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The collapsed cone algorithm for 192Ir dosimetry using phantom-size adaptive multiplescatter point kernels
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Phys. Med. Biol. 60 5313 (http://iopscience.iop.org/0031-9155/60/13/5313) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 130.133.8.114 This content was downloaded on 30/06/2015 at 19:35
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 60 (2015) 5313–5323
Physics in Medicine & Biology doi:10.1088/0031-9155/60/13/5313
The collapsed cone algorithm for 192Ir dosimetry using phantom-size adaptive multiple-scatter point kernels Åsa Carlsson Tedgren1, Mathieu Plamondon2 and Luc Beaulieu2 1
Department of Medical and Health Sciences (IMH) and Center for Medical Image Science and Visualization, Radiation Physics, Linköping University, SE-581 85 Linköping, Sweden and Department of Medical Physics, Karolinska University Hospital, SE 171 76 Stockholm, Sweden 2 Département de Radio-Oncologie et Axe oncologie du Centre de recherche du CHU de Québec, CHU de Québec, Québec, Québec G1R 2J6, Canada and Département de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec, Québec G1V 0A6, Canada E-mail: [email protected] Received 28 January 2015, revised 12 May 2015 Accepted for publication 18 May 2015 Published 24 June 2015 Abstract
The aim of this work was to investigate how dose distributions calculated with the collapsed cone (CC) algorithm depend on the size of the water phantom used in deriving the point kernel for multiple scatter. A research version of the CC algorithm equipped with a set of selectable point kernels for multiple-scatter dose that had initially been derived in water phantoms of various dimensions was used. The new point kernels were generated using EGSnrc in spherical water phantoms of radii 5 cm, 7.5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm. Dose distributions derived with CC in water phantoms of different dimensions and in a CT-based clinical breast geometry were compared to Monte Carlo (MC) simulations using the Geant4based brachytherapy specific MC code Algebra. Agreement with MC within 1% was obtained when the dimensions of the phantom used to derive the multiple-scatter kernel were similar to those of the calculation phantom. Doses are overestimated at phantom edges when kernels are derived in larger phantoms and underestimated when derived in smaller phantoms (by around 2% to 7% depending on distance from source and phantom dimensions). CC agrees well with MC in the high dose region of a breast implant and is superior to TG43 in determining skin doses for all multiple-scatter point kernel sizes. Increased agreement between CC and MC is achieved when the point kernel is comparable to breast dimensions. 0031-9155/15/135313+11$33.00 © 2015 Institute of Physics and Engineering in Medicine Printed in the UK
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The investigated approximation in multiple scatter dose depends on the choice of point kernel in relation to phantom size and yields a significant fraction of the total dose only at distances of several centimeters from a source/implant which correspond to volumes of low doses. The current implementation of the CC algorithm utilizes a point kernel derived in a comparatively large (radius 20 cm) water phantom. A fixed point kernel leads to predictable behaviour of the algorithm with the worst case being a source/implant located well within a patient/phantom for which low doses at phantom edges can be overestimated by 2–5 %. It would be possible to improve the situation by using a point kernel for multiple-scatter dose adapted to the patient/phantom dimensions at hand. Keywords: 192Ir, model-based dose calculation algorithms, collapsed cone superposition, multiple scatter, point kernel (Some figures may appear in colour only in the online journal) I. Introduction Model-based dose calculation algorithms (MBDCAs) capable of performing three-dimensional (3D) dose calculations have long been used to account for patient tissue heterogeneities in planning external beam radiotherapy (EBRT) (see, e.g. Ahnesjö and Aspradakis 1999). Dose calculations for planning brachytherapy (BT) treatments are, however, still generally performed according to the TG43 formalism (Rivard et al 2004), thus assuming that both patient and applicator geometries consist of extended water. Interest in using MBDCAs for BT has recently increased, see e.g. the review by Rivard et al (Rivard et al 2009), the report from AAPM Task Group No. 186 (Beaulieu et al 2012) and the book chapter by Carlsson Tedgren et al (Carlsson Tedgren et al 2012). BT covers the energy region from around 20 keV to about 400 keV, in which the dominant photon interaction process in soft tissue changes from photoelectric absorption to Compton scattering. Effects of changing from the TG43 approach to dose calculations by MBDCAs will therefore be considerably higher at low (50 keV) BT energies. The commonly-used isotope 192Ir has a mean photon energy of around 400 keV, at which energy photon interactions are