and 10cm at polar anglesu590° and 0°, relative to the longaxis of the source, calculated by our simulation code

n

rg

gesion

ofct

is

yl

ct

ono

riath

%

a-c

ec-ergye-asles

nge

Dentsfrac-ateri-

ame

atantra-

70°dd in

atad at

where Ei is the energy of thei th photon in the point ofmeasurement, (men /r)Ei,LiF is the mass energy absorptiocoefficient of LiF at energyEi and (men /r)Ei,water is themass energy absorption coefficient of water at this eneEi .

The above conclusion is in agreement with Mobitet al.40

who found that a LiF TLD rod behaves more like a larrather than a small cavity even forg-ray energies as high athose of60Co and they conclude that a simple approximatis to assume that the TLD response in60Co g-rays is givenby Eq. ~10!. Therefore, the investigation of the variationTLD response is performed by weighing the photon specalculated by our MC code according to Eq.~10!.

A shift of the photon spectrum to the lower energiesobserved as radial distance increases~Fig. 8!. In addition, thespectra at different angles of the same radial distance madifferent due to the different filtration of the cylindricasource~this can also be seen in Fig. 8 where photon speat radial distances of 1 and 10 cm and polar anglesu50°and 90° are presented!. Since the mass energy absorpticoefficient ratio of LiF to water changes significantly at phton energies less than 150 keV,17 the ratio of Eq.~10! isexpected to vary with distance and maybe with angle.

The radial variation of this ratio and the subsequent vation in TLD response was found to be less than 3% overwhole range of radial distances (r<15 cm) @Fig. 9~a!#. Mei-gooni et al.41 and Thomason and Higgins29 found the radialvariation of TLD response up to 8.5% and less than 1respectively.

However, to our knowledge, there are no published davailable on the directional~angular! dependence of the energy spectrum and of the TLD response. In this work, on

Medical Physics, Vol. 25, No. 10, October 1998

y

ra

be

ra

-

-e

,

ta

e

more by means of the weighted MC calculated photon sptra and the ratio of Eq.~10!, an estimation of this dependencis performed. The variation of the weighted mass eneabsorption coefficient ratio of LiF to water and the subsquent variation of TLD response per unit dose to water wfound less than 1%, over the whole range of polar ang(0° – 180°) at the same radial distance, for the whole raof radial distances@Fig. 9~b!#.

Corrections for radial or directional dependence of TLresponse have not been applied on the TLD measuremsince their variation (,3%) is less than the overall error othe measurements~3%!. No corrections were also made fothe finite size of dosimeters since the volume correction ftors for TLD rods are less than 1% at radial distances grethan 1 cm.29 Thus, anisotropy functions were calculated drectly from the ratio of TLD reading at polar angleu relativeto the long source axis, over the reading atu590°.

Our measurements are presented in Fig. 10. In the sfigure measurements of Baltaset al.3 and our MC calcula-tions atr 55 cm have also been plotted for comparison. Dof Baltaset al. are used in Plato BPS, Nucletron treatmeplanning system. They measured anisotropy functions atdial distances of 3, 5 and 7 cm and at angles of 0° – 1using a 0.1 cm3 ionization chamber. Their results were fitteand the average fitted values presented in Fig. 10 are usePlato BPS independently of radial distance. Our TLD dalso present the averaged anisotropy functions measurethe same radial distances~3, 5 and 7 cm! for direct compari-son, and are consistent with both Baltaset al. measurementsand our MC calculations.

romfo

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omsioa

to

ncth-rcm

ng

D-re-ure-n 3%

inub-

ndtheicalnnisthe

hys-po-

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er

so

(o

s

dial

is-also

1983 Karaiskos et al. : Monte Carlo and TLD dosimetry 1983

IV. CONCLUSIONS

Radial dose functions, dose-rate constant and anisotfunctions used in the dose calculation formalism recomended by AAPM Task Group 43 have been calculated,the192Ir microSelectron high dose-rate brachytherapy souusing our analytical MC simulation code.

Radial dose functions depend significantly on phantdimensions near the edge of the phantom where deviationup to 25% are observed. On the other hand, these functdo not indicate strong dependence on source dimensionsencapsulation.

The dose-rate constant is also independent of phandimensions and source design.

Anisotropy functions do not indicate a strong dependeon radial distance and polar angle, for polar angles inrange 30°,u,150°. However, they vary with radial distance at polar angles close to the long axis of the souwhere variations of up to 20% are observed, for the sa

FIG. 9. ~a! Mean mass energy absorption coefficient ratio of LiF to watSEi(men /r)Et,LiF /SEi(men /r)Ei,water, derived by weighting the photonspectra, calculated by our Monte Carlo code, with the mass energy abtion coefficient ratio of LiF to water, (men /r)LiF /(men /r)water, as a functionof radial distance,r , along the perpendicular bisector of the sourceu590°). ~b! The same ratio, calculated in the same way, as a functionpolar angle,u, relative to the long axis of the source, at radial distancer51, 5 and 15 cm.

Medical Physics, Vol. 25, No. 10, October 1998

py-r

e,

ofnsnd

m

ee

e,e

polar angle at different radial distances up to 5 cm. No strodependence on phantom dimensions is observed.

Anisotropy functions were also measured using LiF TL100 rods. The radial and directional dependence of TLDsponse were investigated over the whole range of measment distances and angles and were found to be less thaand 1%, respectively.

Monte Carlo calculations and TLD measurements areagreement to each other and agree with the available plished data.

ACKNOWLEDGMENTS

The authors wish to thank Professor A. Apostolakis aS. Tatsis for their most valuable assistance in preparingexperimental arrangement and H. Papanikolaou for technassistance. Our great appreciation goes to Dr. K. Sarigiafor his useful comments and assistance concerningMonte Carlo calculations.

a!Electronic mail: pkaraisk@cc.uoa.grb!Corresponding author: Angelos Angelopoulos, Nuclear and Particle P

ics Section, Physics Department, University of Athens, Panepistimioulis, Ilisia, 157 71 Athens, Greece. Electronic mail: aangelop@cc.uoa.

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,

rp-

f

FIG. 10. Averaged values of our TLD anisotropy measurements at radistances ofr 53, 5 and 7 cm. Our Monte Carlo calculations atr 55 cm, aswell as Baltaset al. ~Ref. 3! averaged measurements, at same radial dtances, used in Nucletron treatment planning system PLATO BPS, havebeen plotted for direct comparison.

-

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is,at

Sen,’

g,

n c20

ua37

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to6

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n c

on

os

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edrt,’’

s-t.

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on

u,ce,’’

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-.

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37

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f,’’

1984 Karaiskos et al. : Monte Carlo and TLD dosimetry 1984

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