predominantly taking place by Compton scattering and mass energy absorption coefficients of various soft tissues thus vary by only a few percent. The main dosimetric advantage of MBDCAs for 192Ir dosimetry over current practice is their ability to account for 3D effects on dose distributions due to scattered photons in, e.g. the vicinity of air-tissue interfaces and in the penumbral regions of high atomic number shields. Recent studies show moderate differences between MBDCAs and TG43 for implants well within the body such as prostate and unshielded GYN treatments (see, e.g. Mikell et al 2012, Desbiens et al 2013). MBDCAs can be expected to increase dosimetric accuracy in accounting for the reduced contribution of dose from scattered photons when implants are located close to patient surfaces in, e.g. breast and head and neck implants (see, e.g. Poon and Verhaegen 2009) and for the 3D effects of shields of high atomic numbers such as those sometimes used with GYN and rectal applicators (Poon et al 2008, Petrokokkinos et al 2011). MBDCA has hitherto only been implemented in commercially available treatment planning systems (TPS) for the isotope 192Ir. The ACUROS® engine (Transpire, Inc., Gig Harbor, WA) (Zourari et al 2013) is available with the Brachyvision TPS ((BV, Varian Medical Systems, Inc., Palo Alto, CA)). The BT version of the collapsed cone (CC) MBDCA (Carlsson and Ahnesjö 2000a, Carlsson Tedgren and Ahnesjö 2003, Russell et al 2005, Carlsson Tedgren and 5314
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Ahnesjö 2008) has been implemented in the Oncentra® Brachy TPS (Elekta Brachytherapy, Veenendaal, the Netherlands) under the name ACE.1 The CC algorithm is a point kernel convolution/superposition algorithm (Ahnesjö and Aspradakis 1999). Such algorithms are principally capable of calculating dose to the medium for primary and once-scattered photons in heterogeneous geometries without approximations to the physics (Mackie et al 1985, Williamson et al 1991, Carlsson and Ahnesjö 2000b). A possible limitation is, however, their somewhat approximate treatment of dose from multiplyscattered photons which stems from the use of a phantom of fixed size in the initial Monte Carlo (MC) generation of the so-called point kernels, that typically causes an overestimation in dose at the phantom edge ((Williamson et al 1991, Carlsson and Ahnesjö 2000b). Dose from multiply-scattered photons add a significant fraction to the total dose at distances 4–6 cm away from 192Ir implants/sources, i.e. in low dose regions which is why this limitation is expected to be of low clinical significance. The worst situations could be that of a source/ implant located centrally in a comparatively small phantom for which there is interest in high dose accuracy at the phantom surface, several centimeters from the implant. A clinical example of this scenario is breast BT. Breast dimensions are smaller than the size of the phantom used for generating the current, fixed multiple-scatter point kernel and, even when sources are implanted relatively deep within the breast, interest in accurate determination of the skin-dose located several centimeters away from the target is still comparatively high. The aim of this work was to investigate results of dose calculations with the CC algorithm in water phantoms of varying dimensions, using a set of different point kernels for multiplescatter, initially derived in water phantoms of different dimensions. An early research version of the ACE algorithm (version 0.4.0) that allowed use of selectable different point kernels was used. The Geant4-based ALGEBRA Monte Carlo (MC) code (Afsharpour et al 2012) was used to derive benchmark dose distributions. Results will be presented for water phantoms of various dimensions as well as for a clinical breast implant. II. Materials and methods II.A. Generation of point kernels for multiple scatter
A set of point kernels for multiple-scatter dose was generated using EGSnrc v V4-r2-3-2 in spherical water phantoms of radii 5 cm, 7.5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm. The point kernels were generated and fitted to double exponential functions following the methodology described in detail by Carlsson and Ahnesjö (Carlsson and Ahnesjö 2000b). Throughout this work we will refer to dose from photons that have scattered more than once outside the source as multiple-scatter dose (the term residual scatter has earlier sometimes been used as a synonym). II.B. Phantoms and patient geometries for dose calculations
The results of the CC algorithm is to be benchmarked against full MC simulations and thus to be performed in the same geometries and for the same source, these are described here. Dose calculations were performed for a MicroSelectron v2 high dose rate (HDR) 192Ir source (Elekta Brachytherapy, Veenendaal, the Netherlands). A set of calculations was performed with the 1 White Paper available at www.elekta.com/dms/elekta/elekta-assets/Elekta-Brachytherapy/oncentra-brachy/ pdfs/888-00638-MKT-5B01-5D-whitepaper-ACE-in-Oncentra-Brachy/Whitepaper:ACE Advanced Collapsed cone Engine.pdf.
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source positioned in the centres of cubic water phantoms of varying dimensions (half-sides of 5 cm, 10 cm, 15 cm, 20 cm and 25 cm). Calculations were also performed for a clinical breast implant based on the retrospective use of DICOM-RT plan information on geometry and source positioning. Values of absorbed dose to medium, Dm,m, were calculated both with CC and MC. II.C. Dose calculations using CC
The version 0.4.0 of the Elekta Collapsed Cone algorithm ACE was used. This version was an early research/test version and by default equipped with a point kernel for multiple scatter generated in a water sphere of radii 50 cm, following the initial version by Carlsson and Ahnesjö (Carlsson and Ahnesjö 2000a). For this study, however, a set of newly-generated multiplescatter point kernels (section II.A) were also available. The MicroSelectron v2 source was implemented using the primary and scatter separation (PSS) formalism for source characterization as described by (Russell et al 2005), using PSS source data from (Taylor and Rogers 2008). The PSS method for characterization of clinical BT sources is based on initial detailed MC simulations of the BT source and is similar to the ‘first-collision source’ described in early applications of the discrete ordinate method for brachytherapy (Daskalov et al 2000), see also the white paper on ACE1. The research version of the CC algorithm used here was set up so that it was possible to study the output of the primary, first- and multiple-scatter dose contributions separately. Scatter generations were defined as described in (Russell et al 2005); a photon is counted as primary until its first interaction outside of the source encapsulation. Transport line tessellations into 1620 directions for the first-scatter and 320 directions for the multiple-scatter dose calculations were used. II.D. Dose calculations using MC
The MC code Algebra (ALgorithm for the heterogeneous dosimetry based on Geant4 for BRAchytherapy) (Afsharpour et al 2012) was used. Algebra’s phase space model of the MicroSelectron v2 192Ir source was used and absorbed dose values were scored using a tracklength estimator assuming charged particle equilibrium (CPE). The phase space model of the 192 Ir source had been benchmarked against data generated by the TG43 formalism through simulations in a large water sphere. Extensive measurements are unfortunately rare in the benchmarking of calculated BT dose distributions; depending on the large difficulties of experimental work in this geometry and photon energy region. The MC code Algebra is based on Geant4 with brachytherapy specific physics settings and additions such as the layered mass geometry, track-length estimator, DICOM-RT support and others. A full description is given in the manuscript by (Afsharpour et al 2012). That manuscript also provides extensive references on the validation and use of the code since 2008. More recently, it has been independently benchmarked against several other MC codes (Ballester et al 2015). To facilitate an in-detail comparison with the CC algorithm, dose scoring with Algebra was set up so that the total dose was divided up into primary, first- and multiple-scatter constituents in the same way as CC (see section II.C). III. Results and discussion III.A. Multiple-scatter point kernels
Point kernels describe the dose distribution in water around a primary-photon interaction point, see e.g. Ahnesjö and Aspradakis (Ahnesjö and Aspradakis 1999). They are generated 5316
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Figure 1. The point kernel for multiple-scatter dose multiplied by 4πri2 as function of the radial distance, ri, from the kernel origin. Curves using the parameter data from a double-exponential fit at 90 degrees angle with the initially impinging primary photons are shown for multiple scatter point kernels generated in spherical water phantoms of outer radii, r, 5 cm, 10 cm and 20 cm.
by MC. Primary photons are forced to interact at a point in a water phantom, 3D dose distributions are generated by scoring the doses around that point. CPE can generally be assumed for treatment planning purposes in BT and, when CPE is fulfilled, it has been shown possible and advantageous to split the kernel superposition process into two subsequent steps; first scatter and multiple scatter (Carlsson and Ahnesjö 2000a, 2000b). Each of these two steps require their own point kernel, for details see (Carlsson and Ahnesjö 2000b). Dose distributions in water phantoms of different dimensions for multiple-scatter point kernels (double exponential fits at 90 degrees angle with the impinging primary photons), generated by forcing both primary and once scattered photons from an 192Ir spectrum to interact at the origin and multiplied by the squared distance from the origin, are shown in figure 1. The double exponential fit used with the multiple-scatter kernels of CC for BT is the same as the double exponential method used in the nuclear engineering field called ‘the Taylor Form for calculation of the build-up factor for photon radiation scattering’ (Taylor 1954, 1968). It is of interest to note that the larger the phantom used for generating the multiple-scatter point kernel, the higher the dose at a given distance. The corresponding distributions for once-scattered photons (not included in figure 1) would show no dependency on phantom dimensions and fall off exponentially with radial distance. The residual-scatter point kernels used here are derived from forcing both primary and once-scattered photons to interact in the kernel origin, see sections 2.2.3 and 2.3 in (Carlsson and Ahnesjö 2000b) for full detail. Parameters for the double exponential fits used to produce the multiple-scatter point kernels of this work (out of which data for 90 degrees angle has been used for figure 1) can be obtained from the authors upon request. III.B. CC versus MC in water phantoms
Figure 2 shows absorbed dose multiplied by distance squared as function of radial distance from a point source as calculated by MC and CC. The phantom is a water cube of half-side 5317
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Figure 2. Total (Dtot ), primary (Dprim ), first-scatter (D1sc ) and multiple-scatter (Dmsc ) doses multiplied by 4πri2 as function of radial distance, ri, from a centrally positioned 192 Ir point source as calculated by MC and CC. The CC multiple-scatter dose has been derived using three different point kernels, initially generated in spheres of outer radii, r, 10 cm, 20 cm and 50 cm.
10 cm in which an 192Ir source is centrally positioned. The dose is shown as divided up into its total (Dtot ), primary (Dprim ), first (D1sc ) and multiple-scatter (Dmsc ) constituents. Three different point kernels (PK) were used for multiple scatter dose; derived in phantoms of outer radii r = 10 cm, r = 20 cm and r = 50 cm respectively. From figure 2 it can be seen how the multiple scatter dose (and hence also the total dose; Dtot = Dprim + D1sc + Dmsc) depends on the choice of multiple-scatter point kernel. It is also seen how best agreement with MC is achieved using the point kernel generated in a phantom of dimensions similar to that used in the calculations (here for figure 2 r = 10 cm). Note also how the multiple-scatter dose is a small fraction of the total and little sensitive to size of generation phantom close to the source which corresponds to the region of highest total dose (note that the doses of figure 2 are shown as multiplied by distance squared). The fraction of the total-dose delivered through multiple-scatter is increasing with distance and the approximation in multiple-scatter is increasing towards the phantom edge. Figures 3(a) and (b) summarize the dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cm and 25 cm. A multiple-scatter point kernel generated in a water sphere of outer radius 50 cm was used with CC for all the distributions in figure 3(a) while a point kernel generated in a water sphere of radius 10 cm was used with CC for all the distributions in figure 3(b). From figure 3(a) it is seen that use of a point kernel for multiple scatter generated in a water sphere of radii 50 cm leads to the following dose differences at the phantom edges for the investigated single source case: +2.5% (phantom halfside 5 cm), +7% (halfside 10 cm), +12% (halfside 15 cm), +15% (halfside 20 cm) and +15 % (halfside 25 cm). It can be noted that the further away the phantom edge, the higher the deviation but also the lower the absolute dose level (192Ir total dose falls off with distance in close correspondence with the inverse square law). 5318
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Figure 3. (left): Dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cm and 25 cm. A multiple-scatter point kernel that was generated in a water sphere of outer radii 50 cm was used with CC for all the distributions. (right): Dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cmm and 25 cm. A multiple-scatter point kernel that was generated in a water sphere of outer radii 10 cm was used with CC for all the distributions.
From figure 3(b) it is seen that use of a point kernel for multiple scatter generated in a water sphere of radii 10 cm leads to the following dose differences at the phantom edges for the investigated single source case: +2.0% (halfside 5 cm), +2% (halfside 10 cm),−4% (halfside 15 cm),−12% (halfside 20 cm) and −20 % (halfside 25 cm). It can be noted that the further away the phantom edge, the higher the deviation but also the lower the absolute dose level (again due to the inverse square law). Figure 4 shows the voxel-by-voxel difference (CC-MC)/ MC as expressed against the local dose for dose calculations in a cubic water phantom of dimensions 10 cm × 10 cm × 10 cm using point kernels for multiple scatter generated in differently dimensioned spherical phantoms. Figure 4 shows (i) that dose differences larger than 1%–3% occur at low dose levels independently of the point kernel used and (ii) that dose deviations go in different directions (overestimation, underestimation) depending on the dimensions of the phantom used in generating the basic point kernel data. It has been shown that local dose differences can be up to +3% at 5 cm and +10% at 15 cm using the largest (radius 50 cm) point kernel, the magnitudes of the differences depending on the interplay between the point kernel used for multiple scatter and the proportion of total dose contributed by multiply scattered photons. III.C. CC and TG43 versus MC in a breast implant
Figure 5 shows results of doses calculated in a breast implanted with a MammoSite BSOL 5 channel implant (prescription dose 3.4 Gy) following the TG43 formalism (full lines), the CC algorithm (long dashed line) with a multiple-scatter point kernel derived in a phantom of radii 50 cm and Algebra simulations (short dashed lines). It can be seen that all methods agree well both within and close to the target region and how TG43 overestimates doses increasingly at distances from the implant while MC and CC agree well also further away in, e.g. the lungs. Figure 6 shows the dose differences with respect to ALgebra MC for TG43, CC with a point kernel of radius 50 cm and CC with a point kernel of radius 10 cm for the same breast geometry as in figure 5. Dose differences in the target region are clinically insignificant for 5319
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Figure 4. Dose differences between CC and MC as a function of the local dose from
a centrally positioned 192Ir source obtained in cubic water phantoms of halfside 10 cm using multiple-scatter point kernels generated in water spheres of outer radii 5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm.
Figure 5. Dose distributions for a MammoSite 192Ir HDR implant as derived using the
TG43 formalism (full lines), ALgebra MC (short dashed lines) and the CC algorithm with a point kernel for multiple scatter generated in a phantom of radius 50 cm (long dashed lines).
all methods. The TG43 method overestimates the dose at the patient skin and in the lung up to more than 20%. CC, using the point kernel generated in a sphere of radius 50 cm, overestimates skin doses by 2%–4% and lung doses by
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The collapsed cone algorithm for 192Ir dosimetry using phantom-size adaptive multiplescatter point kernels
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Phys. Med. Biol. 60 5313 (http://iopscience.iop.org/0031-9155/60/13/5313) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 130.133.8.114 This content was downloaded on 30/06/2015 at 19:35
Please note that terms and conditions apply.
Institute of Physics and Engineering in Medicine Phys. Med. Biol. 60 (2015) 5313–5323
Physics in Medicine & Biology doi:10.1088/0031-9155/60/13/5313
The collapsed cone algorithm for 192Ir dosimetry using phantom-size adaptive multiple-scatter point kernels Åsa Carlsson Tedgren1, Mathieu Plamondon2 and Luc Beaulieu2 1
Department of Medical and Health Sciences (IMH) and Center for Medical Image Science and Visualization, Radiation Physics, Linköping University, SE-581 85 Linköping, Sweden and Department of Medical Physics, Karolinska University Hospital, SE 171 76 Stockholm, Sweden 2 Département de Radio-Oncologie et Axe oncologie du Centre de recherche du CHU de Québec, CHU de Québec, Québec, Québec G1R 2J6, Canada and Département de Physique, de Génie Physique et d’Optique et Centre de Recherche sur le Cancer, Université Laval, Québec, Québec G1V 0A6, Canada E-mail: [email protected] Received 28 January 2015, revised 12 May 2015 Accepted for publication 18 May 2015 Published 24 June 2015 Abstract
The aim of this work was to investigate how dose distributions calculated with the collapsed cone (CC) algorithm depend on the size of the water phantom used in deriving the point kernel for multiple scatter. A research version of the CC algorithm equipped with a set of selectable point kernels for multiple-scatter dose that had initially been derived in water phantoms of various dimensions was used. The new point kernels were generated using EGSnrc in spherical water phantoms of radii 5 cm, 7.5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm. Dose distributions derived with CC in water phantoms of different dimensions and in a CT-based clinical breast geometry were compared to Monte Carlo (MC) simulations using the Geant4based brachytherapy specific MC code Algebra. Agreement with MC within 1% was obtained when the dimensions of the phantom used to derive the multiple-scatter kernel were similar to those of the calculation phantom. Doses are overestimated at phantom edges when kernels are derived in larger phantoms and underestimated when derived in smaller phantoms (by around 2% to 7% depending on distance from source and phantom dimensions). CC agrees well with MC in the high dose region of a breast implant and is superior to TG43 in determining skin doses for all multiple-scatter point kernel sizes. Increased agreement between CC and MC is achieved when the point kernel is comparable to breast dimensions. 0031-9155/15/135313+11$33.00 © 2015 Institute of Physics and Engineering in Medicine Printed in the UK
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The investigated approximation in multiple scatter dose depends on the choice of point kernel in relation to phantom size and yields a significant fraction of the total dose only at distances of several centimeters from a source/implant which correspond to volumes of low doses. The current implementation of the CC algorithm utilizes a point kernel derived in a comparatively large (radius 20 cm) water phantom. A fixed point kernel leads to predictable behaviour of the algorithm with the worst case being a source/implant located well within a patient/phantom for which low doses at phantom edges can be overestimated by 2–5 %. It would be possible to improve the situation by using a point kernel for multiple-scatter dose adapted to the patient/phantom dimensions at hand. Keywords: 192Ir, model-based dose calculation algorithms, collapsed cone superposition, multiple scatter, point kernel (Some figures may appear in colour only in the online journal) I. Introduction Model-based dose calculation algorithms (MBDCAs) capable of performing three-dimensional (3D) dose calculations have long been used to account for patient tissue heterogeneities in planning external beam radiotherapy (EBRT) (see, e.g. Ahnesjö and Aspradakis 1999). Dose calculations for planning brachytherapy (BT) treatments are, however, still generally performed according to the TG43 formalism (Rivard et al 2004), thus assuming that both patient and applicator geometries consist of extended water. Interest in using MBDCAs for BT has recently increased, see e.g. the review by Rivard et al (Rivard et al 2009), the report from AAPM Task Group No. 186 (Beaulieu et al 2012) and the book chapter by Carlsson Tedgren et al (Carlsson Tedgren et al 2012). BT covers the energy region from around 20 keV to about 400 keV, in which the dominant photon interaction process in soft tissue changes from photoelectric absorption to Compton scattering. Effects of changing from the TG43 approach to dose calculations by MBDCAs will therefore be considerably higher at low (50 keV) BT energies. The commonly-used isotope 192Ir has a mean photon energy of around 400 keV, at which energy photon interactions are predominantly taking place by Compton scattering and mass energy absorption coefficients of various soft tissues thus vary by only a few percent. The main dosimetric advantage of MBDCAs for 192Ir dosimetry over current practice is their ability to account for 3D effects on dose distributions due to scattered photons in, e.g. the vicinity of air-tissue interfaces and in the penumbral regions of high atomic number shields. Recent studies show moderate differences between MBDCAs and TG43 for implants well within the body such as prostate and unshielded GYN treatments (see, e.g. Mikell et al 2012, Desbiens et al 2013). MBDCAs can be expected to increase dosimetric accuracy in accounting for the reduced contribution of dose from scattered photons when implants are located close to patient surfaces in, e.g. breast and head and neck implants (see, e.g. Poon and Verhaegen 2009) and for the 3D effects of shields of high atomic numbers such as those sometimes used with GYN and rectal applicators (Poon et al 2008, Petrokokkinos et al 2011). MBDCA has hitherto only been implemented in commercially available treatment planning systems (TPS) for the isotope 192Ir. The ACUROS® engine (Transpire, Inc., Gig Harbor, WA) (Zourari et al 2013) is available with the Brachyvision TPS ((BV, Varian Medical Systems, Inc., Palo Alto, CA)). The BT version of the collapsed cone (CC) MBDCA (Carlsson and Ahnesjö 2000a, Carlsson Tedgren and Ahnesjö 2003, Russell et al 2005, Carlsson Tedgren and 5314
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Ahnesjö 2008) has been implemented in the Oncentra® Brachy TPS (Elekta Brachytherapy, Veenendaal, the Netherlands) under the name ACE.1 The CC algorithm is a point kernel convolution/superposition algorithm (Ahnesjö and Aspradakis 1999). Such algorithms are principally capable of calculating dose to the medium for primary and once-scattered photons in heterogeneous geometries without approximations to the physics (Mackie et al 1985, Williamson et al 1991, Carlsson and Ahnesjö 2000b). A possible limitation is, however, their somewhat approximate treatment of dose from multiplyscattered photons which stems from the use of a phantom of fixed size in the initial Monte Carlo (MC) generation of the so-called point kernels, that typically causes an overestimation in dose at the phantom edge ((Williamson et al 1991, Carlsson and Ahnesjö 2000b). Dose from multiply-scattered photons add a significant fraction to the total dose at distances 4–6 cm away from 192Ir implants/sources, i.e. in low dose regions which is why this limitation is expected to be of low clinical significance. The worst situations could be that of a source/ implant located centrally in a comparatively small phantom for which there is interest in high dose accuracy at the phantom surface, several centimeters from the implant. A clinical example of this scenario is breast BT. Breast dimensions are smaller than the size of the phantom used for generating the current, fixed multiple-scatter point kernel and, even when sources are implanted relatively deep within the breast, interest in accurate determination of the skin-dose located several centimeters away from the target is still comparatively high. The aim of this work was to investigate results of dose calculations with the CC algorithm in water phantoms of varying dimensions, using a set of different point kernels for multiplescatter, initially derived in water phantoms of different dimensions. An early research version of the ACE algorithm (version 0.4.0) that allowed use of selectable different point kernels was used. The Geant4-based ALGEBRA Monte Carlo (MC) code (Afsharpour et al 2012) was used to derive benchmark dose distributions. Results will be presented for water phantoms of various dimensions as well as for a clinical breast implant. II. Materials and methods II.A. Generation of point kernels for multiple scatter
A set of point kernels for multiple-scatter dose was generated using EGSnrc v V4-r2-3-2 in spherical water phantoms of radii 5 cm, 7.5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm. The point kernels were generated and fitted to double exponential functions following the methodology described in detail by Carlsson and Ahnesjö (Carlsson and Ahnesjö 2000b). Throughout this work we will refer to dose from photons that have scattered more than once outside the source as multiple-scatter dose (the term residual scatter has earlier sometimes been used as a synonym). II.B. Phantoms and patient geometries for dose calculations
The results of the CC algorithm is to be benchmarked against full MC simulations and thus to be performed in the same geometries and for the same source, these are described here. Dose calculations were performed for a MicroSelectron v2 high dose rate (HDR) 192Ir source (Elekta Brachytherapy, Veenendaal, the Netherlands). A set of calculations was performed with the 1 White Paper available at www.elekta.com/dms/elekta/elekta-assets/Elekta-Brachytherapy/oncentra-brachy/ pdfs/888-00638-MKT-5B01-5D-whitepaper-ACE-in-Oncentra-Brachy/Whitepaper:ACE Advanced Collapsed cone Engine.pdf.
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source positioned in the centres of cubic water phantoms of varying dimensions (half-sides of 5 cm, 10 cm, 15 cm, 20 cm and 25 cm). Calculations were also performed for a clinical breast implant based on the retrospective use of DICOM-RT plan information on geometry and source positioning. Values of absorbed dose to medium, Dm,m, were calculated both with CC and MC. II.C. Dose calculations using CC
The version 0.4.0 of the Elekta Collapsed Cone algorithm ACE was used. This version was an early research/test version and by default equipped with a point kernel for multiple scatter generated in a water sphere of radii 50 cm, following the initial version by Carlsson and Ahnesjö (Carlsson and Ahnesjö 2000a). For this study, however, a set of newly-generated multiplescatter point kernels (section II.A) were also available. The MicroSelectron v2 source was implemented using the primary and scatter separation (PSS) formalism for source characterization as described by (Russell et al 2005), using PSS source data from (Taylor and Rogers 2008). The PSS method for characterization of clinical BT sources is based on initial detailed MC simulations of the BT source and is similar to the ‘first-collision source’ described in early applications of the discrete ordinate method for brachytherapy (Daskalov et al 2000), see also the white paper on ACE1. The research version of the CC algorithm used here was set up so that it was possible to study the output of the primary, first- and multiple-scatter dose contributions separately. Scatter generations were defined as described in (Russell et al 2005); a photon is counted as primary until its first interaction outside of the source encapsulation. Transport line tessellations into 1620 directions for the first-scatter and 320 directions for the multiple-scatter dose calculations were used. II.D. Dose calculations using MC
The MC code Algebra (ALgorithm for the heterogeneous dosimetry based on Geant4 for BRAchytherapy) (Afsharpour et al 2012) was used. Algebra’s phase space model of the MicroSelectron v2 192Ir source was used and absorbed dose values were scored using a tracklength estimator assuming charged particle equilibrium (CPE). The phase space model of the 192 Ir source had been benchmarked against data generated by the TG43 formalism through simulations in a large water sphere. Extensive measurements are unfortunately rare in the benchmarking of calculated BT dose distributions; depending on the large difficulties of experimental work in this geometry and photon energy region. The MC code Algebra is based on Geant4 with brachytherapy specific physics settings and additions such as the layered mass geometry, track-length estimator, DICOM-RT support and others. A full description is given in the manuscript by (Afsharpour et al 2012). That manuscript also provides extensive references on the validation and use of the code since 2008. More recently, it has been independently benchmarked against several other MC codes (Ballester et al 2015). To facilitate an in-detail comparison with the CC algorithm, dose scoring with Algebra was set up so that the total dose was divided up into primary, first- and multiple-scatter constituents in the same way as CC (see section II.C). III. Results and discussion III.A. Multiple-scatter point kernels
Point kernels describe the dose distribution in water around a primary-photon interaction point, see e.g. Ahnesjö and Aspradakis (Ahnesjö and Aspradakis 1999). They are generated 5316
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Figure 1. The point kernel for multiple-scatter dose multiplied by 4πri2 as function of the radial distance, ri, from the kernel origin. Curves using the parameter data from a double-exponential fit at 90 degrees angle with the initially impinging primary photons are shown for multiple scatter point kernels generated in spherical water phantoms of outer radii, r, 5 cm, 10 cm and 20 cm.
by MC. Primary photons are forced to interact at a point in a water phantom, 3D dose distributions are generated by scoring the doses around that point. CPE can generally be assumed for treatment planning purposes in BT and, when CPE is fulfilled, it has been shown possible and advantageous to split the kernel superposition process into two subsequent steps; first scatter and multiple scatter (Carlsson and Ahnesjö 2000a, 2000b). Each of these two steps require their own point kernel, for details see (Carlsson and Ahnesjö 2000b). Dose distributions in water phantoms of different dimensions for multiple-scatter point kernels (double exponential fits at 90 degrees angle with the impinging primary photons), generated by forcing both primary and once scattered photons from an 192Ir spectrum to interact at the origin and multiplied by the squared distance from the origin, are shown in figure 1. The double exponential fit used with the multiple-scatter kernels of CC for BT is the same as the double exponential method used in the nuclear engineering field called ‘the Taylor Form for calculation of the build-up factor for photon radiation scattering’ (Taylor 1954, 1968). It is of interest to note that the larger the phantom used for generating the multiple-scatter point kernel, the higher the dose at a given distance. The corresponding distributions for once-scattered photons (not included in figure 1) would show no dependency on phantom dimensions and fall off exponentially with radial distance. The residual-scatter point kernels used here are derived from forcing both primary and once-scattered photons to interact in the kernel origin, see sections 2.2.3 and 2.3 in (Carlsson and Ahnesjö 2000b) for full detail. Parameters for the double exponential fits used to produce the multiple-scatter point kernels of this work (out of which data for 90 degrees angle has been used for figure 1) can be obtained from the authors upon request. III.B. CC versus MC in water phantoms
Figure 2 shows absorbed dose multiplied by distance squared as function of radial distance from a point source as calculated by MC and CC. The phantom is a water cube of half-side 5317
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Figure 2. Total (Dtot ), primary (Dprim ), first-scatter (D1sc ) and multiple-scatter (Dmsc ) doses multiplied by 4πri2 as function of radial distance, ri, from a centrally positioned 192 Ir point source as calculated by MC and CC. The CC multiple-scatter dose has been derived using three different point kernels, initially generated in spheres of outer radii, r, 10 cm, 20 cm and 50 cm.
10 cm in which an 192Ir source is centrally positioned. The dose is shown as divided up into its total (Dtot ), primary (Dprim ), first (D1sc ) and multiple-scatter (Dmsc ) constituents. Three different point kernels (PK) were used for multiple scatter dose; derived in phantoms of outer radii r = 10 cm, r = 20 cm and r = 50 cm respectively. From figure 2 it can be seen how the multiple scatter dose (and hence also the total dose; Dtot = Dprim + D1sc + Dmsc) depends on the choice of multiple-scatter point kernel. It is also seen how best agreement with MC is achieved using the point kernel generated in a phantom of dimensions similar to that used in the calculations (here for figure 2 r = 10 cm). Note also how the multiple-scatter dose is a small fraction of the total and little sensitive to size of generation phantom close to the source which corresponds to the region of highest total dose (note that the doses of figure 2 are shown as multiplied by distance squared). The fraction of the total-dose delivered through multiple-scatter is increasing with distance and the approximation in multiple-scatter is increasing towards the phantom edge. Figures 3(a) and (b) summarize the dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cm and 25 cm. A multiple-scatter point kernel generated in a water sphere of outer radius 50 cm was used with CC for all the distributions in figure 3(a) while a point kernel generated in a water sphere of radius 10 cm was used with CC for all the distributions in figure 3(b). From figure 3(a) it is seen that use of a point kernel for multiple scatter generated in a water sphere of radii 50 cm leads to the following dose differences at the phantom edges for the investigated single source case: +2.5% (phantom halfside 5 cm), +7% (halfside 10 cm), +12% (halfside 15 cm), +15% (halfside 20 cm) and +15 % (halfside 25 cm). It can be noted that the further away the phantom edge, the higher the deviation but also the lower the absolute dose level (192Ir total dose falls off with distance in close correspondence with the inverse square law). 5318
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Figure 3. (left): Dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cm and 25 cm. A multiple-scatter point kernel that was generated in a water sphere of outer radii 50 cm was used with CC for all the distributions. (right): Dose differences between CC and MC as function of the distance from a centrally positioned 192Ir source obtained in cubic water phantoms of halfsides 5 cm, 10 cm, 15 cm, 20 cmm and 25 cm. A multiple-scatter point kernel that was generated in a water sphere of outer radii 10 cm was used with CC for all the distributions.
From figure 3(b) it is seen that use of a point kernel for multiple scatter generated in a water sphere of radii 10 cm leads to the following dose differences at the phantom edges for the investigated single source case: +2.0% (halfside 5 cm), +2% (halfside 10 cm),−4% (halfside 15 cm),−12% (halfside 20 cm) and −20 % (halfside 25 cm). It can be noted that the further away the phantom edge, the higher the deviation but also the lower the absolute dose level (again due to the inverse square law). Figure 4 shows the voxel-by-voxel difference (CC-MC)/ MC as expressed against the local dose for dose calculations in a cubic water phantom of dimensions 10 cm × 10 cm × 10 cm using point kernels for multiple scatter generated in differently dimensioned spherical phantoms. Figure 4 shows (i) that dose differences larger than 1%–3% occur at low dose levels independently of the point kernel used and (ii) that dose deviations go in different directions (overestimation, underestimation) depending on the dimensions of the phantom used in generating the basic point kernel data. It has been shown that local dose differences can be up to +3% at 5 cm and +10% at 15 cm using the largest (radius 50 cm) point kernel, the magnitudes of the differences depending on the interplay between the point kernel used for multiple scatter and the proportion of total dose contributed by multiply scattered photons. III.C. CC and TG43 versus MC in a breast implant
Figure 5 shows results of doses calculated in a breast implanted with a MammoSite BSOL 5 channel implant (prescription dose 3.4 Gy) following the TG43 formalism (full lines), the CC algorithm (long dashed line) with a multiple-scatter point kernel derived in a phantom of radii 50 cm and Algebra simulations (short dashed lines). It can be seen that all methods agree well both within and close to the target region and how TG43 overestimates doses increasingly at distances from the implant while MC and CC agree well also further away in, e.g. the lungs. Figure 6 shows the dose differences with respect to ALgebra MC for TG43, CC with a point kernel of radius 50 cm and CC with a point kernel of radius 10 cm for the same breast geometry as in figure 5. Dose differences in the target region are clinically insignificant for 5319
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Figure 4. Dose differences between CC and MC as a function of the local dose from
a centrally positioned 192Ir source obtained in cubic water phantoms of halfside 10 cm using multiple-scatter point kernels generated in water spheres of outer radii 5 cm, 10 cm, 15 cm, 20 cm, 30 cm and 50 cm.
Figure 5. Dose distributions for a MammoSite 192Ir HDR implant as derived using the
TG43 formalism (full lines), ALgebra MC (short dashed lines) and the CC algorithm with a point kernel for multiple scatter generated in a phantom of radius 50 cm (long dashed lines).
all methods. The TG43 method overestimates the dose at the patient skin and in the lung up to more than 20%. CC, using the point kernel generated in a sphere of radius 50 cm, overestimates skin doses by 2%–4% and lung doses by
